Mercurial > octave-antonio
annotate doc/interpreter/linalg.txi @ 8347:fa78cb8d8a5c
corrections for typos
Here is a patch with some corrections for typos and missing/extra
words in the manual.
changeset: 8347:34fd1d1c2294
user: Brian Gough <bjg@gnu.org>
date: Wed Nov 26 11:00:15 2008 -0500
summary: [docs] can not => cannot
| author | Brian Gough<bjg@network-theory.co.uk> |
|---|---|
| date | Thu, 27 Nov 2008 10:28:24 +0100 |
| parents | bbaa5d7d0143 |
| children | cdb4788879b3 |
| rev | line source |
|---|---|
| 6778 | 1 @c Copyright (C) 1996, 1997, 2007 John W. Eaton |
| 7018 | 2 @c |
| 3 @c This file is part of Octave. | |
| 4 @c | |
| 5 @c Octave is free software; you can redistribute it and/or modify it | |
| 6 @c under the terms of the GNU General Public License as published by the | |
| 7 @c Free Software Foundation; either version 3 of the License, or (at | |
| 8 @c your option) any later version. | |
| 9 @c | |
| 10 @c Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 13 @c for more details. | |
| 14 @c | |
| 15 @c You should have received a copy of the GNU General Public License | |
| 16 @c along with Octave; see the file COPYING. If not, see | |
| 17 @c <http://www.gnu.org/licenses/>. | |
| 3294 | 18 |
| 4167 | 19 @node Linear Algebra |
| 3294 | 20 @chapter Linear Algebra |
| 21 | |
| 22 This chapter documents the linear algebra functions of Octave. | |
| 23 Reference material for many of these functions may be found in | |
| 24 Golub and Van Loan, @cite{Matrix Computations, 2nd Ed.}, Johns Hopkins, | |
|
8347
fa78cb8d8a5c
corrections for typos
Brian Gough<bjg@network-theory.co.uk>
parents:
7984
diff
changeset
|
25 1989, and in the @cite{@sc{Lapack} Users' Guide}, SIAM, 1992. |
| 3294 | 26 |
| 27 @menu | |
| 6531 | 28 * Techniques used for Linear Algebra:: |
| 3294 | 29 * Basic Matrix Functions:: |
| 30 * Matrix Factorizations:: | |
| 31 * Functions of a Matrix:: | |
| 32 @end menu | |
| 33 | |
| 6531 | 34 @node Techniques used for Linear Algebra |
| 35 @section Techniques used for Linear Algebra | |
| 36 | |
| 37 Octave includes a poly-morphic solver, that selects an appropriate | |
| 38 matrix factorization depending on the properties of the matrix itself. | |
| 39 Generally, the cost of determining the matrix type is small relative to | |
| 40 the cost of factorizing the matrix itself, but in any case the matrix | |
| 41 type is cached once it is calculated, so that it is not re-determined | |
| 42 each time it is used in a linear equation. | |
| 43 | |
| 44 The selection tree for how the linear equation is solve or a matrix | |
| 45 inverse is form is given by | |
| 46 | |
| 47 @enumerate 1 | |
| 48 @item If the matrix is upper or lower triangular sparse a forward or | |
| 6939 | 49 backward substitution using the @sc{Lapack} xTRTRS function, and goto 4. |
| 6531 | 50 |
| 51 @c Permuted triangular matrices currently disabled in the code | |
| 52 @c | |
| 53 @c @item If the matrix is a upper triangular matrix with column permutations | |
| 54 @c or lower triangular matrix with row permutations, perform a forward or | |
| 55 @c backward substitution, and goto 5. | |
| 56 | |
| 57 @item If the matrix is square, hermitian with a real positive diagonal, | |
| 58 attempt Cholesky factorization using the @sc{Lapack} xPOTRF function. | |
| 59 | |
| 60 @item If the Cholesky factorization failed or the matrix is not | |
| 61 hermitian with a real positive diagonal, and the matrix is square, factorize | |
| 62 using the @sc{Lapack} xGETRF function. | |
| 63 | |
| 64 @item If the matrix is not square, or any of the previous solvers flags | |
| 65 a singular or near singular matrix, find a least squares solution using | |
| 7072 | 66 the @sc{Lapack} xGELSD function. |
| 6531 | 67 @end enumerate |
| 68 | |
| 69 The user can force the type of the matrix with the @code{matrix_type} | |
| 70 function. This overcomes the cost of discovering the type of the matrix. | |
