Merge branch 'master_14.4.1' of github.com:Unidata/awips2 into master_14.4.1

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pythonPackages/metpy

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+Subproject commit db120ecf9d6094c3c0c3f2778d5cd4a4c776c773

pythonPackages/pint

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pythonPackages/python-dateutil/LICENSE

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+dateutil - Extensions to the standard Python datetime module.
+
+Copyright (c) 2003-2011 - Gustavo Niemeyer <gustavo@niemeyer.net>
+Copyright (c) 2012-2014 - Tomi Pieviläinen <tomi.pievilainen@iki.fi>
+Copyright (c) 2014      - Yaron de Leeuw <me@jarondl.net>
+
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+    * Redistributions of source code must retain the above copyright notice,
+      this list of conditions and the following disclaimer.
+    * Redistributions in binary form must reproduce the above copyright notice,
+      this list of conditions and the following disclaimer in the documentation
+      and/or other materials provided with the distribution.
+    * Neither the name of the copyright holder nor the names of its
+      contributors may be used to endorse or promote products derived from
+      this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

pythonPackages/python-dateutil/MANIFEST.in

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+include LICENSE NEWS zonefile_metadata.json updatezinfo.py

pythonPackages/python-dateutil/NEWS

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+Version 2.4.2
+-------------
+- Updated zoneinfo to 2015b.
+- Fixed issue with parsing of tzstr on Python 2.7.x; tzstr will now be decoded
+  if not a unicode type. gh #51 (lp:1331576), gh pr #55.
+- Fix a parser issue where AM and PM tokens were showing up in fuzzy date
+  stamps, triggering inappropriate errors. gh #56 (lp: 1428895), gh pr #63.
+- Missing function "setcachsize" removed from zoneinfo __all__ list by @ryanss,
+  fixing an issue with wildcard imports of dateutil.zoneinfo. (gh pr #66).
+- (PyPi only) Fix an issue with source distributions not including the test
+  suite.
+
+
+Version 2.4.1
+-------------
+
+- Added explicit check for valid hours if AM/PM is specified in parser.
+  (gh pr #22, issue #21)
+- Fix bug in rrule introduced in 2.4.0 where byweekday parameter was not
+  handled properly. (gh pr #35, issue #34)
+- Fix error where parser allowed some invalid dates, overwriting existing hours
+  with the last 2-digit number in the string. (gh pr #32, issue #31)
+- Fix and add test for Python 2.x compatibility with boolean checking of
+  relativedelta objects. Implemented by @nimasmi (gh pr #43) and Cédric Krier 
+  (lp: 1035038)
+- Replaced parse() calls with explicit datetime objects in unit tests unrelated
+  to parser. (gh pr #36)
+- Changed private _byxxx from sets to sorted tuples and fixed one currently
+  unreachable bug in _construct_byset. (gh pr #54)
+- Additional documentation for parser (gh pr #29, #33, #41) and rrule.
+- Formatting fixes to documentation of rrule and README.rst.
+- Updated zoneinfo to 2015a.
+
+Version 2.4.0
+-------------
+
+- Fix an issue with relativedelta and freezegun (lp:1374022)
+- Fix tzinfo in windows for timezones without dst (lp:1010050, gh #2)
+- Ignore missing timezones in windows like in POSIX
+- Fix minimal version requirement for six (gh #6)
+- Many rrule changes and fixes by @pganssle (gh pull requests #13 #14 #17),
+    including defusing some infinite loops (gh #4)
+
+Version 2.3
+-----------
+
+- Cleanup directory structure, moved test.py to dateutil/tests/test.py
+
+- Changed many aspects of dealing with the zone info file. Instead of a cache,
+  all the zones are loaded to memory, but symbolic links are loaded only once,
+  so not much memory is used.
+
+- The package is now zip-safe, and universal-wheelable, thanks to changes in 
+  the handling of the zoneinfo file. 
+
+- Fixed tzwin silently not imported on windows python2
+
+- New maintainer, together with new hosting: GitHub, Travis, Read-The-Docs
+
+Version 2.2
+-----------
+
+- Updated zoneinfo to 2013h
+
+- fuzzy_with_tokens parse addon from Christopher Corley
+
+- Bug with LANG=C fixed by Mike Gilbert
+
+Version 2.1
+-----------
+
+- New maintainer
+
+- Dateutil now works on Python 2.6, 2.7 and 3.2 from same codebase (with six)
+
+- #704047: Ismael Carnales' patch for a new time format
+
+- Small bug fixes, thanks for reporters!
+
+
+Version 2.0
+-----------
+
+- Ported to Python 3, by Brian Jones.  If you need dateutil for Python 2.X,
+  please continue using the 1.X series.
+
+- There's no such thing as a "PSF License".  This source code is now
+  made available under the Simplified BSD license.  See LICENSE for
+  details.
+
+Version 1.5
+-----------
+
+- As reported by Mathieu Bridon, rrules were matching the bysecond rules
+  incorrectly against byminute in some circumstances when the SECONDLY
+  frequency was in use, due to a copy & paste bug.  The problem has been
+  unittested and corrected.
+
+- Adam Ryan reported a problem in the relativedelta implementation which
+  affected the yearday parameter in the month of January specifically.
+  This has been unittested and fixed.
+
+- Updated timezone information.
+
+
+Version 1.4.1
+-------------
+
+- Updated timezone information.
+
+
+Version 1.4
+-----------
+
+- Fixed another parser precision problem on conversion of decimal seconds
+  to microseconds, as reported by Erik Brown.  Now these issues are gone
+  for real since it's not using floating point arithmetic anymore.
+
+- Fixed case where tzrange.utcoffset and tzrange.dst() might fail due
+  to a date being used where a datetime was expected (reported and fixed
+  by Lennart Regebro).
+
+- Prevent tzstr from introducing daylight timings in strings that didn't
+  specify them (reported by Lennart Regebro).
+
+- Calls like gettz("GMT+3") and gettz("UTC-2") will now return the
+  expected values, instead of the TZ variable behavior.
+
+- Fixed DST signal handling in zoneinfo files.  Reported by
+  Nicholas F. Fabry and John-Mark Gurney.
+
+
+Version 1.3
+-----------
+
+- Fixed precision problem on conversion of decimal seconds to
+  microseconds, as reported by Skip Montanaro.
+
+- Fixed bug in constructor of parser, and converted parser classes to
+  new-style classes.  Original report and patch by Michael Elsdörfer.
+
+- Initialize tzid and comps in tz.py, to prevent the code from ever
+  raising a NameError (even with broken files).  Johan Dahlin suggested
+  the fix after a pyflakes run.
+
+- Version is now published in dateutil.__version__, as requested
+  by Darren Dale.
+
+- All code is compatible with new-style division.
+
+
+Version 1.2
+-----------
+
+- Now tzfile will round timezones to full-minutes if necessary,
+  since Python's datetime doesn't support sub-minute offsets.
+  Thanks to Ilpo Nyyssönen for reporting the issue.
+
+- Removed bare string exceptions, as reported and fixed by
+  Wilfredo Sánchez Vega.
+
+- Fix bug in leap count parsing (reported and fixed by Eugene Oden).
+
+
+Version 1.1
+-----------
+
+- Fixed rrule byyearday handling. Abramo Bagnara pointed out that
+  RFC2445 allows negative numbers.
+
+- Fixed --prefix handling in setup.py (by Sidnei da Silva).
+
+- Now tz.gettz() returns a tzlocal instance when not given any
+  arguments and no other timezone information is found.
+
+- Updating timezone information to version 2005q.
+
+
+Version 1.0
+-----------
+
+- Fixed parsing of XXhXXm formatted time after day/month/year
+  has been parsed.
+
+- Added patch by Jeffrey Harris optimizing rrule.__contains__.
+
+
+Version 0.9
+-----------
+
+- Fixed pickling of timezone types, as reported by
+  Andreas Köhler.
+
+- Implemented internal timezone information with binary
+  timezone files [1]. datautil.tz.gettz() function will now
+  try to use the system timezone files, and fallback to
+  the internal versions. It's also possible to ask for
+  the internal versions directly by using
+  dateutil.zoneinfo.gettz().
+
+- New tzwin timezone type, allowing access to Windows
+  internal timezones (contributed by Jeffrey Harris).
+
+- Fixed parsing of unicode date strings.
+
+- Accept parserinfo instances as the parser constructor
+  parameter, besides parserinfo (sub)classes.
+
+- Changed weekday to spell the not-set n value as None
+  instead of 0.
+
+- Fixed other reported bugs.
+
+[1] http://www.twinsun.com/tz/tz-link.htm
+
+
+Version 0.5
+-----------
+
+- Removed FREQ_ prefix from rrule frequency constants
+  WARNING: this breaks compatibility with previous versions.
+
+- Fixed rrule.between() for cases where "after" is achieved
+  before even starting, as reported by Andreas Köhler.
+
+- Fixed two digit zero-year parsing (such as 31-Dec-00), as
+  reported by Jim Abramson, and included test case for this.
+
+- Sort exdate and rdate before iterating over them, so that
+  it's not necessary to sort them before adding to the rruleset,
+  as reported by Nicholas Piper.
+

pythonPackages/python-dateutil/PKG-INFO

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+Metadata-Version: 1.1
+Name: python-dateutil
+Version: 2.4.2
+Summary: Extensions to the standard Python datetime module
+Home-page: https://dateutil.readthedocs.org
+Author: Yaron de Leeuw
+Author-email: me@jarondl.net
+License: Simplified BSD
+Description: 
+        The dateutil module provides powerful extensions to the
+        datetime module available in the Python standard library.
+        
+Platform: UNKNOWN
+Classifier: Development Status :: 5 - Production/Stable
+Classifier: Intended Audience :: Developers
+Classifier: License :: OSI Approved :: BSD License
+Classifier: Programming Language :: Python
+Classifier: Programming Language :: Python :: 2
+Classifier: Programming Language :: Python :: 2.6
+Classifier: Programming Language :: Python :: 2.7
+Classifier: Programming Language :: Python :: 3
+Classifier: Programming Language :: Python :: 3.2
+Classifier: Programming Language :: Python :: 3.3
+Classifier: Programming Language :: Python :: 3.4
+Classifier: Topic :: Software Development :: Libraries
+Requires: six

pythonPackages/python-dateutil/README.rst

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+dateutil - powerful extensions to datetime
+==========================================
+
+.. image:: https://img.shields.io/travis/dateutil/dateutil/master.svg?style=flat-square
+    :target: https://travis-ci.org/dateutil/dateutil
+    :alt: travis build status
+
+.. image:: https://img.shields.io/appveyor/ci/dateutil/dateutil/master.svg?style=flat-square
+    :target: https://ci.appveyor.com/project/dateutil/dateutil
+    :alt: appveyor build status
+
+.. image:: https://img.shields.io/pypi/dd/python-dateutil.svg?style=flat-square
+    :target: https://pypi.python.org/pypi/python-dateutil/
+    :alt: pypi downloads per day
+
+.. image:: https://img.shields.io/pypi/v/python-dateutil.svg?style=flat-square
+    :target: https://pypi.python.org/pypi/python-dateutil/
+    :alt: pypi version
+
+
+
+The `dateutil` module provides powerful extensions to
+the standard `datetime` module, available in Python.
+
+
+Download
+========
+dateutil is available on PyPI
+https://pypi.python.org/pypi/python-dateutil/
+
+The documentation is hosted at:
+https://dateutil.readthedocs.org/
+
+Code
+====
+https://github.com/dateutil/dateutil/
+
+Features
+========
+
+* Computing of relative deltas (next month, next year,
+  next monday, last week of month, etc);
+* Computing of relative deltas between two given
+  date and/or datetime objects;
+* Computing of dates based on very flexible recurrence rules,
+  using a superset of the `iCalendar <https://www.ietf.org/rfc/rfc2445.txt>`_
+  specification. Parsing of RFC strings is supported as well.
+* Generic parsing of dates in almost any string format;
+* Timezone (tzinfo) implementations for tzfile(5) format
+  files (/etc/localtime, /usr/share/zoneinfo, etc), TZ
+  environment string (in all known formats), iCalendar
+  format files, given ranges (with help from relative deltas),
+  local machine timezone, fixed offset timezone, UTC timezone,
+  and Windows registry-based time zones.
+* Internal up-to-date world timezone information based on
+  Olson's database.
+* Computing of Easter Sunday dates for any given year,
+  using Western, Orthodox or Julian algorithms;
+* More than 400 test cases.
+
+Quick example
+=============
+Here's a snapshot, just to give an idea about the power of the
+package. For more examples, look at the documentation.
+
+Suppose you want to know how much time is left, in
+years/months/days/etc, before the next easter happening on a
+year with a Friday 13th in August, and you want to get today's
+date out of the "date" unix system command. Here is the code:
+
+.. doctest:: readmeexample
+
+    >>> from dateutil.relativedelta import *
+    >>> from dateutil.easter import *
+    >>> from dateutil.rrule import *
+    >>> from dateutil.parser import *
+    >>> from datetime import *
+    >>> now = parse("Sat Oct 11 17:13:46 UTC 2003")
+    >>> today = now.date()
+    >>> year = rrule(YEARLY,dtstart=now,bymonth=8,bymonthday=13,byweekday=FR)[0].year
+    >>> rdelta = relativedelta(easter(year), today)
+    >>> print("Today is: %s" % today)
+    Today is: 2003-10-11
+    >>> print("Year with next Aug 13th on a Friday is: %s" % year)
+    Year with next Aug 13th on a Friday is: 2004
+    >>> print("How far is the Easter of that year: %s" % rdelta)
+    How far is the Easter of that year: relativedelta(months=+6)
+    >>> print("And the Easter of that year is: %s" % (today+rdelta))
+    And the Easter of that year is: 2004-04-11
+
+Being exactly 6 months ahead was **really** a coincidence :)
+
+
+Author
+======
+The dateutil module was written by Gustavo Niemeyer <gustavo@niemeyer.net>
+in 2003
+
+It is maintained by:
+
+* Gustavo Niemeyer <gustavo@niemeyer.net> 2003-2011
+* Tomi Pieviläinen <tomi.pievilainen@iki.fi> 2012-2014
+* Yaron de Leeuw <me@jarondl.net> 2014-
+
+Building and releasing
+======================
+When you get the source, it does not contain the internal zoneinfo
+database. To get (and update) the database, run the updatezinfo.py script. Make sure
+that the zic command is in your path, and that you have network connectivity
+to get the latest timezone information from IANA. If you have downloaded
+the timezone data earlier, you can give the tarball as a parameter to
+updatezinfo.py.
+
+
+Testing
+=======
+dateutil has a comprehensive test suite, which can be run simply by running
+`python setup.py test [-q]` in the project root. Note that if you don't have the internal
+zoneinfo database, some tests will fail. Apart from that, all tests should pass.
+
+To easily test dateutil against all supported Python versions, you can use
+`tox <https://tox.readthedocs.org/en/latest/>`_.
+
+All github pull requests are automatically tested using travis.

pythonPackages/python-dateutil/dateutil/__init__.py

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+# -*- coding: utf-8 -*-
+__version__ = "2.4.2"

pythonPackages/python-dateutil/dateutil/easter.py

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+# -*- coding: utf-8 -*-
+"""
+This module offers a generic easter computing method for any given year, using
+Western, Orthodox or Julian algorithms.
+"""
+
+import datetime
+
+__all__ = ["easter", "EASTER_JULIAN", "EASTER_ORTHODOX", "EASTER_WESTERN"]
+
+EASTER_JULIAN = 1
+EASTER_ORTHODOX = 2
+EASTER_WESTERN = 3
+
+
+def easter(year, method=EASTER_WESTERN):
+    """
+    This method was ported from the work done by GM Arts,
+    on top of the algorithm by Claus Tondering, which was
+    based in part on the algorithm of Ouding (1940), as
+    quoted in "Explanatory Supplement to the Astronomical
+    Almanac", P.  Kenneth Seidelmann, editor.
+
+    This algorithm implements three different easter
+    calculation methods:
+
+    1 - Original calculation in Julian calendar, valid in
+        dates after 326 AD
+    2 - Original method, with date converted to Gregorian
+        calendar, valid in years 1583 to 4099
+    3 - Revised method, in Gregorian calendar, valid in
+        years 1583 to 4099 as well
+
+    These methods are represented by the constants:
+
+    EASTER_JULIAN   = 1
+    EASTER_ORTHODOX = 2
+    EASTER_WESTERN  = 3
+
+    The default method is method 3.
+
+    More about the algorithm may be found at:
+
+    http://users.chariot.net.au/~gmarts/eastalg.htm
+
+    and
+
+    http://www.tondering.dk/claus/calendar.html
+
+    """
+
+    if not (1 <= method <= 3):
+        raise ValueError("invalid method")
+
+    # g - Golden year - 1
+    # c - Century
+    # h - (23 - Epact) mod 30
+    # i - Number of days from March 21 to Paschal Full Moon
+    # j - Weekday for PFM (0=Sunday, etc)
+    # p - Number of days from March 21 to Sunday on or before PFM
+    #     (-6 to 28 methods 1 & 3, to 56 for method 2)
+    # e - Extra days to add for method 2 (converting Julian
+    #     date to Gregorian date)
+
+    y = year
+    g = y % 19
+    e = 0
+    if method < 3:
+        # Old method
+        i = (19*g + 15) % 30
+        j = (y + y//4 + i) % 7
+        if method == 2:
+            # Extra dates to convert Julian to Gregorian date
+            e = 10
+            if y > 1600:
+                e = e + y//100 - 16 - (y//100 - 16)//4
+    else:
+        # New method
+        c = y//100
+        h = (c - c//4 - (8*c + 13)//25 + 19*g + 15) % 30
+        i = h - (h//28)*(1 - (h//28)*(29//(h + 1))*((21 - g)//11))
+        j = (y + y//4 + i + 2 - c + c//4) % 7
+
+    # p can be from -6 to 56 corresponding to dates 22 March to 23 May
+    # (later dates apply to method 2, although 23 May never actually occurs)
+    p = i - j + e
+    d = 1 + (p + 27 + (p + 6)//40) % 31
+    m = 3 + (p + 26)//30
+    return datetime.date(int(y), int(m), int(d))

pythonPackages/python-dateutil/dateutil/relativedelta.py

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+# -*- coding: utf-8 -*-
+import datetime
+import calendar
+
+from six import integer_types
+
+__all__ = ["relativedelta", "MO", "TU", "WE", "TH", "FR", "SA", "SU"]
+
+
+class weekday(object):
+    __slots__ = ["weekday", "n"]
+
+    def __init__(self, weekday, n=None):
+        self.weekday = weekday
+        self.n = n
+
+    def __call__(self, n):
+        if n == self.n:
+            return self
+        else:
+            return self.__class__(self.weekday, n)
+
+    def __eq__(self, other):
+        try:
+            if self.weekday != other.weekday or self.n != other.n:
+                return False
+        except AttributeError:
+            return False
+        return True
+
+    def __repr__(self):
+        s = ("MO", "TU", "WE", "TH", "FR", "SA", "SU")[self.weekday]
+        if not self.n:
+            return s
+        else:
+            return "%s(%+d)" % (s, self.n)
+
+MO, TU, WE, TH, FR, SA, SU = weekdays = tuple([weekday(x) for x in range(7)])
+
+
+class relativedelta(object):
+    """
+The relativedelta type is based on the specification of the excellent
+work done by M.-A. Lemburg in his
+`mx.DateTime <http://www.egenix.com/files/python/mxDateTime.html>`_ extension.
+However, notice that this type does *NOT* implement the same algorithm as
+his work. Do *NOT* expect it to behave like mx.DateTime's counterpart.
+
+There are two different ways to build a relativedelta instance. The
+first one is passing it two date/datetime classes::
+
+    relativedelta(datetime1, datetime2)
+
+The second one is passing it any number of the following keyword arguments::
+
+    relativedelta(arg1=x,arg2=y,arg3=z...)
+
+    year, month, day, hour, minute, second, microsecond:
+        Absolute information (argument is singular); adding or subtracting a
+        relativedelta with absolute information does not perform an aritmetic
+        operation, but rather REPLACES the corresponding value in the
+        original datetime with the value(s) in relativedelta.
+
+    years, months, weeks, days, hours, minutes, seconds, microseconds:
+        Relative information, may be negative (argument is plural); adding
+        or subtracting a relativedelta with relative information performs
+        the corresponding aritmetic operation on the original datetime value
+        with the information in the relativedelta.  
+
+    weekday:
+        One of the weekday instances (MO, TU, etc). These instances may
+        receive a parameter N, specifying the Nth weekday, which could
+        be positive or negative (like MO(+1) or MO(-2). Not specifying
+        it is the same as specifying +1. You can also use an integer,
+        where 0=MO.
+
+    leapdays:
+        Will add given days to the date found, if year is a leap
+        year, and the date found is post 28 of february.
+
+    yearday, nlyearday:
+        Set the yearday or the non-leap year day (jump leap days).
+        These are converted to day/month/leapdays information.
+
+Here is the behavior of operations with relativedelta:
+
+1. Calculate the absolute year, using the 'year' argument, or the
+   original datetime year, if the argument is not present.
+
+2. Add the relative 'years' argument to the absolute year.
+
+3. Do steps 1 and 2 for month/months.
+
+4. Calculate the absolute day, using the 'day' argument, or the
+   original datetime day, if the argument is not present. Then,
+   subtract from the day until it fits in the year and month
+   found after their operations.
+
+5. Add the relative 'days' argument to the absolute day. Notice
+   that the 'weeks' argument is multiplied by 7 and added to
+   'days'.
+
+6. Do steps 1 and 2 for hour/hours, minute/minutes, second/seconds,
+   microsecond/microseconds.
+
+7. If the 'weekday' argument is present, calculate the weekday,
+   with the given (wday, nth) tuple. wday is the index of the
+   weekday (0-6, 0=Mon), and nth is the number of weeks to add
+   forward or backward, depending on its signal. Notice that if
+   the calculated date is already Monday, for example, using
+   (0, 1) or (0, -1) won't change the day.
+    """
+
+    def __init__(self, dt1=None, dt2=None,
+                 years=0, months=0, days=0, leapdays=0, weeks=0,
+                 hours=0, minutes=0, seconds=0, microseconds=0,
+                 year=None, month=None, day=None, weekday=None,
+                 yearday=None, nlyearday=None,
+                 hour=None, minute=None, second=None, microsecond=None):
+        if dt1 and dt2:
+            # datetime is a subclass of date. So both must be date
+            if not (isinstance(dt1, datetime.date) and
+                    isinstance(dt2, datetime.date)):
+                raise TypeError("relativedelta only diffs datetime/date")
+            # We allow two dates, or two datetimes, so we coerce them to be
+            # of the same type
+            if (isinstance(dt1, datetime.datetime) !=
+                    isinstance(dt2, datetime.datetime)):
+                if not isinstance(dt1, datetime.datetime):
+                    dt1 = datetime.datetime.fromordinal(dt1.toordinal())
+                elif not isinstance(dt2, datetime.datetime):
+                    dt2 = datetime.datetime.fromordinal(dt2.toordinal())
+            self.years = 0
+            self.months = 0
+            self.days = 0
+            self.leapdays = 0
+            self.hours = 0
+            self.minutes = 0
+            self.seconds = 0
+            self.microseconds = 0
+            self.year = None
+            self.month = None
+            self.day = None
+            self.weekday = None
+            self.hour = None
+            self.minute = None
+            self.second = None
+            self.microsecond = None
+            self._has_time = 0
+
+            months = (dt1.year*12+dt1.month)-(dt2.year*12+dt2.month)
+            self._set_months(months)
+            dtm = self.__radd__(dt2)
+            if dt1 < dt2:
+                while dt1 > dtm:
+                    months += 1
+                    self._set_months(months)
+                    dtm = self.__radd__(dt2)
+            else:
+                while dt1 < dtm:
+                    months -= 1
+                    self._set_months(months)
+                    dtm = self.__radd__(dt2)
+            delta = dt1 - dtm
+            self.seconds = delta.seconds+delta.days*86400
+            self.microseconds = delta.microseconds
+        else:
+            self.years = years
+            self.months = months
+            self.days = days+weeks*7
+            self.leapdays = leapdays
+            self.hours = hours
+            self.minutes = minutes
+            self.seconds = seconds
+            self.microseconds = microseconds
+            self.year = year
+            self.month = month
+            self.day = day
+            self.hour = hour
+            self.minute = minute
+            self.second = second
+            self.microsecond = microsecond
+
+            if isinstance(weekday, integer_types):
+                self.weekday = weekdays[weekday]
+            else:
+                self.weekday = weekday
+
+            yday = 0
+            if nlyearday:
+                yday = nlyearday
+            elif yearday:
+                yday = yearday
+                if yearday > 59:
+                    self.leapdays = -1
+            if yday:
+                ydayidx = [31, 59, 90, 120, 151, 181, 212,
+                           243, 273, 304, 334, 366]
+                for idx, ydays in enumerate(ydayidx):
+                    if yday <= ydays:
+                        self.month = idx+1
+                        if idx == 0:
+                            self.day = yday
+                        else:
+                            self.day = yday-ydayidx[idx-1]
+                        break
+                else:
+                    raise ValueError("invalid year day (%d)" % yday)
+
+        self._fix()
+
+    def _fix(self):
+        if abs(self.microseconds) > 999999:
+            s = self.microseconds//abs(self.microseconds)
+            div, mod = divmod(self.microseconds*s, 1000000)
+            self.microseconds = mod*s
+            self.seconds += div*s
+        if abs(self.seconds) > 59:
+            s = self.seconds//abs(self.seconds)
+            div, mod = divmod(self.seconds*s, 60)
+            self.seconds = mod*s
+            self.minutes += div*s
+        if abs(self.minutes) > 59:
+            s = self.minutes//abs(self.minutes)
+            div, mod = divmod(self.minutes*s, 60)
+            self.minutes = mod*s
+            self.hours += div*s
+        if abs(self.hours) > 23:
+            s = self.hours//abs(self.hours)
+            div, mod = divmod(self.hours*s, 24)
+            self.hours = mod*s
+            self.days += div*s
+        if abs(self.months) > 11:
+            s = self.months//abs(self.months)
+            div, mod = divmod(self.months*s, 12)
+            self.months = mod*s
+            self.years += div*s
+        if (self.hours or self.minutes or self.seconds or self.microseconds
+                or self.hour is not None or self.minute is not None or
+                self.second is not None or self.microsecond is not None):
+            self._has_time = 1
+        else:
+            self._has_time = 0
+
+    def _set_months(self, months):
+        self.months = months
+        if abs(self.months) > 11:
+            s = self.months//abs(self.months)
+            div, mod = divmod(self.months*s, 12)
+            self.months = mod*s
+            self.years = div*s
+        else:
+            self.years = 0
+
+    def __add__(self, other):
+        if isinstance(other, relativedelta):
+            return relativedelta(years=other.years+self.years,
+                                 months=other.months+self.months,
+                                 days=other.days+self.days,
+                                 hours=other.hours+self.hours,
+                                 minutes=other.minutes+self.minutes,
+                                 seconds=other.seconds+self.seconds,
+                                 microseconds=(other.microseconds +
+                                               self.microseconds),
+                                 leapdays=other.leapdays or self.leapdays,
+                                 year=other.year or self.year,
+                                 month=other.month or self.month,
+                                 day=other.day or self.day,
+                                 weekday=other.weekday or self.weekday,
+                                 hour=other.hour or self.hour,
+                                 minute=other.minute or self.minute,
+                                 second=other.second or self.second,
+                                 microsecond=(other.microsecond or
+                                              self.microsecond))
+        if not isinstance(other, datetime.date):
+            raise TypeError("unsupported type for add operation")
+        elif self._has_time and not isinstance(other, datetime.datetime):
+            other = datetime.datetime.fromordinal(other.toordinal())
+        year = (self.year or other.year)+self.years
+        month = self.month or other.month
+        if self.months:
+            assert 1 <= abs(self.months) <= 12
+            month += self.months
+            if month > 12:
+                year += 1
+                month -= 12
+            elif month < 1:
+                year -= 1
+                month += 12
+        day = min(calendar.monthrange(year, month)[1],
+                  self.day or other.day)
+        repl = {"year": year, "month": month, "day": day}
+        for attr in ["hour", "minute", "second", "microsecond"]:
+            value = getattr(self, attr)
+            if value is not None:
+                repl[attr] = value
+        days = self.days
+        if self.leapdays and month > 2 and calendar.isleap(year):
+            days += self.leapdays
+        ret = (other.replace(**repl)
+               + datetime.timedelta(days=days,
+                                    hours=self.hours,
+                                    minutes=self.minutes,
+                                    seconds=self.seconds,
+                                    microseconds=self.microseconds))
+        if self.weekday:
+            weekday, nth = self.weekday.weekday, self.weekday.n or 1
+            jumpdays = (abs(nth)-1)*7
+            if nth > 0:
+                jumpdays += (7-ret.weekday()+weekday) % 7
+            else:
+                jumpdays += (ret.weekday()-weekday) % 7
+                jumpdays *= -1
+            ret += datetime.timedelta(days=jumpdays)
+        return ret
+
+    def __radd__(self, other):
+        return self.__add__(other)
+
+    def __rsub__(self, other):
+        return self.__neg__().__radd__(other)
+
+    def __sub__(self, other):
+        if not isinstance(other, relativedelta):
+            raise TypeError("unsupported type for sub operation")
+        return relativedelta(years=self.years-other.years,
+                             months=self.months-other.months,
+                             days=self.days-other.days,
+                             hours=self.hours-other.hours,
+                             minutes=self.minutes-other.minutes,
+                             seconds=self.seconds-other.seconds,
+                             microseconds=self.microseconds-other.microseconds,
+                             leapdays=self.leapdays or other.leapdays,
+                             year=self.year or other.year,
+                             month=self.month or other.month,
+                             day=self.day or other.day,
+                             weekday=self.weekday or other.weekday,
+                             hour=self.hour or other.hour,
+                             minute=self.minute or other.minute,
+                             second=self.second or other.second,
+                             microsecond=self.microsecond or other.microsecond)
+
+    def __neg__(self):
+        return relativedelta(years=-self.years,
+                             months=-self.months,
+                             days=-self.days,
+                             hours=-self.hours,
+                             minutes=-self.minutes,
+                             seconds=-self.seconds,
+                             microseconds=-self.microseconds,
+                             leapdays=self.leapdays,
+                             year=self.year,
+                             month=self.month,
+                             day=self.day,
+                             weekday=self.weekday,
+                             hour=self.hour,
+                             minute=self.minute,
+                             second=self.second,
+                             microsecond=self.microsecond)
+
+    def __bool__(self):
+        return not (not self.years and
+                    not self.months and
+                    not self.days and
+                    not self.hours and
+                    not self.minutes and
+                    not self.seconds and
+                    not self.microseconds and
+                    not self.leapdays and
+                    self.year is None and
+                    self.month is None and
+                    self.day is None and
+                    self.weekday is None and
+                    self.hour is None and
+                    self.minute is None and
+                    self.second is None and
+                    self.microsecond is None)
+    # Compatibility with Python 2.x
+    __nonzero__ = __bool__
+
+    def __mul__(self, other):
+        f = float(other)
+        return relativedelta(years=int(self.years*f),
+                             months=int(self.months*f),
+                             days=int(self.days*f),
+                             hours=int(self.hours*f),
+                             minutes=int(self.minutes*f),
+                             seconds=int(self.seconds*f),
+                             microseconds=int(self.microseconds*f),
+                             leapdays=self.leapdays,
+                             year=self.year,
+                             month=self.month,
+                             day=self.day,
+                             weekday=self.weekday,
+                             hour=self.hour,
+                             minute=self.minute,
+                             second=self.second,
+                             microsecond=self.microsecond)
+
+    __rmul__ = __mul__
+
+    def __eq__(self, other):
+        if not isinstance(other, relativedelta):
+            return False
+        if self.weekday or other.weekday:
+            if not self.weekday or not other.weekday:
+                return False
+            if self.weekday.weekday != other.weekday.weekday:
+                return False
+            n1, n2 = self.weekday.n, other.weekday.n
+            if n1 != n2 and not ((not n1 or n1 == 1) and (not n2 or n2 == 1)):
+                return False
+        return (self.years == other.years and
+                self.months == other.months and
+                self.days == other.days and
+                self.hours == other.hours and
+                self.minutes == other.minutes and
+                self.seconds == other.seconds and
+                self.leapdays == other.leapdays and
+                self.year == other.year and
+                self.month == other.month and
+                self.day == other.day and
+                self.hour == other.hour and
+                self.minute == other.minute and
+                self.second == other.second and
+                self.microsecond == other.microsecond)
+
+    def __ne__(self, other):
+        return not self.__eq__(other)
+
+    def __div__(self, other):
+        return self.__mul__(1/float(other))
+
+    __truediv__ = __div__
+
+    def __repr__(self):
+        l = []
+        for attr in ["years", "months", "days", "leapdays",
+                     "hours", "minutes", "seconds", "microseconds"]:
+            value = getattr(self, attr)
+            if value:
+                l.append("%s=%+d" % (attr, value))
+        for attr in ["year", "month", "day", "weekday",
+                     "hour", "minute", "second", "microsecond"]:
+            value = getattr(self, attr)
+            if value is not None:
+                l.append("%s=%s" % (attr, repr(value)))
+        return "%s(%s)" % (self.__class__.__name__, ", ".join(l))
+
+# vim:ts=4:sw=4:et

pythonPackages/python-dateutil/dateutil/tz.py

@@ -0,0 +1,986 @@
+# -*- coding: utf-8 -*-
+"""
+This module offers timezone implementations subclassing the abstract
+:py:`datetime.tzinfo` type. There are classes to handle tzfile format files
+(usually are in :file:`/etc/localtime`, :file:`/usr/share/zoneinfo`, etc), TZ
+environment string (in all known formats), given ranges (with help from
+relative deltas), local machine timezone, fixed offset timezone, and UTC
+timezone.
+"""
+import datetime
+import struct
+import time
+import sys
+import os
+
+from six import string_types, PY3
+
+try:
+    from dateutil.tzwin import tzwin, tzwinlocal
+except ImportError:
+    tzwin = tzwinlocal = None
+
+relativedelta = None
+parser = None
+rrule = None
+
+__all__ = ["tzutc", "tzoffset", "tzlocal", "tzfile", "tzrange",
+           "tzstr", "tzical", "tzwin", "tzwinlocal", "gettz"]
+
+
+def tzname_in_python2(myfunc):
+    """Change unicode output into bytestrings in Python 2
+
+    tzname() API changed in Python 3. It used to return bytes, but was changed
+    to unicode strings
+    """
+    def inner_func(*args, **kwargs):
+        if PY3:
+            return myfunc(*args, **kwargs)
+        else:
+            return myfunc(*args, **kwargs).encode()
+    return inner_func
+
+ZERO = datetime.timedelta(0)
+EPOCHORDINAL = datetime.datetime.utcfromtimestamp(0).toordinal()
+
+
+class tzutc(datetime.tzinfo):
+
+    def utcoffset(self, dt):
+        return ZERO
+
+    def dst(self, dt):
+        return ZERO
+
+    @tzname_in_python2
+    def tzname(self, dt):
+        return "UTC"
+
+    def __eq__(self, other):
+        return (isinstance(other, tzutc) or
+                (isinstance(other, tzoffset) and other._offset == ZERO))
+
+    def __ne__(self, other):
+        return not self.__eq__(other)
+
+    def __repr__(self):
+        return "%s()" % self.__class__.__name__
+
+    __reduce__ = object.__reduce__
+
+
+class tzoffset(datetime.tzinfo):
+
+    def __init__(self, name, offset):
+        self._name = name
+        self._offset = datetime.timedelta(seconds=offset)
+
+    def utcoffset(self, dt):
+        return self._offset
+
+    def dst(self, dt):
+        return ZERO
+
+    @tzname_in_python2
+    def tzname(self, dt):
+        return self._name
+
+    def __eq__(self, other):
+        return (isinstance(other, tzoffset) and
+                self._offset == other._offset)
+
+    def __ne__(self, other):
+        return not self.__eq__(other)
+
+    def __repr__(self):
+        return "%s(%s, %s)" % (self.__class__.__name__,
+                               repr(self._name),
+                               self._offset.days*86400+self._offset.seconds)
+
+    __reduce__ = object.__reduce__
+
+
+class tzlocal(datetime.tzinfo):
+
+    _std_offset = datetime.timedelta(seconds=-time.timezone)
+    if time.daylight:
+        _dst_offset = datetime.timedelta(seconds=-time.altzone)
+    else:
+        _dst_offset = _std_offset
+
+    def utcoffset(self, dt):
+        if self._isdst(dt):
+            return self._dst_offset
+        else:
+            return self._std_offset
+
+    def dst(self, dt):
+        if self._isdst(dt):
+            return self._dst_offset-self._std_offset
+        else:
+            return ZERO
+
+    @tzname_in_python2
+    def tzname(self, dt):
+        return time.tzname[self._isdst(dt)]
+
+    def _isdst(self, dt):
+        # We can't use mktime here. It is unstable when deciding if
+        # the hour near to a change is DST or not.
+        #
+        # timestamp = time.mktime((dt.year, dt.month, dt.day, dt.hour,
+        #                         dt.minute, dt.second, dt.weekday(), 0, -1))
+        # return time.localtime(timestamp).tm_isdst
+        #
+        # The code above yields the following result:
+        #
+        # >>> import tz, datetime
+        # >>> t = tz.tzlocal()
+        # >>> datetime.datetime(2003,2,15,23,tzinfo=t).tzname()
+        # 'BRDT'
+        # >>> datetime.datetime(2003,2,16,0,tzinfo=t).tzname()
+        # 'BRST'
+        # >>> datetime.datetime(2003,2,15,23,tzinfo=t).tzname()
+        # 'BRST'
+        # >>> datetime.datetime(2003,2,15,22,tzinfo=t).tzname()
+        # 'BRDT'
+        # >>> datetime.datetime(2003,2,15,23,tzinfo=t).tzname()
+        # 'BRDT'
+        #
+        # Here is a more stable implementation:
+        #
+        timestamp = ((dt.toordinal() - EPOCHORDINAL) * 86400
+                     + dt.hour * 3600
+                     + dt.minute * 60
+                     + dt.second)
+        return time.localtime(timestamp+time.timezone).tm_isdst
+
+    def __eq__(self, other):
+        if not isinstance(other, tzlocal):
+            return False
+        return (self._std_offset == other._std_offset and
+                self._dst_offset == other._dst_offset)
+        return True
+
+    def __ne__(self, other):
+        return not self.__eq__(other)
+
+    def __repr__(self):
+        return "%s()" % self.__class__.__name__
+
+    __reduce__ = object.__reduce__
+
+
+class _ttinfo(object):
+    __slots__ = ["offset", "delta", "isdst", "abbr", "isstd", "isgmt"]
+
+    def __init__(self):
+        for attr in self.__slots__:
+            setattr(self, attr, None)
+
+    def __repr__(self):
+        l = []
+        for attr in self.__slots__:
+            value = getattr(self, attr)
+            if value is not None:
+                l.append("%s=%s" % (attr, repr(value)))
+        return "%s(%s)" % (self.__class__.__name__, ", ".join(l))
+
+    def __eq__(self, other):
+        if not isinstance(other, _ttinfo):
+            return False
+        return (self.offset == other.offset and
+                self.delta == other.delta and
+                self.isdst == other.isdst and
+                self.abbr == other.abbr and
+                self.isstd == other.isstd and
+                self.isgmt == other.isgmt)
+
+    def __ne__(self, other):
+        return not self.__eq__(other)
+
+    def __getstate__(self):
+        state = {}
+        for name in self.__slots__:
+            state[name] = getattr(self, name, None)
+        return state
+
+    def __setstate__(self, state):
+        for name in self.__slots__:
+            if name in state:
+                setattr(self, name, state[name])
+
+
+class tzfile(datetime.tzinfo):
+
+    # http://www.twinsun.com/tz/tz-link.htm
+    # ftp://ftp.iana.org/tz/tz*.tar.gz
+
+    def __init__(self, fileobj, filename=None):
+        file_opened_here = False
+        if isinstance(fileobj, string_types):
+            self._filename = fileobj
+            fileobj = open(fileobj, 'rb')
+            file_opened_here = True
+        elif filename is not None:
+            self._filename = filename
+        elif hasattr(fileobj, "name"):
+            self._filename = fileobj.name
+        else:
+            self._filename = repr(fileobj)
+
+        # From tzfile(5):
+        #
+        # The time zone information files used by tzset(3)
+        # begin with the magic characters "TZif" to identify
+        # them as time zone information files, followed by
+        # sixteen bytes reserved for future use, followed by
+        # six four-byte values of type long, written in a
+        # ``standard'' byte order (the high-order  byte
+        # of the value is written first).
+        try:
+            if fileobj.read(4).decode() != "TZif":
+                raise ValueError("magic not found")
+
+            fileobj.read(16)
+
+            (
+                # The number of UTC/local indicators stored in the file.
+                ttisgmtcnt,
+
+                # The number of standard/wall indicators stored in the file.
+                ttisstdcnt,
+
+                # The number of leap seconds for which data is
+                # stored in the file.
+                leapcnt,
+
+                # The number of "transition times" for which data
+                # is stored in the file.
+                timecnt,
+
+                # The number of "local time types" for which data
+                # is stored in the file (must not be zero).
+                typecnt,
+
+                # The  number  of  characters  of "time zone
+                # abbreviation strings" stored in the file.
+                charcnt,
+
+            ) = struct.unpack(">6l", fileobj.read(24))
+
+            # The above header is followed by tzh_timecnt four-byte
+            # values  of  type long,  sorted  in ascending order.
+            # These values are written in ``standard'' byte order.
+            # Each is used as a transition time (as  returned  by
+            # time(2)) at which the rules for computing local time
+            # change.
+
+            if timecnt:
+                self._trans_list = struct.unpack(">%dl" % timecnt,
+                                                 fileobj.read(timecnt*4))
+            else:
+                self._trans_list = []
+
+            # Next come tzh_timecnt one-byte values of type unsigned
+            # char; each one tells which of the different types of
+            # ``local time'' types described in the file is associated
+            # with the same-indexed transition time. These values
+            # serve as indices into an array of ttinfo structures that
+            # appears next in the file.
+
+            if timecnt:
+                self._trans_idx = struct.unpack(">%dB" % timecnt,
+                                                fileobj.read(timecnt))
+            else:
+                self._trans_idx = []
+
+            # Each ttinfo structure is written as a four-byte value
+            # for tt_gmtoff  of  type long,  in  a  standard  byte
+            # order, followed  by a one-byte value for tt_isdst
+            # and a one-byte  value  for  tt_abbrind.   In  each
+            # structure, tt_gmtoff  gives  the  number  of
+            # seconds to be added to UTC, tt_isdst tells whether
+            # tm_isdst should be set by  localtime(3),  and
+            # tt_abbrind serves  as an index into the array of
+            # time zone abbreviation characters that follow the
+            # ttinfo structure(s) in the file.
+
+            ttinfo = []
+
+            for i in range(typecnt):
+                ttinfo.append(struct.unpack(">lbb", fileobj.read(6)))
+
+            abbr = fileobj.read(charcnt).decode()
+
+            # Then there are tzh_leapcnt pairs of four-byte
+            # values, written in  standard byte  order;  the
+            # first  value  of  each pair gives the time (as
+            # returned by time(2)) at which a leap second
+            # occurs;  the  second  gives the  total  number of
+            # leap seconds to be applied after the given time.
+            # The pairs of values are sorted in ascending order
+            # by time.
+
+            # Not used, for now
+            # if leapcnt:
+            #    leap = struct.unpack(">%dl" % (leapcnt*2),
+            #                         fileobj.read(leapcnt*8))
+
+            # Then there are tzh_ttisstdcnt standard/wall
+            # indicators, each stored as a one-byte value;
+            # they tell whether the transition times associated
+            # with local time types were specified as standard
+            # time or wall clock time, and are used when
+            # a time zone file is used in handling POSIX-style
+            # time zone environment variables.
+
+            if ttisstdcnt:
+                isstd = struct.unpack(">%db" % ttisstdcnt,
+                                      fileobj.read(ttisstdcnt))
+
+            # Finally, there are tzh_ttisgmtcnt UTC/local
+            # indicators, each stored as a one-byte value;
+            # they tell whether the transition times associated
+            # with local time types were specified as UTC or
+            # local time, and are used when a time zone file
+            # is used in handling POSIX-style time zone envi-
+            # ronment variables.
+
+            if ttisgmtcnt:
+                isgmt = struct.unpack(">%db" % ttisgmtcnt,
+                                      fileobj.read(ttisgmtcnt))
+
+            # ** Everything has been read **
+        finally:
+            if file_opened_here:
+                fileobj.close()
+
+        # Build ttinfo list
+        self._ttinfo_list = []
+        for i in range(typecnt):
+            gmtoff, isdst, abbrind = ttinfo[i]
+            # Round to full-minutes if that's not the case. Python's
+            # datetime doesn't accept sub-minute timezones. Check
+            # http://python.org/sf/1447945 for some information.
+            gmtoff = (gmtoff+30)//60*60
+            tti = _ttinfo()
+            tti.offset = gmtoff
+            tti.delta = datetime.timedelta(seconds=gmtoff)
+            tti.isdst = isdst
+            tti.abbr = abbr[abbrind:abbr.find('\x00', abbrind)]
+            tti.isstd = (ttisstdcnt > i and isstd[i] != 0)
+            tti.isgmt = (ttisgmtcnt > i and isgmt[i] != 0)
+            self._ttinfo_list.append(tti)
+
+        # Replace ttinfo indexes for ttinfo objects.
+        trans_idx = []
+        for idx in self._trans_idx:
+            trans_idx.append(self._ttinfo_list[idx])
+        self._trans_idx = tuple(trans_idx)
+
+        # Set standard, dst, and before ttinfos. before will be
+        # used when a given time is before any transitions,
+        # and will be set to the first non-dst ttinfo, or to
+        # the first dst, if all of them are dst.
+        self._ttinfo_std = None
+        self._ttinfo_dst = None
+        self._ttinfo_before = None
+        if self._ttinfo_list:
+            if not self._trans_list:
+                self._ttinfo_std = self._ttinfo_first = self._ttinfo_list[0]
+            else:
+                for i in range(timecnt-1, -1, -1):
+                    tti = self._trans_idx[i]
+                    if not self._ttinfo_std and not tti.isdst:
+                        self._ttinfo_std = tti
+                    elif not self._ttinfo_dst and tti.isdst:
+                        self._ttinfo_dst = tti
+                    if self._ttinfo_std and self._ttinfo_dst:
+                        break
+                else:
+                    if self._ttinfo_dst and not self._ttinfo_std:
+                        self._ttinfo_std = self._ttinfo_dst
+
+                for tti in self._ttinfo_list:
+                    if not tti.isdst:
+                        self._ttinfo_before = tti
+                        break
+                else:
+                    self._ttinfo_before = self._ttinfo_list[0]
+
+        # Now fix transition times to become relative to wall time.
+        #
+        # I'm not sure about this. In my tests, the tz source file
+        # is setup to wall time, and in the binary file isstd and
+        # isgmt are off, so it should be in wall time. OTOH, it's
+        # always in gmt time. Let me know if you have comments
+        # about this.
+        laststdoffset = 0
+        self._trans_list = list(self._trans_list)
+        for i in range(len(self._trans_list)):
+            tti = self._trans_idx[i]
+            if not tti.isdst:
+                # This is std time.
+                self._trans_list[i] += tti.offset
+                laststdoffset = tti.offset
+            else:
+                # This is dst time. Convert to std.
+                self._trans_list[i] += laststdoffset
+        self._trans_list = tuple(self._trans_list)
+
+    def _find_ttinfo(self, dt, laststd=0):
+        timestamp = ((dt.toordinal() - EPOCHORDINAL) * 86400
+                     + dt.hour * 3600
+                     + dt.minute * 60
+                     + dt.second)
+        idx = 0
+        for trans in self._trans_list:
+            if timestamp < trans:
+                break
+            idx += 1
+        else:
+            return self._ttinfo_std
+        if idx == 0:
+            return self._ttinfo_before
+        if laststd:
+            while idx > 0:
+                tti = self._trans_idx[idx-1]
+                if not tti.isdst:
+                    return tti
+                idx -= 1
+            else:
+                return self._ttinfo_std
+        else:
+            return self._trans_idx[idx-1]
+
+    def utcoffset(self, dt):
+        if not self._ttinfo_std:
+            return ZERO
+        return self._find_ttinfo(dt).delta
+
+    def dst(self, dt):
+        if not self._ttinfo_dst:
+            return ZERO
+        tti = self._find_ttinfo(dt)
+        if not tti.isdst:
+            return ZERO
+
+        # The documentation says that utcoffset()-dst() must
+        # be constant for every dt.
+        return tti.delta-self._find_ttinfo(dt, laststd=1).delta
+
+        # An alternative for that would be:
+        #
+        # return self._ttinfo_dst.offset-self._ttinfo_std.offset
+        #
+        # However, this class stores historical changes in the
+        # dst offset, so I belive that this wouldn't be the right
+        # way to implement this.
+
+    @tzname_in_python2
+    def tzname(self, dt):
+        if not self._ttinfo_std:
+            return None
+        return self._find_ttinfo(dt).abbr
+
+    def __eq__(self, other):
+        if not isinstance(other, tzfile):
+            return False
+        return (self._trans_list == other._trans_list and
+                self._trans_idx == other._trans_idx and
+                self._ttinfo_list == other._ttinfo_list)
+
+    def __ne__(self, other):
+        return not self.__eq__(other)
+
+    def __repr__(self):
+        return "%s(%s)" % (self.__class__.__name__, repr(self._filename))
+
+    def __reduce__(self):
+        if not os.path.isfile(self._filename):
+            raise ValueError("Unpickable %s class" % self.__class__.__name__)
+        return (self.__class__, (self._filename,))
+
+
+class tzrange(datetime.tzinfo):
+    def __init__(self, stdabbr, stdoffset=None,
+                 dstabbr=None, dstoffset=None,
+                 start=None, end=None):
+        global relativedelta
+        if not relativedelta:
+            from dateutil import relativedelta
+        self._std_abbr = stdabbr
+        self._dst_abbr = dstabbr
+        if stdoffset is not None:
+            self._std_offset = datetime.timedelta(seconds=stdoffset)
+        else:
+            self._std_offset = ZERO
+        if dstoffset is not None:
+            self._dst_offset = datetime.timedelta(seconds=dstoffset)
+        elif dstabbr and stdoffset is not None:
+            self._dst_offset = self._std_offset+datetime.timedelta(hours=+1)
+        else:
+            self._dst_offset = ZERO
+        if dstabbr and start is None:
+            self._start_delta = relativedelta.relativedelta(
+                hours=+2, month=4, day=1, weekday=relativedelta.SU(+1))
+        else:
+            self._start_delta = start
+        if dstabbr and end is None:
+            self._end_delta = relativedelta.relativedelta(
+                hours=+1, month=10, day=31, weekday=relativedelta.SU(-1))
+        else:
+            self._end_delta = end
+
+    def utcoffset(self, dt):
+        if self._isdst(dt):
+            return self._dst_offset
+        else:
+            return self._std_offset
+
+    def dst(self, dt):
+        if self._isdst(dt):
+            return self._dst_offset-self._std_offset
+        else:
+            return ZERO
+
+    @tzname_in_python2
+    def tzname(self, dt):
+        if self._isdst(dt):
+            return self._dst_abbr
+        else:
+            return self._std_abbr
+
+    def _isdst(self, dt):
+        if not self._start_delta:
+            return False
+        year = datetime.datetime(dt.year, 1, 1)
+        start = year+self._start_delta
+        end = year+self._end_delta
+        dt = dt.replace(tzinfo=None)
+        if start < end:
+            return dt >= start and dt < end
+        else:
+            return dt >= start or dt < end
+
+    def __eq__(self, other):
+        if not isinstance(other, tzrange):
+            return False
+        return (self._std_abbr == other._std_abbr and
+                self._dst_abbr == other._dst_abbr and
+                self._std_offset == other._std_offset and
+                self._dst_offset == other._dst_offset and
+                self._start_delta == other._start_delta and
+                self._end_delta == other._end_delta)
+
+    def __ne__(self, other):
+        return not self.__eq__(other)
+
+    def __repr__(self):
+        return "%s(...)" % self.__class__.__name__
+
+    __reduce__ = object.__reduce__
+
+
+class tzstr(tzrange):
+
+    def __init__(self, s):
+        global parser
+        if not parser:
+            from dateutil import parser
+        self._s = s
+
+        res = parser._parsetz(s)
+        if res is None:
+            raise ValueError("unknown string format")
+
+        # Here we break the compatibility with the TZ variable handling.
+        # GMT-3 actually *means* the timezone -3.
+        if res.stdabbr in ("GMT", "UTC"):
+            res.stdoffset *= -1
+
+        # We must initialize it first, since _delta() needs
+        # _std_offset and _dst_offset set. Use False in start/end
+        # to avoid building it two times.
+        tzrange.__init__(self, res.stdabbr, res.stdoffset,
+                         res.dstabbr, res.dstoffset,
+                         start=False, end=False)
+
+        if not res.dstabbr:
+            self._start_delta = None
+            self._end_delta = None
+        else:
+            self._start_delta = self._delta(res.start)
+            if self._start_delta:
+                self._end_delta = self._delta(res.end, isend=1)
+
+    def _delta(self, x, isend=0):
+        kwargs = {}
+        if x.month is not None:
+            kwargs["month"] = x.month
+            if x.weekday is not None:
+                kwargs["weekday"] = relativedelta.weekday(x.weekday, x.week)
+                if x.week > 0:
+                    kwargs["day"] = 1
+                else:
+                    kwargs["day"] = 31
+            elif x.day:
+                kwargs["day"] = x.day
+        elif x.yday is not None:
+            kwargs["yearday"] = x.yday
+        elif x.jyday is not None:
+            kwargs["nlyearday"] = x.jyday
+        if not kwargs:
+            # Default is to start on first sunday of april, and end
+            # on last sunday of october.
+            if not isend:
+                kwargs["month"] = 4
+                kwargs["day"] = 1
+                kwargs["weekday"] = relativedelta.SU(+1)
+            else:
+                kwargs["month"] = 10
+                kwargs["day"] = 31
+                kwargs["weekday"] = relativedelta.SU(-1)
+        if x.time is not None:
+            kwargs["seconds"] = x.time
+        else:
+            # Default is 2AM.
+            kwargs["seconds"] = 7200
+        if isend:
+            # Convert to standard time, to follow the documented way
+            # of working with the extra hour. See the documentation
+            # of the tzinfo class.
+            delta = self._dst_offset-self._std_offset
+            kwargs["seconds"] -= delta.seconds+delta.days*86400
+        return relativedelta.relativedelta(**kwargs)
+
+    def __repr__(self):
+        return "%s(%s)" % (self.__class__.__name__, repr(self._s))
+
+
+class _tzicalvtzcomp(object):
+    def __init__(self, tzoffsetfrom, tzoffsetto, isdst,
+                 tzname=None, rrule=None):
+        self.tzoffsetfrom = datetime.timedelta(seconds=tzoffsetfrom)
+        self.tzoffsetto = datetime.timedelta(seconds=tzoffsetto)
+        self.tzoffsetdiff = self.tzoffsetto-self.tzoffsetfrom
+        self.isdst = isdst
+        self.tzname = tzname
+        self.rrule = rrule
+
+
+class _tzicalvtz(datetime.tzinfo):
+    def __init__(self, tzid, comps=[]):
+        self._tzid = tzid
+        self._comps = comps
+        self._cachedate = []
+        self._cachecomp = []
+
+    def _find_comp(self, dt):
+        if len(self._comps) == 1:
+            return self._comps[0]
+        dt = dt.replace(tzinfo=None)
+        try:
+            return self._cachecomp[self._cachedate.index(dt)]
+        except ValueError:
+            pass
+        lastcomp = None
+        lastcompdt = None
+        for comp in self._comps:
+            if not comp.isdst:
+                # Handle the extra hour in DST -> STD
+                compdt = comp.rrule.before(dt-comp.tzoffsetdiff, inc=True)
+            else:
+                compdt = comp.rrule.before(dt, inc=True)
+            if compdt and (not lastcompdt or lastcompdt < compdt):
+                lastcompdt = compdt
+                lastcomp = comp
+        if not lastcomp:
+            # RFC says nothing about what to do when a given
+            # time is before the first onset date. We'll look for the
+            # first standard component, or the first component, if
+            # none is found.
+            for comp in self._comps:
+                if not comp.isdst:
+                    lastcomp = comp
+                    break
+            else:
+                lastcomp = comp[0]
+        self._cachedate.insert(0, dt)
+        self._cachecomp.insert(0, lastcomp)
+        if len(self._cachedate) > 10:
+            self._cachedate.pop()
+            self._cachecomp.pop()
+        return lastcomp
+
+    def utcoffset(self, dt):
+        return self._find_comp(dt).tzoffsetto
+
+    def dst(self, dt):
+        comp = self._find_comp(dt)
+        if comp.isdst:
+            return comp.tzoffsetdiff
+        else:
+            return ZERO
+
+    @tzname_in_python2
+    def tzname(self, dt):
+        return self._find_comp(dt).tzname
+
+    def __repr__(self):
+        return "<tzicalvtz %s>" % repr(self._tzid)
+
+    __reduce__ = object.__reduce__
+
+
+class tzical(object):
+    def __init__(self, fileobj):
+        global rrule
+        if not rrule:
+            from dateutil import rrule
+
+        if isinstance(fileobj, string_types):
+            self._s = fileobj
+            # ical should be encoded in UTF-8 with CRLF
+            fileobj = open(fileobj, 'r')
+        elif hasattr(fileobj, "name"):
+            self._s = fileobj.name
+        else:
+            self._s = repr(fileobj)
+
+        self._vtz = {}
+
+        self._parse_rfc(fileobj.read())
+
+    def keys(self):
+        return list(self._vtz.keys())
+
+    def get(self, tzid=None):
+        if tzid is None:
+            keys = list(self._vtz.keys())
+            if len(keys) == 0:
+                raise ValueError("no timezones defined")
+            elif len(keys) > 1:
+                raise ValueError("more than one timezone available")
+            tzid = keys[0]
+        return self._vtz.get(tzid)
+
+    def _parse_offset(self, s):
+        s = s.strip()
+        if not s:
+            raise ValueError("empty offset")
+        if s[0] in ('+', '-'):
+            signal = (-1, +1)[s[0] == '+']
+            s = s[1:]
+        else:
+            signal = +1
+        if len(s) == 4:
+            return (int(s[:2])*3600+int(s[2:])*60)*signal
+        elif len(s) == 6:
+            return (int(s[:2])*3600+int(s[2:4])*60+int(s[4:]))*signal
+        else:
+            raise ValueError("invalid offset: "+s)
+
+    def _parse_rfc(self, s):
+        lines = s.splitlines()
+        if not lines:
+            raise ValueError("empty string")
+
+        # Unfold
+        i = 0
+        while i < len(lines):
+            line = lines[i].rstrip()
+            if not line:
+                del lines[i]
+            elif i > 0 and line[0] == " ":
+                lines[i-1] += line[1:]
+                del lines[i]
+            else:
+                i += 1
+
+        tzid = None
+        comps = []
+        invtz = False
+        comptype = None
+        for line in lines:
+            if not line:
+                continue
+            name, value = line.split(':', 1)
+            parms = name.split(';')
+            if not parms:
+                raise ValueError("empty property name")
+            name = parms[0].upper()
+            parms = parms[1:]
+            if invtz:
+                if name == "BEGIN":
+                    if value in ("STANDARD", "DAYLIGHT"):
+                        # Process component
+                        pass
+                    else:
+                        raise ValueError("unknown component: "+value)
+                    comptype = value
+                    founddtstart = False
+                    tzoffsetfrom = None
+                    tzoffsetto = None
+                    rrulelines = []
+                    tzname = None
+                elif name == "END":
+                    if value == "VTIMEZONE":
+                        if comptype:
+                            raise ValueError("component not closed: "+comptype)
+                        if not tzid:
+                            raise ValueError("mandatory TZID not found")
+                        if not comps:
+                            raise ValueError(
+                                "at least one component is needed")
+                        # Process vtimezone
+                        self._vtz[tzid] = _tzicalvtz(tzid, comps)
+                        invtz = False
+                    elif value == comptype:
+                        if not founddtstart:
+                            raise ValueError("mandatory DTSTART not found")
+                        if tzoffsetfrom is None:
+                            raise ValueError(
+                                "mandatory TZOFFSETFROM not found")
+                        if tzoffsetto is None:
+                            raise ValueError(
+                                "mandatory TZOFFSETFROM not found")
+                        # Process component
+                        rr = None
+                        if rrulelines:
+                            rr = rrule.rrulestr("\n".join(rrulelines),
+                                                compatible=True,
+                                                ignoretz=True,
+                                                cache=True)
+                        comp = _tzicalvtzcomp(tzoffsetfrom, tzoffsetto,
+                                              (comptype == "DAYLIGHT"),
+                                              tzname, rr)
+                        comps.append(comp)
+                        comptype = None
+                    else:
+                        raise ValueError("invalid component end: "+value)
+                elif comptype:
+                    if name == "DTSTART":
+                        rrulelines.append(line)
+                        founddtstart = True
+                    elif name in ("RRULE", "RDATE", "EXRULE", "EXDATE"):
+                        rrulelines.append(line)
+                    elif name == "TZOFFSETFROM":
+                        if parms:
+                            raise ValueError(
+                                "unsupported %s parm: %s " % (name, parms[0]))
+                        tzoffsetfrom = self._parse_offset(value)
+                    elif name == "TZOFFSETTO":
+                        if parms:
+                            raise ValueError(
+                                "unsupported TZOFFSETTO parm: "+parms[0])
+                        tzoffsetto = self._parse_offset(value)
+                    elif name == "TZNAME":
+                        if parms:
+                            raise ValueError(
+                                "unsupported TZNAME parm: "+parms[0])
+                        tzname = value
+                    elif name == "COMMENT":
+                        pass
+                    else:
+                        raise ValueError("unsupported property: "+name)
+                else:
+                    if name == "TZID":
+                        if parms:
+                            raise ValueError(
+                                "unsupported TZID parm: "+parms[0])
+                        tzid = value
+                    elif name in ("TZURL", "LAST-MODIFIED", "COMMENT"):
+                        pass
+                    else:
+                        raise ValueError("unsupported property: "+name)
+            elif name == "BEGIN" and value == "VTIMEZONE":
+                tzid = None
+                comps = []
+                invtz = True
+
+    def __repr__(self):
+        return "%s(%s)" % (self.__class__.__name__, repr(self._s))
+
+if sys.platform != "win32":
+    TZFILES = ["/etc/localtime", "localtime"]
+    TZPATHS = ["/usr/share/zoneinfo", "/usr/lib/zoneinfo", "/etc/zoneinfo"]
+else:
+    TZFILES = []
+    TZPATHS = []
+
+
+def gettz(name=None):
+    tz = None
+    if not name:
+        try:
+            name = os.environ["TZ"]
+        except KeyError:
+            pass
+    if name is None or name == ":":
+        for filepath in TZFILES:
+            if not os.path.isabs(filepath):
+                filename = filepath
+                for path in TZPATHS:
+                    filepath = os.path.join(path, filename)
+                    if os.path.isfile(filepath):
+                        break
+                else:
+                    continue
+            if os.path.isfile(filepath):
+                try:
+                    tz = tzfile(filepath)
+                    break
+                except (IOError, OSError, ValueError):
+                    pass
+        else:
+            tz = tzlocal()
+    else:
+        if name.startswith(":"):
+            name = name[:-1]
+        if os.path.isabs(name):
+            if os.path.isfile(name):
+                tz = tzfile(name)
+            else:
+                tz = None
+        else:
+            for path in TZPATHS:
+                filepath = os.path.join(path, name)
+                if not os.path.isfile(filepath):
+                    filepath = filepath.replace(' ', '_')
+                    if not os.path.isfile(filepath):
+                        continue
+                try:
+                    tz = tzfile(filepath)
+                    break
+                except (IOError, OSError, ValueError):
+                    pass
+            else:
+                tz = None
+                if tzwin is not None:
+                    try:
+                        tz = tzwin(name)
+                    except WindowsError:
+                        tz = None
+                if not tz:
+                    from dateutil.zoneinfo import gettz
+                    tz = gettz(name)
+                if not tz:
+                    for c in name:
+                        # name must have at least one offset to be a tzstr
+                        if c in "0123456789":
+                            try:
+                                tz = tzstr(name)
+                            except ValueError:
+                                pass
+                            break
+                    else:
+                        if name in ("GMT", "UTC"):
+                            tz = tzutc()
+                        elif name in time.tzname:
+                            tz = tzlocal()
+    return tz
+
+# vim:ts=4:sw=4:et

