octave-nkf: doc/interpreter/linalg.txi annotate

annotate doc/interpreter/linalg.txi @ 19630:0e1f5a750d00

maint: Periodic merge of gui-release to default.

author	John W. Eaton <jwe@octave.org>
date	Tue, 20 Jan 2015 10:24:46 -0500
parents	0f9c5a15c8fa 446c46af4b42
children	4197fc428c7d

rev	line source
17744 d63878346099 maint: Update copyright notices for release. John W. Eaton <jwe@octave.org> parents: 17500 diff changeset	1 @c Copyright (C) 1996-2013 John W. Eaton
7018 fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6993 diff changeset	2 @c
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6993 diff changeset	3 @c This file is part of Octave.
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6993 diff changeset	4 @c
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6993 diff changeset	5 @c Octave is free software; you can redistribute it and/or modify it
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6993 diff changeset	6 @c under the terms of the GNU General Public License as published by the
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6993 diff changeset	7 @c Free Software Foundation; either version 3 of the License, or (at
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6993 diff changeset	8 @c your option) any later version.
19627 446c46af4b42 strip trailing whitespace from most source files John W. Eaton <jwe@octave.org> parents: 18406 diff changeset	9 @c
7018 fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6993 diff changeset	10 @c Octave is distributed in the hope that it will be useful, but WITHOUT
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6993 diff changeset	11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6993 diff changeset	12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6993 diff changeset	13 @c for more details.
19627 446c46af4b42 strip trailing whitespace from most source files John W. Eaton <jwe@octave.org> parents: 18406 diff changeset	14 @c
7018 fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6993 diff changeset	15 @c You should have received a copy of the GNU General Public License
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6993 diff changeset	16 @c along with Octave; see the file COPYING. If not, see
fd42779a8428 [project @ 2007-10-13 00:52:12 by jwe] jwe parents: 6993 diff changeset	17 @c <http://www.gnu.org/licenses/>.
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	18
4167 aae05d51353c [project @ 2002-11-12 02:52:50 by jwe] jwe parents: 3428 diff changeset	19 @node Linear Algebra
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	20 @chapter Linear Algebra
18330 200851c87444 Edits to Manual and indicies Michael Godfrey <michaeldgodfrey@gmail.com> parents: 17744 diff changeset	21 @cindex linear algebra
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	22
18406 a4b4cf4c6ece doc: update linear algebra chapter Michael Godfrey <michaeldgodfrey@gmail.com> parents: 18330 diff changeset	23 This chapter documents the linear algebra functions provided in Octave.
19074 0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 18938 diff changeset	24 Reference material for many of these functions may be found in
0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 18938 diff changeset	25 @nospell{Golub and Van Loan}, @cite{Matrix Computations, 2nd Ed.},
0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 18938 diff changeset	26 Johns Hopkins, 1989, and in the @cite{@sc{lapack} Users' Guide}, SIAM, 1992.
0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 18938 diff changeset	27 The @cite{@sc{lapack} Users' Guide} is available at:
18406 a4b4cf4c6ece doc: update linear algebra chapter Michael Godfrey <michaeldgodfrey@gmail.com> parents: 18330 diff changeset	28 @cite{http://www.netlib.org/lapack/lug/}
a4b4cf4c6ece doc: update linear algebra chapter Michael Godfrey <michaeldgodfrey@gmail.com> parents: 18330 diff changeset	29
18855 e275d15c27b5 doc: Periodic spellcheck of documentation. Rik <rik@octave.org> parents: 18854 diff changeset	30 A common text for engineering courses is @nospell{G. Strang},
e275d15c27b5 doc: Periodic spellcheck of documentation. Rik <rik@octave.org> parents: 18854 diff changeset	31 @cite{Linear Algebra and Its Applications, 4th Edition}. It has become a
19186 0f9c5a15c8fa doc: Periodic grammarcheck of documentation. Rik <rik@octave.org> parents: 19099 diff changeset	32 widespread reference for linear algebra. An alternative is P. Lax
18855 e275d15c27b5 doc: Periodic spellcheck of documentation. Rik <rik@octave.org> parents: 18854 diff changeset	33 @cite{Linear Algebra and Its Applications}, and also is a good choice. It
e275d15c27b5 doc: Periodic spellcheck of documentation. Rik <rik@octave.org> parents: 18854 diff changeset	34 claims to be suitable for high school students with substantial mathematical
e275d15c27b5 doc: Periodic spellcheck of documentation. Rik <rik@octave.org> parents: 18854 diff changeset	35 interests as well as first-year undergraduates.
