From bda2ae28f9d657a04ea5a9aad407dc61284dfb9f Mon Sep 17 00:00:00 2001 From: nicolas Date: Wed, 27 Oct 2010 15:55:15 +0000 Subject: [PATCH] --- magick/resample.c | 21 ++++++++++++--------- 1 file changed, 12 insertions(+), 9 deletions(-) diff --git a/magick/resample.c b/magick/resample.c index 5516c0210..6b98005eb 100644 --- a/magick/resample.c +++ b/magick/resample.c @@ -1387,9 +1387,11 @@ static inline void ClampUpAxes(const double dux, * Jinv = U Sigma V^T * * be an SVD decomposition of Jinv. (The SVD is not unique. The - * final ellipse does not depend on the particular SVD.) In - * principle, what we want is to clamp up the entries of the - * diagonal matrix Sigma so that they are at least 1, and then set + * final ellipse does not depend on the particular SVD. It only + * depends on the hermitian factor of the left polar decomposition, + * which is unique.) In principle, what we want is to clamp up the + * entries of the diagonal matrix Sigma so that they are at least 1, + * and then set * * Jinv = U newSigma V^T. * @@ -1417,12 +1419,13 @@ static inline void ClampUpAxes(const double dux, * implemented it for use with (approximate) Gaussian filtering in * his PDL::Transform code (PDL = Perl Data Language). * - * The only (possibly) new math in the following is the selection of - * the largest row of the eigen matrix system in order to stabilize - * the computation in near rank-deficient cases, and the - * corresponding efficient repair of degenerate cases using the norm - * of this largest row. Omitting the "V^T" factor of the SVD may - * also be a new "trick." + * The only new math in the following is the selection of the + * largest row of the eigen matrix system in order to stabilize the + * computation in near rank-deficient cases, and the corresponding + * efficient repair of degenerate cases using the norm of this + * largest row. Omitting the "V^T" factor of the SVD is also a new + * "trick." It corresponds to moving from the SVD to the left polar + * decomposition. */ const double a = dux; const double b = duy; -- 2.50.1