From f6b8e0eae4374f339487a33e3e4fe5462d5816e1 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?J=C3=B6rg=20Frings-F=C3=BCrst?= <debian@jff-webhosting.net>
Date: Sat, 25 Nov 2017 10:16:00 +0100
Subject: New upstream version 2.0.0

---
 numlib/svd.h | 35 +++++++++++++++++++++++++++++++++--
 1 file changed, 33 insertions(+), 2 deletions(-)
 mode change 100644 => 100755 numlib/svd.h

(limited to 'numlib/svd.h')

diff --git a/numlib/svd.h b/numlib/svd.h
old mode 100644
new mode 100755
index 59b080d..6a89210
--- a/numlib/svd.h
+++ b/numlib/svd.h
@@ -13,13 +13,44 @@
 	extern "C" {
 #endif
 
+/*
+
+	U[] decomposes A[]'s columns into orthogonal, singular vectors.
+	U[]'s columns are vectors that sum to 1.0, i.e. they leave a vectors normal unchanged.
+	The inverse of U[] is its transpose.
+	U[]'s columns corresponding to non-zero W[] are the orthonormal vectors that span
+	the (input) RANGE space. Columns corresponding to zero W[] are zero.
+
+	W[] will return singlular values, i.e. the weighting of the singular vectors.
+	It's inverse is is the reciprical of its elements.
+
+	V[] composes the singular vectors back into A[]'s rows.
+	V[]'s columns and rows are orthonormal.
+	V[]'s columns corresponding to non-zero W[] are the orthonormal vectors that span
+	the (output) RANGE space. 
+	v[]'s columns corresponding to zero W[] are the (output) othonormal vectors that span
+	the NULL space.
+	The inverse of V[] is its transpose.
+
+	To re-form, A = U.W.Vt, i.e. multiply by transpose of V.
+
+	i.e. mult. input vector[m] by U[] converts to [n] compact, orthogonal
+	basis vectors. W then scales them appropiately, setting null space
+	vectors to 0. V[] then transforms from the orthogonal basis vectors
+	to A[]'s output space.
+
+	To reveal NULL space, make sure n >= m, since U[] vectors corrsponding
+	to zero's are set to zero.
+
+*/
+
 /* Compute Singular Value Decomposition of A = U.W.Vt */
 /* Return status value: */
 /* 0 - no error */
 /* 1 - m < n error */
 int svdecomp(
-double **a,		/* A[0..m-1][0..n-1], return U[][] */
-double  *w,		/* return W[0..n-1] */
+double **a,		/* A[0..m-1][0..n-1], return U[0..m-1][0..n-1] */
+double  *w,		/* return W[0..n-1] = singular values */
 double **v,		/* return V[0..n-1][0..n-1] (not transpose!) */
 int      m,		/* Number of equations */
 int      n		/* Number of unknowns */
-- 
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