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	36
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	37 @menu
11255 d682cd6669ac Update info-based documentation menus to include new nodes. Rik <octave@nomad.inbox5.com> parents: 10828 diff changeset	38 * Techniques Used for Linear Algebra::
17152 f2a8592b8fbd doc: Shorten some long subsection names in Manual. Rik <rik@octave.org> parents: 14138 diff changeset	39 * Basic Matrix Functions::
f2a8592b8fbd doc: Shorten some long subsection names in Manual. Rik <rik@octave.org> parents: 14138 diff changeset	40 * Matrix Factorizations::
f2a8592b8fbd doc: Shorten some long subsection names in Manual. Rik <rik@octave.org> parents: 14138 diff changeset	41 * Functions of a Matrix::
8817 03b7f618ab3d include docstrings for new functions in the manual John W. Eaton <jwe@octave.org> parents: 8488 diff changeset	42 * Specialized Solvers::
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	43 @end menu
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	44
11255 d682cd6669ac Update info-based documentation menus to include new nodes. Rik <octave@nomad.inbox5.com> parents: 10828 diff changeset	45 @node Techniques Used for Linear Algebra
d682cd6669ac Update info-based documentation menus to include new nodes. Rik <octave@nomad.inbox5.com> parents: 10828 diff changeset	46 @section Techniques Used for Linear Algebra
18330 200851c87444 Edits to Manual and indicies Michael Godfrey <michaeldgodfrey@gmail.com> parents: 17744 diff changeset	47 @cindex linear algebra, techniques
6531 c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	48
18406 a4b4cf4c6ece doc: update linear algebra chapter Michael Godfrey <michaeldgodfrey@gmail.com> parents: 18330 diff changeset	49 Octave includes a polymorphic solver that selects an appropriate matrix
a4b4cf4c6ece doc: update linear algebra chapter Michael Godfrey <michaeldgodfrey@gmail.com> parents: 18330 diff changeset	50 factorization depending on the properties of the matrix itself.
a4b4cf4c6ece doc: update linear algebra chapter Michael Godfrey <michaeldgodfrey@gmail.com> parents: 18330 diff changeset	51 Generally, the cost of determining the matrix type is small relative to
18854 19a140e93b1f doc: Periodic grammarcheck of documentation. Rik <rik@octave.org> parents: 18406 diff changeset	52 the cost of factorizing the matrix itself. In any case the matrix type
18406 a4b4cf4c6ece doc: update linear algebra chapter Michael Godfrey <michaeldgodfrey@gmail.com> parents: 18330 diff changeset	53 is cached once it is calculated so that it is not re-determined each
a4b4cf4c6ece doc: update linear algebra chapter Michael Godfrey <michaeldgodfrey@gmail.com> parents: 18330 diff changeset	54 time it is used in a linear equation.
6531 c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	55
18406 a4b4cf4c6ece doc: update linear algebra chapter Michael Godfrey <michaeldgodfrey@gmail.com> parents: 18330 diff changeset	56 The selection tree for how the linear equation is solved or a matrix
a4b4cf4c6ece doc: update linear algebra chapter Michael Godfrey <michaeldgodfrey@gmail.com> parents: 18330 diff changeset	57 inverse is formed is given by:
6531 c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	58
c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	59 @enumerate 1
18406 a4b4cf4c6ece doc: update linear algebra chapter Michael Godfrey <michaeldgodfrey@gmail.com> parents: 18330 diff changeset	60 @item If the matrix is upper or lower triangular sparse use a forward or
9209 923c7cb7f13f Simplify TeXinfo files by eliminating redundant @iftex followed by @tex construction. Rik <rdrider0-list@yahoo.com> parents: 9065 diff changeset	61 backward substitution using the @sc{lapack} xTRTRS function, and goto 4.
