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<h1>matrix.h</h1><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/*************************************************************************</span>
<a name="l00002"></a>00002 <span class="comment"> * *</span>
<a name="l00003"></a>00003 <span class="comment"> * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *</span>
<a name="l00004"></a>00004 <span class="comment"> * All rights reserved. Email: russ@q12.org Web: www.q12.org *</span>
<a name="l00005"></a>00005 <span class="comment"> * *</span>
<a name="l00006"></a>00006 <span class="comment"> * This library is free software; you can redistribute it and/or *</span>
<a name="l00007"></a>00007 <span class="comment"> * modify it under the terms of EITHER: *</span>
<a name="l00008"></a>00008 <span class="comment"> * (1) The GNU Lesser General Public License as published by the Free *</span>
<a name="l00009"></a>00009 <span class="comment"> * Software Foundation; either version 2.1 of the License, or (at *</span>
<a name="l00010"></a>00010 <span class="comment"> * your option) any later version. The text of the GNU Lesser *</span>
<a name="l00011"></a>00011 <span class="comment"> * General Public License is included with this library in the *</span>
<a name="l00012"></a>00012 <span class="comment"> * file LICENSE.TXT. *</span>
<a name="l00013"></a>00013 <span class="comment"> * (2) The BSD-style license that is included with this library in *</span>
<a name="l00014"></a>00014 <span class="comment"> * the file LICENSE-BSD.TXT. *</span>
<a name="l00015"></a>00015 <span class="comment"> * *</span>
<a name="l00016"></a>00016 <span class="comment"> * This library is distributed in the hope that it will be useful, *</span>
<a name="l00017"></a>00017 <span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of *</span>
<a name="l00018"></a>00018 <span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files *</span>
<a name="l00019"></a>00019 <span class="comment"> * LICENSE.TXT and LICENSE-BSD.TXT for more details. *</span>
<a name="l00020"></a>00020 <span class="comment"> * *</span>
<a name="l00021"></a>00021 <span class="comment"> *************************************************************************/</span>
<a name="l00022"></a>00022
<a name="l00023"></a>00023 <span class="comment">/* optimized and unoptimized vector and matrix functions */</span>
<a name="l00024"></a>00024
<a name="l00025"></a>00025 <span class="preprocessor">#ifndef _ODE_MATRIX_H_</span>
<a name="l00026"></a>00026 <span class="preprocessor"></span><span class="preprocessor">#define _ODE_MATRIX_H_</span>
<a name="l00027"></a>00027 <span class="preprocessor"></span>
<a name="l00028"></a>00028 <span class="preprocessor">#include &lt;ode/common.h&gt;</span>
<a name="l00029"></a>00029
<a name="l00030"></a>00030
<a name="l00031"></a>00031 <span class="preprocessor">#ifdef __cplusplus</span>
<a name="l00032"></a>00032 <span class="preprocessor"></span><span class="keyword">extern</span> <span class="stringliteral">"C"</span> {
<a name="l00033"></a>00033 <span class="preprocessor">#endif</span>
<a name="l00034"></a>00034 <span class="preprocessor"></span>
<a name="l00035"></a>00035
<a name="l00036"></a>00036 <span class="comment">/* set a vector/matrix of size n to all zeros, or to a specific value. */</span>
<a name="l00037"></a>00037
<a name="l00038"></a>00038 ODE_API <span class="keywordtype">void</span> dSetZero (dReal *a, <span class="keywordtype">int</span> n);
<a name="l00039"></a>00039 ODE_API <span class="keywordtype">void</span> dSetValue (dReal *a, <span class="keywordtype">int</span> n, dReal value);
<a name="l00040"></a>00040
<a name="l00041"></a>00041
