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1/*************************************************************************
2 * *
3 * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
4 * All rights reserved. Email: russ@q12.org Web: www.q12.org *
5 * *
6 * This library is free software; you can redistribute it and/or *
7 * modify it under the terms of EITHER: *
8 * (1) The GNU Lesser General Public License as published by the Free *
9 * Software Foundation; either version 2.1 of the License, or (at *
10 * your option) any later version. The text of the GNU Lesser *
11 * General Public License is included with this library in the *
12 * file LICENSE.TXT. *
13 * (2) The BSD-style license that is included with this library in *
14 * the file LICENSE-BSD.TXT. *
15 * *
16 * This library is distributed in the hope that it will be useful, *
17 * but WITHOUT ANY WARRANTY; without even the implied warranty of *
18 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files *
19 * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
20 * *
21 *************************************************************************/
22
23/* optimized and unoptimized vector and matrix functions */
24
25#ifndef _ODE_MATRIX_H_
26#define _ODE_MATRIX_H_
27
28#include <ode/common.h>
29
30
31#ifdef __cplusplus
32extern "C" {
33#endif
34
35
36/* set a vector/matrix of size n to all zeros, or to a specific value. */
37
38ODE_API void dSetZero (dReal *a, int n);
39ODE_API void dSetValue (dReal *a, int n, dReal value);
40
41
42/* get the dot product of two n*1 vectors. if n <= 0 then
43 * zero will be returned (in which case a and b need not be valid).
44 */
45
46ODE_API dReal dDot (const dReal *a, const dReal *b, int n);
47
48
49/* get the dot products of (a0,b), (a1,b), etc and return them in outsum.
50 * all vectors are n*1. if n <= 0 then zeroes will be returned (in which case
51 * the input vectors need not be valid). this function is somewhat faster
52 * than calling dDot() for all of the combinations separately.
53 */
54
55/* NOT INCLUDED in the library for now.
56void dMultidot2 (const dReal *a0, const dReal *a1,
57 const dReal *b, dReal *outsum, int n);
58*/
59
60
61/* matrix multiplication. all matrices are stored in standard row format.
62 * the digit refers to the argument that is transposed:
63 * 0: A = B * C (sizes: A:p*r B:p*q C:q*r)
64 * 1: A = B' * C (sizes: A:p*r B:q*p C:q*r)
65 * 2: A = B * C' (sizes: A:p*r B:p*q C:r*q)
66 * case 1,2 are equivalent to saying that the operation is A=B*C but
67 * B or C are stored in standard column format.
68 */
69
70ODE_API void dMultiply0 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
71ODE_API void dMultiply1 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
72ODE_API void dMultiply2 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
73
74
75/* do an in-place cholesky decomposition on the lower triangle of the n*n
76 * symmetric matrix A (which is stored by rows). the resulting lower triangle
77 * will be such that L*L'=A. return 1 on success and 0 on failure (on failure
78 * the matrix is not positive definite).
79 */
80
81ODE_API int dFactorCholesky (dReal *A, int n);
82
83
84/* solve for x: L*L'*x = b, and put the result back into x.
85 * L is size n*n, b is size n*1. only the lower triangle of L is considered.
86 */
87
88ODE_API void dSolveCholesky (const dReal *L, dReal *b, int n);
89
90
91/* compute the inverse of the n*n positive definite matrix A and put it in
92 * Ainv. this is not especially fast. this returns 1 on success (A was
93 * positive definite) or 0 on failure (not PD).
94 */
95
96ODE_API int dInvertPDMatrix (const dReal *A, dReal *Ainv, int n);
97
98
99/* check whether an n*n matrix A is positive definite, return 1/0 (yes/no).
100 * positive definite means that x'*A*x > 0 for any x. this performs a
101 * cholesky decomposition of A. if the decomposition fails then the matrix
102 * is not positive definite. A is stored by rows. A is not altered.