6531 c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	62
c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	63 @c Permuted triangular matrices currently disabled in the code
c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	64 @c
c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	65 @c @item If the matrix is a upper triangular matrix with column permutations
c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	66 @c or lower triangular matrix with row permutations, perform a forward or
c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	67 @c backward substitution, and goto 5.
c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	68
10828 322f43e0e170 Grammarcheck .txi documentation files. Rik <octave@nomad.inbox5.com> parents: 9709 diff changeset	69 @item If the matrix is square, Hermitian with a real positive diagonal,
11593 1577c6f80926 Use non-breaking spaces between certain adjectives and their nouns in docstrings. Rik <octave@nomad.inbox5.com> parents: 11533 diff changeset	70 attempt Cholesky@tie{}factorization using the @sc{lapack} xPOTRF function.
6531 c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	71
11593 1577c6f80926 Use non-breaking spaces between certain adjectives and their nouns in docstrings. Rik <octave@nomad.inbox5.com> parents: 11533 diff changeset	72 @item If the Cholesky@tie{}factorization failed or the matrix is not
19627 446c46af4b42 strip trailing whitespace from most source files John W. Eaton <jwe@octave.org> parents: 18406 diff changeset	73 Hermitian with a real positive diagonal, and the matrix is square, factorize
9209 923c7cb7f13f Simplify TeXinfo files by eliminating redundant @iftex followed by @tex construction. Rik <rdrider0-list@yahoo.com> parents: 9065 diff changeset	74 using the @sc{lapack} xGETRF function.
6531 c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	75
9065 8207b833557f Cleanup documentation for arith.texi, linalg.texi, nonlin.texi Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	76 @item If the matrix is not square, or any of the previous solvers flags
6531 c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	77 a singular or near singular matrix, find a least squares solution using
9209 923c7cb7f13f Simplify TeXinfo files by eliminating redundant @iftex followed by @tex construction. Rik <rdrider0-list@yahoo.com> parents: 9065 diff changeset	78 the @sc{lapack} xGELSD function.
6531 c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	79 @end enumerate
c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	80
c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	81 The user can force the type of the matrix with the @code{matrix_type}
9065 8207b833557f Cleanup documentation for arith.texi, linalg.texi, nonlin.texi Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	82 function. This overcomes the cost of discovering the type of the matrix.
8347 fa78cb8d8a5c corrections for typos Brian Gough<bjg@network-theory.co.uk> parents: 7984 diff changeset	83 However, it should be noted that identifying the type of the matrix incorrectly
6531 c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	84 will lead to unpredictable results, and so @code{matrix_type} should be
c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	85 used with care.
c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	86
c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	87 It should be noted that the test for whether a matrix is a candidate for
18406 a4b4cf4c6ece doc: update linear algebra chapter Michael Godfrey <michaeldgodfrey@gmail.com> parents: 18330 diff changeset	88 Cholesky@tie{}factorization, performed above, and by the @code{matrix_type}
a4b4cf4c6ece doc: update linear algebra chapter Michael Godfrey <michaeldgodfrey@gmail.com> parents: 18330 diff changeset	89 function, does not make certain that the matrix is
9065 8207b833557f Cleanup documentation for arith.texi, linalg.texi, nonlin.texi Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	90 Hermitian. However, the attempt to factorize the matrix will quickly
18406 a4b4cf4c6ece doc: update linear algebra chapter Michael Godfrey <michaeldgodfrey@gmail.com> parents: 18330 diff changeset	91 detect a non-Hermitian matrix.