<a name="l00042"></a>00042 <span class="comment">/* get the dot product of two n*1 vectors. if n &lt;= 0 then</span>
<a name="l00043"></a>00043 <span class="comment"> * zero will be returned (in which case a and b need not be valid).</span>
<a name="l00044"></a>00044 <span class="comment"> */</span>
<a name="l00045"></a>00045
<a name="l00046"></a>00046 ODE_API dReal dDot (<span class="keyword">const</span> dReal *a, <span class="keyword">const</span> dReal *b, <span class="keywordtype">int</span> n);
<a name="l00047"></a>00047
<a name="l00048"></a>00048
<a name="l00049"></a>00049 <span class="comment">/* get the dot products of (a0,b), (a1,b), etc and return them in outsum.</span>
<a name="l00050"></a>00050 <span class="comment"> * all vectors are n*1. if n &lt;= 0 then zeroes will be returned (in which case</span>
<a name="l00051"></a>00051 <span class="comment"> * the input vectors need not be valid). this function is somewhat faster</span>
<a name="l00052"></a>00052 <span class="comment"> * than calling dDot() for all of the combinations separately.</span>
<a name="l00053"></a>00053 <span class="comment"> */</span>
<a name="l00054"></a>00054
<a name="l00055"></a>00055 <span class="comment">/* NOT INCLUDED in the library for now.</span>
<a name="l00056"></a>00056 <span class="comment">void dMultidot2 (const dReal *a0, const dReal *a1,</span>
<a name="l00057"></a>00057 <span class="comment"> const dReal *b, dReal *outsum, int n);</span>
<a name="l00058"></a>00058 <span class="comment">*/</span>
<a name="l00059"></a>00059
<a name="l00060"></a>00060
<a name="l00061"></a>00061 <span class="comment">/* matrix multiplication. all matrices are stored in standard row format.</span>
<a name="l00062"></a>00062 <span class="comment"> * the digit refers to the argument that is transposed:</span>
<a name="l00063"></a>00063 <span class="comment"> * 0: A = B * C (sizes: A:p*r B:p*q C:q*r)</span>
<a name="l00064"></a>00064 <span class="comment"> * 1: A = B' * C (sizes: A:p*r B:q*p C:q*r)</span>
<a name="l00065"></a>00065 <span class="comment"> * 2: A = B * C' (sizes: A:p*r B:p*q C:r*q)</span>
<a name="l00066"></a>00066 <span class="comment"> * case 1,2 are equivalent to saying that the operation is A=B*C but</span>
<a name="l00067"></a>00067 <span class="comment"> * B or C are stored in standard column format.</span>
<a name="l00068"></a>00068 <span class="comment"> */</span>
<a name="l00069"></a>00069
<a name="l00070"></a>00070 ODE_API <span class="keywordtype">void</span> dMultiply0 (dReal *A, <span class="keyword">const</span> dReal *B, <span class="keyword">const</span> dReal *C, <span class="keywordtype">int</span> p,<span class="keywordtype">int</span> q,<span class="keywordtype">int</span> r);
<a name="l00071"></a>00071 ODE_API <span class="keywordtype">void</span> dMultiply1 (dReal *A, <span class="keyword">const</span> dReal *B, <span class="keyword">const</span> dReal *C, <span class="keywordtype">int</span> p,<span class="keywordtype">int</span> q,<span class="keywordtype">int</span> r);
<a name="l00072"></a>00072 ODE_API <span class="keywordtype">void</span> dMultiply2 (dReal *A, <span class="keyword">const</span> dReal *B, <span class="keyword">const</span> dReal *C, <span class="keywordtype">int</span> p,<span class="keywordtype">int</span> q,<span class="keywordtype">int</span> r);
<a name="l00073"></a>00073
<a name="l00074"></a>00074
<a name="l00075"></a>00075 <span class="comment">/* do an in-place cholesky decomposition on the lower triangle of the n*n</span>
<a name="l00076"></a>00076 <span class="comment"> * symmetric matrix A (which is stored by rows). the resulting lower triangle</span>
<a name="l00077"></a>00077 <span class="comment"> * will be such that L*L'=A. return 1 on success and 0 on failure (on failure</span>