pythonPackages/python-dateutil/dateutil/tzwin.py

@@ -0,0 +1,184 @@
+# This code was originally contributed by Jeffrey Harris.
+import datetime
+import struct
+
+from six.moves import winreg
+
+__all__ = ["tzwin", "tzwinlocal"]
+
+ONEWEEK = datetime.timedelta(7)
+
+TZKEYNAMENT = r"SOFTWARE\Microsoft\Windows NT\CurrentVersion\Time Zones"
+TZKEYNAME9X = r"SOFTWARE\Microsoft\Windows\CurrentVersion\Time Zones"
+TZLOCALKEYNAME = r"SYSTEM\CurrentControlSet\Control\TimeZoneInformation"
+
+
+def _settzkeyname():
+    handle = winreg.ConnectRegistry(None, winreg.HKEY_LOCAL_MACHINE)
+    try:
+        winreg.OpenKey(handle, TZKEYNAMENT).Close()
+        TZKEYNAME = TZKEYNAMENT
+    except WindowsError:
+        TZKEYNAME = TZKEYNAME9X
+    handle.Close()
+    return TZKEYNAME
+
+TZKEYNAME = _settzkeyname()
+
+
+class tzwinbase(datetime.tzinfo):
+    """tzinfo class based on win32's timezones available in the registry."""
+
+    def utcoffset(self, dt):
+        if self._isdst(dt):
+            return datetime.timedelta(minutes=self._dstoffset)
+        else:
+            return datetime.timedelta(minutes=self._stdoffset)
+
+    def dst(self, dt):
+        if self._isdst(dt):
+            minutes = self._dstoffset - self._stdoffset
+            return datetime.timedelta(minutes=minutes)
+        else:
+            return datetime.timedelta(0)
+
+    def tzname(self, dt):
+        if self._isdst(dt):
+            return self._dstname
+        else:
+            return self._stdname
+
+    def list():
+        """Return a list of all time zones known to the system."""
+        handle = winreg.ConnectRegistry(None, winreg.HKEY_LOCAL_MACHINE)
+        tzkey = winreg.OpenKey(handle, TZKEYNAME)
+        result = [winreg.EnumKey(tzkey, i)
+                  for i in range(winreg.QueryInfoKey(tzkey)[0])]
+        tzkey.Close()
+        handle.Close()
+        return result
+    list = staticmethod(list)
+
+    def display(self):
+        return self._display
+
+    def _isdst(self, dt):
+        if not self._dstmonth:
+            # dstmonth == 0 signals the zone has no daylight saving time
+            return False
+        dston = picknthweekday(dt.year, self._dstmonth, self._dstdayofweek,
+                               self._dsthour, self._dstminute,
+                               self._dstweeknumber)
+        dstoff = picknthweekday(dt.year, self._stdmonth, self._stddayofweek,
+                                self._stdhour, self._stdminute,
+                                self._stdweeknumber)
+        if dston < dstoff:
+            return dston <= dt.replace(tzinfo=None) < dstoff
+        else:
+            return not dstoff <= dt.replace(tzinfo=None) < dston
+
+
+class tzwin(tzwinbase):
+
+    def __init__(self, name):
+        self._name = name
+
+        # multiple contexts only possible in 2.7 and 3.1, we still support 2.6
+        with winreg.ConnectRegistry(None, winreg.HKEY_LOCAL_MACHINE) as handle:
+            with winreg.OpenKey(handle,
+                                "%s\%s" % (TZKEYNAME, name)) as tzkey:
+                keydict = valuestodict(tzkey)
+
+        self._stdname = keydict["Std"].encode("iso-8859-1")
+        self._dstname = keydict["Dlt"].encode("iso-8859-1")
+
+        self._display = keydict["Display"]
+
+        # See http://ww_winreg.jsiinc.com/SUBA/tip0300/rh0398.htm
+        tup = struct.unpack("=3l16h", keydict["TZI"])
+        self._stdoffset = -tup[0]-tup[1]          # Bias + StandardBias * -1
+        self._dstoffset = self._stdoffset-tup[2]  # + DaylightBias * -1
+
+        # for the meaning see the win32 TIME_ZONE_INFORMATION structure docs
+        # http://msdn.microsoft.com/en-us/library/windows/desktop/ms725481(v=vs.85).aspx
+        (self._stdmonth,
+         self._stddayofweek,   # Sunday = 0
+         self._stdweeknumber,  # Last = 5
+         self._stdhour,
+         self._stdminute) = tup[4:9]
+
+        (self._dstmonth,
+         self._dstdayofweek,   # Sunday = 0
+         self._dstweeknumber,  # Last = 5
+         self._dsthour,
+         self._dstminute) = tup[12:17]
+
+    def __repr__(self):
+        return "tzwin(%s)" % repr(self._name)
+
+    def __reduce__(self):
+        return (self.__class__, (self._name,))
+
+
+class tzwinlocal(tzwinbase):
+
+    def __init__(self):
+
+        with winreg.ConnectRegistry(None, winreg.HKEY_LOCAL_MACHINE) as handle:
+
+            with winreg.OpenKey(handle, TZLOCALKEYNAME) as tzlocalkey:
+                keydict = valuestodict(tzlocalkey)
+
+            self._stdname = keydict["StandardName"].encode("iso-8859-1")
+            self._dstname = keydict["DaylightName"].encode("iso-8859-1")
+
+            try:
+                with winreg.OpenKey(
+                        handle, "%s\%s" % (TZKEYNAME, self._stdname)) as tzkey:
+                    _keydict = valuestodict(tzkey)
+                    self._display = _keydict["Display"]
+            except OSError:
+                self._display = None
+
+        self._stdoffset = -keydict["Bias"]-keydict["StandardBias"]
+        self._dstoffset = self._stdoffset-keydict["DaylightBias"]
+
+        # See http://ww_winreg.jsiinc.com/SUBA/tip0300/rh0398.htm
+        tup = struct.unpack("=8h", keydict["StandardStart"])
+
+        (self._stdmonth,
+         self._stddayofweek,   # Sunday = 0
+         self._stdweeknumber,  # Last = 5
+         self._stdhour,
+         self._stdminute) = tup[1:6]
+
+        tup = struct.unpack("=8h", keydict["DaylightStart"])
+
+        (self._dstmonth,
+         self._dstdayofweek,   # Sunday = 0
+         self._dstweeknumber,  # Last = 5
+         self._dsthour,
+         self._dstminute) = tup[1:6]
+
+    def __reduce__(self):
+        return (self.__class__, ())
+
+
+def picknthweekday(year, month, dayofweek, hour, minute, whichweek):
+    """dayofweek == 0 means Sunday, whichweek 5 means last instance"""
+    first = datetime.datetime(year, month, 1, hour, minute)
+    weekdayone = first.replace(day=((dayofweek-first.isoweekday()) % 7+1))
+    for n in range(whichweek):
+        dt = weekdayone+(whichweek-n)*ONEWEEK
+        if dt.month == month:
+            return dt
+
+
+def valuestodict(key):
+    """Convert a registry key's values to a dictionary."""
+    dict = {}
+    size = winreg.QueryInfoKey(key)[1]
+    for i in range(size):
+        data = winreg.EnumValue(key, i)
+        dict[data[0]] = data[1]
+    return dict

pythonPackages/python-dateutil/dateutil/zoneinfo/__init__.py

@@ -0,0 +1,108 @@
+# -*- coding: utf-8 -*-
+import logging
+import os
+import warnings
+import tempfile
+import shutil
+from subprocess import check_call
+from tarfile import TarFile
+from pkgutil import get_data
+from io import BytesIO
+from contextlib import closing
+
+from dateutil.tz import tzfile
+
+__all__ = ["gettz", "rebuild"]
+
+_ZONEFILENAME = "dateutil-zoneinfo.tar.gz"
+
+# python2.6 compatability. Note that TarFile.__exit__ != TarFile.close, but
+# it's close enough for python2.6
+_tar_open = TarFile.open
+if not hasattr(TarFile, '__exit__'):
+    def _tar_open(*args, **kwargs):
+        return closing(TarFile.open(*args, **kwargs))
+
+
+class tzfile(tzfile):
+    def __reduce__(self):
+        return (gettz, (self._filename,))
+
+
+def getzoneinfofile_stream():
+    try:
+        return BytesIO(get_data(__name__, _ZONEFILENAME))
+    except IOError as e:  # TODO  switch to FileNotFoundError?
+        warnings.warn("I/O error({0}): {1}".format(e.errno, e.strerror))
+        return None
+
+
+class ZoneInfoFile(object):
+    def __init__(self, zonefile_stream=None):
+        if zonefile_stream is not None:
+            with _tar_open(fileobj=zonefile_stream, mode='r') as tf:
+                # dict comprehension does not work on python2.6
+                # TODO: get back to the nicer syntax when we ditch python2.6
+                # self.zones = {zf.name: tzfile(tf.extractfile(zf),
+                #               filename = zf.name)
+                #              for zf in tf.getmembers() if zf.isfile()}
+                self.zones = dict((zf.name, tzfile(tf.extractfile(zf),
+                                                   filename=zf.name))
+                                  for zf in tf.getmembers() if zf.isfile())
+                # deal with links: They'll point to their parent object. Less
+                # waste of memory
+                # links = {zl.name: self.zones[zl.linkname]
+                #        for zl in tf.getmembers() if zl.islnk() or zl.issym()}
+                links = dict((zl.name, self.zones[zl.linkname])
+                             for zl in tf.getmembers() if
+                             zl.islnk() or zl.issym())
+                self.zones.update(links)
+        else:
+            self.zones = dict()
+
+
+# The current API has gettz as a module function, although in fact it taps into
+# a stateful class. So as a workaround for now, without changing the API, we
+# will create a new "global" class instance the first time a user requests a
+# timezone. Ugly, but adheres to the api.
+#
+# TODO: deprecate this.
+_CLASS_ZONE_INSTANCE = list()
+
+
+def gettz(name):
+    if len(_CLASS_ZONE_INSTANCE) == 0:
+        _CLASS_ZONE_INSTANCE.append(ZoneInfoFile(getzoneinfofile_stream()))
+    return _CLASS_ZONE_INSTANCE[0].zones.get(name)
+
+
+def rebuild(filename, tag=None, format="gz", zonegroups=[]):
+    """Rebuild the internal timezone info in dateutil/zoneinfo/zoneinfo*tar*
+
+    filename is the timezone tarball from ftp.iana.org/tz.
+
+    """
+    tmpdir = tempfile.mkdtemp()
+    zonedir = os.path.join(tmpdir, "zoneinfo")
+    moduledir = os.path.dirname(__file__)
+    try:
+        with _tar_open(filename) as tf:
+            for name in zonegroups:
+                tf.extract(name, tmpdir)
+            filepaths = [os.path.join(tmpdir, n) for n in zonegroups]
+            try:
+                check_call(["zic", "-d", zonedir] + filepaths)
+            except OSError as e:
+                if e.errno == 2:
+                    logging.error(
+                        "Could not find zic. Perhaps you need to install "
+                        "libc-bin or some other package that provides it, "
+                        "or it's not in your PATH?")
+                    raise
+        target = os.path.join(moduledir, _ZONEFILENAME)
+        with _tar_open(target, "w:%s" % format) as tf:
+            for entry in os.listdir(zonedir):
+                entrypath = os.path.join(zonedir, entry)
+                tf.add(entrypath, entry)
+    finally:
+        shutil.rmtree(tmpdir)

pythonPackages/python-dateutil/python_dateutil.egg-info/PKG-INFO

@@ -0,0 +1,26 @@
+Metadata-Version: 1.1
+Name: python-dateutil
+Version: 2.4.2
+Summary: Extensions to the standard Python datetime module
+Home-page: https://dateutil.readthedocs.org
+Author: Yaron de Leeuw
+Author-email: me@jarondl.net
+License: Simplified BSD
+Description: 
+        The dateutil module provides powerful extensions to the
+        datetime module available in the Python standard library.
+        
+Platform: UNKNOWN
+Classifier: Development Status :: 5 - Production/Stable
+Classifier: Intended Audience :: Developers
+Classifier: License :: OSI Approved :: BSD License
+Classifier: Programming Language :: Python
+Classifier: Programming Language :: Python :: 2
+Classifier: Programming Language :: Python :: 2.6
+Classifier: Programming Language :: Python :: 2.7
+Classifier: Programming Language :: Python :: 3
+Classifier: Programming Language :: Python :: 3.2
+Classifier: Programming Language :: Python :: 3.3
+Classifier: Programming Language :: Python :: 3.4
+Classifier: Topic :: Software Development :: Libraries
+Requires: six

pythonPackages/python-dateutil/python_dateutil.egg-info/SOURCES.txt

@@ -0,0 +1,25 @@
+LICENSE
+MANIFEST.in
+NEWS
+README.rst
+setup.cfg
+setup.py
+updatezinfo.py
+zonefile_metadata.json
+dateutil/__init__.py
+dateutil/easter.py
+dateutil/parser.py
+dateutil/relativedelta.py
+dateutil/rrule.py
+dateutil/tz.py
+dateutil/tzwin.py
+dateutil/test/__init__.py
+dateutil/test/test.py
+dateutil/zoneinfo/__init__.py
+dateutil/zoneinfo/dateutil-zoneinfo.tar.gz
+python_dateutil.egg-info/PKG-INFO
+python_dateutil.egg-info/SOURCES.txt
+python_dateutil.egg-info/dependency_links.txt
+python_dateutil.egg-info/requires.txt
+python_dateutil.egg-info/top_level.txt
+python_dateutil.egg-info/zip-safe

pythonPackages/python-dateutil/python_dateutil.egg-info/dependency_links.txt

@@ -0,0 +1 @@
+

pythonPackages/python-dateutil/python_dateutil.egg-info/requires.txt

@@ -0,0 +1 @@
+six >=1.5

pythonPackages/python-dateutil/python_dateutil.egg-info/top_level.txt

@@ -0,0 +1 @@
+dateutil

pythonPackages/python-dateutil/python_dateutil.egg-info/zip-safe

@@ -0,0 +1 @@
+

pythonPackages/python-dateutil/setup.cfg

@@ -0,0 +1,8 @@
+[bdist_wheel]
+universal = 1
+
+[egg_info]
+tag_build = 
+tag_date = 0
+tag_svn_revision = 0
+

pythonPackages/python-dateutil/setup.py

@@ -0,0 +1,51 @@
+#!/usr/bin/python
+from os.path import isfile
+import codecs
+import os
+import re
+
+from setuptools import setup
+
+
+if isfile("MANIFEST"):
+    os.unlink("MANIFEST")
+
+
+TOPDIR = os.path.dirname(__file__) or "."
+VERSION = re.search('__version__ = "([^"]+)"',
+                    codecs.open(TOPDIR + "/dateutil/__init__.py",
+                                encoding='utf-8').read()).group(1)
+
+
+setup(name="python-dateutil",
+      version=VERSION,
+      description="Extensions to the standard Python datetime module",
+      author="Yaron de Leeuw",
+      author_email="me@jarondl.net",
+      url="https://dateutil.readthedocs.org",
+      license="Simplified BSD",
+      long_description="""
+The dateutil module provides powerful extensions to the
+datetime module available in the Python standard library.
+""",
+      packages=["dateutil", "dateutil.zoneinfo"],
+      package_data={"dateutil.zoneinfo": ["dateutil-zoneinfo.tar.gz"]},
+      zip_safe=True,
+      requires=["six"],
+      install_requires=["six >=1.5"],  # XXX fix when packaging is sane again
+      classifiers=[
+          'Development Status :: 5 - Production/Stable',
+          'Intended Audience :: Developers',
+          'License :: OSI Approved :: BSD License',
+          'Programming Language :: Python',
+          'Programming Language :: Python :: 2',
+          'Programming Language :: Python :: 2.6',
+          'Programming Language :: Python :: 2.7',
+          'Programming Language :: Python :: 3',
+          'Programming Language :: Python :: 3.2',
+          'Programming Language :: Python :: 3.3',
+          'Programming Language :: Python :: 3.4',
+          'Topic :: Software Development :: Libraries',
+      ],
+      test_suite="dateutil.test.test"
+      )

pythonPackages/python-dateutil/updatezinfo.py

@@ -0,0 +1,33 @@
+#!/usr/bin/env python
+import os
+import hashlib
+import json
+import io
+
+from six.moves.urllib import request
+
+from dateutil.zoneinfo import rebuild
+
+METADATA_FILE = "zonefile_metadata.json"
+
+
+def main():
+    with io.open(METADATA_FILE, 'r') as f:
+        metadata = json.load(f)
+
+    if not os.path.isfile(metadata['tzdata_file']):
+        print("Downloading tz file from iana")
+        request.urlretrieve(os.path.join(metadata['releases_url'],
+                                         metadata['tzdata_file']),
+                            metadata['tzdata_file'])
+    with open(metadata['tzdata_file'], 'rb') as tzfile:
+        sha_hasher = hashlib.sha512()
+        sha_hasher.update(tzfile.read())
+        sha_512_file = sha_hasher.hexdigest()
+        assert metadata['tzdata_file_sha512'] == sha_512_file, "SHA failed for"
+    print("Updating timezone information...")
+    rebuild(metadata['tzdata_file'], zonegroups=metadata['zonegroups'])
+    print("Done.")
+
+if __name__ == "__main__":
+    main()

pythonPackages/python-dateutil/zonefile_metadata.json

@@ -0,0 +1,21 @@
+{
+    "metadata_version" : 0.1,
+    "releases_url" : "ftp://ftp.iana.org/tz/releases/",
+    "tzdata_file" : "tzdata2015b.tar.gz",
+    "tzdata_file_sha512" : "767782b87e62a8f7a4dbcae595d16a54197c9e04ca974d7016d11f90ebaf2537b804d111f204af9052c68d4670afe0af0af9e5b150867a357fc199bb541368d0",
+    "zonegroups" : [
+        "africa",
+        "antarctica",
+        "asia",
+        "australasia",
+        "europe",
+        "northamerica",
+        "southamerica",
+        "pacificnew",
+        "etcetera",
+        "systemv",
+        "factory",
+        "backzone",
+        "backward"]
+}
+

pythonPackages/scipy-0.8.0/LICENSE.txt

@@ -0,0 +1,31 @@
+Copyright (c) 2001, 2002 Enthought, Inc.
+All rights reserved.
+
+Copyright (c) 2003-2009 SciPy Developers.
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+  a. Redistributions of source code must retain the above copyright notice,
+     this list of conditions and the following disclaimer.
+  b. Redistributions in binary form must reproduce the above copyright
+     notice, this list of conditions and the following disclaimer in the
+     documentation and/or other materials provided with the distribution.
+  c. Neither the name of the Enthought nor the names of its contributors
+     may be used to endorse or promote products derived from this software
+     without specific prior written permission.
+
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR
+ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
+DAMAGE.
+

pythonPackages/scipy-0.8.0/MANIFEST.in

@@ -0,0 +1,19 @@
+# Use .add_data_files and .add_data_dir methods in a appropriate
+# setup.py files to include non-python files such as documentation,
+# data, etc files to distribution. Avoid using MANIFEST.in for that.
+#
+include MANIFEST.in
+include *.txt
+include setupscons.py
+include setupegg.py
+include setup.py
+include scipy/*.py
+# Adding scons build relateed files not found by distutils
+recursive-include scipy SConstruct SConscript
+# Add documentation: we don't use add_data_dir since we do not want to include
+# this at installation, only for sdist-generated tarballs
+include doc/Makefile doc/postprocess.py
+recursive-include doc/release *
+recursive-include doc/source *
+recursive-include doc/sphinxext *
+prune scipy/special/tests/data/boost

pythonPackages/scipy-0.8.0/THANKS.txt

@@ -0,0 +1,77 @@
+SciPy is an open source library of routines for science and engineering
+using Python.  It is a community project sponsored by Enthought, Inc.
+SciPy originated with code contributions by Travis Oliphant, Pearu
+Peterson, and Eric Jones.  Travis Oliphant and Eric Jones each contributed
+about half the initial code.  Pearu Peterson developed f2py, which is the
+integral to wrapping the many Fortran libraries used in SciPy.
+
+Since then many people have contributed to SciPy, both in code development,
+suggestions, and financial support.  Below is a partial list.  If you've
+been left off, please email the "SciPy Developers List" <scipy-dev@scipy.org>.
+
+Please add names as needed so that we can keep up with all the contributors.
+
+Kumar Appaiah for Dolph Chebyshev window.
+Nathan Bell for sparsetools, help with scipy.sparse and scipy.splinalg.
+Robert Cimrman for UMFpack wrapper for sparse matrix module.
+David M. Cooke for improvements to system_info, and LBFGSB wrapper.
+Aric Hagberg for ARPACK wrappers, help with splinalg.eigen.
+Chuck Harris for Zeros package in optimize (1d root-finding algorithms).
+Prabhu Ramachandran for improvements to gui_thread.
+Robert Kern for improvements to stats and bug-fixes.
+Jean-Sebastien Roy for fmin_tnc code which he adapted from Stephen Nash's
+    original Fortran.
+Ed Schofield for Maximum entropy and Monte Carlo modules, help with
+    sparse matrix module.
+Travis Vaught for numerous contributions to annual conference and community
+    web-site and the initial work on stats module clean up.
+Jeff Whitaker for Mac OS X support.
+David Cournapeau for bug-fixes, refactoring of fftpack and cluster,
+    implementing the numscons build, building Windows binaries and
+    adding single precision FFT.
+Damian Eads for hierarchical clustering, dendrogram plotting,
+    distance functions in spatial package, vq documentation.
+Anne Archibald for kd-trees and nearest neighbor in scipy.spatial.
+Pauli Virtanen for Sphinx documentation generation, online documentation
+    framework and interpolation bugfixes.
+Josef Perktold for major improvements to scipy.stats and its test suite and 
+              fixes and tests to optimize.curve_fit and leastsq.
+David Morrill for getting the scoreboard test system up and running.
+Louis Luangkesorn for providing multiple tests for the stats module.
+Jochen Kupper for the zoom feature in the now-deprecated plt plotting module.
+Tiffany Kamm for working on the community web-site.
+Mark Koudritsky for maintaining the web-site.
+Andrew Straw for help with the web-page, documentation, packaging,
+    testing and work on the linalg module.
+Stefan van der Walt for numerous bug-fixes, testing and documentation.
+Jarrod Millman for release management, community coordination, and code
+    clean up.
+Pierre Gerard-Marchant for statistical masked array functionality.
+Alan McIntyre for updating SciPy tests to use the new NumPy test framework.
+Matthew Brett for work on the Matlab file IO, bug-fixes, and improvements
+    to the testing framework.
+Gary Strangman for the scipy.stats package.
+Tiziano Zito for generalized symmetric and hermitian eigenvalue problem
+    solver.
+Chris Burns for bug-fixes.
+Per Brodtkorb for improvements to stats distributions.
+Neilen Marais for testing and bug-fixing in the ARPACK wrappers.
+Johannes Loehnert and Bart Vandereycken for fixes in the linalg
+    module.
+David Huard for improvements to the interpolation interface.
+David Warde-Farley for converting the ndimage docs to ReST.
+Uwe Schmitt for wrapping non-negative least-squares.
+Ondrej Certik for Debian packaging.
+Paul Ivanov for porting Numeric-style C code to the new NumPy API.
+Ariel Rokem for contributions on percentileofscore fixes and tests.
+Yosef Meller for tests in the optimization module.
+
+Institutions
+------------
+
+Enthought for providing resources and finances for development of SciPy.
+Brigham Young University for providing resources for students to work on SciPy.
+Agilent which gave a genereous donation for support of SciPy.
+UC Berkeley for providing travel money and hosting numerous sprints.
+The University of Stellenbosch for funding the development of
+    the SciKits portal.

pythonPackages/scipy-0.8.0/doc/Makefile

@@ -0,0 +1,163 @@
+# Makefile for Sphinx documentation
+#
+
+PYVER =
+PYTHON = python$(PYVER)
+
+# You can set these variables from the command line.
+SPHINXOPTS    =
+SPHINXBUILD   = LANG=C sphinx-build
+PAPER         =
+
+NEED_AUTOSUMMARY = $(shell $(PYTHON) -c 'import sphinx; print sphinx.__version__ < "0.7" and "1" or ""')
+
+# Internal variables.
+PAPEROPT_a4     = -D latex_paper_size=a4
+PAPEROPT_letter = -D latex_paper_size=letter
+ALLSPHINXOPTS   = -d build/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) source
+
+.PHONY: help clean html web pickle htmlhelp latex changes linkcheck \
+        dist dist-build
+
+#------------------------------------------------------------------------------
+
+help:
+	@echo "Please use \`make <target>' where <target> is one of"
+	@echo "  html      to make standalone HTML files"
+	@echo "  pickle    to make pickle files (usable by e.g. sphinx-web)"
+	@echo "  htmlhelp  to make HTML files and a HTML help project"
+	@echo "  latex     to make LaTeX files, you can set PAPER=a4 or PAPER=letter"
+	@echo "  changes   to make an overview over all changed/added/deprecated items"
+	@echo "  linkcheck to check all external links for integrity"
+	@echo "  dist PYVER=... to make a distribution-ready tree"
+	@echo "  upload USER=...  to upload results to docs.scipy.org"
+
+clean:
+	-rm -rf build/* source/generated
+
+
+#------------------------------------------------------------------------------
+# Automated generation of all documents
+#------------------------------------------------------------------------------
+
+# Build the current scipy version, and extract docs from it.
+# We have to be careful of some issues:
+# 
+# - Everything must be done using the same Python version
+# - We must use eggs (otherwise they might override PYTHONPATH on import).
+# - Different versions of easy_install install to different directories (!)
+#
+
+INSTALL_DIR = $(CURDIR)/build/inst-dist/
+INSTALL_PPH = $(INSTALL_DIR)/lib/python$(PYVER)/site-packages:$(INSTALL_DIR)/local/lib/python$(PYVER)/site-packages:$(INSTALL_DIR)/lib/python$(PYVER)/dist-packages:$(INSTALL_DIR)/local/lib/python$(PYVER)/dist-packages
+
+DIST_VARS=PYTHON="PYTHONPATH=$(INSTALL_PPH):$$PYTHONPATH python$(PYVER)" SPHINXBUILD="LANG=C PYTHONPATH=$(INSTALL_PPH):$$PYTHONPATH python$(PYVER) `which sphinx-build`"
+
+UPLOAD_TARGET = $(USER)@docs.scipy.org:/home/docserver/www-root/doc/scipy/
+
+upload:
+	@test -e build/dist || { echo "make dist is required first"; exit 1; }
+	@test output-is-fine -nt build/dist || { \
+		echo "Review the output in build/dist, and do 'touch output-is-fine' before uploading."; exit 1; }
+	rsync -r -z --delete-after -p \
+	    $(if $(shell test -f build/dist/scipy-ref.pdf && echo "y"),, \
+	         --exclude '**-ref.pdf' --exclude '**-user.pdf') \
+	    $(if $(shell test -f build/dist/scipy-chm.zip && echo "y"),, \
+	         --exclude '**-chm.zip') \
+	    build/dist/ $(UPLOAD_TARGET)
+
+dist:
+	make $(DIST_VARS) real-dist
+
+real-dist: dist-build html
+	test -d build/latex || make latex
+	make -C build/latex all-pdf
+	-test -d build/htmlhelp || make htmlhelp-build
+	-rm -rf build/dist
+	mkdir -p build/dist
+	cp -r build/html build/dist/reference
+	touch build/dist/index.html
+	perl -pi -e 's#^\s*(<li><a href=".*?">SciPy.*?Reference Guide.*?&raquo;</li>)\s*$$#<li><a href="/">Numpy and Scipy Documentation</a> &raquo;</li> $$1#;' build/dist/*.html build/dist/*/*.html build/dist/*/*/*.html
+	(cd build/html && zip -9qr ../dist/scipy-html.zip .)
+	cp build/latex/scipy*.pdf build/dist
+	-zip build/dist/scipy-chm.zip build/htmlhelp/scipy.chm
+	cd build/dist && tar czf ../dist.tar.gz *
+	chmod ug=rwX,o=rX -R build/dist
+	find build/dist -type d -print0 | xargs -0r chmod g+s
+
+dist-build:
+	rm -f ../dist/*.egg
+	cd .. && $(PYTHON) setupegg.py bdist_egg
+	install -d $(subst :, ,$(INSTALL_PPH))
+	$(PYTHON) `which easy_install` --prefix=$(INSTALL_DIR) ../dist/*.egg
+
+
+#------------------------------------------------------------------------------
+# Basic Sphinx generation rules for different formats
+#------------------------------------------------------------------------------
+
+generate: build/generate-stamp
+build/generate-stamp: $(wildcard source/*.rst)
+	mkdir -p build
+ifeq ($(NEED_AUTOSUMMARY),1)
+	$(PYTHON) \
+		./sphinxext/autosummary_generate.py source/*.rst \
+		-p dump.xml -o source/generated 
+endif
+	touch build/generate-stamp
+
+html: generate
+	mkdir -p build/html build/doctrees
+	$(SPHINXBUILD) -b html $(ALLSPHINXOPTS) build/html
+	$(PYTHON) postprocess.py html build/html/*.html
+	@echo
+	@echo "Build finished. The HTML pages are in build/html."
+
+pickle: generate
+	mkdir -p build/pickle build/doctrees
+	$(SPHINXBUILD) -b pickle $(ALLSPHINXOPTS) build/pickle
+	@echo
+	@echo "Build finished; now you can process the pickle files or run"
+	@echo "  sphinx-web build/pickle"
+	@echo "to start the sphinx-web server."
+
+web: pickle
+
+htmlhelp: generate
+	mkdir -p build/htmlhelp build/doctrees
+	$(SPHINXBUILD) -b htmlhelp $(ALLSPHINXOPTS) build/htmlhelp
+	@echo
+	@echo "Build finished; now you can run HTML Help Workshop with the" \
+	      ".hhp project file in build/htmlhelp."
+
+htmlhelp-build: htmlhelp build/htmlhelp/scipy.chm
+%.chm: %.hhp
+	-hhc.exe $^
+
+latex: generate
+	mkdir -p build/latex build/doctrees
+	$(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) build/latex
+	$(PYTHON) postprocess.py tex build/latex/*.tex
+	perl -pi -e 's/\t(latex.*|pdflatex) (.*)/\t-$$1 -interaction batchmode $$2/' build/latex/Makefile
+	@echo
+	@echo "Build finished; the LaTeX files are in build/latex."
+	@echo "Run \`make all-pdf' or \`make all-ps' in that directory to" \
+	      "run these through (pdf)latex."
+
+coverage: build
+	mkdir -p build/coverage build/doctrees
+	$(SPHINXBUILD) -b coverage $(ALLSPHINXOPTS) build/coverage
+	@echo "Coverage finished; see c.txt and python.txt in build/coverage"
+
+changes: generate
+	mkdir -p build/changes build/doctrees
+	$(SPHINXBUILD) -b changes $(ALLSPHINXOPTS) build/changes
+	@echo
+	@echo "The overview file is in build/changes."
+
+linkcheck: generate
+	mkdir -p build/linkcheck build/doctrees
+	$(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) build/linkcheck
+	@echo
+	@echo "Link check complete; look for any errors in the above output " \
+	      "or in build/linkcheck/output.txt."