6531 c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	92
4167 aae05d51353c [project @ 2002-11-12 02:52:50 by jwe] jwe parents: 3428 diff changeset	93 @node Basic Matrix Functions
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	94 @section Basic Matrix Functions
18330 200851c87444 Edits to Manual and indicies Michael Godfrey <michaeldgodfrey@gmail.com> parents: 17744 diff changeset	95 @cindex matrix functions, basic
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	96
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	97 @DOCSTRING(balance)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	98
18938 9addb5ad9426 bandwidth.m: Add new function. Massimiliano Fasi <massimiliano.fasi@gmail.com> parents: 18855 diff changeset	99 @DOCSTRING(bandwidth)
9addb5ad9426 bandwidth.m: Add new function. Massimiliano Fasi <massimiliano.fasi@gmail.com> parents: 18855 diff changeset	100
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	101 @DOCSTRING(cond)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	102
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	103 @DOCSTRING(det)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	104
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	105 @DOCSTRING(eig)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	106
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	107 @DOCSTRING(givens)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	108
7984 bbaa5d7d0143 Some documentation updates David Bateman <dbateman@free.fr> parents: 7638 diff changeset	109 @DOCSTRING(planerot)
bbaa5d7d0143 Some documentation updates David Bateman <dbateman@free.fr> parents: 7638 diff changeset	110
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	111 @DOCSTRING(inv)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	112
17500 b66f068e4468 linsolve.m: Use Octave coding conventions. Rik <rik@octave.org> parents: 17152 diff changeset	113 @DOCSTRING(linsolve)
b66f068e4468 linsolve.m: Use Octave coding conventions. Rik <rik@octave.org> parents: 17152 diff changeset	114
6531 c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	115 @DOCSTRING(matrix_type)
c2609d0502bb [project @ 2007-04-17 18:17:40 by jwe] jwe parents: 6502 diff changeset	116
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	117 @DOCSTRING(norm)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	118
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	119 @DOCSTRING(null)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	120
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	121 @DOCSTRING(orth)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	122
12509 e742720c5e71 Add mgorth and gmres functions from Octave Forge Carlo de Falco <kingcrimson@tiscali.it> parents: 12188 diff changeset	123 @DOCSTRING(mgorth)
e742720c5e71 Add mgorth and gmres functions from Octave Forge Carlo de Falco <kingcrimson@tiscali.it> parents: 12188 diff changeset	124
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	125 @DOCSTRING(pinv)
18330 200851c87444 Edits to Manual and indicies Michael Godfrey <michaeldgodfrey@gmail.com> parents: 17744 diff changeset	126 @cindex pseudoinverse
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	127
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	128 @DOCSTRING(rank)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	129
7984 bbaa5d7d0143 Some documentation updates David Bateman <dbateman@free.fr> parents: 7638 diff changeset	130 @DOCSTRING(rcond)
bbaa5d7d0143 Some documentation updates David Bateman <dbateman@free.fr> parents: 7638 diff changeset	131
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	132 @DOCSTRING(trace)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	133
6502 6ab0a8767780 [project @ 2007-04-06 03:32:06 by jwe] jwe parents: 5775 diff changeset	134 @DOCSTRING(rref)
6ab0a8767780 [project @ 2007-04-06 03:32:06 by jwe] jwe parents: 5775 diff changeset	135
4167 aae05d51353c [project @ 2002-11-12 02:52:50 by jwe] jwe parents: 3428 diff changeset	136 @node Matrix Factorizations
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	137 @section Matrix Factorizations
18330 200851c87444 Edits to Manual and indicies Michael Godfrey <michaeldgodfrey@gmail.com> parents: 17744 diff changeset	138 @cindex matrix factorizations
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	139
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	140 @DOCSTRING(chol)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	141
6502 6ab0a8767780 [project @ 2007-04-06 03:32:06 by jwe] jwe parents: 5775 diff changeset	142 @DOCSTRING(cholinv)
