Mercurial > hg > octave-terminal
changeset 13953:642e43164af6
fix behavior of chol (..., 'lower') to be compatible with matlab
* chol.cc: transpose input matrix prior to factorization when
chol (..., 'lower') is invoked so that only the lower triangular
part is used.
author | Carlo de Falco <kingcrimson@tiscali.it> |
---|---|
date | Mon, 28 Nov 2011 12:39:39 +0100 |
parents | acaf33ccc04f |
children | 2ebbc6c9961b |
files | src/DLD-FUNCTIONS/chol.cc |
diffstat | 1 files changed, 109 insertions(+), 5 deletions(-) [+] |
line wrap: on
line diff
--- a/src/DLD-FUNCTIONS/chol.cc +++ b/src/DLD-FUNCTIONS/chol.cc @@ -61,12 +61,13 @@ } DEFUN_DLD (chol, args, nargout, - "-*- texinfo -*-\n\ +"-*- texinfo -*-\n\ @deftypefn {Loadable Function} {@var{R} =} chol (@var{A})\n\ @deftypefnx {Loadable Function} {[@var{R}, @var{p}] =} chol (@var{A})\n\ @deftypefnx {Loadable Function} {[@var{R}, @var{p}, @var{Q}] =} chol (@var{S})\n\ @deftypefnx {Loadable Function} {[@var{R}, @var{p}, @var{Q}] =} chol (@var{S}, 'vector')\n\ @deftypefnx {Loadable Function} {[@var{L}, @dots{}] =} chol (@dots{}, 'lower')\n\ +@deftypefnx {Loadable Function} {[@var{L}, @dots{}] =} chol (@dots{}, 'upper')\n\ @cindex Cholesky factorization\n\ Compute the Cholesky@tie{}factor, @var{R}, of the symmetric positive definite\n\ matrix @var{A}, where\n\ @@ -128,6 +129,9 @@ \n\ @end ifnottex\n\ \n\ +For full matrices, if the 'lower' flag is set only the lower triangular part of the matrix \ +is used for the factorization, otherwise the upper triangular part is used.\n\ +\n\ In general the lower triangular factorization is significantly faster for\n\ sparse matrices.\n\ @seealso{cholinv, chol2inv}\n\ @@ -155,6 +159,10 @@ if (tmp.compare ("vector") == 0) vecout = true; else if (tmp.compare ("lower") == 0) + // FIXME currently the option "lower" is handled by transposing the + // matrix, factorizing it with the lapack function DPOTRF ('U', ...) + // and finally transposing the factor. It would be more efficient to use + // DPOTRF ('L', ...) in this case. LLt = true; else if (tmp.compare ("upper") == 0) LLt = false; @@ -251,7 +259,13 @@ if (! error_state) { octave_idx_type info; - FloatCHOL fact (m, info); + + FloatCHOL fact; + if (LLt) + fact = FloatCHOL (m.transpose (), info); + else + fact = FloatCHOL (m, info); + if (nargout == 2 || info == 0) { retval(1) = info; @@ -271,7 +285,13 @@ if (! error_state) { octave_idx_type info; - FloatComplexCHOL fact (m, info); + + FloatComplexCHOL fact; + if (LLt) + fact = FloatComplexCHOL (m.transpose (), info); + else + fact = FloatComplexCHOL (m, info); + if (nargout == 2 || info == 0) { retval(1) = info; @@ -296,7 +316,13 @@ if (! error_state) { octave_idx_type info; - CHOL fact (m, info); + + CHOL fact; + if (LLt) + fact = CHOL (m.transpose (), info); + else + fact = CHOL (m, info); + if (nargout == 2 || info == 0) { retval(1) = info; @@ -316,7 +342,13 @@ if (! error_state) { octave_idx_type info; - ComplexCHOL fact (m, info); + + ComplexCHOL fact; + if (LLt) + fact = ComplexCHOL (m.transpose (), info); + else + fact = ComplexCHOL (m, info); + if (nargout == 2 || info == 0) { retval(1) = info; @@ -993,6 +1025,78 @@ %! assert(norm(triu(R1)-R1,Inf) == 0) %! assert(norm(A1(p,p) - single(Ac),Inf) < 2e1*eps('single')) %! + +%!test +%! cu = chol (triu (A), 'upper'); +%! cl = chol (tril (A), 'lower'); +%! assert (cu, cl', eps) +%! +%!test +%! cca = chol (Ac); +%! +%! ccal = chol (Ac, 'lower'); +%! ccal2 = chol (tril (Ac), 'lower'); +%! +%! ccau = chol (Ac, 'upper'); +%! ccau2 = chol (triu (Ac), 'upper'); +%! +%! assert (cca'*cca, Ac, eps) +%! assert (ccau'*ccau, Ac, eps) +%! assert (ccau2'*ccau2, Ac, eps) +%! +%! assert (cca, ccal', eps) +%! assert (cca, ccau, eps) +%! assert (cca, ccal2', eps) +%! assert (cca, ccau2, eps) +%! +%!test +%! cca = chol (single (Ac)); +%! +%! ccal = chol (single (Ac), 'lower'); +%! ccal2 = chol (tril (single (Ac)), 'lower'); +%! +%! ccau = chol (single (Ac), 'upper'); +%! ccau2 = chol (triu (single (Ac)), 'upper'); +%! +%! assert (cca'*cca, single (Ac), eps ('single')) +%! assert (ccau'*ccau, single (Ac), eps ('single')) +%! assert (ccau2'*ccau2, single (Ac), eps ('single')) +%! +%! assert (cca, ccal', eps ('single')) +%! assert (cca, ccau, eps ('single')) +%! assert (cca, ccal2', eps ('single')) +%! assert (cca, ccau2, eps ('single')) + +%!test +%! a = [12, 2, 3, 4; +%! 2, 14, 5, 3; +%! 3, 5, 16, 6; +%! 4, 3, 6, 16]; +%! +%! b = [0, 1, 2, 3; +%! -1, 0, 1, 2; +%! -2, -1, 0, 1; +%! -3, -2, -1, 0]; +%! +%! ca = a + i*b; +%! +%! cca = chol (ca); +%! +%! ccal = chol (ca, 'lower'); +%! ccal2 = chol (tril (ca), 'lower'); +%! +%! ccau = chol (ca, 'upper'); +%! ccau2 = chol (triu (ca), 'upper'); +%! +%! assert (cca'*cca, ca, 16*eps) +%! assert (ccau'*ccau, ca, 16*eps) +%! assert (ccau2'*ccau2, ca, 16*eps) +%! +%! assert (cca, ccal', 16*eps) +%! assert (cca, ccau, 16*eps) +%! assert (cca, ccal2', 16*eps) +%! assert (cca, ccau2, 16*eps) + */ DEFUN_DLD (choldelete, args, ,