pythonPackages/scipy-0.8.0/doc/postprocess.py

@@ -0,0 +1,55 @@
+#!/usr/bin/env python
+"""
+%prog MODE FILES...
+
+Post-processes HTML and Latex files output by Sphinx.
+MODE is either 'html' or 'tex'.
+
+"""
+import re, optparse
+
+def main():
+    p = optparse.OptionParser(__doc__)
+    options, args = p.parse_args()
+
+    if len(args) < 1:
+        p.error('no mode given')
+
+    mode = args.pop(0)
+
+    if mode not in ('html', 'tex'):
+        p.error('unknown mode %s' % mode)
+
+    for fn in args:
+        f = open(fn, 'r')
+        try:
+            if mode == 'html':
+                lines = process_html(fn, f.readlines())
+            elif mode == 'tex':
+                lines = process_tex(f.readlines())
+        finally:
+            f.close()
+
+        f = open(fn, 'w')
+        f.write("".join(lines))
+        f.close()
+
+def process_html(fn, lines):
+    return lines
+
+def process_tex(lines):
+    """
+    Remove unnecessary section titles from the LaTeX file,
+    and convert UTF-8 non-breaking spaces to Latex nbsps.
+
+    """
+    new_lines = []
+    for line in lines:
+        if re.match(r'^\\(section|subsection|subsubsection|paragraph|subparagraph){(numpy|scipy)\.', line):
+            pass # skip!
+        else:
+            new_lines.append(line)
+    return new_lines
+
+if __name__ == "__main__":
+    main()

pythonPackages/scipy-0.8.0/doc/release/0.7.0-notes.rst

@@ -0,0 +1,348 @@
+=========================
+SciPy 0.7.0 Release Notes
+=========================
+
+.. contents::
+
+SciPy 0.7.0 is the culmination of 16 months of hard work. It contains
+many new features, numerous bug-fixes, improved test coverage and
+better documentation.  There have been a number of deprecations and
+API changes in this release, which are documented below.  All users
+are encouraged to upgrade to this release, as there are a large number
+of bug-fixes and optimizations.  Moreover, our development attention
+will now shift to bug-fix releases on the 0.7.x branch, and on adding
+new features on the development trunk.  This release requires Python
+2.4 or 2.5 and NumPy 1.2 or greater.
+
+Please note that SciPy is still considered to have "Beta" status, as
+we work toward a SciPy 1.0.0 release.  The 1.0.0 release will mark a
+major milestone in the development of SciPy, after which changing the
+package structure or API will be much more difficult.  Whilst these
+pre-1.0 releases are considered to have "Beta" status, we are
+committed to making them as bug-free as possible.  For example, in
+addition to fixing numerous bugs in this release, we have also doubled
+the number of unit tests since the last release.
+
+However, until the 1.0 release, we are aggressively reviewing and
+refining the functionality, organization, and interface. This is being
+done in an effort to make the package as coherent, intuitive, and
+useful as possible.  To achieve this, we need help from the community
+of users.  Specifically, we need feedback regarding all aspects of the
+project - everything - from which algorithms we implement, to details
+about our function's call signatures.
+
+Over the last year, we have seen a rapid increase in community
+involvement, and numerous infrastructure improvements to lower the
+barrier to contributions (e.g., more explicit coding standards,
+improved testing infrastructure, better documentation tools).  Over
+the next year, we hope to see this trend continue and invite everyone
+to become more involved.
+
+Python 2.6 and 3.0
+------------------
+
+A significant amount of work has gone into making SciPy compatible
+with Python 2.6; however, there are still some issues in this regard.
+The main issue with 2.6 support is NumPy.  On UNIX (including Mac OS
+X), NumPy 1.2.1 mostly works, with a few caveats.  On Windows, there
+are problems related to the compilation process.  The upcoming NumPy
+1.3 release will fix these problems.  Any remaining issues with 2.6
+support for SciPy 0.7 will be addressed in a bug-fix release.
+
+Python 3.0 is not supported at all; it requires NumPy to be ported to
+Python 3.0.  This requires immense effort, since a lot of C code has
+to be ported.  The transition to 3.0 is still under consideration;
+currently, we don't have any timeline or roadmap for this transition.
+
+Major documentation improvements
+--------------------------------
+
+SciPy documentation is greatly improved; you can view a HTML reference
+manual `online <http://docs.scipy.org/>`__ or download it as a PDF
+file. The new reference guide was built using the popular `Sphinx tool
+<http://sphinx.pocoo.org/>`__.
+
+This release also includes an updated tutorial, which hadn't been
+available since SciPy was ported to NumPy in 2005.  Though not
+comprehensive, the tutorial shows how to use several essential parts
+of Scipy.  It also includes the ``ndimage`` documentation from the
+``numarray`` manual.
+
+Nevertheless, more effort is needed on the documentation front.
+Luckily, contributing to Scipy documentation is now easier than
+before: if you find that a part of it requires improvements, and want
+to help us out, please register a user name in our web-based
+documentation editor at http://docs.scipy.org/ and correct the issues.
+
+Running Tests
+-------------
+
+NumPy 1.2 introduced a new testing framework based on `nose
+<http://somethingaboutorange.com/mrl/projects/nose/>`__.  Starting with
+this release, SciPy now uses the new NumPy test framework as well.
+Taking advantage of the new testing framework requires ``nose``
+version 0.10, or later.  One major advantage of the new framework is
+that it greatly simplifies writing unit tests - which has all ready
+paid off, given the rapid increase in tests.  To run the full test
+suite::
+
+    >>> import scipy
+    >>> scipy.test('full')
+
+For more information, please see `The NumPy/SciPy Testing Guide
+<http://projects.scipy.org/scipy/numpy/wiki/TestingGuidelines>`__.
+
+We have also greatly improved our test coverage.  There were just over
+2,000 unit tests in the 0.6.0 release; this release nearly doubles
+that number, with just over 4,000 unit tests.
+
+Building SciPy
+--------------
+
+Support for NumScons has been added. NumScons is a tentative new build
+system for NumPy/SciPy, using `SCons <http://www.scons.org/>`__ at its
+core.
+
+SCons is a next-generation build system, intended to replace the
+venerable ``Make`` with the integrated functionality of
+``autoconf``/``automake`` and ``ccache``.  Scons is written in Python
+and its configuration files are Python scripts.  NumScons is meant to
+replace NumPy's custom version of ``distutils`` providing more
+advanced functionality, such as ``autoconf``, improved fortran
+support, more tools, and support for ``numpy.distutils``/``scons``
+cooperation.
+
+Sandbox Removed
+---------------
+
+While porting SciPy to NumPy in 2005, several packages and modules
+were moved into ``scipy.sandbox``.  The sandbox was a staging ground
+for packages that were undergoing rapid development and whose APIs
+were in flux.  It was also a place where broken code could live.  The
+sandbox has served its purpose well, but was starting to create
+confusion.  Thus ``scipy.sandbox`` was removed.  Most of the code was
+moved into ``scipy``, some code was made into a ``scikit``, and the
+remaining code was just deleted, as the functionality had been
+replaced by other code.
+
+Sparse Matrices
+---------------
+
+Sparse matrices have seen extensive improvements.  There is now
+support for integer dtypes such ``int8``, ``uint32``, etc.  Two new
+sparse formats were added:
+
+* new class ``dia_matrix`` : the sparse DIAgonal format
+* new class ``bsr_matrix`` : the Block CSR format
+
+Several new sparse matrix construction functions were added:
+
+* ``sparse.kron`` : sparse Kronecker product
+* ``sparse.bmat`` : sparse version of ``numpy.bmat``
+* ``sparse.vstack`` : sparse version of ``numpy.vstack``
+* ``sparse.hstack`` : sparse version of ``numpy.hstack``
+
+Extraction of submatrices and nonzero values have been added:
+
+* ``sparse.tril`` : extract lower triangle
+* ``sparse.triu`` : extract upper triangle
+* ``sparse.find`` : nonzero values and their indices
+
+``csr_matrix`` and ``csc_matrix`` now support slicing and fancy
+indexing (e.g., ``A[1:3, 4:7]`` and ``A[[3,2,6,8],:]``).  Conversions
+among all sparse formats are now possible:
+
+* using member functions such as ``.tocsr()`` and ``.tolil()``
+* using the ``.asformat()`` member function, e.g. ``A.asformat('csr')``
+* using constructors ``A = lil_matrix([[1,2]]); B = csr_matrix(A)``
+
+All sparse constructors now accept dense matrices and lists of lists.
+For example:
+
+* ``A = csr_matrix( rand(3,3) )`` and ``B = lil_matrix( [[1,2],[3,4]] )``
+
+The handling of diagonals in the ``spdiags`` function has been changed.
+It now agrees with the MATLAB(TM) function of the same name.
+  
+Numerous efficiency improvements to format conversions and sparse
+matrix arithmetic have been made.  Finally, this release contains
+numerous bugfixes.
+
+Statistics package
+------------------
+
+Statistical functions for masked arrays have been added, and are
+accessible through ``scipy.stats.mstats``. The functions are similar
+to their counterparts in ``scipy.stats`` but they have not yet been
+verified for identical interfaces and algorithms.
+
+Several bugs were fixed for statistical functions, of those,
+``kstest`` and ``percentileofscore`` gained new keyword arguments.
+
+Added deprecation warning for ``mean``, ``median``, ``var``, ``std``,
+``cov``, and ``corrcoef``. These functions should be replaced by their
+numpy counterparts.  Note, however, that some of the default options
+differ between the ``scipy.stats`` and numpy versions of these
+functions.
+
+Numerous bug fixes to ``stats.distributions``: all generic methods now
+work correctly, several methods in individual distributions were
+corrected. However, a few issues remain with higher moments (``skew``,
+``kurtosis``) and entropy.  The maximum likelihood estimator, ``fit``,
+does not work out-of-the-box for some distributions - in some cases,
+starting values have to be carefully chosen, in other cases, the
+generic implementation of the maximum likelihood method might not be
+the numerically appropriate estimation method.
+
+We expect more bugfixes, increases in numerical precision and
+enhancements in the next release of scipy.
+
+Reworking of IO package
+-----------------------
+
+The IO code in both NumPy and SciPy is being extensively
+reworked. NumPy will be where basic code for reading and writing NumPy
+arrays is located, while SciPy will house file readers and writers for
+various data formats (data, audio, video, images, matlab, etc.).
+
+Several functions in ``scipy.io`` have been deprecated and will be
+removed in the 0.8.0 release including ``npfile``, ``save``, ``load``,
+``create_module``, ``create_shelf``, ``objload``, ``objsave``,
+``fopen``, ``read_array``, ``write_array``, ``fread``, ``fwrite``,
+``bswap``, ``packbits``, ``unpackbits``, and ``convert_objectarray``.
+Some of these functions have been replaced by NumPy's raw reading and
+writing capabilities, memory-mapping capabilities, or array methods.
+Others have been moved from SciPy to NumPy, since basic array reading
+and writing capability is now handled by NumPy.
+
+The Matlab (TM) file readers/writers have a number of improvements:
+
+* default version 5
+* v5 writers for structures, cell arrays, and objects
+* v5 readers/writers for function handles and 64-bit integers
+* new struct_as_record keyword argument to ``loadmat``, which loads
+  struct arrays in matlab as record arrays in numpy
+* string arrays have ``dtype='U...'`` instead of ``dtype=object``
+* ``loadmat`` no longer squeezes singleton dimensions, i.e.
+  ``squeeze_me=False`` by default
+
+New Hierarchical Clustering module
+----------------------------------
+
+This module adds new hierarchical clustering functionality to the
+``scipy.cluster`` package. The function interfaces are similar to the
+functions provided MATLAB(TM)'s Statistics Toolbox to help facilitate
+easier migration to the NumPy/SciPy framework. Linkage methods
+implemented include single, complete, average, weighted, centroid,
+median, and ward.
+
+In addition, several functions are provided for computing
+inconsistency statistics, cophenetic distance, and maximum distance
+between descendants. The ``fcluster`` and ``fclusterdata`` functions
+transform a hierarchical clustering into a set of flat clusters. Since
+these flat clusters are generated by cutting the tree into a forest of
+trees, the ``leaders`` function takes a linkage and a flat clustering,
+and finds the root of each tree in the forest. The ``ClusterNode``
+class represents a hierarchical clusterings as a field-navigable tree
+object. ``to_tree`` converts a matrix-encoded hierarchical clustering
+to a ``ClusterNode`` object. Routines for converting between MATLAB
+and SciPy linkage encodings are provided. Finally, a ``dendrogram``
+function plots hierarchical clusterings as a dendrogram, using
+matplotlib.
+
+New Spatial package
+-------------------
+
+The new spatial package contains a collection of spatial algorithms
+and data structures, useful for spatial statistics and clustering
+applications. It includes rapidly compiled code for computing exact
+and approximate nearest neighbors, as well as a pure-python kd-tree
+with the same interface, but that supports annotation and a variety of
+other algorithms. The API for both modules may change somewhat, as
+user requirements become clearer.
+
+It also includes a ``distance`` module, containing a collection of
+distance and dissimilarity functions for computing distances between
+vectors, which is useful for spatial statistics, clustering, and
+kd-trees.  Distance and dissimilarity functions provided include
+Bray-Curtis, Canberra, Chebyshev, City Block, Cosine, Dice, Euclidean,
+Hamming, Jaccard, Kulsinski, Mahalanobis, Matching, Minkowski,
+Rogers-Tanimoto, Russell-Rao, Squared Euclidean, Standardized
+Euclidean, Sokal-Michener, Sokal-Sneath, and Yule.
+
+The ``pdist`` function computes pairwise distance between all
+unordered pairs of vectors in a set of vectors. The ``cdist`` computes
+the distance on all pairs of vectors in the Cartesian product of two
+sets of vectors.  Pairwise distance matrices are stored in condensed
+form; only the upper triangular is stored. ``squareform`` converts
+distance matrices between square and condensed forms.
+
+Reworked fftpack package
+------------------------
+
+FFTW2, FFTW3, MKL and DJBFFT wrappers have been removed. Only (NETLIB)
+fftpack remains. By focusing on one backend, we hope to add new
+features - like float32 support - more easily.
+
+New Constants package
+---------------------
+
+``scipy.constants`` provides a collection of physical constants and
+conversion factors.  These constants are taken from CODATA Recommended
+Values of the Fundamental Physical Constants: 2002. They may be found
+at physics.nist.gov/constants. The values are stored in the dictionary
+physical_constants as a tuple containing the value, the units, and the
+relative precision - in that order. All constants are in SI units,
+unless otherwise stated.  Several helper functions are provided.
+
+New Radial Basis Function module
+--------------------------------
+
+``scipy.interpolate`` now contains a Radial Basis Function module.
+Radial basis functions can be used for smoothing/interpolating
+scattered data in n-dimensions, but should be used with caution for
+extrapolation outside of the observed data range.
+
+New complex ODE integrator
+--------------------------
+
+``scipy.integrate.ode`` now contains a wrapper for the ZVODE
+complex-valued ordinary differential equation solver (by Peter
+N. Brown, Alan C. Hindmarsh, and George D. Byrne).
+
+New generalized symmetric and hermitian eigenvalue problem solver
+-----------------------------------------------------------------
+
+``scipy.linalg.eigh`` now contains wrappers for more LAPACK symmetric
+and hermitian eigenvalue problem solvers. Users can now solve
+generalized problems, select a range of eigenvalues only, and choose
+to use a faster algorithm at the expense of increased memory
+usage. The signature of the ``scipy.linalg.eigh`` changed accordingly.
+
+Bug fixes in the interpolation package
+--------------------------------------
+
+The shape of return values from ``scipy.interpolate.interp1d`` used to
+be incorrect, if interpolated data had more than 2 dimensions and the
+axis keyword was set to a non-default value. This has been fixed.
+Moreover, ``interp1d`` returns now a scalar (0D-array) if the input
+is a scalar. Users of ``scipy.interpolate.interp1d`` may need to
+revise their code if it relies on the previous behavior.
+
+Weave clean up
+--------------
+
+There were numerous improvements to ``scipy.weave``.  ``blitz++`` was
+relicensed by the author to be compatible with the SciPy license.
+``wx_spec.py`` was removed.
+
+Known problems
+--------------
+
+Here are known problems with scipy 0.7.0:
+
+* weave test failures on windows: those are known, and are being revised.
+* weave test failure with gcc 4.3 (std::labs): this is a gcc 4.3 bug. A
+  workaround is to add #include <cstdlib> in
+  scipy/weave/blitz/blitz/funcs.h (line 27). You can make the change in
+  the installed scipy (in site-packages).

pythonPackages/scipy-0.8.0/doc/release/0.8.0-notes.rst

@@ -0,0 +1,263 @@
+=========================
+SciPy 0.8.0 Release Notes
+=========================
+
+.. contents::
+
+SciPy 0.8.0 is the culmination of 17 months of hard work. It contains
+many new features, numerous bug-fixes, improved test coverage and
+better documentation.  There have been a number of deprecations and
+API changes in this release, which are documented below.  All users
+are encouraged to upgrade to this release, as there are a large number
+of bug-fixes and optimizations.  Moreover, our development attention
+will now shift to bug-fix releases on the 0.8.x branch, and on adding
+new features on the development trunk.  This release requires Python
+2.4 - 2.6 and NumPy 1.4.1 or greater.
+
+Please note that SciPy is still considered to have "Beta" status, as
+we work toward a SciPy 1.0.0 release.  The 1.0.0 release will mark a
+major milestone in the development of SciPy, after which changing the
+package structure or API will be much more difficult.  Whilst these
+pre-1.0 releases are considered to have "Beta" status, we are
+committed to making them as bug-free as possible.  
+
+However, until the 1.0 release, we are aggressively reviewing and
+refining the functionality, organization, and interface. This is being
+done in an effort to make the package as coherent, intuitive, and
+useful as possible.  To achieve this, we need help from the community
+of users.  Specifically, we need feedback regarding all aspects of the
+project - everything - from which algorithms we implement, to details
+about our function's call signatures.
+
+Python 3
+========
+
+Python 3 compatibility is planned and is currently technically
+feasible, since Numpy has been ported. However, since the Python 3
+compatible Numpy 1.5 has not been released yet, support for Python 3
+in Scipy is not yet included in Scipy 0.8.  SciPy 0.9, planned for fall 
+2010, will very likely include experimental support for Python 3.
+
+Major documentation improvements
+================================
+
+SciPy documentation is greatly improved.
+
+Deprecated features
+===================
+
+Swapping inputs for correlation functions (scipy.signal)
+--------------------------------------------------------
+
+Concern correlate, correlate2d, convolve and convolve2d. If the second input is
+larger than the first input, the inputs are swapped before calling the
+underlying computation routine. This behavior is deprecated, and will be
+removed in scipy 0.9.0.
+
+Obsolete code deprecated (scipy.misc)
+-------------------------------------
+
+The modules `helpmod`, `ppimport` and `pexec` from `scipy.misc` are deprecated.
+They will be removed from SciPy in version 0.9.
+
+Additional deprecations
+-----------------------
+
+* linalg: The function `solveh_banded` currently returns a tuple containing
+  the Cholesky factorization and the solution to the linear system.  In
+  SciPy 0.9, the return value will be just the solution.
+* The function `constants.codata.find` will generate a DeprecationWarning.
+  In Scipy version 0.8.0, the keyword argument 'disp' was added to the
+  function, with the default value 'True'.  In 0.9.0, the default will be
+  'False'.
+* The `qshape` keyword argument of `signal.chirp` is deprecated.  Use
+  the argument `vertex_zero` instead.
+* Passing the coefficients of a polynomial as the argument `f0` to
+  `signal.chirp` is deprecated.  Use the function `signal.sweep_poly`
+  instead.
+* The `io.recaster` module has been deprecated and will be removed in 0.9.0.
+
+New features
+============
+
+DCT support (scipy.fftpack)
+---------------------------
+
+New realtransforms have been added, namely dct and idct for Discrete Cosine
+Transform; type I, II and III are available.
+
+Single precision support for fft functions (scipy.fftpack)
+----------------------------------------------------------
+
+fft functions can now handle single precision inputs as well: fft(x) will
+return a single precision array if x is single precision.
+
+At the moment, for FFT sizes that are not composites of 2, 3, and 5, the
+transform is computed internally in double precision to avoid rounding error in
+FFTPACK.
+
+Correlation functions now implement the usual definition (scipy.signal)
+-----------------------------------------------------------------------
+
+The outputs should now correspond to their matlab and R counterparts, and do
+what most people expect if the old_behavior=False argument is passed:
+
+* correlate, convolve and their 2d counterparts do not swap their inputs
+  depending on their relative shape anymore;
+* correlation functions now conjugate their second argument while computing
+  the slided sum-products, which correspond to the usual definition of
+  correlation.
+
+Additions and modification to LTI functions (scipy.signal)
+----------------------------------------------------------
+
+* The functions `impulse2` and `step2` were added to `scipy.signal`.
+  They use the function `scipy.signal.lsim2` to compute the impulse and
+  step response of a system, respectively.
+* The function `scipy.signal.lsim2` was changed to pass any additional
+  keyword arguments to the ODE solver.
+
+Improved waveform generators (scipy.signal)
+-------------------------------------------
+
+Several improvements to the `chirp` function in `scipy.signal` were made:
+
+* The waveform generated when `method="logarithmic"` was corrected; it
+  now generates a waveform that is also known as an "exponential" or
+  "geometric" chirp. (See http://en.wikipedia.org/wiki/Chirp.)
+* A new `chirp` method, "hyperbolic", was added.
+* Instead of the keyword `qshape`, `chirp` now uses the keyword
+  `vertex_zero`, a boolean.
+* `chirp` no longer handles an arbitrary polynomial.  This functionality
+  has been moved to a new function, `sweep_poly`.
+
+A new function, `sweep_poly`, was added.
+
+New functions and other changes in scipy.linalg
+-----------------------------------------------
+
+The functions `cho_solve_banded`, `circulant`, `companion`, `hadamard` and
+`leslie` were added to `scipy.linalg`.
+
+The function `block_diag` was enhanced to accept scalar and 1D arguments,
+along with the usual 2D arguments.
+
+New function and changes in scipy.optimize
+------------------------------------------
+
+The `curve_fit` function has been added; it takes a function and uses
+non-linear least squares to fit that to the provided data.
+
+The `leastsq` and `fsolve` functions now return an array of size one instead of
+a scalar when solving for a single parameter.
+
+New sparse least squares solver
+-------------------------------
+
+The `lsqr` function was added to `scipy.sparse`.  `This routine
+<http://www.stanford.edu/group/SOL/software/lsqr.html>`_ finds a
+least-squares solution to a large, sparse, linear system of equations.
+
+ARPACK-based sparse SVD
+-----------------------
+
+A naive implementation of SVD for sparse matrices is available in
+scipy.sparse.linalg.eigen.arpack. It is based on using an symmetric solver on
+<A, A>, and as such may not be very precise.
+
+Alternative behavior available for `scipy.constants.find`
+---------------------------------------------------------
+
+The keyword argument `disp` was added to the function `scipy.constants.find`,
+with the default value `True`.  When `disp` is `True`, the behavior is the
+same as in Scipy version 0.7.  When `False`, the function returns the list of
+keys instead of printing them.  (In SciPy version 0.9, the default will be
+reversed.)
+
+Incomplete sparse LU decompositions
+-----------------------------------
+
+Scipy now wraps SuperLU version 4.0, which supports incomplete sparse LU
+decompositions. These can be accessed via `scipy.sparse.linalg.spilu`.
+Upgrade to SuperLU 4.0 also fixes some known bugs.
+
+Faster matlab file reader and default behavior change
+------------------------------------------------------
+
+We've rewritten the matlab file reader in Cython and it should now read
+matlab files at around the same speed that Matlab does.
+
+The reader reads matlab named and anonymous functions, but it can't
+write them.
+
+Until scipy 0.8.0 we have returned arrays of matlab structs as numpy
+object arrays, where the objects have attributes named for the struct
+fields.  As of 0.8.0, we return matlab structs as numpy structured
+arrays.  You can get the older behavior by using the optional
+``struct_as_record=False`` keyword argument to `scipy.io.loadmat` and
+friends.
+
+There is an inconsistency in the matlab file writer, in that it writes
+numpy 1D arrays as column vectors in matlab 5 files, and row vectors in
+matlab 4 files.  We will change this in the next version, so both write
+row vectors.  There is a `FutureWarning` when calling the writer to warn
+of this change; for now we suggest using the ``oned_as='row'`` keyword
+argument to `scipy.io.savemat` and friends.
+
+Faster evaluation of orthogonal polynomials
+-------------------------------------------
+
+Values of orthogonal polynomials can be evaluated with new vectorized functions
+in `scipy.special`: `eval_legendre`, `eval_chebyt`, `eval_chebyu`,
+`eval_chebyc`, `eval_chebys`, `eval_jacobi`, `eval_laguerre`,
+`eval_genlaguerre`, `eval_hermite`, `eval_hermitenorm`,
+`eval_gegenbauer`, `eval_sh_legendre`, `eval_sh_chebyt`,
+`eval_sh_chebyu`, `eval_sh_jacobi`. This is faster than constructing the
+full coefficient representation of the polynomials, which was previously the
+only available way.
+
+Note that the previous orthogonal polynomial routines will now also invoke this
+feature, when possible.
+
+Lambert W function
+------------------
+
+`scipy.special.lambertw` can now be used for evaluating the Lambert W
+function.
+
+Improved hypergeometric 2F1 function
+------------------------------------
+
+Implementation of `scipy.special.hyp2f1` for real parameters was revised.
+The new version should produce accurate values for all real parameters.
+
+More flexible interface for Radial basis function interpolation
+---------------------------------------------------------------
+
+The `scipy.interpolate.Rbf` class now accepts a callable as input for the
+"function" argument, in addition to the built-in radial basis functions which
+can be selected with a string argument.
+
+Removed features
+================
+
+scipy.stsci: the package was removed
+
+The module `scipy.misc.limits` was removed.
+
+scipy.io
+--------
+
+The IO code in both NumPy and SciPy is being extensively
+reworked. NumPy will be where basic code for reading and writing NumPy
+arrays is located, while SciPy will house file readers and writers for
+various data formats (data, audio, video, images, matlab, etc.).
+
+Several functions in `scipy.io` are removed in the 0.8.0 release including:
+`npfile`, `save`, `load`, `create_module`, `create_shelf`,
+`objload`, `objsave`, `fopen`, `read_array`, `write_array`,
+`fread`, `fwrite`, `bswap`, `packbits`, `unpackbits`, and
+`convert_objectarray`.  Some of these functions have been replaced by NumPy's
+raw reading and writing capabilities, memory-mapping capabilities, or array
+methods.  Others have been moved from SciPy to NumPy, since basic array reading
+and writing capability is now handled by NumPy.

pythonPackages/scipy-0.8.0/doc/source/_templates/autosummary/class.rst

@@ -0,0 +1,23 @@
+{% extends "!autosummary/class.rst" %}
+
+{% block methods %}
+{% if methods %}
+   .. HACK
+      .. autosummary::
+         :toctree:
+      {% for item in methods %}
+         {{ name }}.{{ item }}
+      {%- endfor %}
+{% endif %}
+{% endblock %}
+
+{% block attributes %}
+{% if attributes %}
+   .. HACK
+      .. autosummary::
+         :toctree:
+      {% for item in attributes %}
+         {{ name }}.{{ item }}
+      {%- endfor %}
+{% endif %}
+{% endblock %}

pythonPackages/scipy-0.8.0/doc/source/_templates/indexsidebar.html

@@ -0,0 +1,5 @@
+            <h3>Resources</h3>
+            <ul>
+              <li><a href="http://scipy.org/">Scipy.org website</a></li>
+              <li>&nbsp;</li>
+            </ul>

pythonPackages/scipy-0.8.0/doc/source/_templates/layout.html

@@ -0,0 +1,14 @@
+{% extends "!layout.html" %}
+
+{% block sidebarsearch %}
+{%- if sourcename %}
+<ul class="this-page-menu">
+{%- if 'generated/' in sourcename %}
+  <li><a href="/scipy/docs/{{ sourcename.replace('generated/', '').replace('.txt', '') |e }}">{{_('Edit page')}}</a></li>
+{%- else %}
+  <li><a href="/scipy/docs/scipy-docs/{{ sourcename.replace('.txt', '.rst') |e }}">{{_('Edit page')}}</a></li>
+{%- endif %}
+</ul>
+{%- endif %}
+{{ super() }}
+{% endblock %}

pythonPackages/scipy-0.8.0/doc/source/cluster.hierarchy.rst

@@ -0,0 +1,10 @@
+========================================================
+Hierarchical clustering (:mod:`scipy.cluster.hierarchy`)
+========================================================
+
+.. warning::
+
+   This documentation is work-in-progress and unorganized.
+
+.. automodule:: scipy.cluster.hierarchy
+   :members:

pythonPackages/scipy-0.8.0/doc/source/cluster.rst

@@ -0,0 +1,10 @@
+=========================================
+Clustering package (:mod:`scipy.cluster`)
+=========================================
+
+.. toctree::
+
+   cluster.hierarchy
+   cluster.vq
+
+.. automodule:: scipy.cluster

pythonPackages/scipy-0.8.0/doc/source/cluster.vq.rst

@@ -0,0 +1,6 @@
+====================================================================
+K-means clustering and vector quantization (:mod:`scipy.cluster.vq`)
+====================================================================
+
+.. automodule:: scipy.cluster.vq
+   :members:

pythonPackages/scipy-0.8.0/doc/source/conf.py

@@ -0,0 +1,286 @@
+# -*- coding: utf-8 -*-
+
+import sys, os, re
+
+# If your extensions are in another directory, add it here. If the directory
+# is relative to the documentation root, use os.path.abspath to make it
+# absolute, like shown here.
+sys.path.insert(0, os.path.abspath('../sphinxext'))
+
+# Check Sphinx version
+import sphinx
+if sphinx.__version__ < "0.5":
+    raise RuntimeError("Sphinx 0.5.dev or newer required")
+
+
+# -----------------------------------------------------------------------------
+# General configuration
+# -----------------------------------------------------------------------------
+
+# Add any Sphinx extension module names here, as strings. They can be extensions
+# coming with Sphinx (named 'sphinx.ext.*') or your custom ones.
+extensions = ['sphinx.ext.autodoc', 'sphinx.ext.pngmath', 'numpydoc',
+              'sphinx.ext.intersphinx', 'sphinx.ext.coverage', 'plot_directive']
+
+if sphinx.__version__ >= "0.7":
+    extensions.append('sphinx.ext.autosummary')
+else:
+    extensions.append('autosummary')
+    extensions.append('only_directives')
+
+
+# Add any paths that contain templates here, relative to this directory.
+templates_path = ['_templates']
+
+# The suffix of source filenames.
+source_suffix = '.rst'
+
+# The master toctree document.
+master_doc = 'index'
+
+# General substitutions.
+project = 'SciPy'
+copyright = '2008-2009, The Scipy community'
+
+# The default replacements for |version| and |release|, also used in various
+# other places throughout the built documents.
+#
+import scipy
+# The short X.Y version (including the .devXXXX suffix if present)
+version = re.sub(r'^(\d+\.\d+)\.\d+(.*)', r'\1\2', scipy.__version__)
+if 'dev' in version:
+    # retain the .dev suffix, but clean it up
+    version = re.sub(r'(\.dev\d*).*?$', r'\1', version)
+else:
+    # strip all other suffixes
+    version = re.sub(r'^(\d+\.\d+).*?$', r'\1', version)
+# The full version, including alpha/beta/rc tags.
+release = scipy.__version__
+
+print "Scipy (VERSION %s) (RELEASE %s)" % (version, release)
+
+# There are two options for replacing |today|: either, you set today to some
+# non-false value, then it is used:
+#today = ''
+# Else, today_fmt is used as the format for a strftime call.
+today_fmt = '%B %d, %Y'
+
+# List of documents that shouldn't be included in the build.
+#unused_docs = []
+
+# The reST default role (used for this markup: `text`) to use for all documents.
+default_role = "autolink"
+
+# List of directories, relative to source directories, that shouldn't be searched
+# for source files.
+exclude_dirs = []
+
+# If true, '()' will be appended to :func: etc. cross-reference text.
+add_function_parentheses = False
+
+# If true, the current module name will be prepended to all description
+# unit titles (such as .. function::).
+#add_module_names = True
+
+# If true, sectionauthor and moduleauthor directives will be shown in the
+# output. They are ignored by default.
+show_authors = False
+
+# The name of the Pygments (syntax highlighting) style to use.
+pygments_style = 'sphinx'
+
+
+# -----------------------------------------------------------------------------
+# HTML output
+# -----------------------------------------------------------------------------
+
+# The style sheet to use for HTML and HTML Help pages. A file of that name
+# must exist either in Sphinx' static/ path, or in one of the custom paths
+# given in html_static_path.
+html_style = 'scipy.css'
+
+# The name for this set of Sphinx documents.  If None, it defaults to
+# "<project> v<release> documentation".
+html_title = "%s v%s Reference Guide (DRAFT)" % (project, version)
+
+# The name of an image file (within the static path) to place at the top of
+# the sidebar.
+html_logo = '_static/scipyshiny_small.png'
+
+# Add any paths that contain custom static files (such as style sheets) here,
+# relative to this directory. They are copied after the builtin static files,
+# so a file named "default.css" will overwrite the builtin "default.css".
+html_static_path = ['_static']
+
+# If not '', a 'Last updated on:' timestamp is inserted at every page bottom,
+# using the given strftime format.
+html_last_updated_fmt = '%b %d, %Y'
+
+# Correct index page
+#html_index = "index"
+
+# If true, SmartyPants will be used to convert quotes and dashes to
+# typographically correct entities.
+#html_use_smartypants = True
+
+# Custom sidebar templates, maps document names to template names.
+html_sidebars = {
+    'index': 'indexsidebar.html'
+}
+
+# Additional templates that should be rendered to pages, maps page names to
+# template names.
+html_additional_pages = {}
+
+# If false, no module index is generated.
+html_use_modindex = True
+
+# If true, the reST sources are included in the HTML build as _sources/<name>.
+#html_copy_source = True
+
+# If true, an OpenSearch description file will be output, and all pages will
+# contain a <link> tag referring to it.  The value of this option must be the
+# base URL from which the finished HTML is served.
+#html_use_opensearch = ''
+
+# If nonempty, this is the file name suffix for HTML files (e.g. ".html").
+html_file_suffix = '.html'
+
+# Output file base name for HTML help builder.
+htmlhelp_basename = 'scipy'
+
+# Pngmath should try to align formulas properly
+pngmath_use_preview = True
+
+
+# -----------------------------------------------------------------------------
+# LaTeX output
+# -----------------------------------------------------------------------------
+
+# The paper size ('letter' or 'a4').
+#latex_paper_size = 'letter'
+
+# The font size ('10pt', '11pt' or '12pt').
+#latex_font_size = '10pt'
+
+# Grouping the document tree into LaTeX files. List of tuples
+# (source start file, target name, title, author, document class [howto/manual]).
+_stdauthor = 'Written by the SciPy community'
+latex_documents = [
+  ('index', 'scipy-ref.tex', 'SciPy Reference Guide', _stdauthor, 'manual'),
+#  ('user/index', 'scipy-user.tex', 'SciPy User Guide',
+#   _stdauthor, 'manual'),
+]
+
+# The name of an image file (relative to this directory) to place at the top of
+# the title page.
+#latex_logo = None
+
+# For "manual" documents, if this is true, then toplevel headings are parts,
+# not chapters.
+#latex_use_parts = False
+
+# Additional stuff for the LaTeX preamble.
+latex_preamble = r'''
+\usepackage{amsmath}
+\DeclareUnicodeCharacter{00A0}{\nobreakspace}
+
+% In the parameters section, place a newline after the Parameters
+% header
+\usepackage{expdlist}
+\let\latexdescription=\description
+\def\description{\latexdescription{}{} \breaklabel}
+
+% Make Examples/etc section headers smaller and more compact
+\makeatletter
+\titleformat{\paragraph}{\normalsize\py@HeaderFamily}%
+            {\py@TitleColor}{0em}{\py@TitleColor}{\py@NormalColor}
+\titlespacing*{\paragraph}{0pt}{1ex}{0pt}
+\makeatother
+
+% Fix footer/header
+\renewcommand{\chaptermark}[1]{\markboth{\MakeUppercase{\thechapter.\ #1}}{}}
+\renewcommand{\sectionmark}[1]{\markright{\MakeUppercase{\thesection.\ #1}}}
+'''
+
+# Documents to append as an appendix to all manuals.
+#latex_appendices = []
+
+# If false, no module index is generated.
+latex_use_modindex = False
+
+
+# -----------------------------------------------------------------------------
+# Intersphinx configuration
+# -----------------------------------------------------------------------------
+intersphinx_mapping = {
+        'http://docs.python.org/dev': None,
+        'http://docs.scipy.org/doc/numpy': None,
+}
+
+
+# -----------------------------------------------------------------------------
+# Numpy extensions
+# -----------------------------------------------------------------------------
+
+# If we want to do a phantom import from an XML file for all autodocs
+phantom_import_file = 'dump.xml'
+
+# Edit links
+#numpydoc_edit_link = '`Edit </pydocweb/doc/%(full_name)s/>`__'
+
+# -----------------------------------------------------------------------------
+# Autosummary
+# -----------------------------------------------------------------------------
+
+if sphinx.__version__ >= "0.7": 
+    import glob
+    autosummary_generate = glob.glob("*.rst")
+
+# -----------------------------------------------------------------------------
+# Coverage checker
+# -----------------------------------------------------------------------------
+coverage_ignore_modules = r"""
+    """.split()
+coverage_ignore_functions = r"""
+    test($|_) (some|all)true bitwise_not cumproduct pkgload
+    generic\.
+    """.split()
+coverage_ignore_classes = r"""
+    """.split()
+
+coverage_c_path = []
+coverage_c_regexes = {}
+coverage_ignore_c_items = {}
+
+
+#------------------------------------------------------------------------------
+# Plot
+#------------------------------------------------------------------------------
+plot_pre_code = """
+import numpy as np
+import scipy as sp
+np.random.seed(123)
+"""
+plot_include_source = True
+plot_formats = [('png', 100), 'pdf']
+
+import math
+phi = (math.sqrt(5) + 1)/2
+
+import matplotlib
+matplotlib.rcParams.update({
+    'font.size': 8,
+    'axes.titlesize': 8,
+    'axes.labelsize': 8,
+    'xtick.labelsize': 8,
+    'ytick.labelsize': 8,
+    'legend.fontsize': 8,
+    'figure.figsize': (3*phi, 3),
+    'figure.subplot.bottom': 0.2,
+    'figure.subplot.left': 0.2,
+    'figure.subplot.right': 0.9,
+    'figure.subplot.top': 0.85,
+    'figure.subplot.wspace': 0.4,
+    'text.usetex': False,
+})

pythonPackages/scipy-0.8.0/doc/source/constants.rst

@@ -0,0 +1,582 @@
+==================================
+Constants (:mod:`scipy.constants`)
+==================================
+
+.. module:: scipy.constants
+
+Physical and mathematical constants and units.
+
+Mathematical constants
+======================
+
+============  =================================================================
+``pi``        Pi
+``golden``    Golden ratio
+============  =================================================================
+
+Physical constants
+==================
+
+=============  =================================================================
+``c``          speed of light in vacuum
+``mu_0``       the magnetic constant :math:`\mu_0`
+``epsilon_0``  the electric constant (vacuum permittivity), :math:`\epsilon_0`
+``h``          the Planck constant :math:`h`
+``hbar``       :math:`\hbar = h/(2\pi)`
+``G``          Newtonian constant of gravitation
+``g``          standard acceleration of gravity
+``e``          elementary charge
+``R``          molar gas constant
+``alpha``      fine-structure constant
+``N_A``        Avogadro constant
+``k``          Boltzmann constant
+``sigma``      Stefan-Boltzmann constant :math:`\sigma`
+``Wien``       Wien displacement law constant
+``Rydberg``    Rydberg constant
+``m_e``        electron mass
+``m_p``        proton mass
+``m_n``        neutron mass
+=============  =================================================================
+
+
+Constants database
+==================
+
+In addition to the above variables containing physical constants,
+:mod:`scipy.constants` also contains a database of additional physical
+constants.
+
+.. autosummary::
+   :toctree: generated/
+
+   value
+   unit
+   precision
+   find
+
+.. data:: physical_constants
+
+   Dictionary of physical constants, of the format
+   ``physical_constants[name] = (value, unit, uncertainty)``.
+
+   Available constants:
+
+   ======================================================================  ====
+   ``alpha particle mass``
+   ``alpha particle mass energy equivalent``
+   ``alpha particle mass energy equivalent in MeV``
+   ``alpha particle mass in u``
+   ``alpha particle molar mass``
+   ``alpha particle-electron mass ratio``
+   ``alpha particle-proton mass ratio``
+   ``Angstrom star``
+   ``atomic mass constant``
+   ``atomic mass constant energy equivalent``
+   ``atomic mass constant energy equivalent in MeV``
+   ``atomic mass unit-electron volt relationship``
+   ``atomic mass unit-hartree relationship``
+   ``atomic mass unit-hertz relationship``
+   ``atomic mass unit-inverse meter relationship``
+   ``atomic mass unit-joule relationship``
+   ``atomic mass unit-kelvin relationship``
+   ``atomic mass unit-kilogram relationship``
+   ``atomic unit of 1st hyperpolarizablity``
+   ``atomic unit of 2nd hyperpolarizablity``
+   ``atomic unit of action``
+   ``atomic unit of charge``
+   ``atomic unit of charge density``
+   ``atomic unit of current``
+   ``atomic unit of electric dipole moment``
+   ``atomic unit of electric field``
+   ``atomic unit of electric field gradient``
+   ``atomic unit of electric polarizablity``
+   ``atomic unit of electric potential``
+   ``atomic unit of electric quadrupole moment``
+   ``atomic unit of energy``
+   ``atomic unit of force``
+   ``atomic unit of length``
+   ``atomic unit of magnetic dipole moment``
+   ``atomic unit of magnetic flux density``
+   ``atomic unit of magnetizability``
+   ``atomic unit of mass``
+   ``atomic unit of momentum``
+   ``atomic unit of permittivity``
+   ``atomic unit of time``
+   ``atomic unit of velocity``
+   ``Avogadro constant``
+   ``Bohr magneton``
+   ``Bohr magneton in eV/T``
+   ``Bohr magneton in Hz/T``
+   ``Bohr magneton in inverse meters per tesla``
+   ``Bohr magneton in K/T``
+   ``Bohr radius``
+   ``Boltzmann constant``
+   ``Boltzmann constant in eV/K``
+   ``Boltzmann constant in Hz/K``
+   ``Boltzmann constant in inverse meters per kelvin``
+   ``characteristic impedance of vacuum``
+   ``classical electron radius``
+   ``Compton wavelength``
+   ``Compton wavelength over 2 pi``
+   ``conductance quantum``
+   ``conventional value of Josephson constant``
+   ``conventional value of von Klitzing constant``
+   ``Cu x unit``
+   ``deuteron magnetic moment``
+   ``deuteron magnetic moment to Bohr magneton ratio``
+   ``deuteron magnetic moment to nuclear magneton ratio``
+   ``deuteron mass``
+   ``deuteron mass energy equivalent``
+   ``deuteron mass energy equivalent in MeV``
+   ``deuteron mass in u``
+   ``deuteron molar mass``
+   ``deuteron rms charge radius``
+   ``deuteron-electron magnetic moment ratio``
+   ``deuteron-electron mass ratio``
+   ``deuteron-neutron magnetic moment ratio``
+   ``deuteron-proton magnetic moment ratio``
+   ``deuteron-proton mass ratio``
+   ``electric constant``
+   ``electron charge to mass quotient``
+   ``electron g factor``
+   ``electron gyromagnetic ratio``
+   ``electron gyromagnetic ratio over 2 pi``
+   ``electron magnetic moment``
+   ``electron magnetic moment anomaly``
+   ``electron magnetic moment to Bohr magneton ratio``
+   ``electron magnetic moment to nuclear magneton ratio``
+   ``electron mass``
+   ``electron mass energy equivalent``
+   ``electron mass energy equivalent in MeV``
+   ``electron mass in u``
+   ``electron molar mass``
+   ``electron to alpha particle mass ratio``
+   ``electron to shielded helion magnetic moment ratio``
+   ``electron to shielded proton magnetic moment ratio``
+   ``electron volt``
+   ``electron volt-atomic mass unit relationship``
+   ``electron volt-hartree relationship``
+   ``electron volt-hertz relationship``
+   ``electron volt-inverse meter relationship``
+   ``electron volt-joule relationship``
+   ``electron volt-kelvin relationship``
+   ``electron volt-kilogram relationship``
+   ``electron-deuteron magnetic moment ratio``
+   ``electron-deuteron mass ratio``
+   ``electron-muon magnetic moment ratio``
+   ``electron-muon mass ratio``
+   ``electron-neutron magnetic moment ratio``
+   ``electron-neutron mass ratio``
+   ``electron-proton magnetic moment ratio``
+   ``electron-proton mass ratio``
+   ``electron-tau mass ratio``
+   ``elementary charge``
+   ``elementary charge over h``
+   ``Faraday constant``
+   ``Faraday constant for conventional electric current``
+   ``Fermi coupling constant``
+   ``fine-structure constant``
+   ``first radiation constant``
+   ``first radiation constant for spectral radiance``
+   ``Hartree energy``
+   ``Hartree energy in eV``
+   ``hartree-atomic mass unit relationship``
+   ``hartree-electron volt relationship``
+   ``hartree-hertz relationship``
+   ``hartree-inverse meter relationship``
+   ``hartree-joule relationship``
+   ``hartree-kelvin relationship``
+   ``hartree-kilogram relationship``
+   ``helion mass``
+   ``helion mass energy equivalent``
+   ``helion mass energy equivalent in MeV``
+   ``helion mass in u``
+   ``helion molar mass``
+   ``helion-electron mass ratio``
+   ``helion-proton mass ratio``
+   ``hertz-atomic mass unit relationship``
+   ``hertz-electron volt relationship``
+   ``hertz-hartree relationship``
+   ``hertz-inverse meter relationship``
+   ``hertz-joule relationship``
+   ``hertz-kelvin relationship``
+   ``hertz-kilogram relationship``
+   ``inverse fine-structure constant``
+   ``inverse meter-atomic mass unit relationship``
+   ``inverse meter-electron volt relationship``
+   ``inverse meter-hartree relationship``
+   ``inverse meter-hertz relationship``
+   ``inverse meter-joule relationship``
+   ``inverse meter-kelvin relationship``
+   ``inverse meter-kilogram relationship``
+   ``inverse of conductance quantum``
+   ``Josephson constant``
+   ``joule-atomic mass unit relationship``
+   ``joule-electron volt relationship``
+   ``joule-hartree relationship``
+   ``joule-hertz relationship``
+   ``joule-inverse meter relationship``
+   ``joule-kelvin relationship``
+   ``joule-kilogram relationship``
+   ``kelvin-atomic mass unit relationship``
+   ``kelvin-electron volt relationship``
+   ``kelvin-hartree relationship``
+   ``kelvin-hertz relationship``
+   ``kelvin-inverse meter relationship``
+   ``kelvin-joule relationship``
+   ``kelvin-kilogram relationship``
+   ``kilogram-atomic mass unit relationship``
+   ``kilogram-electron volt relationship``
+   ``kilogram-hartree relationship``
+   ``kilogram-hertz relationship``
+   ``kilogram-inverse meter relationship``
+   ``kilogram-joule relationship``
+   ``kilogram-kelvin relationship``
+   ``lattice parameter of silicon``
+   ``Loschmidt constant (273.15 K, 101.325 kPa)``
+   ``magnetic constant``
+   ``magnetic flux quantum``
+   ``Mo x unit``
+   ``molar gas constant``
+   ``molar mass constant``
+   ``molar mass of carbon-12``
+   ``molar Planck constant``
+   ``molar Planck constant times c``
+   ``molar volume of ideal gas (273.15 K, 100 kPa)``
+   ``molar volume of ideal gas (273.15 K, 101.325 kPa)``
+   ``molar volume of silicon``
+   ``muon Compton wavelength``
+   ``muon Compton wavelength over 2 pi``
+   ``muon g factor``
+   ``muon magnetic moment``
+   ``muon magnetic moment anomaly``
+   ``muon magnetic moment to Bohr magneton ratio``
+   ``muon magnetic moment to nuclear magneton ratio``
+   ``muon mass``
+   ``muon mass energy equivalent``
+   ``muon mass energy equivalent in MeV``
+   ``muon mass in u``
+   ``muon molar mass``
+   ``muon-electron mass ratio``
+   ``muon-neutron mass ratio``
+   ``muon-proton magnetic moment ratio``
+   ``muon-proton mass ratio``
+   ``muon-tau mass ratio``
+   ``natural unit of action``
+   ``natural unit of action in eV s``
+   ``natural unit of energy``
+   ``natural unit of energy in MeV``
+   ``natural unit of length``
+   ``natural unit of mass``
+   ``natural unit of momentum``
+   ``natural unit of momentum in MeV/c``
+   ``natural unit of time``
+   ``natural unit of velocity``
+   ``neutron Compton wavelength``
+   ``neutron Compton wavelength over 2 pi``
+   ``neutron g factor``
+   ``neutron gyromagnetic ratio``
+   ``neutron gyromagnetic ratio over 2 pi``
+   ``neutron magnetic moment``
+   ``neutron magnetic moment to Bohr magneton ratio``
+   ``neutron magnetic moment to nuclear magneton ratio``
+   ``neutron mass``
+   ``neutron mass energy equivalent``
+   ``neutron mass energy equivalent in MeV``
+   ``neutron mass in u``
+   ``neutron molar mass``
+   ``neutron to shielded proton magnetic moment ratio``
+   ``neutron-electron magnetic moment ratio``
+   ``neutron-electron mass ratio``
+   ``neutron-muon mass ratio``
+   ``neutron-proton magnetic moment ratio``
+   ``neutron-proton mass ratio``
+   ``neutron-tau mass ratio``
+   ``Newtonian constant of gravitation``
+   ``Newtonian constant of gravitation over h-bar c``
+   ``nuclear magneton``
+   ``nuclear magneton in eV/T``
+   ``nuclear magneton in inverse meters per tesla``
+   ``nuclear magneton in K/T``
+   ``nuclear magneton in MHz/T``
+   ``Planck constant``
+   ``Planck constant in eV s``
+   ``Planck constant over 2 pi``
+   ``Planck constant over 2 pi in eV s``
+   ``Planck constant over 2 pi times c in MeV fm``
+   ``Planck length``
+   ``Planck mass``
+   ``Planck temperature``
+   ``Planck time``
+   ``proton charge to mass quotient``
+   ``proton Compton wavelength``
+   ``proton Compton wavelength over 2 pi``
+   ``proton g factor``
+   ``proton gyromagnetic ratio``
+   ``proton gyromagnetic ratio over 2 pi``
+   ``proton magnetic moment``
+   ``proton magnetic moment to Bohr magneton ratio``
+   ``proton magnetic moment to nuclear magneton ratio``
+   ``proton magnetic shielding correction``
+   ``proton mass``
+   ``proton mass energy equivalent``
+   ``proton mass energy equivalent in MeV``
+   ``proton mass in u``
+   ``proton molar mass``
+   ``proton rms charge radius``
+   ``proton-electron mass ratio``
+   ``proton-muon mass ratio``
+   ``proton-neutron magnetic moment ratio``
+   ``proton-neutron mass ratio``
+   ``proton-tau mass ratio``
+   ``quantum of circulation``
+   ``quantum of circulation times 2``
+   ``Rydberg constant``
+   ``Rydberg constant times c in Hz``
+   ``Rydberg constant times hc in eV``
+   ``Rydberg constant times hc in J``
+   ``Sackur-Tetrode constant (1 K, 100 kPa)``
+   ``Sackur-Tetrode constant (1 K, 101.325 kPa)``
+   ``second radiation constant``
+   ``shielded helion gyromagnetic ratio``
+   ``shielded helion gyromagnetic ratio over 2 pi``
+   ``shielded helion magnetic moment``
+   ``shielded helion magnetic moment to Bohr magneton ratio``
+   ``shielded helion magnetic moment to nuclear magneton ratio``
+   ``shielded helion to proton magnetic moment ratio``
+   ``shielded helion to shielded proton magnetic moment ratio``
+   ``shielded proton gyromagnetic ratio``
+   ``shielded proton gyromagnetic ratio over 2 pi``
+   ``shielded proton magnetic moment``
+   ``shielded proton magnetic moment to Bohr magneton ratio``
+   ``shielded proton magnetic moment to nuclear magneton ratio``
+   ``speed of light in vacuum``
+   ``standard acceleration of gravity``
+   ``standard atmosphere``
+   ``Stefan-Boltzmann constant``
+   ``tau Compton wavelength``
+   ``tau Compton wavelength over 2 pi``
+   ``tau mass``
+   ``tau mass energy equivalent``
+   ``tau mass energy equivalent in MeV``
+   ``tau mass in u``
+   ``tau molar mass``
+   ``tau-electron mass ratio``
+   ``tau-muon mass ratio``
+   ``tau-neutron mass ratio``
+   ``tau-proton mass ratio``
+   ``Thomson cross section``
+   ``unified atomic mass unit``
+   ``von Klitzing constant``
+   ``weak mixing angle``
+   ``Wien displacement law constant``
+   ``{220} lattice spacing of silicon``
+   ======================================================================  ====
+
+
+Unit prefixes
+=============
+
+SI
+--
+
+============  =================================================================
+``yotta``     :math:`10^{24}`
+``zetta``     :math:`10^{21}`
+``exa``       :math:`10^{18}`
+``peta``      :math:`10^{15}`
+``tera``      :math:`10^{12}`
+``giga``      :math:`10^{9}`
+``mega``      :math:`10^{6}`
+``kilo``      :math:`10^{3}`
+``hecto``     :math:`10^{2}`
+``deka``      :math:`10^{1}`
+``deci``      :math:`10^{-1}`
+``centi``     :math:`10^{-2}`
+``milli``     :math:`10^{-3}`
+``micro``     :math:`10^{-6}`
+``nano``      :math:`10^{-9}`
+``pico``      :math:`10^{-12}`
+``femto``     :math:`10^{-15}`
+``atto``      :math:`10^{-18}`
+``zepto``     :math:`10^{-21}`
+============  =================================================================
+
+
+Binary
+------
+
+============  =================================================================
+``kibi``      :math:`2^{10}`
+``mebi``      :math:`2^{20}`
+``gibi``      :math:`2^{30}`
+``tebi``      :math:`2^{40}`
+``pebi``      :math:`2^{50}`
+``exbi``      :math:`2^{60}`
+``zebi``      :math:`2^{70}`
+``yobi``      :math:`2^{80}`
+============  =================================================================
+
+Units
+=====
+
+Weight
+------
+
+=================  ============================================================
+``gram``           :math:`10^{-3}` kg
+``metric_ton``     :math:`10^{3}` kg
+``grain``          one grain in kg
+``lb``             one pound (avoirdupous) in kg
+``oz``             one ounce in kg
+``stone``          one stone in kg
+``grain``          one grain in kg
+``long_ton``       one long ton in kg
+``short_ton``      one short ton in kg
+``troy_ounce``     one Troy ounce in kg
+``troy_pound``     one Troy pound in kg
+``carat``          one carat in kg
+``m_u``            atomic mass constant (in kg)
+=================  ============================================================
+
+Angle
+-----
+
+=================  ============================================================
+``degree``         degree in radians
+``arcmin``         arc minute in radians
+``arcsec``         arc second in radians
+=================  ============================================================
+
+
+Time
+----
+
+=================  ============================================================
+``minute``         one minute in seconds
+``hour``           one hour in seconds
+``day``            one day in seconds
+``week``           one week in seconds
+``year``           one year (365 days) in seconds
+``Julian_year``    one Julian year (365.25 days) in seconds
+=================  ============================================================
+
+
+Length
+------
+
+=================  ============================================================
+``inch``           one inch in meters
+``foot``           one foot in meters
+``yard``           one yard in meters
+``mile``           one mile in meters
+``mil``            one mil in meters
+``pt``             one point in meters
+``survey_foot``    one survey foot in meters
+``survey_mile``    one survey mile in meters
+``nautical_mile``  one nautical mile in meters
+``fermi``          one Fermi in meters
+``angstrom``       one Ångström in meters
+``micron``         one micron in meters
+``au``             one astronomical unit in meters
+``light_year``     one light year in meters
+``parsec``         one parsec in meters
+=================  ============================================================
+
+Pressure
+--------
+
+=================  ============================================================
+``atm``            standard atmosphere in pascals
+``bar``            one bar in pascals
+``torr``           one torr (mmHg) in pascals
+``psi``            one psi in pascals
+=================  ============================================================
+
+Area
+----
+
+=================  ============================================================
+``hectare``        one hectare in square meters
+``acre``           one acre in square meters
+=================  ============================================================
+
+
+Volume
+------
+
+===================    ========================================================
+``liter``              one liter in cubic meters
+``gallon``             one gallon (US) in cubic meters
+``gallon_imp``         one gallon (UK) in cubic meters
+``fluid_ounce``        one fluid ounce (US) in cubic meters
+``fluid_ounce_imp``    one fluid ounce (UK) in cubic meters
+``bbl``                one barrel in cubic meters
+===================    ========================================================
+
+Speed
+-----
+
+=================    ==========================================================
+``kmh``              kilometers per hour in meters per second
+``mph``              miles per hour in meters per second
+``mach``             one Mach (approx., at 15 °C, 1 atm) in meters per second
+``knot``             one knot in meters per second
+=================    ==========================================================
+
+
+Temperature
+-----------
+
+=====================  =======================================================
+``zero_Celsius``       zero of Celsius scale in Kelvin
+``degree_Fahrenheit``  one Fahrenheit (only differences) in Kelvins
+=====================  =======================================================
+
+.. autosummary::
+   :toctree: generated/
+
+   C2K
+   K2C
+   F2C
+   C2F
+   F2K
+   K2F
+
+Energy
+------
+
+====================  =======================================================
+``eV``                one electron volt in Joules
+``calorie``           one calorie (thermochemical) in Joules
+``calorie_IT``        one calorie (International Steam Table calorie, 1956) in Joules
+``erg``               one erg in Joules
+``Btu``               one British thermal unit (International Steam Table) in Joules
+``Btu_th``            one British thermal unit (thermochemical) in Joules
+``ton_TNT``           one ton of TNT in Joules
+====================  =======================================================
+
+Power
+-----
+
+====================  =======================================================
+``hp``                one horsepower in watts
+====================  =======================================================
+
+Force
+-----
+
+====================  =======================================================
+``dyn``               one dyne in newtons
+``lbf``               one pound force in newtons
+``kgf``               one kilogram force in newtons
+====================  =======================================================
+
+Optics
+------
+
+.. autosummary::
+   :toctree: generated/
+
+   lambda2nu
+   nu2lambda