6ab0a8767780 [project @ 2007-04-06 03:32:06 by jwe] jwe parents: 5775 diff changeset	143
6ab0a8767780 [project @ 2007-04-06 03:32:06 by jwe] jwe parents: 5775 diff changeset	144 @DOCSTRING(chol2inv)
6ab0a8767780 [project @ 2007-04-06 03:32:06 by jwe] jwe parents: 5775 diff changeset	145
7638 2df457529cfa implement expm1 and log1p functions Jaroslav Hajek <highegg@gmail.com> parents: 7072 diff changeset	146 @DOCSTRING(cholupdate)
2df457529cfa implement expm1 and log1p functions Jaroslav Hajek <highegg@gmail.com> parents: 7072 diff changeset	147
8817 03b7f618ab3d include docstrings for new functions in the manual John W. Eaton <jwe@octave.org> parents: 8488 diff changeset	148 @DOCSTRING(cholinsert)
03b7f618ab3d include docstrings for new functions in the manual John W. Eaton <jwe@octave.org> parents: 8488 diff changeset	149
03b7f618ab3d include docstrings for new functions in the manual John W. Eaton <jwe@octave.org> parents: 8488 diff changeset	150 @DOCSTRING(choldelete)
03b7f618ab3d include docstrings for new functions in the manual John W. Eaton <jwe@octave.org> parents: 8488 diff changeset	151
03b7f618ab3d include docstrings for new functions in the manual John W. Eaton <jwe@octave.org> parents: 8488 diff changeset	152 @DOCSTRING(cholshift)
03b7f618ab3d include docstrings for new functions in the manual John W. Eaton <jwe@octave.org> parents: 8488 diff changeset	153
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	154 @DOCSTRING(hess)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	155
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	156 @DOCSTRING(lu)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	157
9709 f8e2e9fdaa8f document luupdate Jaroslav Hajek <highegg@gmail.com> parents: 9209 diff changeset	158 @DOCSTRING(luupdate)
f8e2e9fdaa8f document luupdate Jaroslav Hajek <highegg@gmail.com> parents: 9209 diff changeset	159
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	160 @DOCSTRING(qr)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	161
7638 2df457529cfa implement expm1 and log1p functions Jaroslav Hajek <highegg@gmail.com> parents: 7072 diff changeset	162 @DOCSTRING(qrupdate)
2df457529cfa implement expm1 and log1p functions Jaroslav Hajek <highegg@gmail.com> parents: 7072 diff changeset	163
2df457529cfa implement expm1 and log1p functions Jaroslav Hajek <highegg@gmail.com> parents: 7072 diff changeset	164 @DOCSTRING(qrinsert)
2df457529cfa implement expm1 and log1p functions Jaroslav Hajek <highegg@gmail.com> parents: 7072 diff changeset	165
2df457529cfa implement expm1 and log1p functions Jaroslav Hajek <highegg@gmail.com> parents: 7072 diff changeset	166 @DOCSTRING(qrdelete)
2df457529cfa implement expm1 and log1p functions Jaroslav Hajek <highegg@gmail.com> parents: 7072 diff changeset	167
8817 03b7f618ab3d include docstrings for new functions in the manual John W. Eaton <jwe@octave.org> parents: 8488 diff changeset	168 @DOCSTRING(qrshift)
03b7f618ab3d include docstrings for new functions in the manual John W. Eaton <jwe@octave.org> parents: 8488 diff changeset	169
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	170 @DOCSTRING(qz)
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3294 diff changeset	171
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	172 @DOCSTRING(qzhess)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	173
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	174 @DOCSTRING(schur)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	175
12188 1e206c8713a7 Add function rsf2csf to documentation. Rik <octave@nomad.inbox5.com> parents: 11593 diff changeset	176 @DOCSTRING(rsf2csf)
1e206c8713a7 Add function rsf2csf to documentation. Rik <octave@nomad.inbox5.com> parents: 11593 diff changeset	177
7984 bbaa5d7d0143 Some documentation updates David Bateman <dbateman@free.fr> parents: 7638 diff changeset	178 @DOCSTRING(subspace)
bbaa5d7d0143 Some documentation updates David Bateman <dbateman@free.fr> parents: 7638 diff changeset	179
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	180 @DOCSTRING(svd)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	181
11533 06c80c90a246 Add undocumented function svd_driver to documentation. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	182 @DOCSTRING(svd_driver)
06c80c90a246 Add undocumented function svd_driver to documentation. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	183
5775 ace8d8d26933 [project @ 2006-04-24 19:13:06 by jwe] jwe parents: 4167 diff changeset	184 @c FIXME -- should there be a new section here?