<a name="l00078"></a>00078 <span class="comment"> * the matrix is not positive definite).</span>
<a name="l00079"></a>00079 <span class="comment"> */</span>
<a name="l00080"></a>00080
<a name="l00081"></a>00081 ODE_API <span class="keywordtype">int</span> dFactorCholesky (dReal *A, <span class="keywordtype">int</span> n);
<a name="l00082"></a>00082
<a name="l00083"></a>00083
<a name="l00084"></a>00084 <span class="comment">/* solve for x: L*L'*x = b, and put the result back into x.</span>
<a name="l00085"></a>00085 <span class="comment"> * L is size n*n, b is size n*1. only the lower triangle of L is considered.</span>
<a name="l00086"></a>00086 <span class="comment"> */</span>
<a name="l00087"></a>00087
<a name="l00088"></a>00088 ODE_API <span class="keywordtype">void</span> dSolveCholesky (<span class="keyword">const</span> dReal *L, dReal *b, <span class="keywordtype">int</span> n);
<a name="l00089"></a>00089
<a name="l00090"></a>00090
<a name="l00091"></a>00091 <span class="comment">/* compute the inverse of the n*n positive definite matrix A and put it in</span>
<a name="l00092"></a>00092 <span class="comment"> * Ainv. this is not especially fast. this returns 1 on success (A was</span>
<a name="l00093"></a>00093 <span class="comment"> * positive definite) or 0 on failure (not PD).</span>
<a name="l00094"></a>00094 <span class="comment"> */</span>
<a name="l00095"></a>00095
<a name="l00096"></a>00096 ODE_API <span class="keywordtype">int</span> dInvertPDMatrix (<span class="keyword">const</span> dReal *A, dReal *Ainv, <span class="keywordtype">int</span> n);
<a name="l00097"></a>00097
<a name="l00098"></a>00098
<a name="l00099"></a>00099 <span class="comment">/* check whether an n*n matrix A is positive definite, return 1/0 (yes/no).</span>
<a name="l00100"></a>00100 <span class="comment"> * positive definite means that x'*A*x &gt; 0 for any x. this performs a</span>
<a name="l00101"></a>00101 <span class="comment"> * cholesky decomposition of A. if the decomposition fails then the matrix</span>
<a name="l00102"></a>00102 <span class="comment"> * is not positive definite. A is stored by rows. A is not altered.</span>
<a name="l00103"></a>00103 <span class="comment"> */</span>
<a name="l00104"></a>00104
<a name="l00105"></a>00105 ODE_API <span class="keywordtype">int</span> dIsPositiveDefinite (<span class="keyword">const</span> dReal *A, <span class="keywordtype">int</span> n);
<a name="l00106"></a>00106
<a name="l00107"></a>00107
<a name="l00108"></a>00108 <span class="comment">/* factorize a matrix A into L*D*L', where L is lower triangular with ones on</span>
<a name="l00109"></a>00109 <span class="comment"> * the diagonal, and D is diagonal.</span>
<a name="l00110"></a>00110 <span class="comment"> * A is an n*n matrix stored by rows, with a leading dimension of n rounded</span>
<a name="l00111"></a>00111 <span class="comment"> * up to 4. L is written into the strict lower triangle of A (the ones are not</span>
<a name="l00112"></a>00112 <span class="comment"> * written) and the reciprocal of the diagonal elements of D are written into</span>
<a name="l00113"></a>00113 <span class="comment"> * d.</span>
<a name="l00114"></a>00114 <span class="comment"> */</span>
<a name="l00115"></a>00115 ODE_API <span class="keywordtype">void</span> dFactorLDLT (dReal *A, dReal *d, <span class="keywordtype">int</span> n, <span class="keywordtype">int</span> nskip);
<a name="l00116"></a>00116
<a name="l00117"></a>00117
<a name="l00118"></a>00118 <span class="comment">/* solve L*x=b, where L is n*n lower triangular with ones on the diagonal,</span>
<a name="l00119"></a>00119 <span class="comment"> * and x,b are n*1. b is overwritten with x.</span>