pythonPackages/scipy-0.8.0/doc/source/fftpack.rst

@@ -0,0 +1,77 @@
+Fourier transforms (:mod:`scipy.fftpack`)
+=========================================
+
+.. module:: scipy.fftpack
+
+Fast Fourier transforms
+-----------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   fft
+   ifft
+   fftn
+   ifftn
+   fft2
+   ifft2
+   rfft
+   irfft
+
+Differential and pseudo-differential operators
+----------------------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   diff
+   tilbert
+   itilbert
+   hilbert
+   ihilbert
+   cs_diff
+   sc_diff
+   ss_diff
+   cc_diff
+   shift
+
+Helper functions
+----------------
+
+.. autosummary::
+   :toctree: generated/
+
+   fftshift
+   ifftshift
+   dftfreq
+   rfftfreq
+
+Convolutions (:mod:`scipy.fftpack.convolve`)
+--------------------------------------------
+
+.. module:: scipy.fftpack.convolve
+
+.. autosummary::
+   :toctree: generated/
+
+   convolve
+   convolve_z
+   init_convolution_kernel
+   destroy_convolve_cache
+
+
+Other (:mod:`scipy.fftpack._fftpack`)
+-------------------------------------
+
+.. module:: scipy.fftpack._fftpack
+
+.. autosummary::
+   :toctree: generated/
+
+   drfft
+   zfft
+   zrfft
+   zfftnd
+   destroy_drfft_cache
+   destroy_zfft_cache
+   destroy_zfftnd_cache

pythonPackages/scipy-0.8.0/doc/source/index.rst

@@ -0,0 +1,44 @@
+SciPy
+=====
+
+:Release: |version|
+:Date: |today|
+
+SciPy (pronounced "Sigh Pie") is open-source software for mathematics,
+science, and engineering.
+
+.. toctree::
+   :maxdepth: 2
+
+   tutorial/index
+
+.. toctree::
+   :maxdepth: 1
+
+   release
+
+Reference
+---------
+
+.. toctree::
+   :maxdepth: 1
+
+   cluster
+   constants
+   fftpack
+   integrate
+   interpolate
+   io
+   linalg
+   maxentropy
+   misc
+   ndimage
+   odr
+   optimize
+   signal
+   sparse
+   sparse.linalg
+   spatial
+   special
+   stats
+   weave

pythonPackages/scipy-0.8.0/doc/source/integrate.rst

@@ -0,0 +1,44 @@
+=============================================
+Integration and ODEs (:mod:`scipy.integrate`)
+=============================================
+
+.. module:: scipy.integrate
+
+
+Integrating functions, given function object
+============================================
+
+.. autosummary::
+   :toctree: generated/
+
+   quad
+   dblquad
+   tplquad
+   fixed_quad
+   quadrature
+   romberg
+
+Integrating functions, given fixed samples
+==========================================
+
+.. autosummary::
+   :toctree: generated/
+
+   trapz
+   cumtrapz
+   simps
+   romb
+
+.. seealso::
+
+   :mod:`scipy.special` for orthogonal polynomials (special) for Gaussian
+   quadrature roots and weights for other weighting factors and regions.
+
+Integrators of ODE systems
+==========================
+
+.. autosummary::
+   :toctree: generated/
+
+   odeint
+   ode

pythonPackages/scipy-0.8.0/doc/source/interpolate.rst

@@ -0,0 +1,100 @@
+========================================
+Interpolation (:mod:`scipy.interpolate`)
+========================================
+
+.. module:: scipy.interpolate
+
+Univariate interpolation
+========================
+
+.. autosummary::
+   :toctree: generated/
+
+   interp1d
+   BarycentricInterpolator
+   KroghInterpolator
+   PiecewisePolynomial
+   barycentric_interpolate
+   krogh_interpolate
+   piecewise_polynomial_interpolate
+
+
+Multivariate interpolation
+==========================
+
+.. autosummary::
+   :toctree: generated/
+
+   interp2d
+   Rbf
+
+
+1-D Splines
+===========
+
+.. autosummary::
+   :toctree: generated/
+
+   UnivariateSpline
+   InterpolatedUnivariateSpline
+   LSQUnivariateSpline
+
+The above univariate spline classes have the following methods:
+
+
+.. autosummary::
+   :toctree: generated/
+
+   UnivariateSpline.__call__
+   UnivariateSpline.derivatives
+   UnivariateSpline.integral
+   UnivariateSpline.roots
+   UnivariateSpline.get_coeffs
+   UnivariateSpline.get_knots
+   UnivariateSpline.get_residual
+   UnivariateSpline.set_smoothing_factor
+
+
+Low-level interface to FITPACK functions:
+
+.. autosummary::
+   :toctree: generated/
+
+   splrep
+   splprep
+   splev
+   splint
+   sproot
+   spalde
+   bisplrep
+   bisplev
+
+
+2-D Splines
+===========
+
+.. seealso:: scipy.ndimage.map_coordinates
+
+.. autosummary::
+   :toctree: generated/
+
+   BivariateSpline
+   SmoothBivariateSpline
+   LSQBivariateSpline
+
+Low-level interface to FITPACK functions:
+
+.. autosummary::
+   :toctree: generated/
+
+   bisplrep
+   bisplev
+
+Additional tools
+================
+
+.. autosummary::
+   :toctree: generated/
+
+   lagrange
+   approximate_taylor_polynomial

pythonPackages/scipy-0.8.0/doc/source/io.rst

@@ -0,0 +1,67 @@
+==================================
+Input and output (:mod:`scipy.io`)
+==================================
+
+.. seealso:: :ref:`numpy-reference.routines.io` (in Numpy)
+
+.. module:: scipy.io
+
+MATLAB® files
+=============
+
+.. autosummary::
+   :toctree: generated/
+
+   loadmat
+   savemat
+
+Matrix Market files
+===================
+
+.. autosummary::
+   :toctree: generated/
+
+   mminfo
+   mmread
+   mmwrite
+
+Other
+=====
+
+.. autosummary::
+   :toctree: generated/
+
+   save_as_module
+   npfile
+
+Wav sound files (:mod:`scipy.io.wavfile`)
+=========================================
+
+.. module:: scipy.io.wavfile
+
+.. autosummary::
+   :toctree: generated/
+
+   read
+   write
+
+Arff files (:mod:`scipy.io.arff`)
+=================================
+
+.. automodule:: scipy.io.arff
+
+.. autosummary::
+   :toctree: generated/
+
+   loadarff
+
+Netcdf (:mod:`scipy.io.netcdf`)
+===============================
+
+.. module:: scipy.io.netcdf
+
+.. autosummary::
+   :toctree: generated/
+
+   netcdf_file
+   netcdf_variable

pythonPackages/scipy-0.8.0/doc/source/linalg.rst

@@ -0,0 +1,95 @@
+====================================
+Linear algebra (:mod:`scipy.linalg`)
+====================================
+
+.. module:: scipy.linalg
+
+Basics
+======
+
+.. autosummary::
+   :toctree: generated/
+
+   inv
+   solve
+   solve_banded
+   solveh_banded
+   det
+   norm
+   lstsq
+   pinv
+   pinv2
+
+Eigenvalue Problem
+==================
+
+.. autosummary::
+   :toctree: generated/
+
+   eig
+   eigvals
+   eigh
+   eigvalsh
+   eig_banded
+   eigvals_banded
+
+Decompositions
+==============
+
+.. autosummary::
+   :toctree: generated/
+
+   lu
+   lu_factor
+   lu_solve
+   svd
+   svdvals
+   diagsvd
+   orth
+   cholesky
+   cholesky_banded
+   cho_factor
+   cho_solve
+   cho_solve_banded
+   qr
+   schur
+   rsf2csf
+   hessenberg
+
+Matrix Functions
+================
+
+.. autosummary::
+   :toctree: generated/
+
+   expm
+   expm2
+   expm3
+   logm
+   cosm
+   sinm
+   tanm
+   coshm
+   sinhm
+   tanhm
+   signm
+   sqrtm
+   funm
+
+Special Matrices
+================
+
+.. autosummary::
+   :toctree: generated/
+
+   block_diag
+   circulant
+   companion
+   hadamard
+   hankel
+   kron
+   leslie
+   toeplitz
+   tri
+   tril
+   triu

pythonPackages/scipy-0.8.0/doc/source/misc.rst

@@ -0,0 +1,10 @@
+==========================================
+Miscellaneous routines (:mod:`scipy.misc`)
+==========================================
+
+.. warning::
+
+   This documentation is work-in-progress and unorganized.
+
+.. automodule:: scipy.misc
+   :members:

pythonPackages/scipy-0.8.0/doc/source/ndimage.rst

@@ -0,0 +1,122 @@
+=========================================================
+Multi-dimensional image processing (:mod:`scipy.ndimage`)
+=========================================================
+
+.. module:: scipy.ndimage
+
+Functions for multi-dimensional image processing.
+
+Filters :mod:`scipy.ndimage.filters`
+====================================
+
+.. module:: scipy.ndimage.filters
+
+.. autosummary::
+   :toctree: generated/
+
+   convolve
+   convolve1d
+   correlate
+   correlate1d
+   gaussian_filter
+   gaussian_filter1d
+   gaussian_gradient_magnitude
+   gaussian_laplace
+   generic_filter
+   generic_filter1d
+   generic_gradient_magnitude
+   generic_laplace
+   laplace
+   maximum_filter
+   maximum_filter1d
+   median_filter
+   minimum_filter
+   minimum_filter1d
+   percentile_filter
+   prewitt
+   rank_filter
+   sobel
+   uniform_filter
+   uniform_filter1d
+
+Fourier filters :mod:`scipy.ndimage.fourier`
+============================================
+
+.. module:: scipy.ndimage.fourier
+
+.. autosummary::
+   :toctree: generated/
+
+   fourier_ellipsoid
+   fourier_gaussian
+   fourier_shift
+   fourier_uniform
+
+Interpolation :mod:`scipy.ndimage.interpolation`
+================================================
+
+.. module:: scipy.ndimage.interpolation
+
+.. autosummary::
+   :toctree: generated/
+
+   affine_transform
+   geometric_transform
+   map_coordinates
+   rotate
+   shift
+   spline_filter
+   spline_filter1d
+   zoom
+
+Measurements :mod:`scipy.ndimage.measurements`
+==============================================
+
+.. module:: scipy.ndimage.measurements
+
+.. autosummary::
+   :toctree: generated/
+
+   center_of_mass
+   extrema
+   find_objects
+   histogram
+   label
+   maximum
+   maximum_position
+   mean
+   minimum
+   minimum_position
+   standard_deviation
+   sum
+   variance
+   watershed_ift
+
+Morphology :mod:`scipy.ndimage.morphology`
+==========================================
+
+.. module:: scipy.ndimage.morphology
+
+.. autosummary::
+   :toctree: generated/
+
+   binary_closing
+   binary_dilation
+   binary_erosion
+   binary_fill_holes
+   binary_hit_or_miss
+   binary_opening
+   binary_propagation
+   black_tophat
+   distance_transform_bf
+   distance_transform_cdt
+   distance_transform_edt
+   generate_binary_structure
+   grey_closing
+   grey_dilation
+   grey_erosion
+   grey_opening
+   iterate_structure
+   morphological_gradient
+   morphological_laplace
+   white_tophat

pythonPackages/scipy-0.8.0/doc/source/odr.rst

@@ -0,0 +1,33 @@
+=================================================
+Orthogonal distance regression (:mod:`scipy.odr`)
+=================================================
+
+.. automodule:: scipy.odr
+
+.. autoclass:: Data
+
+   .. automethod:: set_meta
+
+.. autoclass:: Model
+
+   .. automethod:: set_meta
+
+.. autoclass:: ODR
+
+   .. automethod:: restart
+
+   .. automethod:: run
+
+   .. automethod:: set_iprint
+
+   .. automethod:: set_job
+
+.. autoclass:: Output
+
+   .. automethod:: pprint
+
+.. autoexception:: odr_error
+
+.. autoexception:: odr_stop
+
+.. autofunction:: odr

pythonPackages/scipy-0.8.0/doc/source/optimize.rst

@@ -0,0 +1,111 @@
+=====================================================
+Optimization and root finding (:mod:`scipy.optimize`)
+=====================================================
+
+.. module:: scipy.optimize
+
+Optimization
+============
+
+General-purpose
+---------------
+
+.. autosummary::
+   :toctree: generated/
+
+   fmin
+   fmin_powell
+   fmin_cg
+   fmin_bfgs
+   fmin_ncg
+   leastsq
+
+
+Constrained (multivariate)
+--------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   fmin_l_bfgs_b
+   fmin_tnc
+   fmin_cobyla
+   fmin_slsqp
+   nnls
+
+Global
+------
+
+.. autosummary::
+   :toctree: generated/
+
+   anneal
+   brute
+
+Scalar function minimizers
+--------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   fminbound
+   golden
+   bracket
+   brent
+
+Fitting
+=======
+
+.. autosummary::
+   :toctree: generated/
+
+   curve_fit
+
+Root finding
+============
+
+.. autosummary::
+   :toctree: generated/
+
+   fsolve
+
+Scalar function solvers
+-----------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   brentq
+   brenth
+   ridder
+   bisect
+   newton
+
+Fixed point finding:
+
+.. autosummary::
+   :toctree: generated/
+
+   fixed_point
+
+General-purpose nonlinear (multidimensional)
+--------------------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   broyden1
+   broyden2
+   broyden3
+   broyden_generalized
+   anderson
+   anderson2
+
+Utility Functions
+=================
+
+.. autosummary::
+   :toctree: generated/
+
+   line_search
+   check_grad

pythonPackages/scipy-0.8.0/doc/source/release.rst

@@ -0,0 +1,5 @@
+*************
+Release Notes
+*************
+
+.. include:: ../release/0.8.0-notes.rst

pythonPackages/scipy-0.8.0/doc/source/signal.rst

@@ -0,0 +1,168 @@
+=======================================
+Signal processing (:mod:`scipy.signal`)
+=======================================
+
+.. module:: scipy.signal
+
+Convolution
+===========
+
+.. autosummary::
+   :toctree: generated/
+
+   convolve
+   correlate
+   fftconvolve
+   convolve2d
+   correlate2d
+   sepfir2d
+
+B-splines
+=========
+
+.. autosummary::
+   :toctree: generated/
+
+   bspline
+   gauss_spline
+   cspline1d
+   qspline1d
+   cspline2d
+   qspline2d
+   spline_filter
+
+Filtering
+=========
+
+.. autosummary::
+   :toctree: generated/
+
+   order_filter
+   medfilt
+   medfilt2d
+   wiener
+
+   symiirorder1
+   symiirorder2
+   lfilter
+   lfiltic
+
+   deconvolve
+
+   hilbert
+   get_window
+
+   decimate
+   detrend
+   resample
+
+Filter design
+=============
+
+.. autosummary::
+   :toctree: generated/
+
+   bilinear
+   firwin
+   freqs
+   freqz
+   iirdesign
+   iirfilter
+   kaiserord
+   remez
+
+   unique_roots
+   residue
+   residuez
+   invres
+
+Matlab-style IIR filter design
+==============================
+
+.. autosummary::
+   :toctree: generated/
+
+   butter
+   buttord
+   cheby1
+   cheb1ord
+   cheby2
+   cheb2ord
+   ellip
+   ellipord
+   bessel
+
+Linear Systems
+==============
+
+.. autosummary::
+   :toctree: generated/
+
+   lti
+   lsim
+   lsim2
+   impulse
+   impulse2
+   step
+   step2
+
+LTI Representations
+===================
+
+.. autosummary::
+   :toctree: generated/
+
+   tf2zpk
+   zpk2tf
+   tf2ss
+   ss2tf
+   zpk2ss
+   ss2zpk
+
+Waveforms
+=========
+
+.. autosummary::
+   :toctree: generated/
+
+   chirp
+   gausspulse
+   sawtooth
+   square
+   sweep_poly
+
+Window functions
+================
+
+.. autosummary::
+   :toctree: generated/
+
+   get_window
+   barthann
+   bartlett
+   blackman
+   blackmanharris
+   bohman
+   boxcar
+   chebwin
+   flattop
+   gaussian
+   general_gaussian
+   hamming
+   hann
+   kaiser
+   nuttall
+   parzen
+   slepian
+   triang
+
+Wavelets
+========
+
+.. autosummary::
+   :toctree: generated/
+
+   cascade
+   daub
+   morlet
+   qmf

pythonPackages/scipy-0.8.0/doc/source/sparse.linalg.rst

@@ -0,0 +1,10 @@
+==================================================
+Sparse linear algebra (:mod:`scipy.sparse.linalg`)
+==================================================
+
+.. warning::
+
+   This documentation is work-in-progress and unorganized.
+
+.. automodule:: scipy.sparse.linalg
+   :members:

pythonPackages/scipy-0.8.0/doc/source/sparse.rst

@@ -0,0 +1,64 @@
+=====================================
+Sparse matrices (:mod:`scipy.sparse`)
+=====================================
+
+.. automodule:: scipy.sparse
+
+
+Sparse matrix classes
+=====================
+
+.. autosummary::
+   :toctree: generated/
+
+   csc_matrix
+   csr_matrix
+   bsr_matrix
+   lil_matrix
+   dok_matrix
+   coo_matrix
+   dia_matrix
+
+
+Functions
+=========
+
+Building sparse matrices:
+
+.. autosummary::
+   :toctree: generated/
+
+   eye
+   identity
+   kron
+   kronsum
+   lil_eye
+   lil_diags
+   spdiags
+   tril
+   triu
+   bmat
+   hstack
+   vstack
+
+Identifying sparse matrices:
+
+.. autosummary::
+   :toctree: generated/
+
+   issparse
+   isspmatrix
+   isspmatrix_csc
+   isspmatrix_csr
+   isspmatrix_bsr
+   isspmatrix_lil
+   isspmatrix_dok
+   isspmatrix_coo
+   isspmatrix_dia
+
+Exceptions
+==========
+
+.. autoexception:: SparseEfficiencyWarning
+
+.. autoexception:: SparseWarning

pythonPackages/scipy-0.8.0/doc/source/spatial.distance.rst

@@ -0,0 +1,6 @@
+=====================================================
+Distance computations (:mod:`scipy.spatial.distance`)
+=====================================================
+
+.. automodule:: scipy.spatial.distance
+   :members:

pythonPackages/scipy-0.8.0/doc/source/spatial.rst

@@ -0,0 +1,14 @@
+=============================================================
+Spatial algorithms and data structures (:mod:`scipy.spatial`)
+=============================================================
+
+.. warning::
+
+   This documentation is work-in-progress and unorganized.
+
+.. toctree::
+
+   spatial.distance
+
+.. automodule:: scipy.spatial
+   :members:

pythonPackages/scipy-0.8.0/doc/source/special.rst

@@ -0,0 +1,512 @@
+========================================
+Special functions (:mod:`scipy.special`)
+========================================
+
+.. module:: scipy.special
+
+Nearly all of the functions below are universal functions and follow
+broadcasting and automatic array-looping rules. Exceptions are noted.
+
+Error handling
+==============
+
+Errors are handled by returning nans, or other appropriate values.
+Some of the special function routines will print an error message
+when an error occurs.  By default this printing
+is disabled.  To enable such messages use errprint(1)
+To disable such messages use errprint(0).
+
+Example:
+    >>> print scipy.special.bdtr(-1,10,0.3)
+    >>> scipy.special.errprint(1)
+    >>> print scipy.special.bdtr(-1,10,0.3)
+
+.. autosummary::
+   :toctree: generated/
+
+   errprint
+   errstate
+
+Available functions
+===================
+
+Airy functions
+--------------
+
+.. autosummary::
+   :toctree: generated/
+
+   airy
+   airye
+   ai_zeros
+   bi_zeros
+
+
+Elliptic Functions and Integrals
+--------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   ellipj
+   ellipk
+   ellipkinc
+   ellipe
+   ellipeinc
+
+Bessel Functions
+----------------
+
+.. autosummary::
+   :toctree: generated/
+
+   jn
+   jv
+   jve
+   yn
+   yv
+   yve
+   kn
+   kv
+   kve
+   iv
+   ive
+   hankel1
+   hankel1e
+   hankel2
+   hankel2e
+
+The following is not an universal function:
+
+.. autosummary::
+   :toctree: generated/
+
+   lmbda
+
+Zeros of Bessel Functions
+^^^^^^^^^^^^^^^^^^^^^^^^^
+
+These are not universal functions:
+
+.. autosummary::
+   :toctree: generated/
+
+   jnjnp_zeros
+   jnyn_zeros
+   jn_zeros
+   jnp_zeros
+   yn_zeros
+   ynp_zeros
+   y0_zeros
+   y1_zeros
+   y1p_zeros
+
+Faster versions of common Bessel Functions
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   j0
+   j1
+   y0
+   y1
+   i0
+   i0e
+   i1
+   i1e
+   k0
+   k0e
+   k1
+   k1e
+
+Integrals of Bessel Functions
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   itj0y0
+   it2j0y0
+   iti0k0
+   it2i0k0
+   besselpoly
+
+Derivatives of Bessel Functions
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. autosummary::
+   :toctree: generated/
+
+   jvp
+   yvp
+   kvp
+   ivp
+   h1vp
+   h2vp
+
+Spherical Bessel Functions
+^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+These are not universal functions:
+
+.. autosummary::
+   :toctree: generated/
+
+   sph_jn
+   sph_yn
+   sph_jnyn
+   sph_in
+   sph_kn
+   sph_inkn
+
+Riccati-Bessel Functions
+^^^^^^^^^^^^^^^^^^^^^^^^
+
+These are not universal functions:
+
+.. autosummary::
+   :toctree: generated/
+
+   riccati_jn
+   riccati_yn
+
+Struve Functions
+----------------
+
+.. autosummary::
+   :toctree: generated/
+
+   struve
+   modstruve
+   itstruve0
+   it2struve0
+   itmodstruve0
+
+
+Raw Statistical Functions
+-------------------------
+
+.. seealso:: :mod:`scipy.stats`: Friendly versions of these functions.
+
+.. autosummary::
+   :toctree: generated/
+
+   bdtr
+   bdtrc
+   bdtri
+   btdtr
+   btdtri
+   fdtr
+   fdtrc
+   fdtri
+   gdtr
+   gdtrc
+   gdtria
+   gdtrib
+   gdtrix
+   nbdtr
+   nbdtrc
+   nbdtri
+   pdtr
+   pdtrc
+   pdtri
+   stdtr
+   stdtridf
+   stdtrit
+   chdtr
+   chdtrc
+   chdtri
+   ndtr
+   ndtri
+   smirnov
+   smirnovi
+   kolmogorov
+   kolmogi
+   tklmbda
+
+Gamma and Related Functions
+---------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   gamma
+   gammaln
+   gammainc
+   gammaincinv
+   gammaincc
+   gammainccinv
+   beta
+   betaln
+   betainc
+   betaincinv
+   psi
+   rgamma
+   polygamma
+   multigammaln
+
+
+Error Function and Fresnel Integrals
+------------------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   erf
+   erfc
+   erfinv
+   erfcinv
+   erf_zeros
+   fresnel
+   fresnel_zeros
+   modfresnelp
+   modfresnelm
+
+These are not universal functions:
+
+.. autosummary::
+   :toctree: generated/
+
+   fresnelc_zeros
+   fresnels_zeros
+
+Legendre Functions
+------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   lpmv
+   sph_harm
+
+These are not universal functions:
+
+.. autosummary::
+   :toctree: generated/
+
+   lpn
+   lqn
+   lpmn
+   lqmn
+
+Orthogonal polynomials
+----------------------
+
+The following functions evaluate values of orthogonal polynomials:
+
+.. autosummary::
+   :toctree: generated/
+
+   eval_legendre
+   eval_chebyt
+   eval_chebyu
+   eval_chebyc
+   eval_chebys
+   eval_jacobi
+   eval_laguerre
+   eval_genlaguerre
+   eval_hermite
+   eval_hermitenorm
+   eval_gegenbauer
+   eval_sh_legendre
+   eval_sh_chebyt
+   eval_sh_chebyu
+   eval_sh_jacobi
+
+The functions below, in turn, return :ref:`orthopoly1d` objects, which
+functions similarly as :ref:`numpy.poly1d`.  The :ref:`orthopoly1d`
+class also has an attribute ``weights`` which returns the roots, weights,
+and total weights for the appropriate form of Gaussian quadrature.
+These are returned in an ``n x 3`` array with roots in the first column,
+weights in the second column, and total weights in the final column.
+
+.. autosummary::
+   :toctree: generated/
+
+   legendre
+   chebyt
+   chebyu
+   chebyc
+   chebys
+   jacobi
+   laguerre
+   genlaguerre
+   hermite
+   hermitenorm
+   gegenbauer
+   sh_legendre
+   sh_chebyt
+   sh_chebyu
+   sh_jacobi
+
+.. warning::
+
+   Large-order polynomials obtained from these functions
+   are numerically unstable.
+
+   ``orthopoly1d`` objects are converted to ``poly1d``, when doing
+   arithmetic.  ``numpy.poly1d`` works in power basis and cannot
+   represent high-order polynomials accurately, which can cause
+   significant inaccuracy.
+
+
+Hypergeometric Functions
+------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   hyp2f1
+   hyp1f1
+   hyperu
+   hyp0f1
+   hyp2f0
+   hyp1f2
+   hyp3f0
+
+
+Parabolic Cylinder Functions
+----------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   pbdv
+   pbvv
+   pbwa
+
+These are not universal functions:
+
+.. autosummary::
+   :toctree: generated/
+
+   pbdv_seq
+   pbvv_seq
+   pbdn_seq
+
+Mathieu and Related Functions
+-----------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   mathieu_a
+   mathieu_b
+
+These are not universal functions:
+
+.. autosummary::
+   :toctree: generated/
+
+   mathieu_even_coef
+   mathieu_odd_coef
+
+The following return both function and first derivative:
+
+.. autosummary::
+   :toctree: generated/
+
+   mathieu_cem
+   mathieu_sem
+   mathieu_modcem1
+   mathieu_modcem2
+   mathieu_modsem1
+   mathieu_modsem2
+
+Spheroidal Wave Functions
+-------------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   pro_ang1
+   pro_rad1
+   pro_rad2
+   obl_ang1
+   obl_rad1
+   obl_rad2
+   pro_cv
+   obl_cv
+   pro_cv_seq
+   obl_cv_seq
+
+The following functions require pre-computed characteristic value:
+
+.. autosummary::
+   :toctree: generated/
+
+   pro_ang1_cv
+   pro_rad1_cv
+   pro_rad2_cv
+   obl_ang1_cv
+   obl_rad1_cv
+   obl_rad2_cv
+
+Kelvin Functions
+----------------
+
+.. autosummary::
+   :toctree: generated/
+
+   kelvin
+   kelvin_zeros
+   ber
+   bei
+   berp
+   beip
+   ker
+   kei
+   kerp
+   keip
+
+These are not universal functions:
+
+.. autosummary::
+   :toctree: generated/
+
+   ber_zeros
+   bei_zeros
+   berp_zeros
+   beip_zeros
+   ker_zeros
+   kei_zeros
+   kerp_zeros
+   keip_zeros
+
+Other Special Functions
+-----------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   expn
+   exp1
+   expi
+   wofz
+   dawsn
+   shichi
+   sici
+   spence
+   lambertw
+   zeta
+   zetac
+
+Convenience Functions
+---------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   cbrt
+   exp10
+   exp2
+   radian
+   cosdg
+   sindg
+   tandg
+   cotdg
+   log1p
+   expm1
+   cosm1
+   round

pythonPackages/scipy-0.8.0/doc/source/stats.mstats.rst

@@ -0,0 +1,81 @@
+.. module:: scipy.stats.mstats
+
+===================================================================
+Statistical functions for masked arrays (:mod:`scipy.stats.mstats`)
+===================================================================
+
+This module contains a large number of statistical functions that can
+be used with masked arrays.
+
+Most of these functions are similar to those in scipy.stats but might
+have small differences in the API or in the algorithm used. Since this
+is a relatively new package, some API changes are still possible.
+
+.. autosummary::
+   :toctree: generated/
+
+   argstoarray
+   betai
+   chisquare
+   count_tied_groups
+   describe
+   f_oneway
+   f_value_wilks_lambda
+   find_repeats
+   friedmanchisquare
+   gmean
+   hmean
+   kendalltau
+   kendalltau_seasonal
+   kruskalwallis
+   kruskalwallis
+   ks_twosamp
+   ks_twosamp
+   kurtosis
+   kurtosistest
+   linregress
+   mannwhitneyu
+   plotting_positions
+   mode
+   moment
+   mquantiles
+   msign
+   normaltest
+   obrientransform
+   pearsonr
+   plotting_positions
+   pointbiserialr
+   rankdata
+   samplestd
+   samplevar
+   scoreatpercentile
+   sem
+   signaltonoise
+   skew
+   skewtest
+   spearmanr
+   std
+   stderr
+   theilslopes
+   threshold
+   tmax
+   tmean
+   tmin
+   trim
+   trima
+   trimboth
+   trimmed_stde
+   trimr
+   trimtail
+   tsem
+   ttest_onesamp
+   ttest_ind
+   ttest_onesamp
+   ttest_rel
+   tvar
+   var
+   variation
+   winsorize
+   z
+   zmap
+   zs

pythonPackages/scipy-0.8.0/doc/source/stats.rst

@@ -0,0 +1,284 @@
+.. module:: scipy.stats
+
+==========================================
+Statistical functions (:mod:`scipy.stats`)
+==========================================
+
+This module contains a large number of probability distributions as
+well as a growing library of statistical functions.
+
+Each included continuous distribution is an instance of the class rv_continous:
+
+.. autosummary::
+   :toctree: generated/
+
+   rv_continuous
+   rv_continuous.pdf
+   rv_continuous.cdf
+   rv_continuous.sf
+   rv_continuous.ppf
+   rv_continuous.isf
+   rv_continuous.stats
+
+Each discrete distribution is an instance of the class rv_discrete:
+
+.. autosummary::
+   :toctree: generated/
+
+   rv_discrete
+   rv_discrete.pmf
+   rv_discrete.cdf
+   rv_discrete.sf
+   rv_discrete.ppf
+   rv_discrete.isf
+   rv_discrete.stats
+
+Continuous distributions
+========================
+
+.. autosummary::
+   :toctree: generated/
+
+   norm
+   alpha
+   anglit
+   arcsine
+   beta
+   betaprime
+   bradford
+   burr
+   fisk
+   cauchy
+   chi
+   chi2
+   cosine
+   dgamma
+   dweibull
+   erlang
+   expon
+   exponweib
+   exponpow
+   fatiguelife
+   foldcauchy
+   f
+   foldnorm
+   fretchet_r
+   fretcher_l
+   genlogistic
+   genpareto
+   genexpon
+   genextreme
+   gausshyper
+   gamma
+   gengamma
+   genhalflogistic
+   gompertz
+   gumbel_r
+   gumbel_l
+   halfcauchy
+   halflogistic
+   halfnorm
+   hypsecant
+   invgamma
+   invnorm
+   invweibull
+   johnsonsb
+   johnsonsu
+   laplace
+   logistic
+   loggamma
+   loglaplace
+   lognorm
+   gilbrat
+   lomax
+   maxwell
+   mielke
+   nakagami
+   ncx2
+   ncf
+   t
+   nct
+   pareto
+   powerlaw
+   powerlognorm
+   powernorm
+   rdist
+   reciprocal
+   rayleigh
+   rice
+   recipinvgauss
+   semicircular
+   triang
+   truncexpon
+   truncnorm
+   tukeylambda
+   uniform
+   von_mises
+   wald
+   weibull_min
+   weibull_max
+   wrapcauchy
+   ksone
+   kstwobign
+
+Discrete distributions
+======================
+
+.. autosummary::
+   :toctree: generated/
+
+   binom
+   bernoulli
+   nbinom
+   geom
+   hypergeom
+   logser
+   poisson
+   planck
+   boltzmann
+   randint
+   zipf
+   dlaplace
+
+Statistical functions
+=====================
+
+Several of these functions have a similar version in scipy.stats.mstats
+which work for masked arrays.
+
+.. autosummary::
+   :toctree: generated/
+
+   gmean
+   hmean
+   mean
+   cmedian
+   median
+   mode
+   tmean
+   tvar
+   tmin
+   tmax
+   tstd
+   tsem
+   moment
+   variation
+   skew
+   kurtosis
+   describe
+   skewtest
+   kurtosistest
+   normaltest
+
+
+.. autosummary::
+   :toctree: generated/
+
+   itemfreq
+   scoreatpercentile
+   percentileofscore
+   histogram2
+   histogram
+   cumfreq
+   relfreq
+
+.. autosummary::
+   :toctree: generated/
+
+   obrientransform
+   samplevar
+   samplestd
+   signaltonoise
+   bayes_mvs
+   var
+   std
+   stderr
+   sem
+   z
+   zs
+   zmap
+
+.. autosummary::
+   :toctree: generated/
+
+   threshold
+   trimboth
+   trim1
+   cov
+   corrcoef
+
+.. autosummary::
+   :toctree: generated/
+
+   f_oneway
+   pearsonr
+   spearmanr
+   pointbiserialr
+   kendalltau
+   linregress
+
+.. autosummary::
+   :toctree: generated/
+
+   ttest_1samp
+   ttest_ind
+   ttest_rel
+   kstest
+   chisquare
+   ks_2samp
+   mannwhitneyu
+   tiecorrect
+   ranksums
+   wilcoxon
+   kruskal
+   friedmanchisquare
+
+.. autosummary::
+   :toctree: generated/
+
+   ansari
+   bartlett
+   levene
+   shapiro
+   anderson
+   binom_test
+   fligner
+   mood
+   oneway
+
+
+.. autosummary::
+   :toctree: generated/
+
+   glm
+   anova
+
+Plot-tests
+==========
+
+.. autosummary::
+   :toctree: generated/
+
+   probplot
+   ppcc_max
+   ppcc_plot
+
+
+Masked statistics functions
+===========================
+
+.. toctree::
+
+   stats.mstats
+
+
+Univariate and multivariate kernel density estimation (:mod:`scipy.stats.kde`)
+==============================================================================
+
+.. autosummary::
+   :toctree: generated/
+
+   gaussian_kde
+
+For many more stat related functions install the software R and the
+interface package rpy.

pythonPackages/scipy-0.8.0/doc/source/tutorial/basic.rst

@@ -0,0 +1,302 @@
+Basic functions in Numpy (and top-level scipy)
+==============================================
+
+.. sectionauthor:: Travis E. Oliphant
+
+.. currentmodule:: numpy
+
+.. contents::
+
+Interaction with Numpy
+------------------------
+
+To begin with, all of the Numpy functions have been subsumed into the
+:mod:`scipy` namespace so that all of those functions are available
+without additionally importing Numpy. In addition, the universal
+functions (addition, subtraction, division) have been altered to not
+raise exceptions if floating-point errors are encountered; instead,
+NaN's and Inf's are returned in the arrays. To assist in detection of
+these events, several functions (:func:`sp.isnan`, :func:`sp.isfinite`,
+:func:`sp.isinf`) are available.
+
+Finally, some of the basic functions like log, sqrt, and inverse trig
+functions have been modified to return complex numbers instead of
+NaN's where appropriate (*i.e.* ``sp.sqrt(-1)`` returns ``1j``).
+
+
+Top-level scipy routines
+------------------------
+
+The purpose of the top level of scipy is to collect general-purpose
+routines that the other sub-packages can use and to provide a simple
+replacement for Numpy. Anytime you might think to import Numpy, you
+can import scipy instead and remove yourself from direct dependence on
+Numpy. These routines are divided into several files for
+organizational purposes, but they are all available under the numpy
+namespace (and the scipy namespace). There are routines for type
+handling and type checking, shape and matrix manipulation, polynomial
+processing, and other useful functions. Rather than giving a detailed
+description of each of these functions (which is available in the
+Numpy Reference Guide or by using the :func:`help`, :func:`info` and
+:func:`source` commands), this tutorial will discuss some of the more
+useful commands which require a little introduction to use to their
+full potential.
+
+
+Type handling
+^^^^^^^^^^^^^
+
+Note the difference between :func:`sp.iscomplex`/:func:`sp.isreal` and
+:func:`sp.iscomplexobj`/:func:`sp.isrealobj`. The former command is
+array based and returns byte arrays of ones and zeros providing the
+result of the element-wise test. The latter command is object based
+and returns a scalar describing the result of the test on the entire
+object.
+
+Often it is required to get just the real and/or imaginary part of a
+complex number. While complex numbers and arrays have attributes that
+return those values, if one is not sure whether or not the object will
+be complex-valued, it is better to use the functional forms
+:func:`sp.real` and :func:`sp.imag` . These functions succeed for anything
+that can be turned into a Numpy array. Consider also the function
+:func:`sp.real_if_close` which transforms a complex-valued number with
+tiny imaginary part into a real number.
+
+Occasionally the need to check whether or not a number is a scalar
+(Python (long)int, Python float, Python complex, or rank-0 array)
+occurs in coding. This functionality is provided in the convenient
+function :func:`sp.isscalar` which returns a 1 or a 0.
+
+Finally, ensuring that objects are a certain Numpy type occurs often
+enough that it has been given a convenient interface in SciPy through
+the use of the :obj:`sp.cast` dictionary. The dictionary is keyed by the
+type it is desired to cast to and the dictionary stores functions to
+perform the casting. Thus, ``sp.cast['f'](d)`` returns an array
+of :class:`sp.float32` from *d*. This function is also useful as an easy
+way to get a scalar of a certain type::
+
+    >>> sp.cast['f'](sp.pi)
+    array(3.1415927410125732, dtype=float32)
+
+Index Tricks
+^^^^^^^^^^^^
+
+There are some class instances that make special use of the slicing
+functionality to provide efficient means for array construction. This
+part will discuss the operation of :obj:`sp.mgrid` , :obj:`sp.ogrid` ,
+:obj:`sp.r_` , and :obj:`sp.c_` for quickly constructing arrays.
+
+One familiar with Matlab may complain that it is difficult to
+construct arrays from the interactive session with Python. Suppose,
+for example that one wants to construct an array that begins with 3
+followed by 5 zeros and then contains 10 numbers spanning the range -1
+to 1 (inclusive on both ends). Before SciPy, you would need to enter
+something like the following
+
+    >>> concatenate(([3],[0]*5,arange(-1,1.002,2/9.0)))
+
+With the :obj:`r_` command one can enter this as
+
+    >>> r_[3,[0]*5,-1:1:10j]
+
+which can ease typing and make for more readable code. Notice how
+objects are concatenated, and the slicing syntax is (ab)used to
+construct ranges. The other term that deserves a little explanation is
+the use of the complex number 10j as the step size in the slicing
+syntax. This non-standard use allows the number to be interpreted as
+the number of points to produce in the range rather than as a step
+size (note we would have used the long integer notation, 10L, but this
+notation may go away in Python as the integers become unified). This
+non-standard usage may be unsightly to some, but it gives the user the
+ability to quickly construct complicated vectors in a very readable
+fashion. When the number of points is specified in this way, the end-
+point is inclusive.
+
+The "r" stands for row concatenation because if the objects between
+commas are 2 dimensional arrays, they are stacked by rows (and thus
+must have commensurate columns). There is an equivalent command
+:obj:`c_` that stacks 2d arrays by columns but works identically to
+:obj:`r_` for 1d arrays.
+
+Another very useful class instance which makes use of extended slicing
+notation is the function :obj:`mgrid`. In the simplest case, this
+function can be used to construct 1d ranges as a convenient substitute
+for arange. It also allows the use of complex-numbers in the step-size
+to indicate the number of points to place between the (inclusive)
+end-points. The real purpose of this function however is to produce N,
+N-d arrays which provide coordinate arrays for an N-dimensional
+volume. The easiest way to understand this is with an example of its
+usage:
+
+    >>> mgrid[0:5,0:5]
+    array([[[0, 0, 0, 0, 0],
+            [1, 1, 1, 1, 1],
+            [2, 2, 2, 2, 2],
+            [3, 3, 3, 3, 3],
+            [4, 4, 4, 4, 4]],
+           [[0, 1, 2, 3, 4],
+            [0, 1, 2, 3, 4],
+            [0, 1, 2, 3, 4],
+            [0, 1, 2, 3, 4],
+            [0, 1, 2, 3, 4]]])
+    >>> mgrid[0:5:4j,0:5:4j]
+    array([[[ 0.    ,  0.    ,  0.    ,  0.    ],
+            [ 1.6667,  1.6667,  1.6667,  1.6667],
+            [ 3.3333,  3.3333,  3.3333,  3.3333],
+            [ 5.    ,  5.    ,  5.    ,  5.    ]],
+           [[ 0.    ,  1.6667,  3.3333,  5.    ],
+            [ 0.    ,  1.6667,  3.3333,  5.    ],
+            [ 0.    ,  1.6667,  3.3333,  5.    ],
+            [ 0.    ,  1.6667,  3.3333,  5.    ]]])
+
+Having meshed arrays like this is sometimes very useful. However, it
+is not always needed just to evaluate some N-dimensional function over
+a grid due to the array-broadcasting rules of Numpy and SciPy. If this
+is the only purpose for generating a meshgrid, you should instead use
+the function :obj:`ogrid` which generates an "open "grid using NewAxis
+judiciously to create N, N-d arrays where only one dimension in each
+array has length greater than 1. This will save memory and create the
+same result if the only purpose for the meshgrid is to generate sample
+points for evaluation of an N-d function.
+
+
+Shape manipulation
+^^^^^^^^^^^^^^^^^^
+
+In this category of functions are routines for squeezing out length-
+one dimensions from N-dimensional arrays, ensuring that an array is at
+least 1-, 2-, or 3-dimensional, and stacking (concatenating) arrays by
+rows, columns, and "pages "(in the third dimension). Routines for
+splitting arrays (roughly the opposite of stacking arrays) are also
+available.
+
+
+Polynomials
+^^^^^^^^^^^
+
+There are two (interchangeable) ways to deal with 1-d polynomials in
+SciPy. The first is to use the :class:`poly1d` class from Numpy. This
+class accepts coefficients or polynomial roots to initialize a
+polynomial. The polynomial object can then be manipulated in algebraic
+expressions, integrated, differentiated, and evaluated. It even prints
+like a polynomial:
+
+    >>> p = poly1d([3,4,5])
+    >>> print p
+       2
+    3 x + 4 x + 5
+    >>> print p*p
+       4      3      2
+    9 x + 24 x + 46 x + 40 x + 25
+    >>> print p.integ(k=6)
+     3     2
+    x + 2 x + 5 x + 6
+    >>> print p.deriv()
+    6 x + 4
+    >>> p([4,5])
+    array([ 69, 100])
+
+The other way to handle polynomials is as an array of coefficients
+with the first element of the array giving the coefficient of the
+highest power. There are explicit functions to add, subtract,
+multiply, divide, integrate, differentiate, and evaluate polynomials
+represented as sequences of coefficients.
+
+
+Vectorizing functions (vectorize)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+One of the features that NumPy provides is a class :obj:`vectorize` to
+convert an ordinary Python function which accepts scalars and returns
+scalars into a "vectorized-function" with the same broadcasting rules
+as other Numpy functions (*i.e.* the Universal functions, or
+ufuncs). For example, suppose you have a Python function named
+:obj:`addsubtract` defined as:
+
+    >>> def addsubtract(a,b):
+    ...    if a > b:
+    ...        return a - b
+    ...    else:
+    ...        return a + b
+
+which defines a function of two scalar variables and returns a scalar
+result. The class vectorize can be used to "vectorize "this function so that ::
+
+    >>> vec_addsubtract = vectorize(addsubtract)
+
+returns a function which takes array arguments and returns an array
+result:
+
+    >>> vec_addsubtract([0,3,6,9],[1,3,5,7])
+    array([1, 6, 1, 2])
+
+This particular function could have been written in vector form
+without the use of :obj:`vectorize` . But, what if the function you have written is the result of some
+optimization or integration routine. Such functions can likely only be
+vectorized using ``vectorize.``
+
+
+Other useful functions
+^^^^^^^^^^^^^^^^^^^^^^
+
+There are several other functions in the scipy_base package including
+most of the other functions that are also in the Numpy package. The
+reason for duplicating these functions is to allow SciPy to
+potentially alter their original interface and make it easier for
+users to know how to get access to functions
+
+    >>> from scipy import *
+
+Functions which should be mentioned are :obj:`mod(x,y)` which can
+replace ``x % y`` when it is desired that the result take the sign of
+*y* instead of *x* . Also included is :obj:`fix` which always rounds
+to the nearest integer towards zero. For doing phase processing, the
+functions :func:`angle`, and :obj:`unwrap` are also useful. Also, the
+:obj:`linspace` and :obj:`logspace` functions return equally spaced samples
+in a linear or log scale.  Finally, it's useful to be aware of the indexing
+capabilities of Numpy. Mention should be made of the new
+function :obj:`select` which extends the functionality of :obj:`where` to
+include multiple conditions and multiple choices. The calling
+convention is ``select(condlist,choicelist,default=0).`` :obj:`select` is
+a vectorized form of the multiple if-statement. It allows rapid
+construction of a function which returns an array of results based on
+a list of conditions. Each element of the return array is taken from
+the array in a ``choicelist`` corresponding to the first condition in
+``condlist`` that is true. For example
+
+    >>> x = r_[-2:3]
+    >>> x
+    array([-2, -1,  0,  1,  2])
+    >>> select([x > 3, x >= 0],[0,x+2])
+    array([0, 0, 2, 3, 4])
+
+
+Common functions
+----------------
+
+Some functions depend on sub-packages of SciPy but should be available
+from the top-level of SciPy due to their common use. These are
+functions that might have been placed in scipy_base except for their
+dependence on other sub-packages of SciPy. For example the
+:obj:`factorial` and :obj:`comb` functions compute :math:`n!` and
+:math:`n!/k!(n-k)!` using either exact integer arithmetic (thanks to
+Python's Long integer object), or by using floating-point precision
+and the gamma function.  The functions :obj:`rand` and :obj:`randn`
+are used so often that they warranted a place at the top level. There
+are convenience functions for the interactive use: :obj:`disp`
+(similar to print), and :obj:`who` (returns a list of defined
+variables and memory consumption--upper bounded). Another function
+returns a common image used in image processing: :obj:`lena`.
+
+Finally, two functions are provided that are useful for approximating
+derivatives of functions using discrete-differences. The function
+:obj:`central_diff_weights` returns weighting coefficients for an
+equally-spaced :math:`N`-point approximation to the derivative of
+order *o*. These weights must be multiplied by the function
+corresponding to these points and the results added to obtain the
+derivative approximation. This function is intended for use when only
+samples of the function are avaiable. When the function is an object
+that can be handed to a routine and evaluated, the function
+:obj:`derivative` can be used to automatically evaluate the object at
+the correct points to obtain an N-point approximation to the *o*-th
+derivative at a given point.

pythonPackages/scipy-0.8.0/doc/source/tutorial/examples/1-1

@@ -0,0 +1,55 @@
+>>> sp.info(optimize.fmin)
+ fmin(func, x0, args=(), xtol=0.0001, ftol=0.0001, maxiter=None, maxfun=None,
+      full_output=0, disp=1, retall=0, callback=None)
+
+Minimize a function using the downhill simplex algorithm.
+
+:Parameters:
+
+  func : callable func(x,*args)
+      The objective function to be minimized.
+  x0 : ndarray
+      Initial guess.
+  args : tuple
+      Extra arguments passed to func, i.e. ``f(x,*args)``.
+  callback : callable
+      Called after each iteration, as callback(xk), where xk is the
+      current parameter vector.
+
+:Returns: (xopt, {fopt, iter, funcalls, warnflag})
+
+  xopt : ndarray
+      Parameter that minimizes function.
+  fopt : float
+      Value of function at minimum: ``fopt = func(xopt)``.
+  iter : int
+      Number of iterations performed.
+  funcalls : int
+      Number of function calls made.
+  warnflag : int
+      1 : Maximum number of function evaluations made.
+      2 : Maximum number of iterations reached.
+  allvecs : list
+      Solution at each iteration.
+
+*Other Parameters*:
+
+  xtol : float
+      Relative error in xopt acceptable for convergence.
+  ftol : number
+      Relative error in func(xopt) acceptable for convergence.
+  maxiter : int
+      Maximum number of iterations to perform.
+  maxfun : number
+      Maximum number of function evaluations to make.
+  full_output : bool
+      Set to True if fval and warnflag outputs are desired.
+  disp : bool
+      Set to True to print convergence messages.
+  retall : bool
+      Set to True to return list of solutions at each iteration.
+
+:Notes:
+
+    Uses a Nelder-Mead simplex algorithm to find the minimum of
+    function of one or more variables.

pythonPackages/scipy-0.8.0/doc/source/tutorial/examples/4-1

@@ -0,0 +1,25 @@
+>>> help(integrate)
+ Methods for Integrating Functions given function object.
+
+   quad          -- General purpose integration.
+   dblquad       -- General purpose double integration.
+   tplquad       -- General purpose triple integration.
+   fixed_quad    -- Integrate func(x) using Gaussian quadrature of order n.
+   quadrature    -- Integrate with given tolerance using Gaussian quadrature.
+   romberg       -- Integrate func using Romberg integration.
+
+ Methods for Integrating Functions given fixed samples.
+
+   trapz         -- Use trapezoidal rule to compute integral from samples.
+   cumtrapz      -- Use trapezoidal rule to cumulatively compute integral.
+   simps         -- Use Simpson's rule to compute integral from samples.
+   romb          -- Use Romberg Integration to compute integral from
+                    (2**k + 1) evenly-spaced samples.
+
+   See the special module's orthogonal polynomials (special) for Gaussian
+      quadrature roots and weights for other weighting factors and regions.
+
+ Interface to numerical integrators of ODE systems.
+
+   odeint        -- General integration of ordinary differential equations.
+   ode           -- Integrate ODE using VODE and ZVODE routines.