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8347
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Brian Gough<bjg@network-theory.co.uk>
parents:
7984
diff
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71 However, it should be noted that identifying the type of the matrix incorrectly |
| 6531 | 72 will lead to unpredictable results, and so @code{matrix_type} should be |
| 73 used with care. | |
| 74 | |
| 75 It should be noted that the test for whether a matrix is a candidate for | |
| 76 Cholesky factorization, performed above and by the @code{matrix_type} | |
| 77 function, does not give a certainty that the matrix is | |
| 78 Hermitian. However, the attempt to factorize the matrix will quickly | |
| 79 flag a non-Hermitian matrix. | |
| 80 | |
| 4167 | 81 @node Basic Matrix Functions |
| 3294 | 82 @section Basic Matrix Functions |
| 83 | |
| 3373 | 84 @DOCSTRING(balance) |
| 3294 | 85 |
| 3373 | 86 @DOCSTRING(cond) |
| 3294 | 87 |
| 3373 | 88 @DOCSTRING(det) |
| 3294 | 89 |
| 3428 | 90 @DOCSTRING(dmult) |
| 91 | |
| 92 @DOCSTRING(dot) | |
| 93 | |
| 3373 | 94 @DOCSTRING(eig) |
| 3294 | 95 |
| 3373 | 96 @DOCSTRING(givens) |
| 3294 | 97 |
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98 @DOCSTRING(planerot) |
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99 |
| 3373 | 100 @DOCSTRING(inv) |
| 3294 | 101 |
| 6531 | 102 @DOCSTRING(matrix_type) |
| 103 | |
| 3373 | 104 @DOCSTRING(norm) |
| 3294 | 105 |
| 3373 | 106 @DOCSTRING(null) |
| 3294 | 107 |
| 3373 | 108 @DOCSTRING(orth) |
| 3294 | 109 |
| 3373 | 110 @DOCSTRING(pinv) |
| 3294 | 111 |
| 3373 | 112 @DOCSTRING(rank) |
| 3294 | 113 |
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114 @DOCSTRING(rcond) |
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115 |
| 3373 | 116 @DOCSTRING(trace) |
| 3294 | 117 |
| 6502 | 118 @DOCSTRING(rref) |
| 119 | |
| 4167 | 120 @node Matrix Factorizations |
| 3294 | 121 @section Matrix Factorizations |
| 122 | |
| 3373 | 123 @DOCSTRING(chol) |
| 3294 | 124 |
| 6502 | 125 @DOCSTRING(cholinv) |
| 126 | |
| 127 @DOCSTRING(chol2inv) | |
| 128 | |
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129 @DOCSTRING(cholupdate) |
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130 |
| 3373 | 131 @DOCSTRING(hess) |
| 3294 | 132 |
| 3373 | 133 @DOCSTRING(lu) |
| 3294 | 134 |
| 3373 | 135 @DOCSTRING(qr) |
| 3294 | 136 |
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137 @DOCSTRING(qrupdate) |
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parents:
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138 |
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139 @DOCSTRING(qrinsert) |
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Jaroslav Hajek <highegg@gmail.com>
parents:
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140 |
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parents:
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141 @DOCSTRING(qrdelete) |
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Jaroslav Hajek <highegg@gmail.com>
parents:
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142 |
| 3373 | 143 @DOCSTRING(qz) |
| 3372 | 144 |
| 3373 | 145 @DOCSTRING(qzhess) |
| 3294 | 146 |
| 3373 | 147 @DOCSTRING(schur) |
| 3294 | 148 |
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149 @DOCSTRING(subspace) |
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150 |
| 3373 | 151 @DOCSTRING(svd) |
| 3294 | 152 |
| 5775 | 153 @c FIXME -- should there be a new section here? |
| 3428 | 154 |
| 155 @DOCSTRING(housh) | |
| 156 | |
| 157 @DOCSTRING(krylov) | |
| 158 | |
| 4167 | 159 @node Functions of a Matrix |
| 3294 | 160 @section Functions of a Matrix |
| 161 | |
| 3373 | 162 @DOCSTRING(expm) |
| 3294 | 163 |
| 3373 | 164 @DOCSTRING(logm) |
| 3294 | 165 |
| 3373 | 166 @DOCSTRING(sqrtm) |
| 3294 | 167 |
| 3373 | 168 @DOCSTRING(kron) |
| 3294 | 169 |
| 3373 | 170 @DOCSTRING(syl) |