From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 30 Oct 2016 20:27:45 +0000 (-0400)
Subject: Add the condition_number() function to the matrices module.
X-Git-Tag: 0.1.0~111
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=ed86c0467de2f8903d9a18c28fa478412cd9a52e;p=dunshire.git

Add the condition_number() function to the matrices module.
---

diff --git a/dunshire/matrices.py b/dunshire/matrices.py
index 66c2176..2d4bb17 100644
--- a/dunshire/matrices.py
+++ b/dunshire/matrices.py
@@ -5,7 +5,7 @@ class:`cvxopt.base.matrix` class).
 
 from math import sqrt
 from cvxopt import matrix
-from cvxopt.lapack import gees, syevr
+from cvxopt.lapack import gees, gesdd, syevr
 
 from . import options
 
@@ -388,3 +388,57 @@ def vec(mat):
 
     """
     return matrix(mat, (len(mat), 1))
+
+
+def condition_number(mat):
+    """
+    Return the condition number of the given matrix.
+
+    The condition number of a matrix quantifies how hard it is to do
+    numerical computation with that matrix. It is usually defined as
+    the ratio of the norm of the matrix to the norm of its inverse, and
+    therefore depends on the norm used. One way to compute the condition
+    number with respect to the 2-norm is as the ratio of the matrix's
+    largest and smallest singular values. Since we have easy access to
+    those singular values, that is the algorithm we use.
+
+    The larger the condition number is, the worse the matrix is.
+
+    Parameters
+    ----------
+    mat : matrix
+        The matrix whose condition number you want.
+
+    Returns
+    -------
+
+    float
+        The nonnegative condition number of ``mat``.
+
+    Examples
+    --------
+
+    >>> condition_number(identity(1, typecode='d'))
+    1.0
+    >>> condition_number(identity(2, typecode='d'))
+    1.0
+    >>> condition_number(identity(3, typecode='d'))
+    1.0
+
+    >>> A = matrix([[2,1],[1,2]], tc='d')
+    >>> abs(condition_number(A) - 3.0) < options.ABS_TOL
+    True
+
+    >>> A = matrix([[2,1j],[-1j,2]], tc='z')
+    >>> abs(condition_number(A) - 3.0) < options.ABS_TOL
+    True
+
+    """
+    num_eigs = min(mat.size)
+    eigs = matrix(0, (num_eigs,1), tc='d')
+    gesdd(mat, eigs)
+
+    if len(eigs) > 0:
+        return eigs[0]/eigs[-1]
+    else:
+        return 0