pythonPackages/scipy-0.8.0/doc/source/tutorial/examples/5-1

@@ -0,0 +1,91 @@
+from scipy import optimize
+>>> info(optimize)
+Optimization Tools
+==================
+
+ A collection of general-purpose optimization routines.
+
+   fmin        --  Nelder-Mead Simplex algorithm
+                     (uses only function calls)
+   fmin_powell --  Powell's (modified) level set method (uses only
+                     function calls)
+   fmin_cg     --  Non-linear (Polak-Ribiere) conjugate gradient algorithm
+                     (can use function and gradient).
+   fmin_bfgs   --  Quasi-Newton method (Broydon-Fletcher-Goldfarb-Shanno);
+                     (can use function and gradient)
+   fmin_ncg    --  Line-search Newton Conjugate Gradient (can use
+                     function, gradient and Hessian).
+   leastsq     --  Minimize the sum of squares of M equations in
+                     N unknowns given a starting estimate.
+
+
+  Constrained Optimizers (multivariate)
+
+   fmin_l_bfgs_b -- Zhu, Byrd, and Nocedal's L-BFGS-B constrained optimizer
+                      (if you use this please quote their papers -- see help)
+
+   fmin_tnc      -- Truncated Newton Code originally written by Stephen Nash and
+                      adapted to C by Jean-Sebastien Roy.
+
+   fmin_cobyla   -- Constrained Optimization BY Linear Approximation
+
+
+  Global Optimizers
+
+   anneal      --  Simulated Annealing
+   brute       --  Brute force searching optimizer
+
+
+  Scalar function minimizers
+
+   fminbound   --  Bounded minimization of a scalar function.
+   brent       --  1-D function minimization using Brent method.
+   golden      --  1-D function minimization using Golden Section method
+   bracket     --  Bracket a minimum (given two starting points)
+
+
+ Also a collection of general-purpose root-finding routines.
+
+   fsolve      --  Non-linear multi-variable equation solver.
+
+
+  Scalar function solvers
+
+   brentq      --  quadratic interpolation Brent method
+   brenth      --  Brent method (modified by Harris with hyperbolic
+                     extrapolation)
+   ridder      --  Ridder's method
+   bisect      --  Bisection method
+   newton      --  Secant method or Newton's method
+
+   fixed_point --  Single-variable fixed-point solver.
+
+ A collection of general-purpose nonlinear multidimensional solvers.
+
+   broyden1            --  Broyden's first method - is a quasi-Newton-Raphson
+                           method for updating an approximate Jacobian and then
+                           inverting it
+   broyden2            --  Broyden's second method - the same as broyden1, but
+                           updates the inverse Jacobian directly
+   broyden3            --  Broyden's second method - the same as broyden2, but
+                           instead of directly computing the inverse Jacobian,
+                           it remembers how to construct it using vectors, and
+                           when computing inv(J)*F, it uses those vectors to
+                           compute this product, thus avoding the expensive NxN
+                           matrix multiplication.
+   broyden_generalized --  Generalized Broyden's method, the same as broyden2,
+                           but instead of approximating the full NxN Jacobian,
+                           it construct it at every iteration in a way that
+                           avoids the NxN matrix multiplication.  This is not
+                           as precise as broyden3.
+   anderson            --  extended Anderson method, the same as the
+                           broyden_generalized, but added w_0^2*I to before
+                           taking inversion to improve the stability
+   anderson2           --  the Anderson method, the same as anderson, but
+                           formulated differently
+
+ Utility Functions
+
+   line_search --  Return a step that satisfies the strong Wolfe conditions.
+   check_grad  --  Check the supplied derivative using finite difference
+                     techniques.

pythonPackages/scipy-0.8.0/doc/source/tutorial/examples/normdiscr_plot1.py

@@ -0,0 +1,45 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy import stats
+
+npoints = 20 # number of integer support points of the distribution minus 1
+npointsh = npoints / 2
+npointsf = float(npoints)
+nbound = 4 #bounds for the truncated normal
+normbound = (1 + 1 / npointsf) * nbound #actual bounds of truncated normal
+grid = np.arange(-npointsh, npointsh+2, 1) #integer grid
+gridlimitsnorm = (grid-0.5) / npointsh * nbound #bin limits for the truncnorm
+gridlimits = grid - 0.5
+grid = grid[:-1]
+probs = np.diff(stats.truncnorm.cdf(gridlimitsnorm, -normbound, normbound))
+gridint = grid
+normdiscrete = stats.rv_discrete(
+                        values=(gridint, np.round(probs, decimals=7)),
+                        name='normdiscrete')
+   
+   
+n_sample = 500
+np.random.seed(87655678) #fix the seed for replicability
+rvs = normdiscrete.rvs(size=n_sample)
+rvsnd=rvs
+f,l = np.histogram(rvs, bins=gridlimits)
+sfreq = np.vstack([gridint, f, probs*n_sample]).T
+fs = sfreq[:,1] / float(n_sample)
+ft = sfreq[:,2] / float(n_sample)
+nd_std = np.sqrt(normdiscrete.stats(moments='v'))
+
+ind = gridint  # the x locations for the groups
+width = 0.35       # the width of the bars
+
+plt.subplot(111)
+rects1 = plt.bar(ind, ft, width, color='b')
+rects2 = plt.bar(ind+width, fs, width, color='r')
+normline = plt.plot(ind+width/2.0, stats.norm.pdf(ind, scale=nd_std),
+                    color='b')
+
+plt.ylabel('Frequency')
+plt.title('Frequency and Probability of normdiscrete')
+plt.xticks(ind+width, ind )
+plt.legend((rects1[0], rects2[0]), ('true', 'sample'))
+
+plt.show()

pythonPackages/scipy-0.8.0/doc/source/tutorial/examples/normdiscr_plot2.py

@@ -0,0 +1,48 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy import stats
+
+npoints = 20 # number of integer support points of the distribution minus 1
+npointsh = npoints / 2
+npointsf = float(npoints)
+nbound = 4 #bounds for the truncated normal
+normbound = (1 + 1 / npointsf) * nbound #actual bounds of truncated normal
+grid = np.arange(-npointsh, npointsh+2,1) #integer grid
+gridlimitsnorm = (grid - 0.5) / npointsh * nbound #bin limits for the truncnorm
+gridlimits = grid - 0.5
+grid = grid[:-1]
+probs = np.diff(stats.truncnorm.cdf(gridlimitsnorm, -normbound, normbound))
+gridint = grid
+normdiscrete = stats.rv_discrete(
+                        values=(gridint, np.round(probs, decimals=7)),
+                        name='normdiscrete')
+   
+n_sample = 500
+np.random.seed(87655678) #fix the seed for replicability
+rvs = normdiscrete.rvs(size=n_sample)
+rvsnd = rvs
+f,l = np.histogram(rvs,bins=gridlimits)
+sfreq = np.vstack([gridint,f,probs*n_sample]).T
+fs = sfreq[:,1] / float(n_sample)
+ft = sfreq[:,2] / float(n_sample)
+fs = sfreq[:,1].cumsum() / float(n_sample)
+ft = sfreq[:,2].cumsum() / float(n_sample)
+nd_std = np.sqrt(normdiscrete.stats(moments='v'))
+
+
+ind = gridint  # the x locations for the groups
+width = 0.35   # the width of the bars
+
+plt.figure()
+plt.subplot(111)
+rects1 = plt.bar(ind, ft, width, color='b')
+rects2 = plt.bar(ind+width, fs, width, color='r')
+normline = plt.plot(ind+width/2.0, stats.norm.cdf(ind+0.5,scale=nd_std),
+                    color='b')
+
+plt.ylabel('cdf')
+plt.title('Cumulative Frequency and CDF of normdiscrete')
+plt.xticks(ind+width, ind )
+plt.legend( (rects1[0], rects2[0]), ('true', 'sample') )
+
+plt.show()

pythonPackages/scipy-0.8.0/doc/source/tutorial/fftpack.rst

@@ -0,0 +1,145 @@
+Fourier Transforms (:mod:`scipy.fftpack`)
+=========================================
+
+.. sectionauthor:: Scipy Developers
+
+.. currentmodule:: scipy.fftpack
+
+.. warning::
+
+   This is currently a stub page
+
+
+.. contents::
+
+
+Fourier analysis is fundamentally a method for expressing a function as a
+sum of periodic components, and for recovering the signal from those
+components.  When both the function and its Fourier transform are
+replaced with discretized counterparts, it is called the discrete Fourier
+transform (DFT).  The DFT has become a mainstay of numerical computing in
+part because of a very fast algorithm for computing it, called the Fast
+Fourier Transform (FFT), which was known to Gauss (1805) and was brought
+to light in its current form by Cooley and Tukey [CT]_.  Press et al. [NR]_
+provide an accessible introduction to Fourier analysis and its
+applications.
+
+
+Fast Fourier transforms
+-----------------------
+
+One dimensional discrete Fourier transforms
+-------------------------------------------
+
+fft, ifft, rfft, irfft
+
+
+Two and n dimensional discrete Fourier transforms
+-------------------------------------------------
+
+fft in more than one dimension
+
+
+Discrete Cosine Transforms
+--------------------------
+
+
+Return the Discrete Cosine Transform [Mak]_ of arbitrary type sequence ``x``.
+
+For a single dimension array ``x``, ``dct(x, norm='ortho')`` is equal to
+matlab ``dct(x)``.
+
+There are theoretically 8 types of the DCT [WP]_, only the first 3 types are
+implemented in scipy. 'The' DCT generally refers to DCT type 2, and 'the'
+Inverse DCT generally refers to DCT type 3.
+
+type I
+~~~~~~
+
+There are several definitions of the DCT-I; we use the following
+(for ``norm=None``):
+
+.. math::
+   :nowrap:
+
+    \[ y_k = x_0 + (-1)^k x_{N-1} + 2\sum_{n=1}^{N-2} x_n
+    \cos\left({\pi nk\over N-1}\right),
+    \qquad 0 \le k < N. \]
+
+Only None is supported as normalization mode for DCT-I. Note also that the
+DCT-I is only supported for input size > 1
+
+type II
+~~~~~~~
+
+There are several definitions of the DCT-II; we use the following
+(for ``norm=None``):
+
+.. math::
+   :nowrap:
+
+    \[ y_k = 2 \sum_{n=0}^{N-1} x_n
+    \cos \left({\pi(2n+1)k \over 2N} \right)
+    \qquad 0 \le k < N.\]
+
+If ``norm='ortho'``, :math:`y_k` is multiplied by a scaling factor `f`:
+
+.. math::
+   :nowrap:
+
+    \[f = \begin{cases} \sqrt{1/(4N)}, & \text{if $k = 0$} \\
+       \sqrt{1/(2N)}, & \text{otherwise} \end{cases} \]
+
+
+Which makes the corresponding matrix of coefficients orthonormal
+(`OO' = Id`).
+
+type III
+~~~~~~~~
+
+There are several definitions, we use the following
+(for ``norm=None``):
+
+.. math::
+   :nowrap:
+
+    \[ y_k = x_0 + 2 \sum_{n=1}^{N-1} x_n
+    \cos\left({\pi n(2k+1) \over 2N}\right)
+    \qquad 0 \le k < N,\]
+
+or, for ``norm='ortho'``:
+
+.. math::
+   :nowrap:
+
+    \[ y_k = {x_0\over\sqrt{N}} + {1\over\sqrt{N}} \sum_{n=1}^{N-1}
+    x_n \cos\left({\pi n(2k+1) \over 2N}\right)
+    \qquad 0 \le k < N.\]
+
+The (unnormalized) DCT-III is the inverse of the (unnormalized) DCT-II, up
+to a factor `2N`. The orthonormalized DCT-III is exactly the inverse of the
+orthonormalized DCT-II.
+
+References
+~~~~~~~~~~
+
+.. [CT] Cooley, James W., and John W. Tukey, 1965, "An algorithm for the
+        machine calculation of complex Fourier series," *Math. Comput.*
+        19: 297-301.
+
+.. [NR] Press, W., Teukolsky, S., Vetterline, W.T., and Flannery, B.P.,
+        2007, *Numerical Recipes: The Art of Scientific Computing*, ch.
+        12-13.  Cambridge Univ. Press, Cambridge, UK.
+
+.. [Mak] J. Makhoul, 1980, 'A Fast Cosine Transform in One and Two Dimensions',
+       `IEEE Transactions on acoustics, speech and signal processing`
+       vol. 28(1), pp. 27-34, http://dx.doi.org/10.1109/TASSP.1980.1163351
+
+.. [WP] http://en.wikipedia.org/wiki/Discrete_cosine_transform
+
+
+FFT convolution
+---------------
+
+scipy.fftpack.convolve performs a convolution of two one-dimensional
+arrays in frequency domain.

pythonPackages/scipy-0.8.0/doc/source/tutorial/general.rst

@@ -0,0 +1,129 @@
+============
+Introduction
+============
+
+.. contents::
+
+SciPy is a collection of mathematical algorithms and convenience
+functions built on the Numpy extension for Python. It adds
+significant power to the interactive Python session by exposing the
+user to high-level commands and classes for the manipulation and
+visualization of data. With SciPy, an interactive Python session
+becomes a data-processing and system-prototyping environment rivaling
+sytems such as Matlab, IDL, Octave, R-Lab, and SciLab.
+
+The additional power of using SciPy within Python, however, is that a
+powerful programming language is also available for use in developing
+sophisticated programs and specialized applications. Scientific
+applications written in SciPy benefit from the development of
+additional modules in numerous niche's of the software landscape by
+developers across the world. Everything from parallel programming to
+web and data-base subroutines and classes have been made available to
+the Python programmer. All of this power is available in addition to
+the mathematical libraries in SciPy.
+
+This document provides a tutorial for the first-time user of SciPy to
+help get started with some of the features available in this powerful
+package. It is assumed that the user has already installed the
+package. Some general Python facility is also assumed such as could be
+acquired by working through the Tutorial in the Python distribution.
+For further introductory help the user is directed to the Numpy
+documentation.
+
+For brevity and convenience, we will often assume that the main
+packages (numpy, scipy, and matplotlib) have been imported as::
+
+    >>> import numpy as np
+    >>> import scipy as sp
+    >>> import matplotlib as mpl
+    >>> import matplotlib.pyplot as plt
+
+These are the import conventions that our community has adopted
+after discussion on public mailing lists.  You will see these
+conventions used throughout NumPy and SciPy source code and
+documentation.  While we obviously don't require you to follow
+these conventions in your own code, it is highly recommended.
+
+SciPy Organization
+------------------
+
+SciPy is organized into subpackages covering different scientific
+computing domains. These are summarized in the following table:
+
+.. currentmodule:: scipy
+
+==================  ======================================================
+Subpackage          Description
+==================  ======================================================
+:mod:`cluster`      Clustering algorithms
+:mod:`constants`    Physical and mathematical constants
+:mod:`fftpack`      Fast Fourier Transform routines
+:mod:`integrate`    Integration and ordinary differential equation solvers
+:mod:`interpolate`  Interpolation and smoothing splines
+:mod:`io`           Input and Output
+:mod:`linalg`       Linear algebra
+:mod:`maxentropy`   Maximum entropy methods
+:mod:`ndimage`      N-dimensional image processing
+:mod:`odr`          Orthogonal distance regression
+:mod:`optimize`     Optimization and root-finding routines
+:mod:`signal`       Signal processing
+:mod:`sparse`       Sparse matrices and associated routines
+:mod:`spatial`      Spatial data structures and algorithms
+:mod:`special`      Special functions
+:mod:`stats`        Statistical distributions and functions
+:mod:`weave`        C/C++ integration
+==================  ======================================================
+
+Scipy sub-packages need to be imported separately, for example::
+
+    >>> from scipy import linalg, optimize
+
+Because of their ubiquitousness, some of the functions in these
+subpackages are also made available in the scipy namespace to ease
+their use in interactive sessions and programs. In addition, many
+basic array functions from :mod:`numpy` are also available at the
+top-level of the :mod:`scipy` package. Before looking at the
+sub-packages individually, we will first look at some of these common
+functions.
+
+Finding Documentation
+---------------------
+
+Scipy and Numpy have HTML and PDF versions of their documentation
+available at http://docs.scipy.org/, which currently details nearly
+all available functionality. However, this documentation is still
+work-in-progress, and some parts may be incomplete or sparse. As
+we are a volunteer organization and depend on the community for
+growth, your participation - everything from providing feedback to
+improving the documentation and code - is welcome and actively
+encouraged.
+
+Python also provides the facility of documentation strings. The
+functions and classes available in SciPy use this method for on-line
+documentation. There are two methods for reading these messages and
+getting help. Python provides the command :func:`help` in the pydoc
+module. Entering this command with no arguments (i.e. ``>>> help`` )
+launches an interactive help session that allows searching through the
+keywords and modules available to all of Python. Running the command
+help with an object as the argument displays the calling signature,
+and the documentation string of the object.
+
+The pydoc method of help is sophisticated but uses a pager to display
+the text. Sometimes this can interfere with the terminal you are
+running the interactive session within. A scipy-specific help system
+is also available under the command ``sp.info``. The signature and
+documentation string for the object passed to the ``help`` command are
+printed to standard output (or to a writeable object passed as the
+third argument). The second keyword argument of ``sp.info`` defines
+the maximum width of the line for printing. If a module is passed as
+the argument to help than a list of the functions and classes defined
+in that module is printed. For example:
+
+.. literalinclude:: examples/1-1
+
+Another useful command is :func:`source`. When given a function
+written in Python as an argument, it prints out a listing of the
+source code for that function. This can be helpful in learning about
+an algorithm or understanding exactly what a function is doing with
+its arguments. Also don't forget about the Python command ``dir``
+which can be used to look at the namespace of a module or package.

pythonPackages/scipy-0.8.0/doc/source/tutorial/index.rst

@@ -0,0 +1,22 @@
+**************
+SciPy Tutorial
+**************
+
+.. sectionauthor:: Travis E. Oliphant
+
+.. toctree::
+   :maxdepth: 1
+
+   general
+   basic
+   special
+   integrate
+   optimize
+   interpolate
+   fftpack
+   signal
+   linalg
+   stats
+   ndimage
+   io
+   weave

pythonPackages/scipy-0.8.0/doc/source/tutorial/integrate.rst

@@ -0,0 +1,280 @@
+Integration (:mod:`scipy.integrate`)
+====================================
+
+.. sectionauthor:: Travis E. Oliphant
+
+.. currentmodule:: scipy.integrate
+
+The :mod:`scipy.integrate` sub-package provides several integration
+techniques including an ordinary differential equation integrator. An
+overview of the module is provided by the help command:
+
+.. literalinclude:: examples/4-1
+
+
+General integration (:func:`quad`)
+----------------------------------
+
+The function :obj:`quad` is provided to integrate a function of one
+variable between two points. The points can be :math:`\pm\infty`
+(:math:`\pm` ``inf``) to indicate infinite limits. For example,
+suppose you wish to integrate a bessel function ``jv(2.5,x)`` along
+the interval :math:`[0,4.5].`
+
+.. math::
+   :nowrap:
+
+    \[ I=\int_{0}^{4.5}J_{2.5}\left(x\right)\, dx.\]
+
+This could be computed using :obj:`quad`:
+
+    >>> result = integrate.quad(lambda x: special.jv(2.5,x), 0, 4.5)
+    >>> print result
+    (1.1178179380783249, 7.8663172481899801e-09)
+    
+    >>> I = sqrt(2/pi)*(18.0/27*sqrt(2)*cos(4.5)-4.0/27*sqrt(2)*sin(4.5)+
+        sqrt(2*pi)*special.fresnel(3/sqrt(pi))[0])
+    >>> print I
+    1.117817938088701
+    
+    >>> print abs(result[0]-I)
+    1.03761443881e-11
+
+The first argument to quad is a "callable" Python object (*i.e* a
+function, method, or class instance). Notice the use of a lambda-
+function in this case as the argument. The next two arguments are the
+limits of integration. The return value is a tuple, with the first
+element holding the estimated value of the integral and the second
+element holding an upper bound on the error. Notice, that in this
+case, the true value of this integral is
+
+.. math::
+   :nowrap:
+
+    \[ I=\sqrt{\frac{2}{\pi}}\left(\frac{18}{27}\sqrt{2}\cos\left(4.5\right)-\frac{4}{27}\sqrt{2}\sin\left(4.5\right)+\sqrt{2\pi}\textrm{Si}\left(\frac{3}{\sqrt{\pi}}\right)\right),\]
+
+where
+
+.. math::
+   :nowrap:
+
+    \[ \textrm{Si}\left(x\right)=\int_{0}^{x}\sin\left(\frac{\pi}{2}t^{2}\right)\, dt.\]
+
+is the Fresnel sine integral. Note that the numerically-computed
+integral is within :math:`1.04\times10^{-11}` of the exact result --- well below the reported error bound.
+
+Infinite inputs are also allowed in :obj:`quad` by using :math:`\pm`
+``inf`` as one of the arguments. For example, suppose that a numerical
+value for the exponential integral:
+
+.. math::
+   :nowrap:
+
+    \[ E_{n}\left(x\right)=\int_{1}^{\infty}\frac{e^{-xt}}{t^{n}}\, dt.\]
+
+is desired (and the fact that this integral can be computed as
+``special.expn(n,x)`` is forgotten). The functionality of the function
+:obj:`special.expn` can be replicated by defining a new function
+:obj:`vec_expint` based on the routine :obj:`quad`:
+
+    >>> from scipy.integrate import quad
+    >>> def integrand(t,n,x):
+    ...     return exp(-x*t) / t**n
+    
+    >>> def expint(n,x): 
+    ...     return quad(integrand, 1, Inf, args=(n, x))[0]
+    
+    >>> vec_expint = vectorize(expint)
+    
+    >>> vec_expint(3,arange(1.0,4.0,0.5))
+    array([ 0.1097,  0.0567,  0.0301,  0.0163,  0.0089,  0.0049])
+    >>> special.expn(3,arange(1.0,4.0,0.5))
+    array([ 0.1097,  0.0567,  0.0301,  0.0163,  0.0089,  0.0049])
+
+The function which is integrated can even use the quad argument
+(though the error bound may underestimate the error due to possible
+numerical error in the integrand from the use of :obj:`quad` ). The integral in this case is
+
+.. math::
+   :nowrap:
+
+    \[ I_{n}=\int_{0}^{\infty}\int_{1}^{\infty}\frac{e^{-xt}}{t^{n}}\, dt\, dx=\frac{1}{n}.\]
+
+>>> result = quad(lambda x: expint(3, x), 0, inf)
+>>> print result
+(0.33333333324560266, 2.8548934485373678e-09)  
+    
+>>> I3 = 1.0/3.0
+>>> print I3
+0.333333333333   
+    
+>>> print I3 - result[0]
+8.77306560731e-11     
+    
+This last example shows that multiple integration can be handled using
+repeated calls to :func:`quad`. The mechanics of this for double and
+triple integration have been wrapped up into the functions
+:obj:`dblquad` and :obj:`tplquad`. The function, :obj:`dblquad`
+performs double integration. Use the help function to be sure that the
+arguments are defined in the correct order. In addition, the limits on
+all inner integrals are actually functions which can be constant
+functions. An example of using double integration to compute several
+values of :math:`I_{n}` is shown below:
+
+    >>> from scipy.integrate import quad, dblquad
+    >>> def I(n):
+    ...     return dblquad(lambda t, x: exp(-x*t)/t**n, 0, Inf, lambda x: 1, lambda x: Inf) 
+    
+    >>> print I(4)
+    (0.25000000000435768, 1.0518245707751597e-09)
+    >>> print I(3)
+    (0.33333333325010883, 2.8604069919261191e-09) 
+    >>> print I(2)
+    (0.49999999999857514, 1.8855523253868967e-09)
+
+
+Gaussian quadrature (integrate.gauss_quadtol)
+---------------------------------------------
+
+A few functions are also provided in order to perform simple Gaussian
+quadrature over a fixed interval. The first is :obj:`fixed_quad` which
+performs fixed-order Gaussian quadrature. The second function is
+:obj:`quadrature` which performs Gaussian quadrature of multiple
+orders until the difference in the integral estimate is beneath some
+tolerance supplied by the user. These functions both use the module
+:mod:`special.orthogonal` which can calculate the roots and quadrature
+weights of a large variety of orthogonal polynomials (the polynomials
+themselves are available as special functions returning instances of
+the polynomial class --- e.g. :obj:`special.legendre <scipy.special.legendre>`).
+
+
+Integrating using samples
+-------------------------
+
+There are three functions for computing integrals given only samples:
+:obj:`trapz` , :obj:`simps`, and :obj:`romb` . The first two
+functions use Newton-Coates formulas of order 1 and 2 respectively to
+perform integration. These two functions can handle,
+non-equally-spaced samples. The trapezoidal rule approximates the
+function as a straight line between adjacent points, while Simpson's
+rule approximates the function between three adjacent points as a
+parabola.
+
+If the samples are equally-spaced and the number of samples available
+is :math:`2^{k}+1` for some integer :math:`k`, then Romberg
+integration can be used to obtain high-precision estimates of the
+integral using the available samples. Romberg integration uses the
+trapezoid rule at step-sizes related by a power of two and then
+performs Richardson extrapolation on these estimates to approximate
+the integral with a higher-degree of accuracy. (A different interface
+to Romberg integration useful when the function can be provided is
+also available as :func:`romberg`).
+
+
+Ordinary differential equations (:func:`odeint`)
+------------------------------------------------
+
+Integrating a set of ordinary differential equations (ODEs) given
+initial conditions is another useful example. The function
+:obj:`odeint` is available in SciPy for integrating a first-order
+vector differential equation:
+
+.. math::
+   :nowrap:
+
+    \[ \frac{d\mathbf{y}}{dt}=\mathbf{f}\left(\mathbf{y},t\right),\]
+
+given initial conditions :math:`\mathbf{y}\left(0\right)=y_{0}`, where
+:math:`\mathbf{y}` is a length :math:`N` vector and :math:`\mathbf{f}`
+is a mapping from :math:`\mathcal{R}^{N}` to :math:`\mathcal{R}^{N}.`
+A higher-order ordinary differential equation can always be reduced to
+a differential equation of this type by introducing intermediate
+derivatives into the :math:`\mathbf{y}` vector.
+
+For example suppose it is desired to find the solution to the
+following second-order differential equation:
+
+.. math::
+   :nowrap:
+
+    \[ \frac{d^{2}w}{dz^{2}}-zw(z)=0\]
+
+with initial conditions :math:`w\left(0\right)=\frac{1}{\sqrt[3]{3^{2}}\Gamma\left(\frac{2}{3}\right)}` and :math:`\left.\frac{dw}{dz}\right|_{z=0}=-\frac{1}{\sqrt[3]{3}\Gamma\left(\frac{1}{3}\right)}.` It is known that the solution to this differential equation with these
+boundary conditions is the Airy function
+
+.. math::
+   :nowrap:
+
+    \[ w=\textrm{Ai}\left(z\right),\]
+
+which gives a means to check the integrator using :func:`special.airy <scipy.special.airy>`.
+
+First, convert this ODE into standard form by setting
+:math:`\mathbf{y}=\left[\frac{dw}{dz},w\right]` and :math:`t=z`. Thus,
+the differential equation becomes
+
+.. math::
+   :nowrap:
+
+    \[ \frac{d\mathbf{y}}{dt}=\left[\begin{array}{c} ty_{1}\\ y_{0}\end{array}\right]=\left[\begin{array}{cc} 0 & t\\ 1 & 0\end{array}\right]\left[\begin{array}{c} y_{0}\\ y_{1}\end{array}\right]=\left[\begin{array}{cc} 0 & t\\ 1 & 0\end{array}\right]\mathbf{y}.\]
+
+In other words,
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{f}\left(\mathbf{y},t\right)=\mathbf{A}\left(t\right)\mathbf{y}.\]
+
+As an interesting reminder, if :math:`\mathbf{A}\left(t\right)`
+commutes with :math:`\int_{0}^{t}\mathbf{A}\left(\tau\right)\, d\tau`
+under matrix multiplication, then this linear differential equation
+has an exact solution using the matrix exponential:
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{y}\left(t\right)=\exp\left(\int_{0}^{t}\mathbf{A}\left(\tau\right)d\tau\right)\mathbf{y}\left(0\right),\]
+
+However, in this case, :math:`\mathbf{A}\left(t\right)` and its integral do not commute.
+
+There are many optional inputs and outputs available when using odeint
+which can help tune the solver. These additional inputs and outputs
+are not needed much of the time, however, and the three required input
+arguments and the output solution suffice. The required inputs are the
+function defining the derivative, *fprime*, the initial conditions
+vector, *y0*, and the time points to obtain a solution, *t*, (with
+the initial value point as the first element of this sequence).  The
+output to :obj:`odeint` is a matrix where each row contains the
+solution vector at each requested time point (thus, the initial
+conditions are given in the first output row).
+
+The following example illustrates the use of odeint including the
+usage of the *Dfun* option which allows the user to specify a gradient
+(with respect to :math:`\mathbf{y}` ) of the function,
+:math:`\mathbf{f}\left(\mathbf{y},t\right)`.
+
+    >>> from scipy.integrate import odeint
+    >>> from scipy.special import gamma, airy
+    >>> y1_0 = 1.0/3**(2.0/3.0)/gamma(2.0/3.0)
+    >>> y0_0 = -1.0/3**(1.0/3.0)/gamma(1.0/3.0)
+    >>> y0 = [y0_0, y1_0]
+    >>> def func(y, t):
+    ...     return [t*y[1],y[0]]
+    
+    >>> def gradient(y,t):
+    ...     return [[0,t],[1,0]]
+    
+    >>> x = arange(0,4.0, 0.01)
+    >>> t = x
+    >>> ychk = airy(x)[0]
+    >>> y = odeint(func, y0, t)
+    >>> y2 = odeint(func, y0, t, Dfun=gradient)
+    
+    >>> print ychk[:36:6]
+    [ 0.355028  0.339511  0.324068  0.308763  0.293658  0.278806]
+    
+    >>> print y[:36:6,1]
+    [ 0.355028  0.339511  0.324067  0.308763  0.293658  0.278806]
+    
+    >>> print y2[:36:6,1]
+    [ 0.355028  0.339511  0.324067  0.308763  0.293658  0.278806]

pythonPackages/scipy-0.8.0/doc/source/tutorial/interpolate.rst

@@ -0,0 +1,399 @@
+Interpolation (:mod:`scipy.interpolate`)
+========================================
+
+.. sectionauthor:: Travis E. Oliphant
+
+.. currentmodule:: scipy.interpolate
+
+.. contents::
+
+There are two general interpolation facilities available in SciPy. The
+first facility is an interpolation class which performs linear
+1-dimensional interpolation. The second facility is based on the
+FORTRAN library FITPACK and provides functions for 1- and
+2-dimensional (smoothed) cubic-spline interpolation. There are both
+procedural and object-oriented interfaces for the FITPACK library.
+
+
+Linear 1-d interpolation (:class:`interp1d`)
+--------------------------------------------
+
+The interp1d class in scipy.interpolate is a convenient method to
+create a function based on fixed data points which can be evaluated
+anywhere within the domain defined by the given data using linear
+interpolation. An instance of this class is created by passing the 1-d
+vectors comprising the data. The instance of this class defines a
+__call__ method and can therefore by treated like a function which
+interpolates between known data values to obtain unknown values (it
+also has a docstring for help). Behavior at the boundary can be
+specified at instantiation time. The following example demonstrates
+it's use.
+
+.. plot::
+
+   >>> import numpy as np
+   >>> from scipy import interpolate
+
+   >>> x = np.arange(0,10)
+   >>> y = np.exp(-x/3.0)
+   >>> f = interpolate.interp1d(x, y)
+
+   >>> xnew = np.arange(0,9,0.1)
+   >>> import matplotlib.pyplot as plt
+   >>> plt.plot(x,y,'o',xnew,f(xnew),'-')
+
+..   :caption: One-dimensional interpolation using the
+..             class :obj:`interpolate.interp1d`
+
+
+Spline interpolation in 1-d: Procedural (interpolate.splXXX)
+------------------------------------------------------------
+
+Spline interpolation requires two essential steps: (1) a spline
+representation of the curve is computed, and (2) the spline is
+evaluated at the desired points. In order to find the spline
+representation, there are two different ways to represent a curve and
+obtain (smoothing) spline coefficients: directly and parametrically.
+The direct method finds the spline representation of a curve in a two-
+dimensional plane using the function :obj:`splrep`. The
+first two arguments are the only ones required, and these provide the
+:math:`x` and :math:`y` components of the curve. The normal output is
+a 3-tuple, :math:`\left(t,c,k\right)` , containing the knot-points,
+:math:`t` , the coefficients :math:`c` and the order :math:`k` of the
+spline. The default spline order is cubic, but this can be changed
+with the input keyword, *k.*
+
+For curves in :math:`N` -dimensional space the function
+:obj:`splprep` allows defining the curve
+parametrically. For this function only 1 input argument is
+required. This input is a list of :math:`N` -arrays representing the
+curve in :math:`N` -dimensional space. The length of each array is the
+number of curve points, and each array provides one component of the
+:math:`N` -dimensional data point. The parameter variable is given
+with the keword argument, *u,* which defaults to an equally-spaced
+monotonic sequence between :math:`0` and :math:`1` . The default
+output consists of two objects: a 3-tuple, :math:`\left(t,c,k\right)`
+, containing the spline representation and the parameter variable
+:math:`u.`
+
+The keyword argument, *s* , is used to specify the amount of smoothing
+to perform during the spline fit. The default value of :math:`s` is
+:math:`s=m-\sqrt{2m}` where :math:`m` is the number of data-points
+being fit. Therefore, **if no smoothing is desired a value of**
+:math:`\mathbf{s}=0` **should be passed to the routines.**
+
+Once the spline representation of the data has been determined,
+functions are available for evaluating the spline
+(:func:`splev`) and its derivatives
+(:func:`splev`, :func:`spalde`) at any point
+and the integral of the spline between any two points (
+:func:`splint`). In addition, for cubic splines ( :math:`k=3`
+) with 8 or more knots, the roots of the spline can be estimated (
+:func:`sproot`). These functions are demonstrated in the
+example that follows.
+
+.. plot::
+
+   >>> import numpy as np
+   >>> import matplotlib.pyplot as plt
+   >>> from scipy import interpolate
+
+   Cubic-spline
+
+   >>> x = np.arange(0,2*np.pi+np.pi/4,2*np.pi/8)
+   >>> y = np.sin(x)
+   >>> tck = interpolate.splrep(x,y,s=0)
+   >>> xnew = np.arange(0,2*np.pi,np.pi/50)
+   >>> ynew = interpolate.splev(xnew,tck,der=0)
+
+   >>> plt.figure()
+   >>> plt.plot(x,y,'x',xnew,ynew,xnew,np.sin(xnew),x,y,'b')
+   >>> plt.legend(['Linear','Cubic Spline', 'True'])
+   >>> plt.axis([-0.05,6.33,-1.05,1.05])
+   >>> plt.title('Cubic-spline interpolation')
+   >>> plt.show()
+
+   Derivative of spline
+
+   >>> yder = interpolate.splev(xnew,tck,der=1)
+   >>> plt.figure()
+   >>> plt.plot(xnew,yder,xnew,np.cos(xnew),'--')
+   >>> plt.legend(['Cubic Spline', 'True'])
+   >>> plt.axis([-0.05,6.33,-1.05,1.05])
+   >>> plt.title('Derivative estimation from spline')
+   >>> plt.show()
+
+   Integral of spline
+
+   >>> def integ(x,tck,constant=-1):
+   >>>     x = np.atleast_1d(x)
+   >>>     out = np.zeros(x.shape, dtype=x.dtype)
+   >>>     for n in xrange(len(out)):
+   >>>         out[n] = interpolate.splint(0,x[n],tck)
+   >>>     out += constant
+   >>>     return out
+   >>>
+   >>> yint = integ(xnew,tck)
+   >>> plt.figure()
+   >>> plt.plot(xnew,yint,xnew,-np.cos(xnew),'--')
+   >>> plt.legend(['Cubic Spline', 'True'])
+   >>> plt.axis([-0.05,6.33,-1.05,1.05])
+   >>> plt.title('Integral estimation from spline')
+   >>> plt.show()
+
+   Roots of spline
+
+   >>> print interpolate.sproot(tck)
+   [ 0.      3.1416]
+
+   Parametric spline
+
+   >>> t = np.arange(0,1.1,.1)
+   >>> x = np.sin(2*np.pi*t)
+   >>> y = np.cos(2*np.pi*t)
+   >>> tck,u = interpolate.splprep([x,y],s=0)
+   >>> unew = np.arange(0,1.01,0.01)
+   >>> out = interpolate.splev(unew,tck)
+   >>> plt.figure()
+   >>> plt.plot(x,y,'x',out[0],out[1],np.sin(2*np.pi*unew),np.cos(2*np.pi*unew),x,y,'b')
+   >>> plt.legend(['Linear','Cubic Spline', 'True'])
+   >>> plt.axis([-1.05,1.05,-1.05,1.05])
+   >>> plt.title('Spline of parametrically-defined curve')
+   >>> plt.show()
+
+Spline interpolation in 1-d: Object-oriented (:class:`UnivariateSpline`)
+-----------------------------------------------------------------------------
+
+The spline-fitting capabilities described above are also available via
+an objected-oriented interface.  The one dimensional splines are
+objects of the `UnivariateSpline` class, and are created with the
+:math:`x` and :math:`y` components of the curve provided as arguments
+to the constructor.  The class defines __call__, allowing the object
+to be called with the x-axis values at which the spline should be
+evaluated, returning the interpolated y-values.  This is shown in
+the example below for the subclass `InterpolatedUnivariateSpline`.
+The methods :meth:`integral <UnivariateSpline.integral>`,
+:meth:`derivatives <UnivariateSpline.derivatives>`, and
+:meth:`roots <UnivariateSpline.roots>` methods are also available
+on `UnivariateSpline` objects, allowing definite integrals,
+derivatives, and roots to be computed for the spline.
+
+The UnivariateSpline class can also be used to smooth data by
+providing a non-zero value of the smoothing parameter `s`, with the
+same meaning as the `s` keyword of the :obj:`splrep` function
+described above.  This results in a spline that has fewer knots
+than the number of data points, and hence is no longer strictly
+an interpolating spline, but rather a smoothing spline.  If this
+is not desired, the `InterpolatedUnivariateSpline` class is available.
+It is a subclass of `UnivariateSpline` that always passes  through all
+points (equivalent to forcing the smoothing parameter to 0).  This
+class is demonstrated in the example below.
+
+The `LSQUnivarateSpline` is the other subclass of `UnivarateSpline`.
+It allows the user to specify the number and location of internal
+knots as explicitly with the parameter `t`.  This allows creation
+of customized splines with non-linear spacing, to interpolate in
+some domains and smooth in others, or change the character of the
+spline.
+
+
+.. plot::
+
+   >>> import numpy as np
+   >>> import matplotlib.pyplot as plt
+   >>> from scipy import interpolate
+
+   InterpolatedUnivariateSpline
+
+   >>> x = np.arange(0,2*np.pi+np.pi/4,2*np.pi/8)
+   >>> y = np.sin(x)
+   >>> s = interpolate.InterpolatedUnivariateSpline(x,y)
+   >>> xnew = np.arange(0,2*np.pi,np.pi/50)
+   >>> ynew = s(xnew)
+
+   >>> plt.figure()
+   >>> plt.plot(x,y,'x',xnew,ynew,xnew,np.sin(xnew),x,y,'b')
+   >>> plt.legend(['Linear','InterpolatedUnivariateSpline', 'True'])
+   >>> plt.axis([-0.05,6.33,-1.05,1.05])
+   >>> plt.title('InterpolatedUnivariateSpline')
+   >>> plt.show()
+
+   LSQUnivarateSpline with non-uniform knots
+
+   >>> t = [np.pi/2-.1,np.pi/2-.1,3*np.pi/2-.1,3*np.pi/2+.1]
+   >>> s = interpolate.LSQUnivariateSpline(x,y,t)
+   >>> ynew = s(xnew)
+
+   >>> plt.figure()
+   >>> plt.plot(x,y,'x',xnew,ynew,xnew,np.sin(xnew),x,y,'b')
+   >>> plt.legend(['Linear','LSQUnivariateSpline', 'True'])
+   >>> plt.axis([-0.05,6.33,-1.05,1.05])
+   >>> plt.title('Spline with Specified Interior Knots')
+   >>> plt.show()
+
+
+
+Two-dimensional spline representation: Procedural (:func:`bisplrep`)
+--------------------------------------------------------------------
+
+For (smooth) spline-fitting to a two dimensional surface, the function
+:func:`bisplrep` is available. This function takes as required inputs
+the **1-D** arrays *x*, *y*, and *z* which represent points on the
+surface :math:`z=f\left(x,y\right).` The default output is a list
+:math:`\left[tx,ty,c,kx,ky\right]` whose entries represent
+respectively, the components of the knot positions, the coefficients
+of the spline, and the order of the spline in each coordinate. It is
+convenient to hold this list in a single object, *tck,* so that it can
+be passed easily to the function :obj:`bisplev`. The
+keyword, *s* , can be used to change the amount of smoothing performed
+on the data while determining the appropriate spline. The default
+value is :math:`s=m-\sqrt{2m}` where :math:`m` is the number of data
+points in the *x, y,* and *z* vectors. As a result, if no smoothing is
+desired, then :math:`s=0` should be passed to
+:obj:`bisplrep` .
+
+To evaluate the two-dimensional spline and it's partial derivatives
+(up to the order of the spline), the function
+:obj:`bisplev` is required. This function takes as the
+first two arguments **two 1-D arrays** whose cross-product specifies
+the domain over which to evaluate the spline. The third argument is
+the *tck* list returned from :obj:`bisplrep`. If desired,
+the fourth and fifth arguments provide the orders of the partial
+derivative in the :math:`x` and :math:`y` direction respectively.
+
+It is important to note that two dimensional interpolation should not
+be used to find the spline representation of images. The algorithm
+used is not amenable to large numbers of input points. The signal
+processing toolbox contains more appropriate algorithms for finding
+the spline representation of an image. The two dimensional
+interpolation commands are intended for use when interpolating a two
+dimensional function as shown in the example that follows. This
+example uses the :obj:`mgrid <numpy.mgrid>` command in SciPy which is
+useful for defining a "mesh-grid "in many dimensions. (See also the
+:obj:`ogrid <numpy.ogrid>` command if the full-mesh is not
+needed). The number of output arguments and the number of dimensions
+of each argument is determined by the number of indexing objects
+passed in :obj:`mgrid <numpy.mgrid>`.
+
+.. plot::
+
+   >>> import numpy as np
+   >>> from scipy import interpolate
+   >>> import matplotlib.pyplot as plt
+
+   Define function over sparse 20x20 grid
+
+   >>> x,y = np.mgrid[-1:1:20j,-1:1:20j]
+   >>> z = (x+y)*np.exp(-6.0*(x*x+y*y))
+
+   >>> plt.figure()
+   >>> plt.pcolor(x,y,z)
+   >>> plt.colorbar()
+   >>> plt.title("Sparsely sampled function.")
+   >>> plt.show()
+
+   Interpolate function over new 70x70 grid
+
+   >>> xnew,ynew = np.mgrid[-1:1:70j,-1:1:70j]
+   >>> tck = interpolate.bisplrep(x,y,z,s=0)
+   >>> znew = interpolate.bisplev(xnew[:,0],ynew[0,:],tck)
+
+   >>> plt.figure()
+   >>> plt.pcolor(xnew,ynew,znew)
+   >>> plt.colorbar()
+   >>> plt.title("Interpolated function.")
+   >>> plt.show()
+
+..   :caption: Example of two-dimensional spline interpolation.
+
+
+Two-dimensional spline representation: Object-oriented (:class:`BivariateSpline`)
+---------------------------------------------------------------------------------
+
+The :class:`BivariateSpline` class is the 2-dimensional analog of the
+:class:`UnivariateSpline` class.  It and its subclasses implement
+the FITPACK functions described above in an object oriented fashion,
+allowing objects to be instantiated that can be called to compute
+the spline value by passing in the two coordinates as the two
+arguments.
+
+
+Using radial basis functions for smoothing/interpolation
+---------------------------------------------------------
+
+Radial basis functions can be used for smoothing/interpolating scattered
+data in n-dimensions, but should be used with caution for extrapolation
+outside of the observed data range.
+
+1-d Example
+^^^^^^^^^^^
+
+This example compares the usage of the Rbf and UnivariateSpline classes
+from the scipy.interpolate module.
+
+.. plot::
+
+    >>> import numpy as np
+    >>> from scipy.interpolate import Rbf, InterpolatedUnivariateSpline
+    >>> import matplotlib.pyplot as plt
+
+    >>> # setup data
+    >>> x = np.linspace(0, 10, 9)
+    >>> y = np.sin(x)
+    >>> xi = np.linspace(0, 10, 101)
+
+    >>> # use fitpack2 method
+    >>> ius = InterpolatedUnivariateSpline(x, y)
+    >>> yi = ius(xi)
+
+    >>> plt.subplot(2, 1, 1)
+    >>> plt.plot(x, y, 'bo')
+    >>> plt.plot(xi, yi, 'g')
+    >>> plt.plot(xi, np.sin(xi), 'r')
+    >>> plt.title('Interpolation using univariate spline')
+
+    >>> # use RBF method
+    >>> rbf = Rbf(x, y)
+    >>> fi = rbf(xi)
+
+    >>> plt.subplot(2, 1, 2)
+    >>> plt.plot(x, y, 'bo')
+    >>> plt.plot(xi, fi, 'g')
+    >>> plt.plot(xi, np.sin(xi), 'r')
+    >>> plt.title('Interpolation using RBF - multiquadrics')
+    >>> plt.show()
+
+..   :caption: Example of one-dimensional RBF interpolation.
+
+2-d Example
+^^^^^^^^^^^
+
+This example shows how to interpolate scattered 2d data.
+
+.. plot::
+
+    >>> import numpy as np
+    >>> from scipy.interpolate import Rbf
+    >>> import matplotlib.pyplot as plt
+    >>> from matplotlib import cm
+
+    >>> # 2-d tests - setup scattered data
+    >>> x = np.random.rand(100)*4.0-2.0
+    >>> y = np.random.rand(100)*4.0-2.0
+    >>> z = x*np.exp(-x**2-y**2)
+    >>> ti = np.linspace(-2.0, 2.0, 100)
+    >>> XI, YI = np.meshgrid(ti, ti)
+
+    >>> # use RBF
+    >>> rbf = Rbf(x, y, z, epsilon=2)
+    >>> ZI = rbf(XI, YI)
+
+    >>> # plot the result
+    >>> n = plt.normalize(-2., 2.)
+    >>> plt.subplot(1, 1, 1)
+    >>> plt.pcolor(XI, YI, ZI, cmap=cm.jet)
+    >>> plt.scatter(x, y, 100, z, cmap=cm.jet)
+    >>> plt.title('RBF interpolation - multiquadrics')
+    >>> plt.xlim(-2, 2)
+    >>> plt.ylim(-2, 2)
+    >>> plt.colorbar()

pythonPackages/scipy-0.8.0/doc/source/tutorial/io.rst

@@ -0,0 +1,376 @@
+File IO (:mod:`scipy.io`)
+=========================
+
+.. sectionauthor:: Matthew Brett
+
+.. currentmodule:: scipy.io
+
+.. seealso:: :ref:`numpy-reference.routines.io` (in numpy)
+
+Matlab files
+------------
+
+.. autosummary::
+   :toctree: generated/
+
+   loadmat
+   savemat
+
+Getting started:
+
+   >>> import scipy.io as sio
+
+If you are using IPython, try tab completing on ``sio``.  You'll find::
+
+   sio.loadmat
+   sio.savemat
+
+These are the high-level functions you will most likely use.  You'll also find::
+
+   sio.matlab
+
+This is the package from which ``loadmat`` and ``savemat`` are imported.
+Within ``sio.matlab``, you will find the ``mio`` module - containing
+the machinery that ``loadmat`` and ``savemat`` use.  From time to time
+you may find yourself re-using this machinery.
+
+How do I start?
+```````````````
+
+You may have a ``.mat`` file that you want to read into Scipy.  Or, you
+want to pass some variables from Scipy / Numpy into Matlab.
+
+To save us using a Matlab license, let's start in Octave_.  Octave has
+Matlab-compatible save / load functions.  Start Octave (``octave`` at
+the command line for me):
+
+.. sourcecode:: octave
+
+  octave:1> a = 1:12
+  a =
+
+     1   2   3   4   5   6   7   8   9  10  11  12
+
+  octave:2> a = reshape(a, [1 3 4])
+  a =
+
+  ans(:,:,1) =
+
+     1   2   3
+
+  ans(:,:,2) =
+
+     4   5   6
+
+  ans(:,:,3) =
+
+     7   8   9
+
+  ans(:,:,4) =
+
+     10   11   12
+
+
+
+  octave:3> save -6 octave_a.mat a % Matlab 6 compatible
+  octave:4> ls octave_a.mat
+  octave_a.mat
+
+Now, to Python:
+
+  >>> mat_contents = sio.loadmat('octave_a.mat')
+  >>> print mat_contents
+  {'a': array([[[  1.,   4.,   7.,  10.],
+          [  2.,   5.,   8.,  11.],
+          [  3.,   6.,   9.,  12.]]]), '__version__': '1.0', '__header__': 'MATLAB 5.0 MAT-file, written by Octave 3.2.3, 2010-05-30 02:13:40 UTC', '__globals__': []}
+  >>> oct_a = mat_contents['a']
+  >>> print oct_a
+  [[[  1.   4.   7.  10.]
+    [  2.   5.   8.  11.]
+    [  3.   6.   9.  12.]]]
+  >>> print oct_a.shape
+  (1, 3, 4)
+
+Now let's try the other way round:
+
+   >>> import numpy as np
+   >>> vect = np.arange(10)
+   >>> print vect.shape
+   (10,)
+   >>> sio.savemat('np_vector.mat', {'vect':vect})
+   /Users/mb312/usr/local/lib/python2.6/site-packages/scipy/io/matlab/mio.py:196: FutureWarning: Using oned_as default value ('column') This will change to 'row' in future versions
+  oned_as=oned_as)
+
+Then back to Octave:
+
+.. sourcecode:: octave
+
+   octave:5> load np_vector.mat
+   octave:6> vect
+   vect =
+
+     0
+     1
+     2
+     3
+     4
+     5
+     6
+     7
+     8
+     9
+
+   octave:7> size(vect)
+   ans =
+
+      10    1
+
+Note the deprecation warning.  The ``oned_as`` keyword determines the way in
+which one-dimensional vectors are stored.  In the future, this will default
+to ``row`` instead of ``column``:
+
+   >>> sio.savemat('np_vector.mat', {'vect':vect}, oned_as='row')
+
+We can load this in Octave or Matlab:
+
+.. sourcecode:: octave
+
+   octave:8> load np_vector.mat
+   octave:9> vect
+   vect =
+
+     0  1  2  3  4  5  6  7  8  9
+
+   octave:10> size(vect)
+   ans =
+
+       1   10
+
+
+Matlab structs
+``````````````
+
+Matlab structs are a little bit like Python dicts, except the field
+names must be strings.  Any Matlab object can be a value of a field.  As
+for all objects in Matlab, structs are in fact arrays of structs, where
+a single struct is an array of shape (1, 1).
+
+.. sourcecode:: octave
+
+   octave:11> my_struct = struct('field1', 1, 'field2', 2)
+   my_struct =
+   {
+     field1 =  1
+     field2 =  2
+   }
+
+   octave:12> save -6 octave_struct.mat my_struct
+
+We can load this in Python:
+
+   >>> mat_contents = sio.loadmat('octave_struct.mat')
+   >>> print mat_contents
+   {'my_struct': array([[([[1.0]], [[2.0]])]], 
+         dtype=[('field1', '|O8'), ('field2', '|O8')]), '__version__': '1.0', '__header__': 'MATLAB 5.0 MAT-file, written by Octave 3.2.3, 2010-05-30 02:00:26 UTC', '__globals__': []}
+   >>> oct_struct = mat_contents['my_struct']
+   >>> print oct_struct.shape
+   (1, 1)
+   >>> val = oct_struct[0,0]
+   >>> print val
+   ([[1.0]], [[2.0]])
+   >>> print val['field1']
+   [[ 1.]]
+   >>> print val['field2']
+   [[ 2.]]
+   >>> print val.dtype
+   [('field1', '|O8'), ('field2', '|O8')]
+
+In this version of Scipy (0.8.0), Matlab structs come back as numpy
+structured arrays, with fields named for the struct fields.  You can see
+the field names in the ``dtype`` output above.  Note also:
+
+   >>> val = oct_struct[0,0]
+
+and:
+
+.. sourcecode:: octave
+
+  octave:13> size(my_struct)
+  ans =
+
+     1   1
+
+So, in Matlab, the struct array must be at least 2D, and we replicate
+that when we read into Scipy.  If you want all length 1 dimensions
+squeezed out, try this:
+
+   >>> mat_contents = sio.loadmat('octave_struct.mat', squeeze_me=True)
+   >>> oct_struct = mat_contents['my_struct']
+   >>> oct_struct.shape
+   ()
+
+Sometimes, it's more convenient to load the matlab structs as python
+objects rather than numpy structured arrarys - it can make the access
+syntax in python a bit more similar to that in matlab.  In order to do
+this, use the ``struct_as_record=False`` parameter to ``loadmat``. 
+
+   >>> mat_contents = sio.loadmat('octave_struct.mat', struct_as_record=False)
+   >>> oct_struct = mat_contents['my_struct']
+   >>> oct_struct[0,0].field1
+   array([[ 1.]])
+
+``struct_as_record=False`` works nicely with ``squeeze_me``:
+
+   >>> mat_contents = sio.loadmat('octave_struct.mat', struct_as_record=False, squeeze_me=True)
+   >>> oct_struct = mat_contents['my_struct']
+   >>> oct_struct.shape # but no - it's a scalar
+   Traceback (most recent call last):
+     File "<stdin>", line 1, in <module>
+   AttributeError: 'mat_struct' object has no attribute 'shape'
+   >>> print type(oct_struct)
+   <class 'scipy.io.matlab.mio5_params.mat_struct'>
+   >>> print oct_struct.field1
+   1.0
+
+Saving struct arrays can be done in various ways.  One simple method is
+to use dicts:
+
+   >>> a_dict = {'field1': 0.5, 'field2': 'a string'}
+   >>> sio.savemat('saved_struct.mat', {'a_dict': a_dict})
+
+loaded as:
+
+.. sourcecode:: octave
+
+   octave:21> load saved_struct
+   octave:22> a_dict
+   a_dict =
+   {
+     field2 = a string
+     field1 =  0.50000
+   }
+
+You can also save structs back again to Matlab (or Octave in our case)
+like this:
+
+   >>> dt = [('f1', 'f8'), ('f2', 'S10')]
+   >>> arr = np.zeros((2,), dtype=dt)
+   >>> print arr
+   [(0.0, '') (0.0, '')]
+   >>> arr[0]['f1'] = 0.5
+   >>> arr[0]['f2'] = 'python'
+   >>> arr[1]['f1'] = 99
+   >>> arr[1]['f2'] = 'not perl'
+   >>> sio.savemat('np_struct_arr.mat', {'arr': arr})
+
+Matlab cell arrays
+``````````````````
+
+Cell arrays in Matlab are rather like python lists, in the sense that
+the elements in the arrays can contain any type of Matlab object.  In
+fact they are most similar to numpy object arrays, and that is how we
+load them into numpy.
+
+.. sourcecode:: octave
+
+   octave:14> my_cells = {1, [2, 3]}
+   my_cells =
+
+   {
+     [1,1] =  1
+     [1,2] =
+
+        2   3
+
+   }
+
+   octave:15> save -6 octave_cells.mat my_cells
+
+Back to Python:
+
+   >>> mat_contents = sio.loadmat('octave_cells.mat')
+   >>> oct_cells = mat_contents['my_cells']
+   >>> print oct_cells.dtype
+   object
+   >>> val = oct_cells[0,0]
+   >>> print val
+   [[ 1.]]
+   >>> print val.dtype
+   float64
+
+Saving to a Matlab cell array just involves making a numpy object array:
+
+   >>> obj_arr = np.zeros((2,), dtype=np.object)
+   >>> obj_arr[0] = 1
+   >>> obj_arr[1] = 'a string'
+   >>> print obj_arr
+   [1 a string]
+   >>> sio.savemat('np_cells.mat', {'obj_arr':obj_arr})
+
+.. sourcecode:: octave
+
+   octave:16> load np_cells.mat
+   octave:17> obj_arr
+   obj_arr =
+
+   {
+     [1,1] = 1
+     [2,1] = a string
+   }
+
+
+Matrix Market files
+-------------------
+
+.. autosummary::
+   :toctree: generated/
+
+   mminfo
+   mmread
+   mmwrite
+
+Other
+-----
+
+.. autosummary::
+   :toctree: generated/
+
+   save_as_module
+
+Wav sound files (:mod:`scipy.io.wavfile`)
+-----------------------------------------
+
+.. module:: scipy.io.wavfile
+
+.. autosummary::
+   :toctree: generated/
+
+   read
+   write
+
+Arff files (:mod:`scipy.io.arff`)
+---------------------------------
+
+.. automodule:: scipy.io.arff
+
+.. autosummary::
+   :toctree: generated/
+
+   loadarff
+
+Netcdf (:mod:`scipy.io.netcdf`)
+-------------------------------
+
+.. module:: scipy.io.netcdf
+
+.. autosummary::
+   :toctree: generated/
+
+   netcdf_file
+
+Allows reading of  NetCDF files (version of pupynere_ package)
+
+
+.. _pupynere: http://pypi.python.org/pypi/pupynere/
+.. _octave: http://www.gnu.org/software/octave
+.. _matlab: http://www.mathworks.com/