103 */
104
105ODE_API int dIsPositiveDefinite (const dReal *A, int n);
106
107
108/* factorize a matrix A into L*D*L', where L is lower triangular with ones on
109 * the diagonal, and D is diagonal.
110 * A is an n*n matrix stored by rows, with a leading dimension of n rounded
111 * up to 4. L is written into the strict lower triangle of A (the ones are not
112 * written) and the reciprocal of the diagonal elements of D are written into
113 * d.
114 */
115ODE_API void dFactorLDLT (dReal *A, dReal *d, int n, int nskip);
116
117
118/* solve L*x=b, where L is n*n lower triangular with ones on the diagonal,
119 * and x,b are n*1. b is overwritten with x.
120 * the leading dimension of L is `nskip'.
121 */
122ODE_API void dSolveL1 (const dReal *L, dReal *b, int n, int nskip);
123
124
125/* solve L'*x=b, where L is n*n lower triangular with ones on the diagonal,
126 * and x,b are n*1. b is overwritten with x.
127 * the leading dimension of L is `nskip'.
128 */
129ODE_API void dSolveL1T (const dReal *L, dReal *b, int n, int nskip);
130
131
132/* in matlab syntax: a(1:n) = a(1:n) .* d(1:n) */
133
134ODE_API void dVectorScale (dReal *a, const dReal *d, int n);
135
136
137/* given `L', a n*n lower triangular matrix with ones on the diagonal,
138 * and `d', a n*1 vector of the reciprocal diagonal elements of an n*n matrix
139 * D, solve L*D*L'*x=b where x,b are n*1. x overwrites b.
140 * the leading dimension of L is `nskip'.
141 */
142
143ODE_API void dSolveLDLT (const dReal *L, const dReal *d, dReal *b, int n, int nskip);
144
145
146/* given an L*D*L' factorization of an n*n matrix A, return the updated
147 * factorization L2*D2*L2' of A plus the following "top left" matrix:
148 *
149 * [ b a' ] <-- b is a[0]
150 * [ a 0 ] <-- a is a[1..n-1]
151 *
152 * - L has size n*n, its leading dimension is nskip. L is lower triangular
153 * with ones on the diagonal. only the lower triangle of L is referenced.
154 * - d has size n. d contains the reciprocal diagonal elements of D.
155 * - a has size n.
156 * the result is written into L, except that the left column of L and d[0]
157 * are not actually modified. see ldltaddTL.m for further comments.
158 */
159ODE_API void dLDLTAddTL (dReal *L, dReal *d, const dReal *a, int n, int nskip);
160
161
162/* given an L*D*L' factorization of a permuted matrix A, produce a new
163 * factorization for row and column `r' removed.
164 * - A has size n1*n1, its leading dimension in nskip. A is symmetric and
165 * positive definite. only the lower triangle of A is referenced.
166 * A itself may actually be an array of row pointers.
167 * - L has size n2*n2, its leading dimension in nskip. L is lower triangular
168 * with ones on the diagonal. only the lower triangle of L is referenced.
169 * - d has size n2. d contains the reciprocal diagonal elements of D.
170 * - p is a permutation vector. it contains n2 indexes into A. each index
171 * must be in the range 0..n1-1.
172 * - r is the row/column of L to remove.
173 * the new L will be written within the old L, i.e. will have the same leading
174 * dimension. the last row and column of L, and the last element of d, are
175 * undefined on exit.
176 *
177 * a fast O(n^2) algorithm is used. see ldltremove.m for further comments.
178 */
179ODE_API void dLDLTRemove (dReal **A, const int *p, dReal *L, dReal *d,
180 int n1, int n2, int r, int nskip);
181
182
183/* given an n*n matrix A (with leading dimension nskip), remove the r'th row
184 * and column by moving elements. the new matrix will have the same leading
185 * dimension. the last row and column of A are untouched on exit.
186 */
187ODE_API void dRemoveRowCol (dReal *A, int n, int nskip, int r);
188
189
190#ifdef __cplusplus
191}
192#endif
193
194#endif
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