<a name="l00120"></a>00120 <span class="comment"> * the leading dimension of L is `nskip'.</span>
<a name="l00121"></a>00121 <span class="comment"> */</span>
<a name="l00122"></a>00122 ODE_API <span class="keywordtype">void</span> dSolveL1 (<span class="keyword">const</span> dReal *L, dReal *b, <span class="keywordtype">int</span> n, <span class="keywordtype">int</span> nskip);
<a name="l00123"></a>00123
<a name="l00124"></a>00124
<a name="l00125"></a>00125 <span class="comment">/* solve L'*x=b, where L is n*n lower triangular with ones on the diagonal,</span>
<a name="l00126"></a>00126 <span class="comment"> * and x,b are n*1. b is overwritten with x.</span>
<a name="l00127"></a>00127 <span class="comment"> * the leading dimension of L is `nskip'.</span>
<a name="l00128"></a>00128 <span class="comment"> */</span>
<a name="l00129"></a>00129 ODE_API <span class="keywordtype">void</span> dSolveL1T (<span class="keyword">const</span> dReal *L, dReal *b, <span class="keywordtype">int</span> n, <span class="keywordtype">int</span> nskip);
<a name="l00130"></a>00130
<a name="l00131"></a>00131
<a name="l00132"></a>00132 <span class="comment">/* in matlab syntax: a(1:n) = a(1:n) .* d(1:n) */</span>
<a name="l00133"></a>00133
<a name="l00134"></a>00134 ODE_API <span class="keywordtype">void</span> dVectorScale (dReal *a, <span class="keyword">const</span> dReal *d, <span class="keywordtype">int</span> n);
<a name="l00135"></a>00135
<a name="l00136"></a>00136
<a name="l00137"></a>00137 <span class="comment">/* given `L', a n*n lower triangular matrix with ones on the diagonal,</span>
<a name="l00138"></a>00138 <span class="comment"> * and `d', a n*1 vector of the reciprocal diagonal elements of an n*n matrix</span>
<a name="l00139"></a>00139 <span class="comment"> * D, solve L*D*L'*x=b where x,b are n*1. x overwrites b.</span>
<a name="l00140"></a>00140 <span class="comment"> * the leading dimension of L is `nskip'.</span>
<a name="l00141"></a>00141 <span class="comment"> */</span>
<a name="l00142"></a>00142
<a name="l00143"></a>00143 ODE_API <span class="keywordtype">void</span> dSolveLDLT (<span class="keyword">const</span> dReal *L, <span class="keyword">const</span> dReal *d, dReal *b, <span class="keywordtype">int</span> n, <span class="keywordtype">int</span> nskip);
<a name="l00144"></a>00144
<a name="l00145"></a>00145
<a name="l00146"></a>00146 <span class="comment">/* given an L*D*L' factorization of an n*n matrix A, return the updated</span>
<a name="l00147"></a>00147 <span class="comment"> * factorization L2*D2*L2' of A plus the following "top left" matrix:</span>
<a name="l00148"></a>00148 <span class="comment"> *</span>
<a name="l00149"></a>00149 <span class="comment"> * [ b a' ] &lt;-- b is a[0]</span>
<a name="l00150"></a>00150 <span class="comment"> * [ a 0 ] &lt;-- a is a[1..n-1]</span>
<a name="l00151"></a>00151 <span class="comment"> *</span>
<a name="l00152"></a>00152 <span class="comment"> * - L has size n*n, its leading dimension is nskip. L is lower triangular</span>
<a name="l00153"></a>00153 <span class="comment"> * with ones on the diagonal. only the lower triangle of L is referenced.</span>
<a name="l00154"></a>00154 <span class="comment"> * - d has size n. d contains the reciprocal diagonal elements of D.</span>
<a name="l00155"></a>00155 <span class="comment"> * - a has size n.</span>
<a name="l00156"></a>00156 <span class="comment"> * the result is written into L, except that the left column of L and d[0]</span>
<a name="l00157"></a>00157 <span class="comment"> * are not actually modified. see ldltaddTL.m for further comments. </span>
<a name="l00158"></a>00158 <span class="comment"> */</span>