pythonPackages/scipy-0.8.0/doc/source/tutorial/linalg.rst

@@ -0,0 +1,825 @@
+Linear Algebra
+==============
+
+.. sectionauthor:: Travis E. Oliphant
+
+.. currentmodule: scipy
+
+When SciPy is built using the optimized ATLAS LAPACK and BLAS
+libraries, it has very fast linear algebra capabilities. If you dig
+deep enough, all of the raw lapack and blas libraries are available
+for your use for even more speed. In this section, some easier-to-use
+interfaces to these routines are described.
+
+All of these linear algebra routines expect an object that can be
+converted into a 2-dimensional array. The output of these routines is
+also a two-dimensional array. There is a matrix class defined in
+Numpy, which you can initialize with an appropriate Numpy array in
+order to get objects for which multiplication is matrix-multiplication
+instead of the default, element-by-element multiplication.
+
+
+Matrix Class
+------------
+
+The matrix class is initialized with the SciPy command :obj:`mat`
+which is just convenient short-hand for :class:`matrix
+<numpy.matrix>`. If you are going to be doing a lot of matrix-math, it
+is convenient to convert arrays into matrices using this command. One
+advantage of using the :func:`mat` command is that you can enter
+two-dimensional matrices using MATLAB-like syntax with commas or
+spaces separating columns and semicolons separting rows as long as the
+matrix is placed in a string passed to :obj:`mat` .
+
+
+Basic routines
+--------------
+
+
+Finding Inverse
+^^^^^^^^^^^^^^^
+
+The inverse of a matrix :math:`\mathbf{A}` is the matrix
+:math:`\mathbf{B}` such that :math:`\mathbf{AB}=\mathbf{I}` where
+:math:`\mathbf{I}` is the identity matrix consisting of ones down the
+main diagonal.  Usually :math:`\mathbf{B}` is denoted
+:math:`\mathbf{B}=\mathbf{A}^{-1}` . In SciPy, the matrix inverse of
+the Numpy array, A, is obtained using :obj:`linalg.inv` ``(A)`` , or
+using ``A.I`` if ``A`` is a Matrix. For example, let
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{A=}\left[\begin{array}{ccc} 1 & 3 & 5\\ 2 & 5 & 1\\ 2 & 3 & 8\end{array}\right]\]
+
+then
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{A^{-1}=\frac{1}{25}\left[\begin{array}{ccc} -37 & 9 & 22\\ 14 & 2 & -9\\ 4 & -3 & 1\end{array}\right]=\left[\begin{array}{ccc} -1.48 & 0.36 & 0.88\\ 0.56 & 0.08 & -0.36\\ 0.16 & -0.12 & 0.04\end{array}\right].}\]
+
+The following example demonstrates this computation in SciPy
+
+    >>> A = mat('[1 3 5; 2 5 1; 2 3 8]')
+    >>> A
+    matrix([[1, 3, 5],
+            [2, 5, 1],
+            [2, 3, 8]])
+    >>> A.I
+    matrix([[-1.48,  0.36,  0.88],
+            [ 0.56,  0.08, -0.36],
+            [ 0.16, -0.12,  0.04]])
+    >>> from scipy import linalg
+    >>> linalg.inv(A)
+    array([[-1.48,  0.36,  0.88],
+           [ 0.56,  0.08, -0.36],
+           [ 0.16, -0.12,  0.04]])
+    
+Solving linear system
+^^^^^^^^^^^^^^^^^^^^^
+
+Solving linear systems of equations is straightforward using the scipy
+command :obj:`linalg.solve`. This command expects an input matrix and
+a right-hand-side vector. The solution vector is then computed. An
+option for entering a symmetrix matrix is offered which can speed up
+the processing when applicable.  As an example, suppose it is desired
+to solve the following simultaneous equations:
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} x+3y+5z & = & 10\\ 2x+5y+z & = & 8\\ 2x+3y+8z & = & 3\end{eqnarray*}
+
+We could find the solution vector using a matrix inverse:
+
+.. math::
+   :nowrap:
+
+    \[ \left[\begin{array}{c} x\\ y\\ z\end{array}\right]=\left[\begin{array}{ccc} 1 & 3 & 5\\ 2 & 5 & 1\\ 2 & 3 & 8\end{array}\right]^{-1}\left[\begin{array}{c} 10\\ 8\\ 3\end{array}\right]=\frac{1}{25}\left[\begin{array}{c} -232\\ 129\\ 19\end{array}\right]=\left[\begin{array}{c} -9.28\\ 5.16\\ 0.76\end{array}\right].\]
+
+However, it is better to use the linalg.solve command which can be
+faster and more numerically stable. In this case it however gives the
+same answer as shown in the following example:
+
+    >>> A = mat('[1 3 5; 2 5 1; 2 3 8]')
+    >>> b = mat('[10;8;3]')
+    >>> A.I*b
+    matrix([[-9.28],
+            [ 5.16],
+            [ 0.76]])
+    >>> linalg.solve(A,b)
+    array([[-9.28],
+           [ 5.16],
+           [ 0.76]])
+
+
+Finding Determinant
+^^^^^^^^^^^^^^^^^^^
+
+The determinant of a square matrix :math:`\mathbf{A}` is often denoted
+:math:`\left|\mathbf{A}\right|` and is a quantity often used in linear
+algebra. Suppose :math:`a_{ij}` are the elements of the matrix
+:math:`\mathbf{A}` and let :math:`M_{ij}=\left|\mathbf{A}_{ij}\right|`
+be the determinant of the matrix left by removing the
+:math:`i^{\textrm{th}}` row and :math:`j^{\textrm{th}}` column from
+:math:`\mathbf{A}` . Then for any row :math:`i,`
+
+.. math::
+   :nowrap:
+
+    \[ \left|\mathbf{A}\right|=\sum_{j}\left(-1\right)^{i+j}a_{ij}M_{ij}.\]
+
+This is a recursive way to define the determinant where the base case
+is defined by accepting that the determinant of a :math:`1\times1` matrix is the only matrix element. In SciPy the determinant can be
+calculated with :obj:`linalg.det` . For example, the determinant of
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{A=}\left[\begin{array}{ccc} 1 & 3 & 5\\ 2 & 5 & 1\\ 2 & 3 & 8\end{array}\right]\]
+
+is
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \left|\mathbf{A}\right| & = & 1\left|\begin{array}{cc} 5 & 1\\ 3 & 8\end{array}\right|-3\left|\begin{array}{cc} 2 & 1\\ 2 & 8\end{array}\right|+5\left|\begin{array}{cc} 2 & 5\\ 2 & 3\end{array}\right|\\  & = & 1\left(5\cdot8-3\cdot1\right)-3\left(2\cdot8-2\cdot1\right)+5\left(2\cdot3-2\cdot5\right)=-25.\end{eqnarray*}
+
+In SciPy this is computed as shown in this example:
+
+    >>> A = mat('[1 3 5; 2 5 1; 2 3 8]')
+    >>> linalg.det(A)
+    -25.000000000000004
+
+
+Computing norms
+^^^^^^^^^^^^^^^
+
+Matrix and vector norms can also be computed with SciPy. A wide range
+of norm definitions are available using different parameters to the
+order argument of :obj:`linalg.norm` . This function takes a rank-1
+(vectors) or a rank-2 (matrices) array and an optional order argument
+(default is 2). Based on these inputs a vector or matrix norm of the
+requested order is computed.
+
+For vector *x* , the order parameter can be any real number including
+``inf`` or ``-inf``. The computed norm is
+
+.. math::
+   :nowrap:
+
+    \[ \left\Vert \mathbf{x}\right\Vert =\left\{ \begin{array}{cc} \max\left|x_{i}\right| & \textrm{ord}=\textrm{inf}\\ \min\left|x_{i}\right| & \textrm{ord}=-\textrm{inf}\\ \left(\sum_{i}\left|x_{i}\right|^{\textrm{ord}}\right)^{1/\textrm{ord}} & \left|\textrm{ord}\right|<\infty.\end{array}\right.\]
+
+
+
+For matrix :math:`\mathbf{A}` the only valid values for norm are :math:`\pm2,\pm1,` :math:`\pm` inf, and 'fro' (or 'f') Thus,
+
+.. math::
+   :nowrap:
+
+    \[ \left\Vert \mathbf{A}\right\Vert =\left\{ \begin{array}{cc} \max_{i}\sum_{j}\left|a_{ij}\right| & \textrm{ord}=\textrm{inf}\\ \min_{i}\sum_{j}\left|a_{ij}\right| & \textrm{ord}=-\textrm{inf}\\ \max_{j}\sum_{i}\left|a_{ij}\right| & \textrm{ord}=1\\ \min_{j}\sum_{i}\left|a_{ij}\right| & \textrm{ord}=-1\\ \max\sigma_{i} & \textrm{ord}=2\\ \min\sigma_{i} & \textrm{ord}=-2\\ \sqrt{\textrm{trace}\left(\mathbf{A}^{H}\mathbf{A}\right)} & \textrm{ord}=\textrm{'fro'}\end{array}\right.\]
+
+where :math:`\sigma_{i}` are the singular values of :math:`\mathbf{A}` .
+
+
+Solving linear least-squares problems and pseudo-inverses
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Linear least-squares problems occur in many branches of applied
+mathematics. In this problem a set of linear scaling coefficients is
+sought that allow a model to fit data. In particular it is assumed
+that data :math:`y_{i}` is related to data :math:`\mathbf{x}_{i}`
+through a set of coefficients :math:`c_{j}` and model functions
+:math:`f_{j}\left(\mathbf{x}_{i}\right)` via the model
+
+.. math::
+   :nowrap:
+
+    \[ y_{i}=\sum_{j}c_{j}f_{j}\left(\mathbf{x}_{i}\right)+\epsilon_{i}\]
+
+where :math:`\epsilon_{i}` represents uncertainty in the data. The
+strategy of least squares is to pick the coefficients :math:`c_{j}` to
+minimize
+
+.. math::
+   :nowrap:
+
+    \[ J\left(\mathbf{c}\right)=\sum_{i}\left|y_{i}-\sum_{j}c_{j}f_{j}\left(x_{i}\right)\right|^{2}.\]
+
+
+
+Theoretically, a global minimum will occur when
+
+.. math::
+   :nowrap:
+
+    \[ \frac{\partial J}{\partial c_{n}^{*}}=0=\sum_{i}\left(y_{i}-\sum_{j}c_{j}f_{j}\left(x_{i}\right)\right)\left(-f_{n}^{*}\left(x_{i}\right)\right)\]
+
+or
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \sum_{j}c_{j}\sum_{i}f_{j}\left(x_{i}\right)f_{n}^{*}\left(x_{i}\right) & = & \sum_{i}y_{i}f_{n}^{*}\left(x_{i}\right)\\ \mathbf{A}^{H}\mathbf{Ac} & = & \mathbf{A}^{H}\mathbf{y}\end{eqnarray*}
+
+where
+
+.. math::
+   :nowrap:
+
+    \[ \left\{ \mathbf{A}\right\} _{ij}=f_{j}\left(x_{i}\right).\]
+
+When :math:`\mathbf{A^{H}A}` is invertible, then
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{c}=\left(\mathbf{A}^{H}\mathbf{A}\right)^{-1}\mathbf{A}^{H}\mathbf{y}=\mathbf{A}^{\dagger}\mathbf{y}\]
+
+where :math:`\mathbf{A}^{\dagger}` is called the pseudo-inverse of
+:math:`\mathbf{A}.` Notice that using this definition of
+:math:`\mathbf{A}` the model can be written
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{y}=\mathbf{Ac}+\boldsymbol{\epsilon}.\]
+
+The command :obj:`linalg.lstsq` will solve the linear least squares
+problem for :math:`\mathbf{c}` given :math:`\mathbf{A}` and
+:math:`\mathbf{y}` . In addition :obj:`linalg.pinv` or
+:obj:`linalg.pinv2` (uses a different method based on singular value
+decomposition) will find :math:`\mathbf{A}^{\dagger}` given
+:math:`\mathbf{A}.`
+
+The following example and figure demonstrate the use of
+:obj:`linalg.lstsq` and :obj:`linalg.pinv` for solving a data-fitting
+problem. The data shown below were generated using the model:
+
+.. math::
+   :nowrap:
+
+    \[ y_{i}=c_{1}e^{-x_{i}}+c_{2}x_{i}\]
+
+where :math:`x_{i}=0.1i` for :math:`i=1\ldots10` , :math:`c_{1}=5` ,
+and :math:`c_{2}=4.` Noise is added to :math:`y_{i}` and the
+coefficients :math:`c_{1}` and :math:`c_{2}` are estimated using
+linear least squares.
+
+.. plot::
+
+   >>> from numpy import *
+   >>> from scipy import linalg
+   >>> import matplotlib.pyplot as plt
+
+   >>> c1,c2= 5.0,2.0
+   >>> i = r_[1:11]
+   >>> xi = 0.1*i
+   >>> yi = c1*exp(-xi)+c2*xi
+   >>> zi = yi + 0.05*max(yi)*random.randn(len(yi))
+
+   >>> A = c_[exp(-xi)[:,newaxis],xi[:,newaxis]]
+   >>> c,resid,rank,sigma = linalg.lstsq(A,zi)
+
+   >>> xi2 = r_[0.1:1.0:100j]
+   >>> yi2 = c[0]*exp(-xi2) + c[1]*xi2
+
+   >>> plt.plot(xi,zi,'x',xi2,yi2)
+   >>> plt.axis([0,1.1,3.0,5.5])
+   >>> plt.xlabel('$x_i$')
+   >>> plt.title('Data fitting with linalg.lstsq')
+   >>> plt.show()
+
+..   :caption: Example of linear least-squares fit
+
+Generalized inverse
+^^^^^^^^^^^^^^^^^^^
+
+The generalized inverse is calculated using the command
+:obj:`linalg.pinv` or :obj:`linalg.pinv2`. These two commands differ
+in how they compute the generalized inverse.  The first uses the
+linalg.lstsq algorithm while the second uses singular value
+decomposition. Let :math:`\mathbf{A}` be an :math:`M\times N` matrix,
+then if :math:`M>N` the generalized inverse is
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{A}^{\dagger}=\left(\mathbf{A}^{H}\mathbf{A}\right)^{-1}\mathbf{A}^{H}\]
+
+while if :math:`M<N` matrix the generalized inverse is
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{A}^{\#}=\mathbf{A}^{H}\left(\mathbf{A}\mathbf{A}^{H}\right)^{-1}.\]
+
+In both cases for :math:`M=N` , then
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{A}^{\dagger}=\mathbf{A}^{\#}=\mathbf{A}^{-1}\]
+
+as long as :math:`\mathbf{A}` is invertible.
+
+
+Decompositions
+--------------
+
+In many applications it is useful to decompose a matrix using other
+representations. There are several decompositions supported by SciPy.
+
+
+Eigenvalues and eigenvectors
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The eigenvalue-eigenvector problem is one of the most commonly
+employed linear algebra operations. In one popular form, the
+eigenvalue-eigenvector problem is to find for some square matrix
+:math:`\mathbf{A}` scalars :math:`\lambda` and corresponding vectors
+:math:`\mathbf{v}` such that
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{Av}=\lambda\mathbf{v}.\]
+
+For an :math:`N\times N` matrix, there are :math:`N` (not necessarily
+distinct) eigenvalues --- roots of the (characteristic) polynomial
+
+.. math::
+   :nowrap:
+
+    \[ \left|\mathbf{A}-\lambda\mathbf{I}\right|=0.\]
+
+The eigenvectors, :math:`\mathbf{v}` , are also sometimes called right
+eigenvectors to distinguish them from another set of left eigenvectors
+that satisfy
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{v}_{L}^{H}\mathbf{A}=\lambda\mathbf{v}_{L}^{H}\]
+
+or
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{A}^{H}\mathbf{v}_{L}=\lambda^{*}\mathbf{v}_{L}.\]
+
+With it's default optional arguments, the command :obj:`linalg.eig`
+returns :math:`\lambda` and :math:`\mathbf{v}.` However, it can also
+return :math:`\mathbf{v}_{L}` and just :math:`\lambda` by itself (
+:obj:`linalg.eigvals` returns just :math:`\lambda` as well).
+
+In addtion, :obj:`linalg.eig` can also solve the more general eigenvalue problem
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \mathbf{Av} & = & \lambda\mathbf{Bv}\\ \mathbf{A}^{H}\mathbf{v}_{L} & = & \lambda^{*}\mathbf{B}^{H}\mathbf{v}_{L}\end{eqnarray*}
+
+for square matrices :math:`\mathbf{A}` and :math:`\mathbf{B}.` The
+standard eigenvalue problem is an example of the general eigenvalue
+problem for :math:`\mathbf{B}=\mathbf{I}.` When a generalized
+eigenvalue problem can be solved, then it provides a decomposition of
+:math:`\mathbf{A}` as
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{A}=\mathbf{BV}\boldsymbol{\Lambda}\mathbf{V}^{-1}\]
+
+where :math:`\mathbf{V}` is the collection of eigenvectors into
+columns and :math:`\boldsymbol{\Lambda}` is a diagonal matrix of
+eigenvalues.
+
+By definition, eigenvectors are only defined up to a constant scale
+factor. In SciPy, the scaling factor for the eigenvectors is chosen so
+that :math:`\left\Vert \mathbf{v}\right\Vert
+^{2}=\sum_{i}v_{i}^{2}=1.`
+
+As an example, consider finding the eigenvalues and eigenvectors of
+the matrix
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{A}=\left[\begin{array}{ccc} 1 & 5 & 2\\ 2 & 4 & 1\\ 3 & 6 & 2\end{array}\right].\]
+
+The characteristic polynomial is
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \left|\mathbf{A}-\lambda\mathbf{I}\right| & = & \left(1-\lambda\right)\left[\left(4-\lambda\right)\left(2-\lambda\right)-6\right]-\\  &  & 5\left[2\left(2-\lambda\right)-3\right]+2\left[12-3\left(4-\lambda\right)\right]\\  & = & -\lambda^{3}+7\lambda^{2}+8\lambda-3.\end{eqnarray*}
+
+The roots of this polynomial are the eigenvalues of :math:`\mathbf{A}` :
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \lambda_{1} & = & 7.9579\\ \lambda_{2} & = & -1.2577\\ \lambda_{3} & = & 0.2997.\end{eqnarray*}
+
+The eigenvectors corresponding to each eigenvalue can be found using
+the original equation. The eigenvectors associated with these
+eigenvalues can then be found.
+
+    >>> from scipy import linalg
+    >>> A = mat('[1 5 2; 2 4 1; 3 6 2]')
+    >>> la,v = linalg.eig(A)
+    >>> l1,l2,l3 = la
+    >>> print l1, l2, l3
+    (7.95791620491+0j) (-1.25766470568+0j) (0.299748500767+0j)
+    
+    >>> print v[:,0]
+    [-0.5297175  -0.44941741 -0.71932146]
+    >>> print v[:,1]
+    [-0.90730751  0.28662547  0.30763439]
+    >>> print v[:,2]
+    [ 0.28380519 -0.39012063  0.87593408]
+    >>> print sum(abs(v**2),axis=0)
+    [ 1.  1.  1.]
+    
+    >>> v1 = mat(v[:,0]).T
+    >>> print max(ravel(abs(A*v1-l1*v1)))
+    8.881784197e-16
+
+
+Singular value decomposition
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Singular Value Decompostion (SVD) can be thought of as an extension of
+the eigenvalue problem to matrices that are not square. Let
+:math:`\mathbf{A}` be an :math:`M\times N` matrix with :math:`M` and
+:math:`N` arbitrary. The matrices :math:`\mathbf{A}^{H}\mathbf{A}` and
+:math:`\mathbf{A}\mathbf{A}^{H}` are square hermitian matrices [#]_ of
+size :math:`N\times N` and :math:`M\times M` respectively. It is known
+that the eigenvalues of square hermitian matrices are real and
+non-negative. In addtion, there are at most
+:math:`\min\left(M,N\right)` identical non-zero eigenvalues of
+:math:`\mathbf{A}^{H}\mathbf{A}` and :math:`\mathbf{A}\mathbf{A}^{H}.`
+Define these positive eigenvalues as :math:`\sigma_{i}^{2}.` The
+square-root of these are called singular values of :math:`\mathbf{A}.`
+The eigenvectors of :math:`\mathbf{A}^{H}\mathbf{A}` are collected by
+columns into an :math:`N\times N` unitary [#]_ matrix
+:math:`\mathbf{V}` while the eigenvectors of
+:math:`\mathbf{A}\mathbf{A}^{H}` are collected by columns in the
+unitary matrix :math:`\mathbf{U}` , the singular values are collected
+in an :math:`M\times N` zero matrix
+:math:`\mathbf{\boldsymbol{\Sigma}}` with main diagonal entries set to
+the singular values. Then
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{A=U}\boldsymbol{\Sigma}\mathbf{V}^{H}\]
+
+is the singular-value decomposition of :math:`\mathbf{A}.` Every
+matrix has a singular value decomposition. Sometimes, the singular
+values are called the spectrum of :math:`\mathbf{A}.` The command
+:obj:`linalg.svd` will return :math:`\mathbf{U}` ,
+:math:`\mathbf{V}^{H}` , and :math:`\sigma_{i}` as an array of the
+singular values. To obtain the matrix :math:`\mathbf{\Sigma}` use
+:obj:`linalg.diagsvd`. The following example illustrates the use of
+:obj:`linalg.svd` .
+
+    >>> A = mat('[1 3 2; 1 2 3]')
+    >>> M,N = A.shape
+    >>> U,s,Vh = linalg.svd(A)
+    >>> Sig = mat(linalg.diagsvd(s,M,N))
+    >>> U, Vh = mat(U), mat(Vh)
+    >>> print U
+    [[-0.70710678 -0.70710678]
+     [-0.70710678  0.70710678]]
+    >>> print Sig
+    [[ 5.19615242  0.          0.        ]
+     [ 0.          1.          0.        ]]
+    >>> print Vh
+    [[ -2.72165527e-01  -6.80413817e-01  -6.80413817e-01]
+     [ -6.18652536e-16  -7.07106781e-01   7.07106781e-01]
+     [ -9.62250449e-01   1.92450090e-01   1.92450090e-01]]
+    
+    >>> print A
+    [[1 3 2]
+     [1 2 3]]
+    >>> print U*Sig*Vh
+    [[ 1.  3.  2.]
+     [ 1.  2.  3.]]
+
+.. [#] A hermitian matrix :math:`\mathbf{D}` satisfies :math:`\mathbf{D}^{H}=\mathbf{D}.`
+
+.. [#] A unitary matrix :math:`\mathbf{D}` satisfies :math:`\mathbf{D}^{H}\mathbf{D}=\mathbf{I}=\mathbf{D}\mathbf{D}^{H}` so that :math:`\mathbf{D}^{-1}=\mathbf{D}^{H}.`
+
+
+LU decomposition
+^^^^^^^^^^^^^^^^
+
+The LU decompostion finds a representation for the :math:`M\times N` matrix :math:`\mathbf{A}` as
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{A}=\mathbf{PLU}\]
+
+where :math:`\mathbf{P}` is an :math:`M\times M` permutation matrix (a
+permutation of the rows of the identity matrix), :math:`\mathbf{L}` is
+in :math:`M\times K` lower triangular or trapezoidal matrix (
+:math:`K=\min\left(M,N\right)` ) with unit-diagonal, and
+:math:`\mathbf{U}` is an upper triangular or trapezoidal matrix. The
+SciPy command for this decomposition is :obj:`linalg.lu` .
+
+Such a decomposition is often useful for solving many simultaneous
+equations where the left-hand-side does not change but the right hand
+side does. For example, suppose we are going to solve
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{A}\mathbf{x}_{i}=\mathbf{b}_{i}\]
+
+for many different :math:`\mathbf{b}_{i}` . The LU decomposition allows this to be written as
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{PLUx}_{i}=\mathbf{b}_{i}.\]
+
+Because :math:`\mathbf{L}` is lower-triangular, the equation can be
+solved for :math:`\mathbf{U}\mathbf{x}_{i}` and finally
+:math:`\mathbf{x}_{i}` very rapidly using forward- and
+back-substitution. An initial time spent factoring :math:`\mathbf{A}`
+allows for very rapid solution of similar systems of equations in the
+future. If the intent for performing LU decomposition is for solving
+linear systems then the command :obj:`linalg.lu_factor` should be used
+followed by repeated applications of the command
+:obj:`linalg.lu_solve` to solve the system for each new
+right-hand-side.
+
+
+Cholesky decomposition
+^^^^^^^^^^^^^^^^^^^^^^
+
+Cholesky decomposition is a special case of LU decomposition
+applicable to Hermitian positive definite matrices. When
+:math:`\mathbf{A}=\mathbf{A}^{H}` and
+:math:`\mathbf{x}^{H}\mathbf{Ax}\geq0` for all :math:`\mathbf{x}` ,
+then decompositions of :math:`\mathbf{A}` can be found so that
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \mathbf{A} & = & \mathbf{U}^{H}\mathbf{U}\\ \mathbf{A} & = & \mathbf{L}\mathbf{L}^{H}\end{eqnarray*}
+
+where :math:`\mathbf{L}` is lower-triangular and :math:`\mathbf{U}` is
+upper triangular. Notice that :math:`\mathbf{L}=\mathbf{U}^{H}.` The
+command :obj:`linagl.cholesky` computes the cholesky
+factorization. For using cholesky factorization to solve systems of
+equations there are also :obj:`linalg.cho_factor` and
+:obj:`linalg.cho_solve` routines that work similarly to their LU
+decomposition counterparts.
+
+
+QR decomposition
+^^^^^^^^^^^^^^^^
+
+The QR decomposition (sometimes called a polar decomposition) works
+for any :math:`M\times N` array and finds an :math:`M\times M` unitary
+matrix :math:`\mathbf{Q}` and an :math:`M\times N` upper-trapezoidal
+matrix :math:`\mathbf{R}` such that
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{A=QR}.\]
+
+Notice that if the SVD of :math:`\mathbf{A}` is known then the QR decomposition can be found
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{A}=\mathbf{U}\boldsymbol{\Sigma}\mathbf{V}^{H}=\mathbf{QR}\]
+
+implies that :math:`\mathbf{Q}=\mathbf{U}` and
+:math:`\mathbf{R}=\boldsymbol{\Sigma}\mathbf{V}^{H}.` Note, however,
+that in SciPy independent algorithms are used to find QR and SVD
+decompositions. The command for QR decomposition is :obj:`linalg.qr` .
+
+
+Schur decomposition
+^^^^^^^^^^^^^^^^^^^
+
+For a square :math:`N\times N` matrix, :math:`\mathbf{A}` , the Schur
+decomposition finds (not-necessarily unique) matrices
+:math:`\mathbf{T}` and :math:`\mathbf{Z}` such that
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{A}=\mathbf{ZT}\mathbf{Z}^{H}\]
+
+where :math:`\mathbf{Z}` is a unitary matrix and :math:`\mathbf{T}` is
+either upper-triangular or quasi-upper triangular depending on whether
+or not a real schur form or complex schur form is requested.  For a
+real schur form both :math:`\mathbf{T}` and :math:`\mathbf{Z}` are
+real-valued when :math:`\mathbf{A}` is real-valued. When
+:math:`\mathbf{A}` is a real-valued matrix the real schur form is only
+quasi-upper triangular because :math:`2\times2` blocks extrude from
+the main diagonal corresponding to any complex- valued
+eigenvalues. The command :obj:`linalg.schur` finds the Schur
+decomposition while the command :obj:`linalg.rsf2csf` converts
+:math:`\mathbf{T}` and :math:`\mathbf{Z}` from a real Schur form to a
+complex Schur form. The Schur form is especially useful in calculating
+functions of matrices.
+
+The following example illustrates the schur decomposition:
+
+    >>> from scipy import linalg
+    >>> A = mat('[1 3 2; 1 4 5; 2 3 6]')
+    >>> T,Z = linalg.schur(A)
+    >>> T1,Z1 = linalg.schur(A,'complex')
+    >>> T2,Z2 = linalg.rsf2csf(T,Z)
+    >>> print T
+    [[ 9.90012467  1.78947961 -0.65498528]
+     [ 0.          0.54993766 -1.57754789]
+     [ 0.          0.51260928  0.54993766]]
+    >>> print T2
+    [[ 9.90012467 +0.00000000e+00j -0.32436598 +1.55463542e+00j
+      -0.88619748 +5.69027615e-01j]
+     [ 0.00000000 +0.00000000e+00j  0.54993766 +8.99258408e-01j
+       1.06493862 +1.37016050e-17j]
+     [ 0.00000000 +0.00000000e+00j  0.00000000 +0.00000000e+00j
+       0.54993766 -8.99258408e-01j]]
+    >>> print abs(T1-T2) # different
+    [[  1.24357637e-14   2.09205364e+00   6.56028192e-01]
+     [  0.00000000e+00   4.00296604e-16   1.83223097e+00]
+     [  0.00000000e+00   0.00000000e+00   4.57756680e-16]]
+    >>> print abs(Z1-Z2) # different
+    [[ 0.06833781  1.10591375  0.23662249]
+     [ 0.11857169  0.5585604   0.29617525]
+     [ 0.12624999  0.75656818  0.22975038]]
+    >>> T,Z,T1,Z1,T2,Z2 = map(mat,(T,Z,T1,Z1,T2,Z2))
+    >>> print abs(A-Z*T*Z.H) # same
+    [[  1.11022302e-16   4.44089210e-16   4.44089210e-16]
+     [  4.44089210e-16   1.33226763e-15   8.88178420e-16]
+     [  8.88178420e-16   4.44089210e-16   2.66453526e-15]]
+    >>> print abs(A-Z1*T1*Z1.H) # same
+    [[  1.00043248e-15   2.22301403e-15   5.55749485e-15]
+     [  2.88899660e-15   8.44927041e-15   9.77322008e-15]
+     [  3.11291538e-15   1.15463228e-14   1.15464861e-14]]
+    >>> print abs(A-Z2*T2*Z2.H) # same
+    [[  3.34058710e-16   8.88611201e-16   4.18773089e-18]
+     [  1.48694940e-16   8.95109973e-16   8.92966151e-16]
+     [  1.33228956e-15   1.33582317e-15   3.55373104e-15]]
+
+Matrix Functions
+----------------
+
+Consider the function :math:`f\left(x\right)` with Taylor series expansion
+
+.. math::
+   :nowrap:
+
+    \[ f\left(x\right)=\sum_{k=0}^{\infty}\frac{f^{\left(k\right)}\left(0\right)}{k!}x^{k}.\]
+
+A matrix function can be defined using this Taylor series for the
+square matrix :math:`\mathbf{A}` as
+
+.. math::
+   :nowrap:
+
+    \[ f\left(\mathbf{A}\right)=\sum_{k=0}^{\infty}\frac{f^{\left(k\right)}\left(0\right)}{k!}\mathbf{A}^{k}.\]
+
+While, this serves as a useful representation of a matrix function, it
+is rarely the best way to calculate a matrix function.
+
+
+Exponential and logarithm functions
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The matrix exponential is one of the more common matrix functions. It
+can be defined for square matrices as
+
+.. math::
+   :nowrap:
+
+    \[ e^{\mathbf{A}}=\sum_{k=0}^{\infty}\frac{1}{k!}\mathbf{A}^{k}.\]
+
+The command :obj:`linalg.expm3` uses this Taylor series definition to compute the matrix exponential.
+Due to poor convergence properties it is not often used.
+
+Another method to compute the matrix exponential is to find an
+eigenvalue decomposition of :math:`\mathbf{A}` :
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{A}=\mathbf{V}\boldsymbol{\Lambda}\mathbf{V}^{-1}\]
+
+and note that
+
+.. math::
+   :nowrap:
+
+    \[ e^{\mathbf{A}}=\mathbf{V}e^{\boldsymbol{\Lambda}}\mathbf{V}^{-1}\]
+
+where the matrix exponential of the diagonal matrix :math:`\boldsymbol{\Lambda}` is just the exponential of its elements. This method is implemented in :obj:`linalg.expm2` .
+
+The preferred method for implementing the matrix exponential is to use
+scaling and a Padé approximation for :math:`e^{x}` . This algorithm is
+implemented as :obj:`linalg.expm` .
+
+The inverse of the matrix exponential is the matrix logarithm defined
+as the inverse of the matrix exponential.
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{A}\equiv\exp\left(\log\left(\mathbf{A}\right)\right).\]
+
+The matrix logarithm can be obtained with :obj:`linalg.logm` .
+
+
+Trigonometric functions
+^^^^^^^^^^^^^^^^^^^^^^^
+
+The trigonometric functions :math:`\sin` , :math:`\cos` , and
+:math:`\tan` are implemented for matrices in :func:`linalg.sinm`,
+:func:`linalg.cosm`, and :obj:`linalg.tanm` respectively. The matrix
+sin and cosine can be defined using Euler's identity as
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \sin\left(\mathbf{A}\right) & = & \frac{e^{j\mathbf{A}}-e^{-j\mathbf{A}}}{2j}\\ \cos\left(\mathbf{A}\right) & = & \frac{e^{j\mathbf{A}}+e^{-j\mathbf{A}}}{2}.\end{eqnarray*}
+
+The tangent is
+
+.. math::
+   :nowrap:
+
+    \[ \tan\left(x\right)=\frac{\sin\left(x\right)}{\cos\left(x\right)}=\left[\cos\left(x\right)\right]^{-1}\sin\left(x\right)\]
+
+and so the matrix tangent is defined as
+
+.. math::
+   :nowrap:
+
+    \[ \left[\cos\left(\mathbf{A}\right)\right]^{-1}\sin\left(\mathbf{A}\right).\]
+
+
+
+
+Hyperbolic trigonometric functions
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The hyperbolic trigonemetric functions :math:`\sinh` , :math:`\cosh` ,
+and :math:`\tanh` can also be defined for matrices using the familiar
+definitions:
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \sinh\left(\mathbf{A}\right) & = & \frac{e^{\mathbf{A}}-e^{-\mathbf{A}}}{2}\\ \cosh\left(\mathbf{A}\right) & = & \frac{e^{\mathbf{A}}+e^{-\mathbf{A}}}{2}\\ \tanh\left(\mathbf{A}\right) & = & \left[\cosh\left(\mathbf{A}\right)\right]^{-1}\sinh\left(\mathbf{A}\right).\end{eqnarray*}
+
+These matrix functions can be found using :obj:`linalg.sinhm`,
+:obj:`linalg.coshm` , and :obj:`linalg.tanhm`.
+
+
+Arbitrary function
+^^^^^^^^^^^^^^^^^^
+
+Finally, any arbitrary function that takes one complex number and
+returns a complex number can be called as a matrix function using the
+command :obj:`linalg.funm`. This command takes the matrix and an
+arbitrary Python function. It then implements an algorithm from Golub
+and Van Loan's book "Matrix Computations "to compute function applied
+to the matrix using a Schur decomposition.  Note that *the function
+needs to accept complex numbers* as input in order to work with this
+algorithm. For example the following code computes the zeroth-order
+Bessel function applied to a matrix.
+
+    >>> from scipy import special, random, linalg
+    >>> A = random.rand(3,3)
+    >>> B = linalg.funm(A,lambda x: special.jv(0,x))
+    >>> print A
+    [[ 0.72578091  0.34105276  0.79570345]
+     [ 0.65767207  0.73855618  0.541453  ]
+     [ 0.78397086  0.68043507  0.4837898 ]]
+    >>> print B
+    [[ 0.72599893 -0.20545711 -0.22721101]
+     [-0.27426769  0.77255139 -0.23422637]
+     [-0.27612103 -0.21754832  0.7556849 ]]
+    >>> print linalg.eigvals(A)
+    [ 1.91262611+0.j  0.21846476+0.j -0.18296399+0.j]
+    >>> print special.jv(0, linalg.eigvals(A))
+    [ 0.27448286+0.j  0.98810383+0.j  0.99164854+0.j]
+    >>> print linalg.eigvals(B)
+    [ 0.27448286+0.j  0.98810383+0.j  0.99164854+0.j]
+
+Note how, by virtue of how matrix analytic functions are defined,
+the Bessel function has acted on the matrix eigenvalues.
+

