#9011: the numpy SVD decomposition docstring is wrong
------------------------------+---------------------------------------------
Reporter: was | Owner: jason, was
Type: defect | Status: new
Priority: minor | Milestone: sage-4.4.3
Component: linear algebra | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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I decided to actually look at the numpy SVD decomposition in preparation
for my class today, and quickly found that it is wrong.
{{{
sage: import numpy
sage: numpy.linalg.svd?
---
Definition: numpy.linalg.svd(a, full_matrices=1, compute_uv=1)
Docstring:
Singular Value Decomposition.
Factorizes the matrix `a` into two unitary matrices, ``U`` and ``Vh``,
and a 1-dimensional array of singular values, ``s`` (real, non-
negative),
such that ``a == U S Vh``, where ``S`` is the diagonal
matrix ``np.diag(s)``.
----
}}}
The statement that S is the diagonal matrix np.diag(s) is just totally
false if the input matrix a is nonsquare, since S is also non square.
The best fix I could find is to replace np.diag(s) by
{{{
S = numpy.zeros( a )
S[:len(s),:len(s)] = numpy.diag(s)
}}}
Obviously, this should really be reported and patched upstream.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9011>
Sage <http://www.sagemath.org>
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