[Scipy-svn] r5461 - branches/0.7.x/scipy/special
scipy-svn at scipy.org
scipy-svn at scipy.org
Tue Jan 13 03:34:28 EST 2009
Author: stefan
Date: 2009-01-13 02:34:19 -0600 (Tue, 13 Jan 2009)
New Revision: 5461
Modified:
branches/0.7.x/scipy/special/orthogonal.py
Log:
Backport changes to orthogonal docs.
Modified: branches/0.7.x/scipy/special/orthogonal.py
===================================================================
--- branches/0.7.x/scipy/special/orthogonal.py 2009-01-13 08:32:53 UTC (rev 5460)
+++ branches/0.7.x/scipy/special/orthogonal.py 2009-01-13 08:34:19 UTC (rev 5461)
@@ -1,8 +1,3 @@
-#!/usr/bin/env python
-#
-# Author: Travis Oliphant 2000
-# Updated Sep. 2003 (fixed bugs --- tested to be accurate)
-
"""
A collection of functions to find the weights and abscissas for
Gaussian Quadrature.
@@ -14,30 +9,44 @@
Many recursion relations for orthogonal polynomials are given:
-a1n f_n+1 (x) = (a2n + a3n x ) f_n (x) - a4n f_n-1 (x)
+.. math::
+ a1n f_{n+1} (x) = (a2n + a3n x ) f_n (x) - a4n f_{n-1} (x)
+
The recursion relation of interest is
-P_n+1 (x) = (x - A_n) P_n (x) - B_n P_n-1 (x)
+.. math::
-where P has a different normalization than f.
+ P_{n+1} (x) = (x - A_n) P_n (x) - B_n P_{n-1} (x)
+where :math:`P` has a different normalization than :math:`f`.
+
The coefficients can be found as:
-A_n = -a2n / a3n
+.. math::
-B_n = ( a4n / a3n sqrt(h_n-1 / h_n))**2
+ A_n = -a2n / a3n
+ \\qquad
+ B_n = ( a4n / a3n \\sqrt{h_n-1 / h_n})^2
- where
- h_n = int_a^b w(x) f_n(x)^2
+where
+
+.. math::
+
+ h_n = \\int_a^b w(x) f_n(x)^2
+
assume:
-P_0(x) = 1
-P_-1(x) == 0
+.. math::
+
+ P_0 (x) = 1
+ \\qquad
+ P_{-1} (x) == 0
+
For the mathematical background, see [golub.welsch-1969-mathcomp]_ and
[abramowitz.stegun-1965]_.
-Functions:
+Functions::
gen_roots_and_weights -- Generic roots and weights.
j_roots -- Jacobi
@@ -66,7 +75,11 @@
Mathematical Functions: with Formulas, Graphs, and Mathematical
Tables*. Gaithersburg, MD: National Bureau of Standards.
http://www.math.sfu.ca/~cbm/aands/
+
"""
+#
+# Author: Travis Oliphant 2000
+# Updated Sep. 2003 (fixed bugs --- tested to be accurate)
# Scipy imports.
import numpy as np
More information about the Scipy-svn
mailing list