pythonPackages/scipy-0.8.0/doc/source/tutorial/optimize.rst

@@ -0,0 +1,637 @@
+Optimization (optimize)
+=======================
+
+.. sectionauthor:: Travis E. Oliphant
+
+.. currentmodule:: scipy.optimize
+
+There are several classical optimization algorithms provided by SciPy
+in the :mod:`scipy.optimize` package. An overview of the module is
+available using :func:`help` (or :func:`pydoc.help`):
+
+.. literalinclude:: examples/5-1
+
+The first four algorithms are unconstrained minimization algorithms
+(:func:`fmin`: Nelder-Mead simplex, :func:`fmin_bfgs`: BFGS,
+:func:`fmin_ncg`: Newton Conjugate Gradient, and :func:`leastsq`:
+Levenburg-Marquardt). The last algorithm actually finds the roots of a
+general function of possibly many variables. It is included in the
+optimization package because at the (non-boundary) extreme points of a
+function, the gradient is equal to zero.
+
+
+Nelder-Mead Simplex algorithm (:func:`fmin`)
+--------------------------------------------
+
+The simplex algorithm is probably the simplest way to minimize a
+fairly well-behaved function. The simplex algorithm requires only
+function evaluations and is a good choice for simple minimization
+problems. However, because it does not use any gradient evaluations,
+it may take longer to find the minimum. To demonstrate the
+minimization function consider the problem of minimizing the
+Rosenbrock function of :math:`N` variables:
+
+.. math::
+   :nowrap:
+
+    \[ f\left(\mathbf{x}\right)=\sum_{i=1}^{N-1}100\left(x_{i}-x_{i-1}^{2}\right)^{2}+\left(1-x_{i-1}\right)^{2}.\]
+
+The minimum value of this function is 0 which is achieved when :math:`x_{i}=1.` This minimum can be found using the :obj:`fmin` routine as shown in the example below:
+
+    >>> from scipy.optimize import fmin
+    >>> def rosen(x):
+    ...     """The Rosenbrock function"""
+    ...     return sum(100.0*(x[1:]-x[:-1]**2.0)**2.0 + (1-x[:-1])**2.0)
+
+    >>> x0 = [1.3, 0.7, 0.8, 1.9, 1.2]
+    >>> xopt = fmin(rosen, x0, xtol=1e-8)
+    Optimization terminated successfully.
+             Current function value: 0.000000
+             Iterations: 339
+             Function evaluations: 571
+
+    >>> print xopt
+    [ 1.  1.  1.  1.  1.]
+
+Another optimization algorithm that needs only function calls to find
+the minimum is Powell's method available as :func:`fmin_powell`.
+
+
+Broyden-Fletcher-Goldfarb-Shanno algorithm (:func:`fmin_bfgs`)
+--------------------------------------------------------------
+
+In order to converge more quickly to the solution, this routine uses
+the gradient of the objective function. If the gradient is not given
+by the user, then it is estimated using first-differences. The
+Broyden-Fletcher-Goldfarb-Shanno (BFGS) method typically requires
+fewer function calls than the simplex algorithm even when the gradient
+must be estimated.
+
+To demonstrate this algorithm, the Rosenbrock function is again used.
+The gradient of the Rosenbrock function is the vector:
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \frac{\partial f}{\partial x_{j}} & = & \sum_{i=1}^{N}200\left(x_{i}-x_{i-1}^{2}\right)\left(\delta_{i,j}-2x_{i-1}\delta_{i-1,j}\right)-2\left(1-x_{i-1}\right)\delta_{i-1,j}.\\  & = & 200\left(x_{j}-x_{j-1}^{2}\right)-400x_{j}\left(x_{j+1}-x_{j}^{2}\right)-2\left(1-x_{j}\right).\end{eqnarray*}
+
+This expression is valid for the interior derivatives. Special cases
+are
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \frac{\partial f}{\partial x_{0}} & = & -400x_{0}\left(x_{1}-x_{0}^{2}\right)-2\left(1-x_{0}\right),\\ \frac{\partial f}{\partial x_{N-1}} & = & 200\left(x_{N-1}-x_{N-2}^{2}\right).\end{eqnarray*}
+
+A Python function which computes this gradient is constructed by the
+code-segment:
+
+    >>> def rosen_der(x):
+    ...     xm = x[1:-1]
+    ...     xm_m1 = x[:-2]
+    ...     xm_p1 = x[2:]
+    ...     der = zeros_like(x)
+    ...     der[1:-1] = 200*(xm-xm_m1**2) - 400*(xm_p1 - xm**2)*xm - 2*(1-xm)
+    ...     der[0] = -400*x[0]*(x[1]-x[0]**2) - 2*(1-x[0])
+    ...     der[-1] = 200*(x[-1]-x[-2]**2)
+    ...     return der
+
+The calling signature for the BFGS minimization algorithm is similar
+to :obj:`fmin` with the addition of the *fprime* argument. An example
+usage of :obj:`fmin_bfgs` is shown in the following example which
+minimizes the Rosenbrock function.
+
+    >>> from scipy.optimize import fmin_bfgs
+
+    >>> x0 = [1.3, 0.7, 0.8, 1.9, 1.2]
+    >>> xopt = fmin_bfgs(rosen, x0, fprime=rosen_der)
+    Optimization terminated successfully.
+             Current function value: 0.000000
+             Iterations: 53
+             Function evaluations: 65
+             Gradient evaluations: 65
+    >>> print xopt
+    [ 1.  1.  1.  1.  1.]
+
+
+Newton-Conjugate-Gradient (:func:`fmin_ncg`)
+--------------------------------------------
+
+The method which requires the fewest function calls and is therefore
+often the fastest method to minimize functions of many variables is
+:obj:`fmin_ncg`. This method is a modified Newton's method and uses a
+conjugate gradient algorithm to (approximately) invert the local
+Hessian.  Newton's method is based on fitting the function locally to
+a quadratic form:
+
+.. math::
+   :nowrap:
+
+    \[ f\left(\mathbf{x}\right)\approx f\left(\mathbf{x}_{0}\right)+\nabla f\left(\mathbf{x}_{0}\right)\cdot\left(\mathbf{x}-\mathbf{x}_{0}\right)+\frac{1}{2}\left(\mathbf{x}-\mathbf{x}_{0}\right)^{T}\mathbf{H}\left(\mathbf{x}_{0}\right)\left(\mathbf{x}-\mathbf{x}_{0}\right).\]
+
+where :math:`\mathbf{H}\left(\mathbf{x}_{0}\right)` is a matrix of second-derivatives (the Hessian). If the Hessian is
+positive definite then the local minimum of this function can be found
+by setting the gradient of the quadratic form to zero, resulting in
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{x}_{\textrm{opt}}=\mathbf{x}_{0}-\mathbf{H}^{-1}\nabla f.\]
+
+The inverse of the Hessian is evaluted using the conjugate-gradient
+method. An example of employing this method to minimizing the
+Rosenbrock function is given below. To take full advantage of the
+NewtonCG method, a function which computes the Hessian must be
+provided. The Hessian matrix itself does not need to be constructed,
+only a vector which is the product of the Hessian with an arbitrary
+vector needs to be available to the minimization routine. As a result,
+the user can provide either a function to compute the Hessian matrix,
+or a function to compute the product of the Hessian with an arbitrary
+vector.
+
+
+Full Hessian example:
+^^^^^^^^^^^^^^^^^^^^^
+
+The Hessian of the Rosenbrock function is
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} H_{ij}=\frac{\partial^{2}f}{\partial x_{i}\partial x_{j}} & = & 200\left(\delta_{i,j}-2x_{i-1}\delta_{i-1,j}\right)-400x_{i}\left(\delta_{i+1,j}-2x_{i}\delta_{i,j}\right)-400\delta_{i,j}\left(x_{i+1}-x_{i}^{2}\right)+2\delta_{i,j},\\  & = & \left(202+1200x_{i}^{2}-400x_{i+1}\right)\delta_{i,j}-400x_{i}\delta_{i+1,j}-400x_{i-1}\delta_{i-1,j},\end{eqnarray*}
+
+if :math:`i,j\in\left[1,N-2\right]` with :math:`i,j\in\left[0,N-1\right]` defining the :math:`N\times N` matrix. Other non-zero entries of the matrix are
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \frac{\partial^{2}f}{\partial x_{0}^{2}} & = & 1200x_{0}^{2}-400x_{1}+2,\\ \frac{\partial^{2}f}{\partial x_{0}\partial x_{1}}=\frac{\partial^{2}f}{\partial x_{1}\partial x_{0}} & = & -400x_{0},\\ \frac{\partial^{2}f}{\partial x_{N-1}\partial x_{N-2}}=\frac{\partial^{2}f}{\partial x_{N-2}\partial x_{N-1}} & = & -400x_{N-2},\\ \frac{\partial^{2}f}{\partial x_{N-1}^{2}} & = & 200.\end{eqnarray*}
+
+For example, the Hessian when :math:`N=5` is
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{H}=\left[\begin{array}{ccccc} 1200x_{0}^{2}-400x_{1}+2 & -400x_{0} & 0 & 0 & 0\\ -400x_{0} & 202+1200x_{1}^{2}-400x_{2} & -400x_{1} & 0 & 0\\ 0 & -400x_{1} & 202+1200x_{2}^{2}-400x_{3} & -400x_{2} & 0\\ 0 &  & -400x_{2} & 202+1200x_{3}^{2}-400x_{4} & -400x_{3}\\ 0 & 0 & 0 & -400x_{3} & 200\end{array}\right].\]
+
+The code which computes this Hessian along with the code to minimize
+the function using :obj:`fmin_ncg` is shown in the following example:
+
+    >>> from scipy.optimize import fmin_ncg
+    >>> def rosen_hess(x):
+    ...     x = asarray(x)
+    ...     H = diag(-400*x[:-1],1) - diag(400*x[:-1],-1)
+    ...     diagonal = zeros_like(x)
+    ...     diagonal[0] = 1200*x[0]-400*x[1]+2
+    ...     diagonal[-1] = 200
+    ...     diagonal[1:-1] = 202 + 1200*x[1:-1]**2 - 400*x[2:]
+    ...     H = H + diag(diagonal)
+    ...     return H
+
+    >>> x0 = [1.3, 0.7, 0.8, 1.9, 1.2]
+    >>> xopt = fmin_ncg(rosen, x0, rosen_der, fhess=rosen_hess, avextol=1e-8)
+    Optimization terminated successfully.
+             Current function value: 0.000000
+             Iterations: 23
+             Function evaluations: 26
+             Gradient evaluations: 23
+             Hessian evaluations: 23
+    >>> print xopt
+    [ 1.  1.  1.  1.  1.]
+
+
+Hessian product example:
+^^^^^^^^^^^^^^^^^^^^^^^^
+
+For larger minimization problems, storing the entire Hessian matrix
+can consume considerable time and memory. The Newton-CG algorithm only
+needs the product of the Hessian times an arbitrary vector. As a
+result, the user can supply code to compute this product rather than
+the full Hessian by setting the *fhess_p* keyword to the desired
+function. The *fhess_p* function should take the minimization vector as
+the first argument and the arbitrary vector as the second
+argument. Any extra arguments passed to the function to be minimized
+will also be passed to this function. If possible, using Newton-CG
+with the hessian product option is probably the fastest way to
+minimize the function.
+
+In this case, the product of the Rosenbrock Hessian with an arbitrary
+vector is not difficult to compute. If :math:`\mathbf{p}` is the arbitrary vector, then :math:`\mathbf{H}\left(\mathbf{x}\right)\mathbf{p}` has elements:
+
+.. math::
+   :nowrap:
+
+    \[ \mathbf{H}\left(\mathbf{x}\right)\mathbf{p}=\left[\begin{array}{c} \left(1200x_{0}^{2}-400x_{1}+2\right)p_{0}-400x_{0}p_{1}\\ \vdots\\ -400x_{i-1}p_{i-1}+\left(202+1200x_{i}^{2}-400x_{i+1}\right)p_{i}-400x_{i}p_{i+1}\\ \vdots\\ -400x_{N-2}p_{N-2}+200p_{N-1}\end{array}\right].\]
+
+Code which makes use of the *fhess_p* keyword to minimize the
+Rosenbrock function using :obj:`fmin_ncg` follows:
+
+    >>> from scipy.optimize import fmin_ncg
+    >>> def rosen_hess_p(x,p):
+    ...     x = asarray(x)
+    ...     Hp = zeros_like(x)
+    ...     Hp[0] = (1200*x[0]**2 - 400*x[1] + 2)*p[0] - 400*x[0]*p[1]
+    ...     Hp[1:-1] = -400*x[:-2]*p[:-2]+(202+1200*x[1:-1]**2-400*x[2:])*p[1:-1] \
+    ...                -400*x[1:-1]*p[2:]
+    ...     Hp[-1] = -400*x[-2]*p[-2] + 200*p[-1]
+    ...     return Hp
+
+    >>> x0 = [1.3, 0.7, 0.8, 1.9, 1.2]
+    >>> xopt = fmin_ncg(rosen, x0, rosen_der, fhess_p=rosen_hess_p, avextol=1e-8)
+    Optimization terminated successfully.
+             Current function value: 0.000000
+             Iterations: 22
+             Function evaluations: 25
+             Gradient evaluations: 22
+             Hessian evaluations: 54
+    >>> print xopt
+    [ 1.  1.  1.  1.  1.]
+
+
+Least-square fitting (:func:`leastsq`)
+--------------------------------------
+
+All of the previously-explained minimization procedures can be used to
+solve a least-squares problem provided the appropriate objective
+function is constructed. For example, suppose it is desired to fit a
+set of data :math:`\left\{\mathbf{x}_{i}, \mathbf{y}_{i}\right\}`
+to a known model,
+:math:`\mathbf{y}=\mathbf{f}\left(\mathbf{x},\mathbf{p}\right)`
+where :math:`\mathbf{p}` is a vector of parameters for the model that
+need to be found. A common method for determining which parameter
+vector gives the best fit to the data is to minimize the sum of squares
+of the residuals. The residual is usually defined for each observed
+data-point as
+
+.. math::
+   :nowrap:
+
+    \[ e_{i}\left(\mathbf{p},\mathbf{y}_{i},\mathbf{x}_{i}\right)=\left\Vert \mathbf{y}_{i}-\mathbf{f}\left(\mathbf{x}_{i},\mathbf{p}\right)\right\Vert .\]
+
+An objective function to pass to any of the previous minization
+algorithms to obtain a least-squares fit is.
+
+.. math::
+   :nowrap:
+
+    \[ J\left(\mathbf{p}\right)=\sum_{i=0}^{N-1}e_{i}^{2}\left(\mathbf{p}\right).\]
+
+
+
+The :obj:`leastsq` algorithm performs this squaring and summing of the
+residuals automatically. It takes as an input argument the vector
+function :math:`\mathbf{e}\left(\mathbf{p}\right)` and returns the
+value of :math:`\mathbf{p}` which minimizes
+:math:`J\left(\mathbf{p}\right)=\mathbf{e}^{T}\mathbf{e}`
+directly. The user is also encouraged to provide the Jacobian matrix
+of the function (with derivatives down the columns or across the
+rows). If the Jacobian is not provided, it is estimated.
+
+An example should clarify the usage. Suppose it is believed some
+measured data follow a sinusoidal pattern
+
+.. math::
+   :nowrap:
+
+    \[ y_{i}=A\sin\left(2\pi kx_{i}+\theta\right)\]
+
+where the parameters :math:`A,` :math:`k` , and :math:`\theta` are unknown. The residual vector is
+
+.. math::
+   :nowrap:
+
+    \[ e_{i}=\left|y_{i}-A\sin\left(2\pi kx_{i}+\theta\right)\right|.\]
+
+By defining a function to compute the residuals and (selecting an
+appropriate starting position), the least-squares fit routine can be
+used to find the best-fit parameters :math:`\hat{A},\,\hat{k},\,\hat{\theta}`.
+This is shown in the following example:
+
+.. plot::
+
+   >>> from numpy import *
+   >>> x = arange(0,6e-2,6e-2/30)
+   >>> A,k,theta = 10, 1.0/3e-2, pi/6
+   >>> y_true = A*sin(2*pi*k*x+theta)
+   >>> y_meas = y_true + 2*random.randn(len(x))
+
+   >>> def residuals(p, y, x):
+   ...     A,k,theta = p
+   ...     err = y-A*sin(2*pi*k*x+theta)
+   ...     return err
+
+   >>> def peval(x, p):
+   ...     return p[0]*sin(2*pi*p[1]*x+p[2])
+
+   >>> p0 = [8, 1/2.3e-2, pi/3]
+   >>> print array(p0)
+   [  8.      43.4783   1.0472]
+
+   >>> from scipy.optimize import leastsq
+   >>> plsq = leastsq(residuals, p0, args=(y_meas, x))
+   >>> print plsq[0]
+   [ 10.9437  33.3605   0.5834]
+
+   >>> print array([A, k, theta])
+   [ 10.      33.3333   0.5236]
+
+   >>> import matplotlib.pyplot as plt
+   >>> plt.plot(x,peval(x,plsq[0]),x,y_meas,'o',x,y_true)
+   >>> plt.title('Least-squares fit to noisy data')
+   >>> plt.legend(['Fit', 'Noisy', 'True'])
+   >>> plt.show()
+
+..   :caption: Least-square fitting to noisy data using
+..             :obj:`scipy.optimize.leastsq`
+
+
+.. _tutorial-sqlsp:
+
+Sequential Least-square fitting with constraints (:func:`fmin_slsqp`)
+---------------------------------------------------------------------
+
+This module implements the Sequential Least SQuares Programming optimization algorithm (SLSQP).
+
+.. math::
+   :nowrap:
+
+     \begin{eqnarray*} \min F(x) \\ \text{subject to } & C_j(X) =  0  ,  &j = 1,...,\text{MEQ}\\
+            & C_j(x) \geq 0  ,  &j = \text{MEQ}+1,...,M\\
+           &  XL  \leq x \leq XU , &I = 1,...,N. \end{eqnarray*}
+
+The following script shows examples for how constraints can be specified.
+
+::
+
+    """
+    This script tests fmin_slsqp using Example 14.4 from Numerical Methods for
+    Engineers by Steven Chapra and Raymond Canale.  This example maximizes the
+    function f(x) = 2*x*y + 2*x - x**2 - 2*y**2, which has a maximum at x=2,y=1.
+    """
+
+    from scipy.optimize import fmin_slsqp
+    from numpy import array, asfarray, finfo,ones, sqrt, zeros
+
+
+    def testfunc(d,*args):
+        """
+        Arguments:
+        d     - A list of two elements, where d[0] represents x and
+                d[1] represents y in the following equation.
+        sign - A multiplier for f.  Since we want to optimize it, and the scipy
+               optimizers can only minimize functions, we need to multiply it by
+               -1 to achieve the desired solution
+        Returns:
+        2*x*y + 2*x - x**2 - 2*y**2
+
+        """
+        try:
+            sign = args[0]
+        except:
+            sign = 1.0
+        x = d[0]
+        y = d[1]
+        return sign*(2*x*y + 2*x - x**2 - 2*y**2)
+
+    def testfunc_deriv(d,*args):
+        """ This is the derivative of testfunc, returning a numpy array
+        representing df/dx and df/dy
+
+        """
+        try:
+            sign = args[0]
+        except:
+            sign = 1.0
+        x = d[0]
+        y = d[1]
+        dfdx = sign*(-2*x + 2*y + 2)
+        dfdy = sign*(2*x - 4*y)
+        return array([ dfdx, dfdy ],float)
+
+
+    from time import time
+
+    print '\n\n'
+
+    print "Unbounded optimization. Derivatives approximated."
+    t0 = time()
+    x = fmin_slsqp(testfunc, [-1.0,1.0], args=(-1.0,), iprint=2, full_output=1)
+    print "Elapsed time:", 1000*(time()-t0), "ms"
+    print "Results",x
+    print "\n\n"
+
+    print "Unbounded optimization.  Derivatives provided."
+    t0 = time()
+    x = fmin_slsqp(testfunc, [-1.0,1.0], args=(-1.0,), iprint=2, full_output=1)
+    print "Elapsed time:", 1000*(time()-t0), "ms"
+    print "Results",x
+    print "\n\n"
+
+    print "Bound optimization.  Derivatives approximated."
+    t0 = time()
+    x = fmin_slsqp(testfunc, [-1.0,1.0], args=(-1.0,),
+                   eqcons=[lambda x, y: x[0]-x[1] ], iprint=2, full_output=1)
+    print "Elapsed time:", 1000*(time()-t0), "ms"
+    print "Results",x
+    print "\n\n"
+
+    print "Bound optimization (equality constraints).  Derivatives provided."
+    t0 = time()
+    x = fmin_slsqp(testfunc, [-1.0,1.0], fprime=testfunc_deriv, args=(-1.0,),
+                   eqcons=[lambda x, y: x[0]-x[1] ], iprint=2, full_output=1)
+    print "Elapsed time:", 1000*(time()-t0), "ms"
+    print "Results",x
+    print "\n\n"
+
+    print "Bound optimization (equality and inequality constraints)."
+    print "Derivatives provided."
+
+    t0 = time()
+    x = fmin_slsqp(testfunc,[-1.0,1.0], fprime=testfunc_deriv, args=(-1.0,),
+                   eqcons=[lambda x, y: x[0]-x[1] ],
+                   ieqcons=[lambda x, y: x[0]-.5], iprint=2, full_output=1)
+    print "Elapsed time:", 1000*(time()-t0), "ms"
+    print "Results",x
+    print "\n\n"
+
+
+    def test_eqcons(d,*args):
+        try:
+            sign = args[0]
+        except:
+            sign = 1.0
+        x = d[0]
+        y = d[1]
+        return array([ x**3-y ])
+
+
+    def test_ieqcons(d,*args):
+        try:
+            sign = args[0]
+        except:
+            sign = 1.0
+        x = d[0]
+        y = d[1]
+        return array([ y-1 ])
+
+    print "Bound optimization (equality and inequality constraints)."
+    print "Derivatives provided via functions."
+    t0 = time()
+    x = fmin_slsqp(testfunc, [-1.0,1.0], fprime=testfunc_deriv, args=(-1.0,),
+                   f_eqcons=test_eqcons, f_ieqcons=test_ieqcons,
+                   iprint=2, full_output=1)
+    print "Elapsed time:", 1000*(time()-t0), "ms"
+    print "Results",x
+    print "\n\n"
+
+
+    def test_fprime_eqcons(d,*args):
+        try:
+            sign = args[0]
+        except:
+            sign = 1.0
+        x = d[0]
+        y = d[1]
+        return array([ 3.0*(x**2.0), -1.0 ])
+
+
+    def test_fprime_ieqcons(d,*args):
+        try:
+            sign = args[0]
+        except:
+            sign = 1.0
+        x = d[0]
+        y = d[1]
+        return array([ 0.0, 1.0 ])
+
+    print "Bound optimization (equality and inequality constraints)."
+    print "Derivatives provided via functions."
+    print "Constraint jacobians provided via functions"
+    t0 = time()
+    x = fmin_slsqp(testfunc,[-1.0,1.0], fprime=testfunc_deriv, args=(-1.0,),
+                   f_eqcons=test_eqcons, f_ieqcons=test_ieqcons,
+                   fprime_eqcons=test_fprime_eqcons,
+                   fprime_ieqcons=test_fprime_ieqcons, iprint=2, full_output=1)
+    print "Elapsed time:", 1000*(time()-t0), "ms"
+    print "Results",x
+    print "\n\n"
+
+
+
+
+Scalar function minimizers
+--------------------------
+
+Often only the minimum of a scalar function is needed (a scalar
+function is one that takes a scalar as input and returns a scalar
+output). In these circumstances, other optimization techniques have
+been developed that can work faster.
+
+
+Unconstrained minimization (:func:`brent`)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+There are actually two methods that can be used to minimize a scalar
+function (:obj:`brent` and :func:`golden`), but :obj:`golden` is
+included only for academic purposes and should rarely be used. The
+brent method uses Brent's algorithm for locating a minimum. Optimally
+a bracket should be given which contains the minimum desired. A
+bracket is a triple :math:`\left(a,b,c\right)` such that
+:math:`f\left(a\right)>f\left(b\right)<f\left(c\right)` and
+:math:`a<b<c` . If this is not given, then alternatively two starting
+points can be chosen and a bracket will be found from these points
+using a simple marching algorithm. If these two starting points are
+not provided 0 and 1 will be used (this may not be the right choice
+for your function and result in an unexpected minimum being returned).
+
+
+Bounded minimization (:func:`fminbound`)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Thus far all of the minimization routines described have been
+unconstrained minimization routines. Very often, however, there are
+constraints that can be placed on the solution space before
+minimization occurs. The :obj:`fminbound` function is an example of a
+constrained minimization procedure that provides a rudimentary
+interval constraint for scalar functions. The interval constraint
+allows the minimization to occur only between two fixed endpoints.
+
+For example, to find the minimum of :math:`J_{1}\left(x\right)` near :math:`x=5` , :obj:`fminbound` can be called using the interval :math:`\left[4,7\right]` as a constraint. The result is :math:`x_{\textrm{min}}=5.3314` :
+
+    >>> from scipy.special import j1
+    >>> from scipy.optimize import fminbound
+    >>> xmin = fminbound(j1, 4, 7)
+    >>> print xmin
+    5.33144184241
+
+
+Root finding
+------------
+
+
+Sets of equations
+^^^^^^^^^^^^^^^^^
+
+To find the roots of a polynomial, the command :obj:`roots
+<scipy.roots>` is useful. To find a root of a set of non-linear
+equations, the command :obj:`fsolve` is needed. For example, the
+following example finds the roots of the single-variable
+transcendental equation
+
+.. math::
+   :nowrap:
+
+    \[ x+2\cos\left(x\right)=0,\]
+
+and the set of non-linear equations
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} x_{0}\cos\left(x_{1}\right) & = & 4,\\ x_{0}x_{1}-x_{1} & = & 5.\end{eqnarray*}
+
+The results are :math:`x=-1.0299` and :math:`x_{0}=6.5041,\, x_{1}=0.9084` .
+
+    >>> def func(x):
+    ...     return x + 2*cos(x)
+
+    >>> def func2(x):
+    ...     out = [x[0]*cos(x[1]) - 4]
+    ...     out.append(x[1]*x[0] - x[1] - 5)
+    ...     return out
+
+    >>> from scipy.optimize import fsolve
+    >>> x0 = fsolve(func, 0.3)
+    >>> print x0
+    -1.02986652932
+
+    >>> x02 = fsolve(func2, [1, 1])
+    >>> print x02
+    [ 6.50409711  0.90841421]
+
+
+
+Scalar function root finding
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+If one has a single-variable equation, there are four different root
+finder algorithms that can be tried. Each of these root finding
+algorithms requires the endpoints of an interval where a root is
+suspected (because the function changes signs). In general
+:obj:`brentq` is the best choice, but the other methods may be useful
+in certain circumstances or for academic purposes.
+
+
+Fixed-point solving
+^^^^^^^^^^^^^^^^^^^
+
+A problem closely related to finding the zeros of a function is the
+problem of finding a fixed-point of a function. A fixed point of a
+function is the point at which evaluation of the function returns the
+point: :math:`g\left(x\right)=x.` Clearly the fixed point of :math:`g`
+is the root of :math:`f\left(x\right)=g\left(x\right)-x.`
+Equivalently, the root of :math:`f` is the fixed_point of
+:math:`g\left(x\right)=f\left(x\right)+x.` The routine
+:obj:`fixed_point` provides a simple iterative method using Aitkens
+sequence acceleration to estimate the fixed point of :math:`g` given a
+starting point.

pythonPackages/scipy-0.8.0/doc/source/tutorial/signal.rst

@@ -0,0 +1,544 @@
+Signal Processing (signal)
+==========================
+
+.. sectionauthor:: Travis E. Oliphant
+
+The signal processing toolbox currently contains some filtering
+functions, a limited set of filter design tools, and a few B-spline
+interpolation algorithms for one- and two-dimensional data. While the
+B-spline algorithms could technically be placed under the
+interpolation category, they are included here because they only work
+with equally-spaced data and make heavy use of filter-theory and
+transfer-function formalism to provide a fast B-spline transform. To
+understand this section you will need to understand that a signal in
+SciPy is an array of real or complex numbers.
+
+
+B-splines
+---------
+
+A B-spline is an approximation of a continuous function over a finite-
+domain in terms of B-spline coefficients and knot points. If the knot-
+points are equally spaced with spacing :math:`\Delta x` , then the B-spline approximation to a 1-dimensional function is the
+finite-basis expansion.
+
+.. math::
+   :nowrap:
+
+    \[ y\left(x\right)\approx\sum_{j}c_{j}\beta^{o}\left(\frac{x}{\Delta x}-j\right).\]
+
+In two dimensions with knot-spacing :math:`\Delta x` and :math:`\Delta y` , the function representation is
+
+.. math::
+   :nowrap:
+
+    \[ z\left(x,y\right)\approx\sum_{j}\sum_{k}c_{jk}\beta^{o}\left(\frac{x}{\Delta x}-j\right)\beta^{o}\left(\frac{y}{\Delta y}-k\right).\]
+
+In these expressions, :math:`\beta^{o}\left(\cdot\right)` is the space-limited B-spline basis function of order, :math:`o` . The requirement of equally-spaced knot-points and equally-spaced
+data points, allows the development of fast (inverse-filtering)
+algorithms for determining the coefficients, :math:`c_{j}` , from sample-values, :math:`y_{n}` . Unlike the general spline interpolation algorithms, these algorithms
+can quickly find the spline coefficients for large images.
+
+The advantage of representing a set of samples via B-spline basis
+functions is that continuous-domain operators (derivatives, re-
+sampling, integral, etc.) which assume that the data samples are drawn
+from an underlying continuous function can be computed with relative
+ease from the spline coefficients. For example, the second-derivative
+of a spline is
+
+.. math::
+   :nowrap:
+
+    \[ y{}^{\prime\prime}\left(x\right)=\frac{1}{\Delta x^{2}}\sum_{j}c_{j}\beta^{o\prime\prime}\left(\frac{x}{\Delta x}-j\right).\]
+
+Using the property of B-splines that
+
+.. math::
+   :nowrap:
+
+    \[ \frac{d^{2}\beta^{o}\left(w\right)}{dw^{2}}=\beta^{o-2}\left(w+1\right)-2\beta^{o-2}\left(w\right)+\beta^{o-2}\left(w-1\right)\]
+
+it can be seen that
+
+.. math::
+   :nowrap:
+
+    \[ y^{\prime\prime}\left(x\right)=\frac{1}{\Delta x^{2}}\sum_{j}c_{j}\left[\beta^{o-2}\left(\frac{x}{\Delta x}-j+1\right)-2\beta^{o-2}\left(\frac{x}{\Delta x}-j\right)+\beta^{o-2}\left(\frac{x}{\Delta x}-j-1\right)\right].\]
+
+If :math:`o=3` , then at the sample points,
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \Delta x^{2}\left.y^{\prime}\left(x\right)\right|_{x=n\Delta x} & = & \sum_{j}c_{j}\delta_{n-j+1}-2c_{j}\delta_{n-j}+c_{j}\delta_{n-j-1},\\  & = & c_{n+1}-2c_{n}+c_{n-1}.\end{eqnarray*}
+
+Thus, the second-derivative signal can be easily calculated from the
+spline fit. if desired, smoothing splines can be found to make the
+second-derivative less sensitive to random-errors.
+
+The savvy reader will have already noticed that the data samples are
+related to the knot coefficients via a convolution operator, so that
+simple convolution with the sampled B-spline function recovers the
+original data from the spline coefficients. The output of convolutions
+can change depending on how boundaries are handled (this becomes
+increasingly more important as the number of dimensions in the data-
+set increases). The algorithms relating to B-splines in the signal-
+processing sub package assume mirror-symmetric boundary conditions.
+Thus, spline coefficients are computed based on that assumption, and
+data-samples can be recovered exactly from the spline coefficients by
+assuming them to be mirror-symmetric also.
+
+Currently the package provides functions for determining second- and
+third-order cubic spline coefficients from equally spaced samples in
+one- and two-dimensions (:func:`signal.qspline1d`,
+:func:`signal.qspline2d`, :func:`signal.cspline1d`,
+:func:`signal.cspline2d`). The package also supplies a function (
+:obj:`signal.bspline` ) for evaluating the bspline basis function,
+:math:`\beta^{o}\left(x\right)` for arbitrary order and :math:`x.` For
+large :math:`o` , the B-spline basis function can be approximated well
+by a zero-mean Gaussian function with standard-deviation equal to
+:math:`\sigma_{o}=\left(o+1\right)/12` :
+
+.. math::
+   :nowrap:
+
+    \[ \beta^{o}\left(x\right)\approx\frac{1}{\sqrt{2\pi\sigma_{o}^{2}}}\exp\left(-\frac{x^{2}}{2\sigma_{o}}\right).\]
+
+A function to compute this Gaussian for arbitrary :math:`x` and
+:math:`o` is also available ( :obj:`signal.gauss_spline` ). The
+following code and Figure uses spline-filtering to compute an
+edge-image (the second-derivative of a smoothed spline) of Lena's face
+which is an array returned by the command :func:`lena`. The command
+:obj:`signal.sepfir2d` was used to apply a separable two-dimensional
+FIR filter with mirror- symmetric boundary conditions to the spline
+coefficients. This function is ideally suited for reconstructing
+samples from spline coefficients and is faster than
+:obj:`signal.convolve2d` which convolves arbitrary two-dimensional
+filters and allows for choosing mirror-symmetric boundary conditions.
+
+.. plot::
+
+   >>> from numpy import *
+   >>> from scipy import signal, misc
+   >>> import matplotlib.pyplot as plt
+
+   >>> image = misc.lena().astype(float32)
+   >>> derfilt = array([1.0,-2,1.0],float32)
+   >>> ck = signal.cspline2d(image,8.0)
+   >>> deriv = signal.sepfir2d(ck, derfilt, [1]) + \
+   >>>         signal.sepfir2d(ck, [1], derfilt)
+
+   Alternatively we could have done::
+
+       laplacian = array([[0,1,0],[1,-4,1],[0,1,0]],float32)
+       deriv2 = signal.convolve2d(ck,laplacian,mode='same',boundary='symm')
+
+   >>> plt.figure()
+   >>> plt.imshow(image)
+   >>> plt.gray()
+   >>> plt.title('Original image')
+   >>> plt.show()
+
+   >>> plt.figure()
+   >>> plt.imshow(deriv)
+   >>> plt.gray()
+   >>> plt.title('Output of spline edge filter')
+   >>> plt.show()
+
+..   :caption: Example of using smoothing splines to filter images.
+
+
+Filtering
+---------
+
+Filtering is a generic name for any system that modifies an input
+signal in some way. In SciPy a signal can be thought of as a Numpy
+array. There are different kinds of filters for different kinds of
+operations. There are two broad kinds of filtering operations: linear
+and non-linear. Linear filters can always be reduced to multiplication
+of the flattened Numpy array by an appropriate matrix resulting in
+another flattened Numpy array. Of course, this is not usually the best
+way to compute the filter as the matrices and vectors involved may be
+huge. For example filtering a :math:`512 \times 512` image with this
+method would require multiplication of a :math:`512^2 \times 512^2`
+matrix with a :math:`512^2` vector. Just trying to store the
+:math:`512^2 \times 512^2` matrix using a standard Numpy array would
+require :math:`68,719,476,736` elements. At 4 bytes per element this
+would require :math:`256\textrm{GB}` of memory. In most applications
+most of the elements of this matrix are zero and a different method
+for computing the output of the filter is employed.
+
+
+Convolution/Correlation
+^^^^^^^^^^^^^^^^^^^^^^^
+
+Many linear filters also have the property of shift-invariance. This
+means that the filtering operation is the same at different locations
+in the signal and it implies that the filtering matrix can be
+constructed from knowledge of one row (or column) of the matrix alone.
+In this case, the matrix multiplication can be accomplished using
+Fourier transforms.
+
+Let :math:`x\left[n\right]` define a one-dimensional signal indexed by the integer :math:`n.` Full convolution of two one-dimensional signals can be expressed as
+
+.. math::
+   :nowrap:
+
+    \[ y\left[n\right]=\sum_{k=-\infty}^{\infty}x\left[k\right]h\left[n-k\right].\]
+
+This equation can only be implemented directly if we limit the
+sequences to finite support sequences that can be stored in a
+computer, choose :math:`n=0` to be the starting point of both
+sequences, let :math:`K+1` be that value for which
+:math:`y\left[n\right]=0` for all :math:`n>K+1` and :math:`M+1` be
+that value for which :math:`x\left[n\right]=0` for all :math:`n>M+1` ,
+then the discrete convolution expression is
+
+.. math::
+   :nowrap:
+
+    \[ y\left[n\right]=\sum_{k=\max\left(n-M,0\right)}^{\min\left(n,K\right)}x\left[k\right]h\left[n-k\right].\]
+
+For convenience assume :math:`K\geq M.` Then, more explicitly the output of this operation is
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} y\left[0\right] & = & x\left[0\right]h\left[0\right]\\ y\left[1\right] & = & x\left[0\right]h\left[1\right]+x\left[1\right]h\left[0\right]\\ y\left[2\right] & = & x\left[0\right]h\left[2\right]+x\left[1\right]h\left[1\right]+x\left[2\right]h\left[0\right]\\ \vdots & \vdots & \vdots\\ y\left[M\right] & = & x\left[0\right]h\left[M\right]+x\left[1\right]h\left[M-1\right]+\cdots+x\left[M\right]h\left[0\right]\\ y\left[M+1\right] & = & x\left[1\right]h\left[M\right]+x\left[2\right]h\left[M-1\right]+\cdots+x\left[M+1\right]h\left[0\right]\\ \vdots & \vdots & \vdots\\ y\left[K\right] & = & x\left[K-M\right]h\left[M\right]+\cdots+x\left[K\right]h\left[0\right]\\ y\left[K+1\right] & = & x\left[K+1-M\right]h\left[M\right]+\cdots+x\left[K\right]h\left[1\right]\\ \vdots & \vdots & \vdots\\ y\left[K+M-1\right] & = & x\left[K-1\right]h\left[M\right]+x\left[K\right]h\left[M-1\right]\\ y\left[K+M\right] & = & x\left[K\right]h\left[M\right].\end{eqnarray*}
+
+Thus, the full discrete convolution of two finite sequences of lengths :math:`K+1` and :math:`M+1` respectively results in a finite sequence of length :math:`K+M+1=\left(K+1\right)+\left(M+1\right)-1.`
+
+One dimensional convolution is implemented in SciPy with the function
+``signal.convolve`` . This function takes as inputs the signals
+:math:`x,` :math:`h` , and an optional flag and returns the signal
+:math:`y.` The optional flag allows for specification of which part of
+the output signal to return. The default value of 'full' returns the
+entire signal. If the flag has a value of 'same' then only the middle
+:math:`K` values are returned starting at :math:`y\left[\left\lfloor
+\frac{M-1}{2}\right\rfloor \right]` so that the output has the same
+length as the largest input. If the flag has a value of 'valid' then
+only the middle :math:`K-M+1=\left(K+1\right)-\left(M+1\right)+1`
+output values are returned where :math:`z` depends on all of the
+values of the smallest input from :math:`h\left[0\right]` to
+:math:`h\left[M\right].` In other words only the values
+:math:`y\left[M\right]` to :math:`y\left[K\right]` inclusive are
+returned.
+
+This same function ``signal.convolve`` can actually take :math:`N`
+-dimensional arrays as inputs and will return the :math:`N`
+-dimensional convolution of the two arrays. The same input flags are
+available for that case as well.
+
+Correlation is very similar to convolution except for the minus sign
+becomes a plus sign. Thus
+
+.. math::
+   :nowrap:
+
+    \[ w\left[n\right]=\sum_{k=-\infty}^{\infty}y\left[k\right]x\left[n+k\right]\]
+
+is the (cross) correlation of the signals :math:`y` and :math:`x.` For finite-length signals with :math:`y\left[n\right]=0` outside of the range :math:`\left[0,K\right]` and :math:`x\left[n\right]=0` outside of the range :math:`\left[0,M\right],` the summation can simplify to
+
+.. math::
+   :nowrap:
+
+    \[ w\left[n\right]=\sum_{k=\max\left(0,-n\right)}^{\min\left(K,M-n\right)}y\left[k\right]x\left[n+k\right].\]
+
+Assuming again that :math:`K\geq M` this is
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} w\left[-K\right] & = & y\left[K\right]x\left[0\right]\\ w\left[-K+1\right] & = & y\left[K-1\right]x\left[0\right]+y\left[K\right]x\left[1\right]\\ \vdots & \vdots & \vdots\\ w\left[M-K\right] & = & y\left[K-M\right]x\left[0\right]+y\left[K-M+1\right]x\left[1\right]+\cdots+y\left[K\right]x\left[M\right]\\ w\left[M-K+1\right] & = & y\left[K-M-1\right]x\left[0\right]+\cdots+y\left[K-1\right]x\left[M\right]\\ \vdots & \vdots & \vdots\\ w\left[-1\right] & = & y\left[1\right]x\left[0\right]+y\left[2\right]x\left[1\right]+\cdots+y\left[M+1\right]x\left[M\right]\\ w\left[0\right] & = & y\left[0\right]x\left[0\right]+y\left[1\right]x\left[1\right]+\cdots+y\left[M\right]x\left[M\right]\\ w\left[1\right] & = & y\left[0\right]x\left[1\right]+y\left[1\right]x\left[2\right]+\cdots+y\left[M-1\right]x\left[M\right]\\ w\left[2\right] & = & y\left[0\right]x\left[2\right]+y\left[1\right]x\left[3\right]+\cdots+y\left[M-2\right]x\left[M\right]\\ \vdots & \vdots & \vdots\\ w\left[M-1\right] & = & y\left[0\right]x\left[M-1\right]+y\left[1\right]x\left[M\right]\\ w\left[M\right] & = & y\left[0\right]x\left[M\right].\end{eqnarray*}
+
+
+
+The SciPy function ``signal.correlate`` implements this
+operation. Equivalent flags are available for this operation to return
+the full :math:`K+M+1` length sequence ('full') or a sequence with the
+same size as the largest sequence starting at
+:math:`w\left[-K+\left\lfloor \frac{M-1}{2}\right\rfloor \right]`
+('same') or a sequence where the values depend on all the values of
+the smallest sequence ('valid'). This final option returns the
+:math:`K-M+1` values :math:`w\left[M-K\right]` to
+:math:`w\left[0\right]` inclusive.
+
+The function :obj:`signal.correlate` can also take arbitrary :math:`N`
+-dimensional arrays as input and return the :math:`N` -dimensional
+convolution of the two arrays on output.
+
+When :math:`N=2,` :obj:`signal.correlate` and/or
+:obj:`signal.convolve` can be used to construct arbitrary image
+filters to perform actions such as blurring, enhancing, and
+edge-detection for an image.
+
+Convolution is mainly used for filtering when one of the signals is
+much smaller than the other ( :math:`K\gg M` ), otherwise linear
+filtering is more easily accomplished in the frequency domain (see
+Fourier Transforms).
+
+
+Difference-equation filtering
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+A general class of linear one-dimensional filters (that includes
+convolution filters) are filters described by the difference equation
+
+.. math::
+   :nowrap:
+
+    \[ \sum_{k=0}^{N}a_{k}y\left[n-k\right]=\sum_{k=0}^{M}b_{k}x\left[n-k\right]\]
+
+where :math:`x\left[n\right]` is the input sequence and
+:math:`y\left[n\right]` is the output sequence. If we assume initial
+rest so that :math:`y\left[n\right]=0` for :math:`n<0` , then this
+kind of filter can be implemented using convolution.  However, the
+convolution filter sequence :math:`h\left[n\right]` could be infinite
+if :math:`a_{k}\neq0` for :math:`k\geq1.` In addition, this general
+class of linear filter allows initial conditions to be placed on
+:math:`y\left[n\right]` for :math:`n<0` resulting in a filter that
+cannot be expressed using convolution.
+
+The difference equation filter can be thought of as finding :math:`y\left[n\right]` recursively in terms of it's previous values
+
+.. math::
+   :nowrap:
+
+    \[ a_{0}y\left[n\right]=-a_{1}y\left[n-1\right]-\cdots-a_{N}y\left[n-N\right]+\cdots+b_{0}x\left[n\right]+\cdots+b_{M}x\left[n-M\right].\]
+
+Often :math:`a_{0}=1` is chosen for normalization. The implementation
+in SciPy of this general difference equation filter is a little more
+complicated then would be implied by the previous equation. It is
+implemented so that only one signal needs to be delayed. The actual
+implementation equations are (assuming :math:`a_{0}=1` ).
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} y\left[n\right] & = & b_{0}x\left[n\right]+z_{0}\left[n-1\right]\\ z_{0}\left[n\right] & = & b_{1}x\left[n\right]+z_{1}\left[n-1\right]-a_{1}y\left[n\right]\\ z_{1}\left[n\right] & = & b_{2}x\left[n\right]+z_{2}\left[n-1\right]-a_{2}y\left[n\right]\\ \vdots & \vdots & \vdots\\ z_{K-2}\left[n\right] & = & b_{K-1}x\left[n\right]+z_{K-1}\left[n-1\right]-a_{K-1}y\left[n\right]\\ z_{K-1}\left[n\right] & = & b_{K}x\left[n\right]-a_{K}y\left[n\right],\end{eqnarray*}
+
+where :math:`K=\max\left(N,M\right).` Note that :math:`b_{K}=0` if
+:math:`K>M` and :math:`a_{K}=0` if :math:`K>N.` In this way, the
+output at time :math:`n` depends only on the input at time :math:`n`
+and the value of :math:`z_{0}` at the previous time. This can always
+be calculated as long as the :math:`K` values
+:math:`z_{0}\left[n-1\right]\ldots z_{K-1}\left[n-1\right]` are
+computed and stored at each time step.
+
+The difference-equation filter is called using the command
+:obj:`signal.lfilter` in SciPy. This command takes as inputs the
+vector :math:`b,` the vector, :math:`a,` a signal :math:`x` and
+returns the vector :math:`y` (the same length as :math:`x` ) computed
+using the equation given above. If :math:`x` is :math:`N`
+-dimensional, then the filter is computed along the axis provided. If,
+desired, initial conditions providing the values of
+:math:`z_{0}\left[-1\right]` to :math:`z_{K-1}\left[-1\right]` can be
+provided or else it will be assumed that they are all zero. If initial
+conditions are provided, then the final conditions on the intermediate
+variables are also returned. These could be used, for example, to
+restart the calculation in the same state.
+
+Sometimes it is more convenient to express the initial conditions in
+terms of the signals :math:`x\left[n\right]` and
+:math:`y\left[n\right].` In other words, perhaps you have the values
+of :math:`x\left[-M\right]` to :math:`x\left[-1\right]` and the values
+of :math:`y\left[-N\right]` to :math:`y\left[-1\right]` and would like
+to determine what values of :math:`z_{m}\left[-1\right]` should be
+delivered as initial conditions to the difference-equation filter. It
+is not difficult to show that for :math:`0\leq m<K,`
+
+.. math::
+   :nowrap:
+
+    \[ z_{m}\left[n\right]=\sum_{p=0}^{K-m-1}\left(b_{m+p+1}x\left[n-p\right]-a_{m+p+1}y\left[n-p\right]\right).\]
+
+Using this formula we can find the intial condition vector :math:`z_{0}\left[-1\right]` to :math:`z_{K-1}\left[-1\right]` given initial conditions on :math:`y` (and :math:`x` ). The command :obj:`signal.lfiltic` performs this function.
+
+
+Other filters
+^^^^^^^^^^^^^
+
+The signal processing package provides many more filters as well.
+
+
+Median Filter
+"""""""""""""
+
+A median filter is commonly applied when noise is markedly non-
+Gaussian or when it is desired to preserve edges. The median filter
+works by sorting all of the array pixel values in a rectangular region
+surrounding the point of interest. The sample median of this list of
+neighborhood pixel values is used as the value for the output array.
+The sample median is the middle array value in a sorted list of
+neighborhood values. If there are an even number of elements in the
+neighborhood, then the average of the middle two values is used as the
+median. A general purpose median filter that works on N-dimensional
+arrays is :obj:`signal.medfilt` . A specialized version that works
+only for two-dimensional arrays is available as
+:obj:`signal.medfilt2d` .
+
+
+Order Filter
+""""""""""""
+
+A median filter is a specific example of a more general class of
+filters called order filters. To compute the output at a particular
+pixel, all order filters use the array values in a region surrounding
+that pixel. These array values are sorted and then one of them is
+selected as the output value. For the median filter, the sample median
+of the list of array values is used as the output. A general order
+filter allows the user to select which of the sorted values will be
+used as the output. So, for example one could choose to pick the
+maximum in the list or the minimum. The order filter takes an
+additional argument besides the input array and the region mask that
+specifies which of the elements in the sorted list of neighbor array
+values should be used as the output. The command to perform an order
+filter is :obj:`signal.order_filter` .
+
+
+Wiener filter
+"""""""""""""
+
+The Wiener filter is a simple deblurring filter for denoising images.
+This is not the Wiener filter commonly described in image
+reconstruction problems but instead it is a simple, local-mean filter.
+Let :math:`x` be the input signal, then the output is
+
+
+
+.. math::
+   :nowrap:
+
+    \[ y=\left\{ \begin{array}{cc} \frac{\sigma^{2}}{\sigma_{x}^{2}}m_{x}+\left(1-\frac{\sigma^{2}}{\sigma_{x}^{2}}\right)x & \sigma_{x}^{2}\geq\sigma^{2},\\ m_{x} & \sigma_{x}^{2}<\sigma^{2}.\end{array}\right.\]
+
+Where :math:`m_{x}` is the local estimate of the mean and
+:math:`\sigma_{x}^{2}` is the local estimate of the variance. The
+window for these estimates is an optional input parameter (default is
+:math:`3\times3` ). The parameter :math:`\sigma^{2}` is a threshold
+noise parameter. If :math:`\sigma` is not given then it is estimated
+as the average of the local variances.
+
+
+Hilbert filter
+""""""""""""""
+
+The Hilbert transform constructs the complex-valued analytic signal
+from a real signal. For example if :math:`x=\cos\omega n` then
+:math:`y=\textrm{hilbert}\left(x\right)` would return (except near the
+edges) :math:`y=\exp\left(j\omega n\right).` In the frequency domain,
+the hilbert transform performs
+
+.. math::
+   :nowrap:
+
+    \[ Y=X\cdot H\]
+
+where :math:`H` is 2 for positive frequencies, :math:`0` for negative frequencies and :math:`1` for zero-frequencies.
+
+.. XXX: TODO
+..
+.. Detrend
+.. """""""
+..
+.. Filter design
+.. -------------
+..
+..
+.. Finite-impulse response design
+.. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+..
+..
+.. Inifinite-impulse response design
+.. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+..
+..
+.. Analog filter frequency response
+.. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+..
+..
+.. Digital filter frequency response
+.. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+..
+..
+.. Linear Time-Invariant Systems
+.. -----------------------------
+..
+..
+.. LTI Object
+.. ^^^^^^^^^^
+..
+..
+.. Continuous-Time Simulation
+.. ^^^^^^^^^^^^^^^^^^^^^^^^^^
+..
+..
+.. Step response
+.. ^^^^^^^^^^^^^
+..
+..
+.. Impulse response
+.. ^^^^^^^^^^^^^^^^
+..
+..
+.. Input/Output
+.. ============
+..
+..
+.. Binary
+.. ------
+..
+..
+.. Arbitrary binary input and output (fopen)
+.. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+..
+..
+.. Read and write Matlab .mat files
+.. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+..
+..
+.. Saving workspace
+.. ^^^^^^^^^^^^^^^^
+..
+..
+.. Text-file
+.. ---------
+..
+..
+.. Read text-files (read_array)
+.. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+..
+..
+.. Write a text-file (write_array)
+.. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+..
+..
+.. Fourier Transforms
+.. ==================
+..
+..
+.. One-dimensional
+.. ---------------
+..
+..
+.. Two-dimensional
+.. ---------------
+..
+..
+.. N-dimensional
+.. -------------
+..
+..
+.. Shifting
+.. --------
+..
+..
+.. Sample frequencies
+.. ------------------
+..
+..
+.. Hilbert transform
+.. -----------------
+..
+..
+.. Tilbert transform
+.. -----------------

pythonPackages/scipy-0.8.0/doc/source/tutorial/special.rst

@@ -0,0 +1,23 @@
+Special functions (:mod:`scipy.special`)
+========================================
+
+.. sectionauthor:: Travis E. Oliphant
+
+.. currentmodule:: scipy.special
+
+The main feature of the :mod:`scipy.special` package is the definition of
+numerous special functions of mathematical physics. Available
+functions include airy, elliptic, bessel, gamma, beta, hypergeometric,
+parabolic cylinder, mathieu, spheroidal wave, struve, and
+kelvin. There are also some low-level stats functions that are not
+intended for general use as an easier interface to these functions is
+provided by the ``stats`` module. Most of these functions can take
+array arguments and return array results following the same
+broadcasting rules as other math functions in Numerical Python. Many
+of these functions also accept complex numbers as input. For a
+complete list of the available functions with a one-line description
+type ``>>> help(special).`` Each function also has its own
+documentation accessible using help.  If you don't see a function you
+need, consider writing it and contributing it to the library. You can
+write the function in either C, Fortran, or Python. Look in the source
+code of the library for examples of each of these kinds of functions.