3428 5b77cf82393c [project @ 2000-01-14 02:54:53 by jwe] jwe parents: 3373 diff changeset	185
5b77cf82393c [project @ 2000-01-14 02:54:53 by jwe] jwe parents: 3373 diff changeset	186 @DOCSTRING(housh)
5b77cf82393c [project @ 2000-01-14 02:54:53 by jwe] jwe parents: 3373 diff changeset	187
5b77cf82393c [project @ 2000-01-14 02:54:53 by jwe] jwe parents: 3373 diff changeset	188 @DOCSTRING(krylov)
5b77cf82393c [project @ 2000-01-14 02:54:53 by jwe] jwe parents: 3373 diff changeset	189
4167 aae05d51353c [project @ 2002-11-12 02:52:50 by jwe] jwe parents: 3428 diff changeset	190 @node Functions of a Matrix
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	191 @section Functions of a Matrix
18330 200851c87444 Edits to Manual and indicies Michael Godfrey <michaeldgodfrey@gmail.com> parents: 17744 diff changeset	192 @cindex matrix, functions of
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	193
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	194 @DOCSTRING(expm)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	195
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	196 @DOCSTRING(logm)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	197
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	198 @DOCSTRING(sqrtm)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	199
3373 36405da8e173 [project @ 1999-11-23 20:54:17 by jwe] jwe parents: 3372 diff changeset	200 @DOCSTRING(kron)
3294 bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe] jwe parents: diff changeset	201
12572 dffd30f12752 Add blkmm function to documentation. Rik <octave@nomad.inbox5.com> parents: 12520 diff changeset	202 @DOCSTRING(blkmm)
dffd30f12752 Add blkmm function to documentation. Rik <octave@nomad.inbox5.com> parents: 12520 diff changeset	203
19099 d20c81d3cd21 Deprecate syl, add new function sylvester. Rik <rik@octave.org> parents: 19074 diff changeset	204 @DOCSTRING(sylvester)
8817 03b7f618ab3d include docstrings for new functions in the manual John W. Eaton <jwe@octave.org> parents: 8488 diff changeset	205
03b7f618ab3d include docstrings for new functions in the manual John W. Eaton <jwe@octave.org> parents: 8488 diff changeset	206 @node Specialized Solvers
03b7f618ab3d include docstrings for new functions in the manual John W. Eaton <jwe@octave.org> parents: 8488 diff changeset	207 @section Specialized Solvers
18330 200851c87444 Edits to Manual and indicies Michael Godfrey <michaeldgodfrey@gmail.com> parents: 17744 diff changeset	208 @cindex matrix, specialized solvers
8817 03b7f618ab3d include docstrings for new functions in the manual John W. Eaton <jwe@octave.org> parents: 8488 diff changeset	209
13021 d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: 12572 diff changeset	210 @DOCSTRING(bicg)
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method Carlo de Falco <kingcrimson@tiscali.it> parents: 12572 diff changeset	211
8817 03b7f618ab3d include docstrings for new functions in the manual John W. Eaton <jwe@octave.org> parents: 8488 diff changeset	212 @DOCSTRING(bicgstab)
03b7f618ab3d include docstrings for new functions in the manual John W. Eaton <jwe@octave.org> parents: 8488 diff changeset	213
03b7f618ab3d include docstrings for new functions in the manual John W. Eaton <jwe@octave.org> parents: 8488 diff changeset	214 @DOCSTRING(cgs)
12509 e742720c5e71 Add mgorth and gmres functions from Octave Forge Carlo de Falco <kingcrimson@tiscali.it> parents: 12188 diff changeset	215
e742720c5e71 Add mgorth and gmres functions from Octave Forge Carlo de Falco <kingcrimson@tiscali.it> parents: 12188 diff changeset	216 @DOCSTRING(gmres)
18854 19a140e93b1f doc: Periodic grammarcheck of documentation. Rik <rik@octave.org> parents: 18406 diff changeset	217

Mercurial > octave-nkf

annotate doc/interpreter/linalg.txi @ 19630:0e1f5a750d00