<a name="l00159"></a>00159 ODE_API <span class="keywordtype">void</span> dLDLTAddTL (dReal *L, dReal *d, <span class="keyword">const</span> dReal *a, <span class="keywordtype">int</span> n, <span class="keywordtype">int</span> nskip);
<a name="l00160"></a>00160
<a name="l00161"></a>00161
<a name="l00162"></a>00162 <span class="comment">/* given an L*D*L' factorization of a permuted matrix A, produce a new</span>
<a name="l00163"></a>00163 <span class="comment"> * factorization for row and column `r' removed.</span>
<a name="l00164"></a>00164 <span class="comment"> * - A has size n1*n1, its leading dimension in nskip. A is symmetric and</span>
<a name="l00165"></a>00165 <span class="comment"> * positive definite. only the lower triangle of A is referenced.</span>
<a name="l00166"></a>00166 <span class="comment"> * A itself may actually be an array of row pointers.</span>
<a name="l00167"></a>00167 <span class="comment"> * - L has size n2*n2, its leading dimension in nskip. L is lower triangular</span>
<a name="l00168"></a>00168 <span class="comment"> * with ones on the diagonal. only the lower triangle of L is referenced.</span>
<a name="l00169"></a>00169 <span class="comment"> * - d has size n2. d contains the reciprocal diagonal elements of D.</span>
<a name="l00170"></a>00170 <span class="comment"> * - p is a permutation vector. it contains n2 indexes into A. each index</span>
<a name="l00171"></a>00171 <span class="comment"> * must be in the range 0..n1-1.</span>
<a name="l00172"></a>00172 <span class="comment"> * - r is the row/column of L to remove.</span>
<a name="l00173"></a>00173 <span class="comment"> * the new L will be written within the old L, i.e. will have the same leading</span>
<a name="l00174"></a>00174 <span class="comment"> * dimension. the last row and column of L, and the last element of d, are</span>
<a name="l00175"></a>00175 <span class="comment"> * undefined on exit.</span>
<a name="l00176"></a>00176 <span class="comment"> *</span>
<a name="l00177"></a>00177 <span class="comment"> * a fast O(n^2) algorithm is used. see ldltremove.m for further comments.</span>
<a name="l00178"></a>00178 <span class="comment"> */</span>
<a name="l00179"></a>00179 ODE_API <span class="keywordtype">void</span> dLDLTRemove (dReal **A, <span class="keyword">const</span> <span class="keywordtype">int</span> *p, dReal *L, dReal *d,
<a name="l00180"></a>00180 <span class="keywordtype">int</span> n1, <span class="keywordtype">int</span> n2, <span class="keywordtype">int</span> r, <span class="keywordtype">int</span> nskip);
<a name="l00181"></a>00181
<a name="l00182"></a>00182
<a name="l00183"></a>00183 <span class="comment">/* given an n*n matrix A (with leading dimension nskip), remove the r'th row</span>
<a name="l00184"></a>00184 <span class="comment"> * and column by moving elements. the new matrix will have the same leading</span>
<a name="l00185"></a>00185 <span class="comment"> * dimension. the last row and column of A are untouched on exit.</span>
<a name="l00186"></a>00186 <span class="comment"> */</span>
<a name="l00187"></a>00187 ODE_API <span class="keywordtype">void</span> dRemoveRowCol (dReal *A, <span class="keywordtype">int</span> n, <span class="keywordtype">int</span> nskip, <span class="keywordtype">int</span> r);
<a name="l00188"></a>00188
<a name="l00189"></a>00189
<a name="l00190"></a>00190 <span class="preprocessor">#ifdef __cplusplus</span>
<a name="l00191"></a>00191 <span class="preprocessor"></span>}
<a name="l00192"></a>00192 <span class="preprocessor">#endif</span>
<a name="l00193"></a>00193 <span class="preprocessor"></span>
<a name="l00194"></a>00194 <span class="preprocessor">#endif</span>
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