pythonPackages/scipy-0.8.0/doc/source/tutorial/stats.rst

@@ -0,0 +1,579 @@
+Statistics
+==========
+
+.. sectionauthor:: Travis E. Oliphant
+
+Introduction
+------------
+
+SciPy has a tremendous number of basic statistics routines with more
+easily added by the end user (if you create one please contribute it).
+All of the statistics functions are located in the sub-package
+:mod:`scipy.stats` and a fairly complete listing of these functions
+can be had using ``info(stats)``.
+
+Random Variables
+^^^^^^^^^^^^^^^^
+
+There are two general distribution classes that have been implemented
+for encapsulating
+:ref:`continuous random variables <continuous-random-variables>`
+and
+:ref:`discrete random variables <discrete-random-variables>`
+. Over 80 continuous random variables  and 10 discrete random
+variables have been implemented using these classes. The list of the
+random variables available is in the docstring for the stats sub-
+package.
+
+
+Note: The following is work in progress
+
+Distributions
+-------------
+
+
+First some imports
+
+    >>> import numpy as np
+    >>> from scipy import stats
+    >>> import warnings
+    >>> warnings.simplefilter('ignore', DeprecationWarning)
+
+We can obtain the list of available distribution through introspection:
+
+    >>> dist_continu = [d for d in dir(stats) if
+    ...                 isinstance(getattr(stats,d), stats.rv_continuous)]
+    >>> dist_discrete = [d for d in dir(stats) if
+    ...                  isinstance(getattr(stats,d), stats.rv_discrete)]
+    >>> print 'number of continuous distributions:', len(dist_continu)
+    number of continuous distributions: 84
+    >>> print 'number of discrete distributions:  ', len(dist_discrete)
+    number of discrete distributions:   12
+
+
+
+
+Distributions can be used in one of two ways, either by passing all distribution
+parameters to each method call or by freezing the parameters for the instance
+of the distribution. As an example, we can get the median of the distribution by using
+the percent point function, ppf, which is the inverse of the cdf:
+
+    >>> print stats.nct.ppf(0.5, 10, 2.5)
+    2.56880722561
+    >>> my_nct = stats.nct(10, 2.5)
+    >>> print my_nct.ppf(0.5)
+    2.56880722561
+
+``help(stats.nct)`` prints the complete docstring of the distribution. Instead
+we can print just some basic information::
+
+    >>> print stats.nct.extradoc #contains the distribution specific docs
+    Non-central Student T distribution
+
+                                     df**(df/2) * gamma(df+1)
+    nct.pdf(x,df,nc) = --------------------------------------------------
+                       2**df*exp(nc**2/2)*(df+x**2)**(df/2) * gamma(df/2)
+    for df > 0, nc > 0.
+
+
+    >>> print 'number of arguments: %d, shape parameters: %s'% (stats.nct.numargs,
+    ...                                                         stats.nct.shapes)
+    number of arguments: 2, shape parameters: df,nc
+    >>> print 'bounds of distribution lower: %s, upper: %s' % (stats.nct.a,
+    ...                                                        stats.nct.b)
+    bounds of distribution lower: -1.#INF, upper: 1.#INF
+
+We can list all methods and properties of the distribution with
+``dir(stats.nct)``. Some of the methods are private methods, that are
+not named as such, i.e. no leading underscore, for example veccdf or
+xa and xb are for internal calculation. The main methods we can see
+when we list the methods of the frozen distribution:
+
+    >>> print dir(my_nct) #reformatted
+        ['__class__', '__delattr__', '__dict__', '__doc__', '__getattribute__',
+        '__hash__', '__init__', '__module__', '__new__', '__reduce__', '__reduce_ex__',
+        '__repr__', '__setattr__', '__str__', '__weakref__', 'args', 'cdf', 'dist',
+        'entropy', 'isf', 'kwds', 'moment', 'pdf', 'pmf', 'ppf', 'rvs', 'sf', 'stats']
+
+
+The main public methods are:
+
+* rvs:   Random Variates
+* pdf:   Probability Density Function
+* cdf:   Cumulative Distribution Function
+* sf:    Survival Function (1-CDF)
+* ppf:   Percent Point Function (Inverse of CDF)
+* isf:   Inverse Survival Function (Inverse of SF)
+* stats: Return mean, variance, (Fisher's) skew, or (Fisher's) kurtosis
+* moment: non-central moments of the distribution
+
+The main additional methods of the not frozen distribution are related to the estimation
+of distrition parameters:
+
+* fit:   maximum likelihood estimation of distribution parameters, including location
+         and scale
+* fit_loc_scale: estimation of location and scale when shape parameters are given
+* nnlf:  negative log likelihood function
+* expect: Calculate the expectation of a function against the pdf or pmf
+
+All continuous distributions take `loc` and `scale` as keyword
+parameters to adjust the location and scale of the distribution,
+e.g. for the standard normal distribution location is the mean and
+scale is the standard deviation. The standardized distribution for a
+random variable `x` is obtained through ``(x - loc) / scale``.
+
+Discrete distribution have most of the same basic methods, however
+pdf is replaced the probability mass function `pmf`, no estimation
+methods, such as fit, are available, and scale is not a valid
+keyword parameter. The location parameter, keyword `loc` can be used
+to shift the distribution.
+
+The basic methods, pdf, cdf, sf, ppf, and isf are vectorized with
+``np.vectorize``, and the usual numpy broadcasting is applied. For
+example, we can calculate the critical values for the upper tail of
+the t distribution for different probabilites and degrees of freedom.
+
+    >>> stats.t.isf([0.1, 0.05, 0.01], [[10], [11]])
+    array([[ 1.37218364,  1.81246112,  2.76376946],
+           [ 1.36343032,  1.79588482,  2.71807918]])
+
+Here, the first row are the critical values for 10 degrees of freedom and the second row
+is for 11 d.o.f., i.e. this is the same as
+
+    >>> stats.t.isf([0.1, 0.05, 0.01], 10)
+    array([ 1.37218364,  1.81246112,  2.76376946])
+    >>> stats.t.isf([0.1, 0.05, 0.01], 11)
+    array([ 1.36343032,  1.79588482,  2.71807918])
+
+If both, probabilities and degrees of freedom have the same array shape, then element
+wise matching is used. As an example, we can obtain the 10% tail for 10 d.o.f., the 5% tail
+for 11 d.o.f. and the 1% tail for 12 d.o.f. by
+
+    >>> stats.t.isf([0.1, 0.05, 0.01], [10, 11, 12])
+    array([ 1.37218364,  1.79588482,  2.68099799])
+
+
+
+Performance and Remaining Issues
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The performance of the individual methods, in terms of speed, varies
+widely by distribution and method. The results of a method are
+obtained in one of two ways, either by explicit calculation or by a
+generic algorithm that is independent of the specific distribution.
+Explicit calculation, requires that the method is directly specified
+for the given distribution, either through analytic formulas or
+through special functions in scipy.special or numpy.random for
+`rvs`. These are usually relatively fast calculations. The generic
+methods are used if the distribution does not specify any explicit
+calculation. To define a distribution, only one of pdf or cdf is
+necessary, all other methods can be derived using numeric integration
+and root finding. These indirect methods can be very slow. As an
+example, ``rgh = stats.gausshyper.rvs(0.5, 2, 2, 2, size=100)`` creates
+random variables in a very indirect way and takes about 19 seconds
+for 100 random variables on my computer, while one million random
+variables from the standard normal or from the t distribution take
+just above one second.
+
+
+The distributions in scipy.stats have recently been corrected and improved
+and gained a considerable test suite, however a few issues remain:
+
+* skew and kurtosis, 3rd and 4th moments and entropy are not thoroughly
+  tested and some coarse testing indicates that there are still some
+  incorrect results left.
+* the distributions have been tested over some range of parameters,
+  however in some corner ranges, a few incorrect results may remain.
+* the maximum likelihood estimation in `fit` does not work with
+  default starting parameters for all distributions and the user
+  needs to supply good starting parameters. Also, for some
+  distribution using a maximum likelihood estimator might
+  inherently not be the best choice.
+
+
+The next example shows how to build our own discrete distribution,
+and more examples for the usage of the distributions are shown below
+together with the statistical tests.
+
+
+
+Example: discrete distribution rv_discrete
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+In the following we use stats.rv_discrete to generate a discrete distribution
+that has the probabilites of the truncated normal for the intervalls
+centered around the integers.
+
+
+    >>> npoints = 20 # number of integer support points of the distribution minus 1
+    >>> npointsh = npoints / 2
+    >>> npointsf = float(npoints)
+    >>> nbound = 4 # bounds for the truncated normal
+    >>> normbound = (1+1/npointsf) * nbound # actual bounds of truncated normal
+    >>> grid = np.arange(-npointsh, npointsh+2, 1) # integer grid
+    >>> gridlimitsnorm = (grid-0.5) / npointsh * nbound # bin limits for the truncnorm
+    >>> gridlimits = grid - 0.5
+    >>> grid = grid[:-1]
+    >>> probs = np.diff(stats.truncnorm.cdf(gridlimitsnorm, -normbound, normbound))
+    >>> gridint = grid
+    >>> normdiscrete = stats.rv_discrete(values = (gridint,
+    ...              np.round(probs, decimals=7)), name='normdiscrete')
+
+From the docstring of rv_discrete:
+ "You can construct an aribtrary discrete rv where P{X=xk} = pk by
+ passing to the rv_discrete initialization method (through the values=
+ keyword) a tuple of sequences (xk, pk) which describes only those
+ values of X (xk) that occur with nonzero probability (pk)."
+
+There are some requirements for this distribution to work. The
+keyword `name` is required. The support points of the distribution
+xk have to be integers. Also, I needed  to limit the number of
+decimals. If the last two requirements are not satisfied an
+exception may be raised or the resulting numbers may be incorrect.
+
+After defining the distribution, we obtain access to all methods of
+discrete distributions.
+
+    >>> print 'mean = %6.4f, variance = %6.4f, skew = %6.4f, kurtosis = %6.4f'% \
+    ...       normdiscrete.stats(moments =  'mvsk')
+    mean = -0.0000, variance = 6.3302, skew = 0.0000, kurtosis = -0.0076
+
+    >>> nd_std = np.sqrt(normdiscrete.stats(moments =  'v'))
+
+**Generate a random sample and compare observed frequencies with probabilities**
+
+    >>> n_sample = 500
+    >>> np.random.seed(87655678) # fix the seed for replicability
+    >>> rvs = normdiscrete.rvs(size=n_sample)
+    >>> rvsnd = rvs
+    >>> f, l = np.histogram(rvs, bins=gridlimits)
+    >>> sfreq = np.vstack([gridint, f, probs*n_sample]).T
+    >>> print sfreq
+    [[ -1.00000000e+01   0.00000000e+00   2.95019349e-02]
+     [ -9.00000000e+00   0.00000000e+00   1.32294142e-01]
+     [ -8.00000000e+00   0.00000000e+00   5.06497902e-01]
+     [ -7.00000000e+00   2.00000000e+00   1.65568919e+00]
+     [ -6.00000000e+00   1.00000000e+00   4.62125309e+00]
+     [ -5.00000000e+00   9.00000000e+00   1.10137298e+01]
+     [ -4.00000000e+00   2.60000000e+01   2.24137683e+01]
+     [ -3.00000000e+00   3.70000000e+01   3.89503370e+01]
+     [ -2.00000000e+00   5.10000000e+01   5.78004747e+01]
+     [ -1.00000000e+00   7.10000000e+01   7.32455414e+01]
+     [  0.00000000e+00   7.40000000e+01   7.92618251e+01]
+     [  1.00000000e+00   8.90000000e+01   7.32455414e+01]
+     [  2.00000000e+00   5.50000000e+01   5.78004747e+01]
+     [  3.00000000e+00   5.00000000e+01   3.89503370e+01]
+     [  4.00000000e+00   1.70000000e+01   2.24137683e+01]
+     [  5.00000000e+00   1.10000000e+01   1.10137298e+01]
+     [  6.00000000e+00   4.00000000e+00   4.62125309e+00]
+     [  7.00000000e+00   3.00000000e+00   1.65568919e+00]
+     [  8.00000000e+00   0.00000000e+00   5.06497902e-01]
+     [  9.00000000e+00   0.00000000e+00   1.32294142e-01]
+     [  1.00000000e+01   0.00000000e+00   2.95019349e-02]]
+
+
+.. plot:: examples/normdiscr_plot1.py
+   :align: center
+   :include-source: 0
+
+
+.. plot:: examples/normdiscr_plot2.py
+   :align: center
+   :include-source: 0
+
+
+Next, we can test, whether our sample was generated by our normdiscrete
+distribution. This also verifies, whether the random numbers are generated
+correctly
+
+The chisquare test requires that there are a minimum number of observations
+in each bin. We combine the tail bins into larger bins so that they contain
+enough observations.
+
+    >>> f2 = np.hstack([f[:5].sum(), f[5:-5], f[-5:].sum()])
+    >>> p2 = np.hstack([probs[:5].sum(), probs[5:-5], probs[-5:].sum()])
+    >>> ch2, pval = stats.chisquare(f2, p2*n_sample)
+
+    >>> print 'chisquare for normdiscrete: chi2 = %6.3f pvalue = %6.4f' % (ch2, pval)
+    chisquare for normdiscrete: chi2 = 12.466 pvalue = 0.4090
+
+The pvalue in this case is high, so we can be quite confident that
+our random sample was actually generated by the distribution.
+
+
+
+Analysing One Sample
+--------------------
+
+First, we create some random variables. We set a seed so that in each run
+we get identical results to look at. As an example we take a sample from
+the Student t distribution:
+
+    >>> np.random.seed(282629734)
+    >>> x = stats.t.rvs(10, size=1000)
+
+Here, we set the required shape parameter of the t distribution, which
+in statistics corresponds to the degrees of freedom, to 10. Using size=100 means
+that our sample consists of 1000 independently drawn (pseudo) random numbers.
+Since we did not specify the keyword arguments `loc` and `scale`, those are
+set to their default values zero and one.
+
+Descriptive Statistics
+^^^^^^^^^^^^^^^^^^^^^^
+
+`x` is a numpy array, and we have direct access to all array methods, e.g.
+
+    >>> print x.max(), x.min()  # equivalent to np.max(x), np.min(x)
+    5.26327732981 -3.78975572422
+    >>> print x.mean(), x.var() # equivalent to np.mean(x), np.var(x)
+    0.0140610663985 1.28899386208
+
+
+How do the some sample properties compare to their theoretical counterparts?
+
+    >>> m, v, s, k = stats.t.stats(10, moments='mvsk')
+    >>> n, (smin, smax), sm, sv, ss, sk = stats.describe(x)
+
+    >>> print 'distribution:',
+    distribution:
+    >>> sstr = 'mean = %6.4f, variance = %6.4f, skew = %6.4f, kurtosis = %6.4f'
+    >>> print sstr %(m, v, s ,k)
+    mean = 0.0000, variance = 1.2500, skew = 0.0000, kurtosis = 1.0000
+    >>> print 'sample:      ',
+    sample:
+    >>> print sstr %(sm, sv, ss, sk)
+    mean = 0.0141, variance = 1.2903, skew = 0.2165, kurtosis = 1.0556
+
+Note: stats.describe uses the unbiased estimator for the variance, while
+np.var is the biased estimator.
+
+
+For our sample the sample statistics differ a by a small amount from
+their theoretical counterparts.
+
+
+T-test and KS-test
+^^^^^^^^^^^^^^^^^^
+
+We can use the t-test to test whether the mean of our sample differs
+in a statistcally significant way from the theoretical expectation.
+
+    >>> print 't-statistic = %6.3f pvalue = %6.4f' %  stats.ttest_1samp(x, m)
+    t-statistic =  0.391 pvalue = 0.6955
+
+The pvalue is 0.7, this means that with an alpha error of, for
+example, 10%, we cannot reject the hypothesis that the sample mean
+is equal to zero, the expectation of the standard t-distribution.
+
+
+As an exercise, we can calculate our ttest also directly without
+using the provided function, which should give us the same answer,
+and so it does:
+
+    >>> tt = (sm-m)/np.sqrt(sv/float(n))  # t-statistic for mean
+    >>> pval = stats.t.sf(np.abs(tt), n-1)*2  # two-sided pvalue = Prob(abs(t)>tt)
+    >>> print 't-statistic = %6.3f pvalue = %6.4f' % (tt, pval)
+    t-statistic =  0.391 pvalue = 0.6955
+
+The Kolmogorov-Smirnov test can be used to test the hypothesis that
+the sample comes from the standard t-distribution
+
+    >>> print 'KS-statistic D = %6.3f pvalue = %6.4f' % stats.kstest(x, 't', (10,))
+    KS-statistic D =  0.016 pvalue = 0.9606
+
+Again the p-value is high enough that we cannot reject the
+hypothesis that the random sample really is distributed according to the
+t-distribution. In real applications, we don't know what the
+underlying distribution is. If we perform the Kolmogorov-Smirnov
+test of our sample against the standard normal distribution, then we
+also cannot reject the hypothesis that our sample was generated by the
+normal distribution given that in this example the p-value is almost 40%.
+
+    >>> print 'KS-statistic D = %6.3f pvalue = %6.4f' % stats.kstest(x,'norm')
+    KS-statistic D =  0.028 pvalue = 0.3949
+
+However, the standard normal distribution has a variance of 1, while our
+sample has a variance of 1.29. If we standardize our sample and test it
+against the normal distribution, then the p-value is again large enough
+that we cannot reject the hypothesis that the sample came form the
+normal distribution.
+
+    >>> d, pval = stats.kstest((x-x.mean())/x.std(), 'norm')
+    >>> print 'KS-statistic D = %6.3f pvalue = %6.4f' % (d, pval)
+    KS-statistic D =  0.032 pvalue = 0.2402
+
+Note: The Kolmogorov-Smirnov test assumes that we test against a
+distribution with given parameters, since in the last case we
+estimated mean and variance, this assumption is violated, and the
+distribution of the test statistic on which the p-value is based, is
+not correct.
+
+Tails of the distribution
+^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Finally, we can check the upper tail of the distribution. We can use
+the percent point function ppf, which is the inverse of the cdf
+function, to obtain the critical values, or, more directly, we can use
+the inverse of the survival function
+
+    >>> crit01, crit05, crit10 = stats.t.ppf([1-0.01, 1-0.05, 1-0.10], 10)
+    >>> print 'critical values from ppf at 1%%, 5%% and 10%% %8.4f %8.4f %8.4f'% (crit01, crit05, crit10)
+    critical values from ppf at 1%, 5% and 10%   2.7638   1.8125   1.3722
+    >>> print 'critical values from isf at 1%%, 5%% and 10%% %8.4f %8.4f %8.4f'% tuple(stats.t.isf([0.01,0.05,0.10],10))
+    critical values from isf at 1%, 5% and 10%   2.7638   1.8125   1.3722
+
+    >>> freq01 = np.sum(x>crit01) / float(n) * 100
+    >>> freq05 = np.sum(x>crit05) / float(n) * 100
+    >>> freq10 = np.sum(x>crit10) / float(n) * 100
+    >>> print 'sample %%-frequency at 1%%, 5%% and 10%% tail %8.4f %8.4f %8.4f'% (freq01, freq05, freq10)
+    sample %-frequency at 1%, 5% and 10% tail   1.4000   5.8000  10.5000
+
+In all three cases, our sample has more weight in the top tail than the
+underlying distribution.
+We can briefly check a larger sample to see if we get a closer match. In this
+case the empirical frequency is quite close to the theoretical probability,
+but if we repeat this several times the fluctuations are still pretty large.
+
+    >>> freq05l = np.sum(stats.t.rvs(10, size=10000) > crit05) / 10000.0 * 100
+    >>> print 'larger sample %%-frequency at 5%% tail %8.4f'% freq05l
+    larger sample %-frequency at 5% tail   4.8000
+
+We can also compare it with the tail of the normal distribution, which
+has less weight in the tails:
+
+    >>> print 'tail prob. of normal at 1%%, 5%% and 10%% %8.4f %8.4f %8.4f'% \
+    ...       tuple(stats.norm.sf([crit01, crit05, crit10])*100)
+    tail prob. of normal at 1%, 5% and 10%   0.2857   3.4957   8.5003
+
+The chisquare test can be used to test, whether for a finite number of bins,
+the observed frequencies differ significantly from the probabilites of the
+hypothesized distribution.
+
+    >>> quantiles = [0.0, 0.01, 0.05, 0.1, 1-0.10, 1-0.05, 1-0.01, 1.0]
+    >>> crit = stats.t.ppf(quantiles, 10)
+    >>> print crit
+    [       -Inf -2.76376946 -1.81246112 -1.37218364  1.37218364  1.81246112
+      2.76376946         Inf]
+    >>> n_sample = x.size
+    >>> freqcount = np.histogram(x, bins=crit)[0]
+    >>> tprob = np.diff(quantiles)
+    >>> nprob = np.diff(stats.norm.cdf(crit))
+    >>> tch, tpval = stats.chisquare(freqcount, tprob*n_sample)
+    >>> nch, npval = stats.chisquare(freqcount, nprob*n_sample)
+    >>> print 'chisquare for t:      chi2 = %6.3f pvalue = %6.4f' % (tch, tpval)
+    chisquare for t:      chi2 =  2.300 pvalue = 0.8901
+    >>> print 'chisquare for normal: chi2 = %6.3f pvalue = %6.4f' % (nch, npval)
+    chisquare for normal: chi2 = 64.605 pvalue = 0.0000
+
+We see that the standard normal distribution is clearly rejected while the
+standard t-distribution cannot be rejected. Since the variance of our sample
+differs from both standard distribution, we can again redo the test taking
+the estimate for scale and location into account.
+
+The fit method of the distributions can be used to estimate the parameters
+of the distribution, and the test is repeated using probabilites of the
+estimated distribution.
+
+    >>> tdof, tloc, tscale = stats.t.fit(x)
+    >>> nloc, nscale = stats.norm.fit(x)
+    >>> tprob = np.diff(stats.t.cdf(crit, tdof, loc=tloc, scale=tscale))
+    >>> nprob = np.diff(stats.norm.cdf(crit, loc=nloc, scale=nscale))
+    >>> tch, tpval = stats.chisquare(freqcount, tprob*n_sample)
+    >>> nch, npval = stats.chisquare(freqcount, nprob*n_sample)
+    >>> print 'chisquare for t:      chi2 = %6.3f pvalue = %6.4f' % (tch, tpval)
+    chisquare for t:      chi2 =  1.577 pvalue = 0.9542
+    >>> print 'chisquare for normal: chi2 = %6.3f pvalue = %6.4f' % (nch, npval)
+    chisquare for normal: chi2 = 11.084 pvalue = 0.0858
+
+Taking account of the estimated parameters, we can still reject the
+hypothesis that our sample came from a normal distribution (at the 5% level),
+but again, with a p-value of 0.95, we cannot reject the t distribution.
+
+
+
+Special tests for normal distributions
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Since the normal distribution is the most common distribution in statistics,
+there are several additional functions available to test whether a sample
+could have been drawn from a normal distribution
+
+First we can test if skew and kurtosis of our sample differ significantly from
+those of a normal distribution:
+
+    >>> print 'normal skewtest teststat = %6.3f pvalue = %6.4f' % stats.skewtest(x)
+    normal skewtest teststat =  2.785 pvalue = 0.0054
+    >>> print 'normal kurtosistest teststat = %6.3f pvalue = %6.4f' % stats.kurtosistest(x)
+    normal kurtosistest teststat =  4.757 pvalue = 0.0000
+
+These two tests are combined in the normality test
+
+    >>> print 'normaltest teststat = %6.3f pvalue = %6.4f' % stats.normaltest(x)
+    normaltest teststat = 30.379 pvalue = 0.0000
+
+In all three tests the p-values are very low and we can reject the hypothesis
+that the our sample has skew and kurtosis of the normal distribution.
+
+Since skew and kurtosis of our sample are based on central moments, we get
+exactly the same results if we test the standardized sample:
+
+    >>> print 'normaltest teststat = %6.3f pvalue = %6.4f' % \
+    ...                      stats.normaltest((x-x.mean())/x.std())
+    normaltest teststat = 30.379 pvalue = 0.0000
+
+Because normality is rejected so strongly, we can check whether the
+normaltest gives reasonable results for other cases:
+
+    >>> print 'normaltest teststat = %6.3f pvalue = %6.4f' % stats.normaltest(stats.t.rvs(10, size=100))
+    normaltest teststat =  4.698 pvalue = 0.0955
+    >>> print 'normaltest teststat = %6.3f pvalue = %6.4f' % stats.normaltest(stats.norm.rvs(size=1000))
+    normaltest teststat =  0.613 pvalue = 0.7361
+
+When testing for normality of a small sample of t-distributed observations
+and a large sample of normal distributed observation, then in neither case
+can we reject the null hypothesis that the sample comes from a normal
+distribution. In the first case this is because the test is not powerful
+enough to distinguish a t and a normally distributed random variable in a
+small sample.
+
+
+Comparing two samples
+---------------------
+
+In the following, we are given two samples, which can come either from the
+same or from different distribution, and we want to test whether these
+samples have the same statistical properties.
+
+Comparing means
+^^^^^^^^^^^^^^^
+
+Test with sample with identical means:
+
+    >>> rvs1 = stats.norm.rvs(loc=5, scale=10, size=500)
+    >>> rvs2 = stats.norm.rvs(loc=5, scale=10, size=500)
+    >>> stats.ttest_ind(rvs1, rvs2)
+    (-0.54890361750888583, 0.5831943748663857)
+
+
+Test with sample with different means:
+
+    >>> rvs3 = stats.norm.rvs(loc=8, scale=10, size=500)
+    >>> stats.ttest_ind(rvs1, rvs3)
+    (-4.5334142901750321, 6.507128186505895e-006)
+
+
+
+Kolmogorov-Smirnov test for two samples ks_2samp
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+For the example where both samples are drawn from the same distribution,
+we cannot reject the null hypothesis since the pvalue is high
+
+    >>> stats.ks_2samp(rvs1, rvs2)
+    (0.025999999999999995, 0.99541195173064878)
+
+In the second example, with different location, i.e. means, we can
+reject the null hypothesis since the pvalue is below 1%
+
+    >>> stats.ks_2samp(rvs1, rvs3)
+    (0.11399999999999999, 0.0027132103661283141)

pythonPackages/scipy-0.8.0/doc/source/tutorial/stats/discrete.rst

@@ -0,0 +1,690 @@
+.. _discrete-random-variables:
+
+
+==================================
+Discrete Statistical Distributions
+==================================
+
+Discrete random variables take on only a countable number of values.
+The commonly used distributions are included in SciPy and described in
+this document. Each discrete distribution can take one extra integer
+parameter: :math:`L.` The relationship between the general distribution
+:math:`p` and the standard distribution :math:`p_{0}` is
+
+.. math::
+   :nowrap:
+
+    \[ p\left(x\right)=p_{0}\left(x-L\right)\]
+
+which allows for shifting of the input. When a distribution generator
+is initialized, the discrete distribution can either specify the
+beginning and ending (integer) values :math:`a` and :math:`b` which must be such that
+
+.. math::
+   :nowrap:
+
+    \[ p_{0}\left(x\right)=0\quad x<a\textrm{ or }x>b\]
+
+in which case, it is assumed that the pdf function is specified on the
+integers :math:`a+mk\leq b` where :math:`k` is a non-negative integer ( :math:`0,1,2,\ldots` ) and :math:`m` is a positive integer multiplier. Alternatively, the two lists :math:`x_{k}` and :math:`p\left(x_{k}\right)` can be provided directly in which case a dictionary is set up
+internally to evaulate probabilities and generate random variates.
+
+
+Probability Mass Function (PMF)
+-------------------------------
+
+The probability mass function of a random variable X is defined as the
+probability that the random variable takes on a particular value.
+
+.. math::
+   :nowrap:
+
+    \[ p\left(x_{k}\right)=P\left[X=x_{k}\right]\]
+
+This is also sometimes called the probability density function,
+although technically
+
+.. math::
+   :nowrap:
+
+    \[ f\left(x\right)=\sum_{k}p\left(x_{k}\right)\delta\left(x-x_{k}\right)\]
+
+is the probability density function for a discrete distribution [#]_ .
+
+
+
+.. [#]
+    XXX: Unknown layout Plain Layout: Note that we will be using :math:`p` to represent the probability mass function and a parameter (a
+    XXX: probability). The usage should be obvious from context.
+
+
+
+Cumulative Distribution Function (CDF)
+--------------------------------------
+
+The cumulative distribution function is
+
+.. math::
+   :nowrap:
+
+    \[ F\left(x\right)=P\left[X\leq x\right]=\sum_{x_{k}\leq x}p\left(x_{k}\right)\]
+
+and is also useful to be able to compute. Note that
+
+.. math::
+   :nowrap:
+
+    \[ F\left(x_{k}\right)-F\left(x_{k-1}\right)=p\left(x_{k}\right)\]
+
+
+
+
+Survival Function
+-----------------
+
+The survival function is just
+
+.. math::
+   :nowrap:
+
+    \[ S\left(x\right)=1-F\left(x\right)=P\left[X>k\right]\]
+
+the probability that the random variable is strictly larger than :math:`k` .
+
+
+Percent Point Function (Inverse CDF)
+------------------------------------
+
+The percent point function is the inverse of the cumulative
+distribution function and is
+
+.. math::
+   :nowrap:
+
+    \[ G\left(q\right)=F^{-1}\left(q\right)\]
+
+for discrete distributions, this must be modified for cases where
+there is no :math:`x_{k}` such that :math:`F\left(x_{k}\right)=q.` In these cases we choose :math:`G\left(q\right)` to be the smallest value :math:`x_{k}=G\left(q\right)` for which :math:`F\left(x_{k}\right)\geq q` . If :math:`q=0` then we define :math:`G\left(0\right)=a-1` . This definition allows random variates to be defined in the same way
+as with continuous rv's using the inverse cdf on a uniform
+distribution to generate random variates.
+
+
+Inverse survival function
+-------------------------
+
+The inverse survival function is the inverse of the survival function
+
+.. math::
+   :nowrap:
+
+    \[ Z\left(\alpha\right)=S^{-1}\left(\alpha\right)=G\left(1-\alpha\right)\]
+
+and is thus the smallest non-negative integer :math:`k` for which :math:`F\left(k\right)\geq1-\alpha` or the smallest non-negative integer :math:`k` for which :math:`S\left(k\right)\leq\alpha.`
+
+
+Hazard functions
+----------------
+
+If desired, the hazard function and the cumulative hazard function
+could be defined as
+
+.. math::
+   :nowrap:
+
+    \[ h\left(x_{k}\right)=\frac{p\left(x_{k}\right)}{1-F\left(x_{k}\right)}\]
+
+and
+
+.. math::
+   :nowrap:
+
+    \[ H\left(x\right)=\sum_{x_{k}\leq x}h\left(x_{k}\right)=\sum_{x_{k}\leq x}\frac{F\left(x_{k}\right)-F\left(x_{k-1}\right)}{1-F\left(x_{k}\right)}.\]
+
+
+
+
+Moments
+-------
+
+Non-central moments are defined using the PDF
+
+.. math::
+   :nowrap:
+
+    \[ \mu_{m}^{\prime}=E\left[X^{m}\right]=\sum_{k}x_{k}^{m}p\left(x_{k}\right).\]
+
+Central moments are computed similarly :math:`\mu=\mu_{1}^{\prime}`
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \mu_{m}=E\left[\left(X-\mu\right)^{m}\right] & = & \sum_{k}\left(x_{k}-\mu\right)^{m}p\left(x_{k}\right)\\  & = & \sum_{k=0}^{m}\left(-1\right)^{m-k}\left(\begin{array}{c} m\\ k\end{array}\right)\mu^{m-k}\mu_{k}^{\prime}\end{eqnarray*}
+
+The mean is the first moment
+
+.. math::
+   :nowrap:
+
+    \[ \mu=\mu_{1}^{\prime}=E\left[X\right]=\sum_{k}x_{k}p\left(x_{k}\right)\]
+
+the variance is the second central moment
+
+.. math::
+   :nowrap:
+
+    \[ \mu_{2}=E\left[\left(X-\mu\right)^{2}\right]=\sum_{x_{k}}x_{k}^{2}p\left(x_{k}\right)-\mu^{2}.\]
+
+Skewness is defined as
+
+.. math::
+   :nowrap:
+
+    \[ \gamma_{1}=\frac{\mu_{3}}{\mu_{2}^{3/2}}\]
+
+while (Fisher) kurtosis is
+
+.. math::
+   :nowrap:
+
+    \[ \gamma_{2}=\frac{\mu_{4}}{\mu_{2}^{2}}-3,\]
+
+so that a normal distribution has a kurtosis of zero.
+
+
+Moment generating function
+--------------------------
+
+The moment generating funtion is defined as
+
+.. math::
+   :nowrap:
+
+    \[ M_{X}\left(t\right)=E\left[e^{Xt}\right]=\sum_{x_{k}}e^{x_{k}t}p\left(x_{k}\right)\]
+
+Moments are found as the derivatives of the moment generating function
+evaluated at :math:`0.`
+
+
+Fitting data
+------------
+
+To fit data to a distribution, maximizing the likelihood function is
+common. Alternatively, some distributions have well-known minimum
+variance unbiased estimators. These will be chosen by default, but the
+likelihood function will always be available for minimizing.
+
+If :math:`f_{i}\left(k;\boldsymbol{\theta}\right)` is the PDF of a random-variable where :math:`\boldsymbol{\theta}` is a vector of parameters ( *e.g.* :math:`L` and :math:`S` ), then for a collection of :math:`N` independent samples from this distribution, the joint distribution the
+random vector :math:`\mathbf{k}` is
+
+.. math::
+   :nowrap:
+
+    \[ f\left(\mathbf{k};\boldsymbol{\theta}\right)=\prod_{i=1}^{N}f_{i}\left(k_{i};\boldsymbol{\theta}\right).\]
+
+The maximum likelihood estimate of the parameters :math:`\boldsymbol{\theta}` are the parameters which maximize this function with :math:`\mathbf{x}` fixed and given by the data:
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \hat{\boldsymbol{\theta}} & = & \arg\max_{\boldsymbol{\theta}}f\left(\mathbf{k};\boldsymbol{\theta}\right)\\  & = & \arg\min_{\boldsymbol{\theta}}l_{\mathbf{k}}\left(\boldsymbol{\theta}\right).\end{eqnarray*}
+
+Where
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} l_{\mathbf{k}}\left(\boldsymbol{\theta}\right) & = & -\sum_{i=1}^{N}\log f\left(k_{i};\boldsymbol{\theta}\right)\\  & = & -N\overline{\log f\left(k_{i};\boldsymbol{\theta}\right)}\end{eqnarray*}
+
+
+
+
+Standard notation for mean
+--------------------------
+
+We will use
+
+.. math::
+   :nowrap:
+
+    \[ \overline{y\left(\mathbf{x}\right)}=\frac{1}{N}\sum_{i=1}^{N}y\left(x_{i}\right)\]
+
+where :math:`N` should be clear from context.
+
+
+Combinations
+------------
+
+Note that
+
+.. math::
+   :nowrap:
+
+    \[ k!=k\cdot\left(k-1\right)\cdot\left(k-2\right)\cdot\cdots\cdot1=\Gamma\left(k+1\right)\]
+
+and has special cases of
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} 0! & \equiv & 1\\ k! & \equiv & 0\quad k<0\end{eqnarray*}
+
+and
+
+.. math::
+   :nowrap:
+
+    \[ \left(\begin{array}{c} n\\ k\end{array}\right)=\frac{n!}{\left(n-k\right)!k!}.\]
+
+If :math:`n<0` or :math:`k<0` or :math:`k>n` we define :math:`\left(\begin{array}{c} n\\ k\end{array}\right)=0`
+
+
+Bernoulli
+=========
+
+A Bernoulli random variable of parameter :math:`p` takes one of only two values :math:`X=0` or :math:`X=1` . The probability of success ( :math:`X=1` ) is :math:`p` , and the probability of failure ( :math:`X=0` ) is :math:`1-p.` It can be thought of as a binomial random variable with :math:`n=1` . The PMF is :math:`p\left(k\right)=0` for :math:`k\neq0,1` and
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} p\left(k;p\right) & = & \begin{cases} 1-p & k=0\\ p & k=1\end{cases}\\ F\left(x;p\right) & = & \begin{cases} 0 & x<0\\ 1-p & 0\le x<1\\ 1 & 1\leq x\end{cases}\\ G\left(q;p\right) & = & \begin{cases} 0 & 0\leq q<1-p\\ 1 & 1-p\leq q\leq1\end{cases}\\ \mu & = & p\\ \mu_{2} & = & p\left(1-p\right)\\ \gamma_{3} & = & \frac{1-2p}{\sqrt{p\left(1-p\right)}}\\ \gamma_{4} & = & \frac{1-6p\left(1-p\right)}{p\left(1-p\right)}\end{eqnarray*}
+
+
+
+
+
+.. math::
+   :nowrap:
+
+    \[ M\left(t\right)=1-p\left(1-e^{t}\right)\]
+
+
+
+
+
+.. math::
+   :nowrap:
+
+    \[ \mu_{m}^{\prime}=p\]
+
+
+
+
+
+.. math::
+   :nowrap:
+
+    \[ h\left[X\right]=p\log p+\left(1-p\right)\log\left(1-p\right)\]
+
+
+
+
+Binomial
+========
+
+A binomial random variable with parameters :math:`\left(n,p\right)` can be described as the sum of :math:`n` independent Bernoulli random variables of parameter :math:`p;`
+
+.. math::
+   :nowrap:
+
+    \[ Y=\sum_{i=1}^{n}X_{i}.\]
+
+Therefore, this random variable counts the number of successes in :math:`n` independent trials of a random experiment where the probability of
+success is :math:`p.`
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} p\left(k;n,p\right) & = & \left(\begin{array}{c} n\\ k\end{array}\right)p^{k}\left(1-p\right)^{n-k}\,\, k\in\left\{ 0,1,\ldots n\right\} ,\\ F\left(x;n,p\right) & = & \sum_{k\leq x}\left(\begin{array}{c} n\\ k\end{array}\right)p^{k}\left(1-p\right)^{n-k}=I_{1-p}\left(n-\left\lfloor x\right\rfloor ,\left\lfloor x\right\rfloor +1\right)\quad x\geq0\end{eqnarray*}
+
+where the incomplete beta integral is
+
+.. math::
+   :nowrap:
+
+    \[ I_{x}\left(a,b\right)=\frac{\Gamma\left(a+b\right)}{\Gamma\left(a\right)\Gamma\left(b\right)}\int_{0}^{x}t^{a-1}\left(1-t\right)^{b-1}dt.\]
+
+Now
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \mu & = & np\\ \mu_{2} & = & np\left(1-p\right)\\ \gamma_{1} & = & \frac{1-2p}{\sqrt{np\left(1-p\right)}}\\ \gamma_{2} & = & \frac{1-6p\left(1-p\right)}{np\left(1-p\right)}.\end{eqnarray*}
+
+
+
+.. math::
+   :nowrap:
+
+    \[ M\left(t\right)=\left[1-p\left(1-e^{t}\right)\right]^{n}\]
+
+
+
+
+Boltzmann (truncated Planck)
+============================
+
+
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} p\left(k;N,\lambda\right) & = & \frac{1-e^{-\lambda}}{1-e^{-\lambda N}}\exp\left(-\lambda k\right)\quad k\in\left\{ 0,1,\ldots,N-1\right\} \\ F\left(x;N,\lambda\right) & = & \left\{ \begin{array}{cc} 0 & x<0\\ \frac{1-\exp\left[-\lambda\left(\left\lfloor x\right\rfloor +1\right)\right]}{1-\exp\left(-\lambda N\right)} & 0\leq x\leq N-1\\ 1 & x\geq N-1\end{array}\right.\\ G\left(q,\lambda\right) & = & \left\lceil -\frac{1}{\lambda}\log\left[1-q\left(1-e^{-\lambda N}\right)\right]-1\right\rceil \end{eqnarray*}
+
+Define :math:`z=e^{-\lambda}`
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \mu & = & \frac{z}{1-z}-\frac{Nz^{N}}{1-z^{N}}\\ \mu_{2} & = & \frac{z}{\left(1-z\right)^{2}}-\frac{N^{2}z^{N}}{\left(1-z^{N}\right)^{2}}\\ \gamma_{1} & = & \frac{z\left(1+z\right)\left(\frac{1-z^{N}}{1-z}\right)^{3}-N^{3}z^{N}\left(1+z^{N}\right)}{\left[z\left(\frac{1-z^{N}}{1-z}\right)^{2}-N^{2}z^{N}\right]^{3/2}}\\ \gamma_{2} & = & \frac{z\left(1+4z+z^{2}\right)\left(\frac{1-z^{N}}{1-z}\right)^{4}-N^{4}z^{N}\left(1+4z^{N}+z^{2N}\right)}{\left[z\left(\frac{1-z^{N}}{1-z}\right)^{2}-N^{2}z^{N}\right]^{2}}\end{eqnarray*}
+
+
+
+.. math::
+   :nowrap:
+
+    \[ M\left(t\right)=\frac{1-e^{N\left(t-\lambda\right)}}{1-e^{t-\lambda}}\frac{1-e^{-\lambda}}{1-e^{-\lambda N}}\]
+
+
+
+
+Planck (discrete exponential)
+=============================
+
+Named Planck because of its relationship to the black-body problem he
+solved.
+
+
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} p\left(k;\lambda\right) & = & \left(1-e^{-\lambda}\right)e^{-\lambda k}\quad k\lambda\geq0\\ F\left(x;\lambda\right) & = & 1-e^{-\lambda\left(\left\lfloor x\right\rfloor +1\right)}\quad x\lambda\geq0\\ G\left(q;\lambda\right) & = & \left\lceil -\frac{1}{\lambda}\log\left[1-q\right]-1\right\rceil .\end{eqnarray*}
+
+
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \mu & = & \frac{1}{e^{\lambda}-1}\\ \mu_{2} & = & \frac{e^{-\lambda}}{\left(1-e^{-\lambda}\right)^{2}}\\ \gamma_{1} & = & 2\cosh\left(\frac{\lambda}{2}\right)\\ \gamma_{2} & = & 4+2\cosh\left(\lambda\right)\end{eqnarray*}
+
+
+
+
+
+.. math::
+   :nowrap:
+
+    \[ M\left(t\right)=\frac{1-e^{-\lambda}}{1-e^{t-\lambda}}\]
+
+
+
+.. math::
+   :nowrap:
+
+    \[ h\left[X\right]=\frac{\lambda e^{-\lambda}}{1-e^{-\lambda}}-\log\left(1-e^{-\lambda}\right)\]
+
+
+
+
+Poisson
+=======
+
+The Poisson random variable counts the number of successes in :math:`n` independent Bernoulli trials in the limit as :math:`n\rightarrow\infty` and :math:`p\rightarrow0` where the probability of success in each trial is :math:`p` and :math:`np=\lambda\geq0` is a constant. It can be used to approximate the Binomial random
+variable or in it's own right to count the number of events that occur
+in the interval :math:`\left[0,t\right]` for a process satisfying certain "sparsity "constraints. The functions are
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} p\left(k;\lambda\right) & = & e^{-\lambda}\frac{\lambda^{k}}{k!}\quad k\geq0,\\ F\left(x;\lambda\right) & = & \sum_{n=0}^{\left\lfloor x\right\rfloor }e^{-\lambda}\frac{\lambda^{n}}{n!}=\frac{1}{\Gamma\left(\left\lfloor x\right\rfloor +1\right)}\int_{\lambda}^{\infty}t^{\left\lfloor x\right\rfloor }e^{-t}dt,\\ \mu & = & \lambda\\ \mu_{2} & = & \lambda\\ \gamma_{1} & = & \frac{1}{\sqrt{\lambda}}\\ \gamma_{2} & = & \frac{1}{\lambda}.\end{eqnarray*}
+
+
+
+
+
+.. math::
+   :nowrap:
+
+    \[ M\left(t\right)=\exp\left[\lambda\left(e^{t}-1\right)\right].\]
+
+
+
+
+Geometric
+=========
+
+The geometric random variable with parameter :math:`p\in\left(0,1\right)` can be defined as the number of trials required to obtain a success
+where the probability of success on each trial is :math:`p` . Thus,
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} p\left(k;p\right) & = & \left(1-p\right)^{k-1}p\quad k\geq1\\ F\left(x;p\right) & = & 1-\left(1-p\right)^{\left\lfloor x\right\rfloor }\quad x\geq1\\ G\left(q;p\right) & = & \left\lceil \frac{\log\left(1-q\right)}{\log\left(1-p\right)}\right\rceil \\ \mu & = & \frac{1}{p}\\ \mu_{2} & = & \frac{1-p}{p^{2}}\\ \gamma_{1} & = & \frac{2-p}{\sqrt{1-p}}\\ \gamma_{2} & = & \frac{p^{2}-6p+6}{1-p}.\end{eqnarray*}
+
+
+
+
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} M\left(t\right) & = & \frac{p}{e^{-t}-\left(1-p\right)}\end{eqnarray*}
+
+
+
+
+Negative Binomial
+=================
+
+The negative binomial random variable with parameters :math:`n` and :math:`p\in\left(0,1\right)` can be defined as the number of *extra* independent trials (beyond :math:`n` ) required to accumulate a total of :math:`n` successes where the probability of a success on each trial is :math:`p.` Equivalently, this random variable is the number of failures
+encoutered while accumulating :math:`n` successes during independent trials of an experiment that succeeds
+with probability :math:`p.` Thus,
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} p\left(k;n,p\right) & = & \left(\begin{array}{c} k+n-1\\ n-1\end{array}\right)p^{n}\left(1-p\right)^{k}\quad k\geq0\\ F\left(x;n,p\right) & = & \sum_{i=0}^{\left\lfloor x\right\rfloor }\left(\begin{array}{c} i+n-1\\ i\end{array}\right)p^{n}\left(1-p\right)^{i}\quad x\geq0\\  & = & I_{p}\left(n,\left\lfloor x\right\rfloor +1\right)\quad x\geq0\\ \mu & = & n\frac{1-p}{p}\\ \mu_{2} & = & n\frac{1-p}{p^{2}}\\ \gamma_{1} & = & \frac{2-p}{\sqrt{n\left(1-p\right)}}\\ \gamma_{2} & = & \frac{p^{2}+6\left(1-p\right)}{n\left(1-p\right)}.\end{eqnarray*}
+
+Recall that :math:`I_{p}\left(a,b\right)` is the incomplete beta integral.
+
+
+Hypergeometric
+==============
+
+The hypergeometric random variable with parameters :math:`\left(M,n,N\right)` counts the number of "good "objects in a sample of size :math:`N` chosen without replacement from a population of :math:`M` objects where :math:`n` is the number of "good "objects in the total population.
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} p\left(k;N,n,M\right) & = & \frac{\left(\begin{array}{c} n\\ k\end{array}\right)\left(\begin{array}{c} M-n\\ N-k\end{array}\right)}{\left(\begin{array}{c} M\\ N\end{array}\right)}\quad N-\left(M-n\right)\leq k\leq\min\left(n,N\right)\\ F\left(x;N,n,M\right) & = & \sum_{k=0}^{\left\lfloor x\right\rfloor }\frac{\left(\begin{array}{c} m\\ k\end{array}\right)\left(\begin{array}{c} N-m\\ n-k\end{array}\right)}{\left(\begin{array}{c} N\\ n\end{array}\right)},\\ \mu & = & \frac{nN}{M}\\ \mu_{2} & = & \frac{nN\left(M-n\right)\left(M-N\right)}{M^{2}\left(M-1\right)}\\ \gamma_{1} & = & \frac{\left(M-2n\right)\left(M-2N\right)}{M-2}\sqrt{\frac{M-1}{nN\left(M-m\right)\left(M-n\right)}}\\ \gamma_{2} & = & \frac{g\left(N,n,M\right)}{nN\left(M-n\right)\left(M-3\right)\left(M-2\right)\left(N-M\right)}\end{eqnarray*}
+
+where (defining :math:`m=M-n` )
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} g\left(N,n,M\right) & = & m^{3}-m^{5}+3m^{2}n-6m^{3}n+m^{4}n+3mn^{2}\\  &  & -12m^{2}n^{2}+8m^{3}n^{2}+n^{3}-6mn^{3}+8m^{2}n^{3}\\  &  & +mn^{4}-n^{5}-6m^{3}N+6m^{4}N+18m^{2}nN\\  &  & -6m^{3}nN+18mn^{2}N-24m^{2}n^{2}N-6n^{3}N\\  &  & -6mn^{3}N+6n^{4}N+6m^{2}N^{2}-6m^{3}N^{2}-24mnN^{2}\\  &  & +12m^{2}nN^{2}+6n^{2}N^{2}+12mn^{2}N^{2}-6n^{3}N^{2}.\end{eqnarray*}
+
+
+
+
+Zipf (Zeta)
+===========
+
+A random variable has the zeta distribution (also called the zipf
+distribution) with parameter :math:`\alpha>1` if it's probability mass function is given by
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} p\left(k;\alpha\right) & = & \frac{1}{\zeta\left(\alpha\right)k^{\alpha}}\quad k\geq1\end{eqnarray*}
+
+where
+
+.. math::
+   :nowrap:
+
+    \[ \zeta\left(\alpha\right)=\sum_{n=1}^{\infty}\frac{1}{n^{\alpha}}\]
+
+is the Riemann zeta function. Other functions of this distribution are
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} F\left(x;\alpha\right) & = & \frac{1}{\zeta\left(\alpha\right)}\sum_{k=1}^{\left\lfloor x\right\rfloor }\frac{1}{k^{\alpha}}\\ \mu & = & \frac{\zeta_{1}}{\zeta_{0}}\quad\alpha>2\\ \mu_{2} & = & \frac{\zeta_{2}\zeta_{0}-\zeta_{1}^{2}}{\zeta_{0}^{2}}\quad\alpha>3\\ \gamma_{1} & = & \frac{\zeta_{3}\zeta_{0}^{2}-3\zeta_{0}\zeta_{1}\zeta_{2}+2\zeta_{1}^{3}}{\left[\zeta_{2}\zeta_{0}-\zeta_{1}^{2}\right]^{3/2}}\quad\alpha>4\\ \gamma_{2} & = & \frac{\zeta_{4}\zeta_{0}^{3}-4\zeta_{3}\zeta_{1}\zeta_{0}^{2}+12\zeta_{2}\zeta_{1}^{2}\zeta_{0}-6\zeta_{1}^{4}-3\zeta_{2}^{2}\zeta_{0}^{2}}{\left(\zeta_{2}\zeta_{0}-\zeta_{1}^{2}\right)^{2}}.\end{eqnarray*}
+
+
+
+
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} M\left(t\right) & = & \frac{\textrm{Li}_{\alpha}\left(e^{t}\right)}{\zeta\left(\alpha\right)}\end{eqnarray*}
+
+where :math:`\zeta_{i}=\zeta\left(\alpha-i\right)` and :math:`\textrm{Li}_{n}\left(z\right)` is the :math:`n^{\textrm{th}}` polylogarithm function of :math:`z` defined as
+
+.. math::
+   :nowrap:
+
+    \[ \textrm{Li}_{n}\left(z\right)\equiv\sum_{k=1}^{\infty}\frac{z^{k}}{k^{n}}\]
+
+
+
+.. math::
+   :nowrap:
+
+    \[ \mu_{n}^{\prime}=\left.M^{\left(n\right)}\left(t\right)\right|_{t=0}=\left.\frac{\textrm{Li}_{\alpha-n}\left(e^{t}\right)}{\zeta\left(a\right)}\right|_{t=0}=\frac{\zeta\left(\alpha-n\right)}{\zeta\left(\alpha\right)}\]
+
+
+
+
+Logarithmic (Log-Series, Series)
+================================
+
+The logarimthic distribution with parameter :math:`p` has a probability mass function with terms proportional to the Taylor
+series expansion of :math:`\log\left(1-p\right)`
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} p\left(k;p\right) & = & -\frac{p^{k}}{k\log\left(1-p\right)}\quad k\geq1\\ F\left(x;p\right) & = & -\frac{1}{\log\left(1-p\right)}\sum_{k=1}^{\left\lfloor x\right\rfloor }\frac{p^{k}}{k}=1+\frac{p^{1+\left\lfloor x\right\rfloor }\Phi\left(p,1,1+\left\lfloor x\right\rfloor \right)}{\log\left(1-p\right)}\end{eqnarray*}
+
+where
+
+.. math::
+   :nowrap:
+
+    \[ \Phi\left(z,s,a\right)=\sum_{k=0}^{\infty}\frac{z^{k}}{\left(a+k\right)^{s}}\]
+
+is the Lerch Transcendent. Also define :math:`r=\log\left(1-p\right)`
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \mu & = & -\frac{p}{\left(1-p\right)r}\\ \mu_{2} & = & -\frac{p\left[p+r\right]}{\left(1-p\right)^{2}r^{2}}\\ \gamma_{1} & = & -\frac{2p^{2}+3pr+\left(1+p\right)r^{2}}{r\left(p+r\right)\sqrt{-p\left(p+r\right)}}r\\ \gamma_{2} & = & -\frac{6p^{3}+12p^{2}r+p\left(4p+7\right)r^{2}+\left(p^{2}+4p+1\right)r^{3}}{p\left(p+r\right)^{2}}.\end{eqnarray*}
+
+
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} M\left(t\right) & = & -\frac{1}{\log\left(1-p\right)}\sum_{k=1}^{\infty}\frac{e^{tk}p^{k}}{k}\\  & = & \frac{\log\left(1-pe^{t}\right)}{\log\left(1-p\right)}\end{eqnarray*}
+
+Thus,
+
+.. math::
+   :nowrap:
+
+    \[ \mu_{n}^{\prime}=\left.M^{\left(n\right)}\left(t\right)\right|_{t=0}=\left.\frac{\textrm{Li}_{1-n}\left(pe^{t}\right)}{\log\left(1-p\right)}\right|_{t=0}=-\frac{\textrm{Li}_{1-n}\left(p\right)}{\log\left(1-p\right)}.\]
+
+
+
+
+Discrete Uniform (randint)
+==========================
+
+The discrete uniform distribution with parameters :math:`\left(a,b\right)` constructs a random variable that has an equal probability of being
+any one of the integers in the half-open range :math:`[a,b).` If :math:`a` is not given it is assumed to be zero and the only parameter is :math:`b.` Therefore,
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} p\left(k;a,b\right) & = & \frac{1}{b-a}\quad a\leq k<b\\ F\left(x;a,b\right) & = & \frac{\left\lfloor x\right\rfloor -a}{b-a}\quad a\leq x\leq b\\ G\left(q;a,b\right) & = & \left\lceil q\left(b-a\right)+a\right\rceil \\ \mu & = & \frac{b+a-1}{2}\\ \mu_{2} & = & \frac{\left(b-a-1\right)\left(b-a+1\right)}{12}\\ \gamma_{1} & = & 0\\ \gamma_{2} & = & -\frac{6}{5}\frac{\left(b-a\right)^{2}+1}{\left(b-a-1\right)\left(b-a+1\right)}.\end{eqnarray*}
+
+
+
+
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} M\left(t\right) & = & \frac{1}{b-a}\sum_{k=a}^{b-1}e^{tk}\\  & = & \frac{e^{bt}-e^{at}}{\left(b-a\right)\left(e^{t}-1\right)}\end{eqnarray*}
+
+
+
+
+Discrete Laplacian
+==================
+
+Defined over all integers for :math:`a>0`
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} p\left(k\right) & = & \tanh\left(\frac{a}{2}\right)e^{-a\left|k\right|},\\ F\left(x\right) & = & \left\{ \begin{array}{cc} \frac{e^{a\left(\left\lfloor x\right\rfloor +1\right)}}{e^{a}+1} & \left\lfloor x\right\rfloor <0,\\ 1-\frac{e^{-a\left\lfloor x\right\rfloor }}{e^{a}+1} & \left\lfloor x\right\rfloor \geq0.\end{array}\right.\\ G\left(q\right) & = & \left\{ \begin{array}{cc} \left\lceil \frac{1}{a}\log\left[q\left(e^{a}+1\right)\right]-1\right\rceil  & q<\frac{1}{1+e^{-a}},\\ \left\lceil -\frac{1}{a}\log\left[\left(1-q\right)\left(1+e^{a}\right)\right]\right\rceil  & q\geq\frac{1}{1+e^{-a}}.\end{array}\right.\end{eqnarray*}
+
+
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} M\left(t\right) & = & \tanh\left(\frac{a}{2}\right)\sum_{k=-\infty}^{\infty}e^{tk}e^{-a\left|k\right|}\\  & = & C\left(1+\sum_{k=1}^{\infty}e^{-\left(t+a\right)k}+\sum_{1}^{\infty}e^{\left(t-a\right)k}\right)\\  & = & \tanh\left(\frac{a}{2}\right)\left(1+\frac{e^{-\left(t+a\right)}}{1-e^{-\left(t+a\right)}}+\frac{e^{t-a}}{1-e^{t-a}}\right)\\  & = & \frac{\tanh\left(\frac{a}{2}\right)\sinh a}{\cosh a-\cosh t}.\end{eqnarray*}
+
+Thus,
+
+.. math::
+   :nowrap:
+
+    \[ \mu_{n}^{\prime}=M^{\left(n\right)}\left(0\right)=\left[1+\left(-1\right)^{n}\right]\textrm{Li}_{-n}\left(e^{-a}\right)\]
+
+where :math:`\textrm{Li}_{-n}\left(z\right)` is the polylogarithm function of order :math:`-n` evaluated at :math:`z.`
+
+.. math::
+   :nowrap:
+
+    \[ h\left[X\right]=-\log\left(\tanh\left(\frac{a}{2}\right)\right)+\frac{a}{\sinh a}\]
+
+
+
+
+Discrete Gaussian*
+==================
+
+Defined for all :math:`\mu` and :math:`\lambda>0` and :math:`k`
+
+.. math::
+   :nowrap:
+
+    \[ p\left(k;\mu,\lambda\right)=\frac{1}{Z\left(\lambda\right)}\exp\left[-\lambda\left(k-\mu\right)^{2}\right]\]
+
+where
+
+.. math::
+   :nowrap:
+
+    \[ Z\left(\lambda\right)=\sum_{k=-\infty}^{\infty}\exp\left[-\lambda k^{2}\right]\]
+
+
+
+.. math::
+   :nowrap:
+
+    \begin{eqnarray*} \mu & = & \mu\\ \mu_{2} & = & -\frac{\partial}{\partial\lambda}\log Z\left(\lambda\right)\\  & = & G\left(\lambda\right)e^{-\lambda}\end{eqnarray*}
+
+where :math:`G\left(0\right)\rightarrow\infty` and :math:`G\left(\infty\right)\rightarrow2` with a minimum less than 2 near :math:`\lambda=1`
+
+.. math::
+   :nowrap:
+
+    \[ G\left(\lambda\right)=\frac{1}{Z\left(\lambda\right)}\sum_{k=-\infty}^{\infty}k^{2}\exp\left[-\lambda\left(k+1\right)\left(k-1\right)\right]\]

pythonPackages/scipy-0.8.0/doc/source/weave.rst

@@ -0,0 +1,19 @@
+======================================
+C/C++ integration (:mod:`scipy.weave`)
+======================================
+
+.. warning::
+
+   This documentation is work-in-progress and unorganized.
+
+.. automodule:: scipy.weave
+   :members:
+
+
+.. autosummary::
+   :toctree: generated/
+
+   inline
+   blitz
+   ext_tools
+   accelerate