1 /*************************************************************************
3 * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
4 * All rights reserved. Email: russ@q12.org Web: www.q12.org *
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 *
13 * (2) The BSD-style license that is included with this library in *
14 * the file LICENSE-BSD.TXT. *
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. *
21 *************************************************************************/
23 /* optimized and unoptimized vector and matrix functions */
25 #ifndef _ODE_MATRIX_H_
26 #define _ODE_MATRIX_H_
28 #include <ode/common.h>
36 /* set a vector/matrix of size n to all zeros, or to a specific value. */
38 ODE_API void dSetZero (dReal *a, int n);
39 ODE_API void dSetValue (dReal *a, int n, dReal value);
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).
46 ODE_API dReal dDot (const dReal *a, const dReal *b, int n);
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.
55 /* NOT INCLUDED in the library for now.
56 void dMultidot2 (const dReal *a0, const dReal *a1,
57 const dReal *b, dReal *outsum, int n);
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.
70 ODE_API void dMultiply0 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
71 ODE_API void dMultiply1 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
72 ODE_API void dMultiply2 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
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).
81 ODE_API int dFactorCholesky (dReal *A, int n);
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.
88 ODE_API void dSolveCholesky (const dReal *L, dReal *b, int n);
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).
96 ODE_API int dInvertPDMatrix (const dReal *A, dReal *Ainv, int n);
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.
105 ODE_API int dIsPositiveDefinite (const dReal *A, int n);
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
115 ODE_API void dFactorLDLT (dReal *A, dReal *d, int n, int nskip);
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'.
122 ODE_API void dSolveL1 (const dReal *L, dReal *b, int n, int nskip);
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'.
129 ODE_API void dSolveL1T (const dReal *L, dReal *b, int n, int nskip);
132 /* in matlab syntax: a(1:n) = a(1:n) .* d(1:n) */
134 ODE_API void dVectorScale (dReal *a, const dReal *d, int n);
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'.
143 ODE_API void dSolveLDLT (const dReal *L, const dReal *d, dReal *b, int n, int nskip);
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:
149 * [ b a' ] <-- b is a[0]
150 * [ a 0 ] <-- a is a[1..n-1]
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.
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.
159 ODE_API void dLDLTAddTL (dReal *L, dReal *d, const dReal *a, int n, int nskip);
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
177 * a fast O(n^2) algorithm is used. see ldltremove.m for further comments.
179 ODE_API void dLDLTRemove (dReal **A, const int *p, dReal *L, dReal *d,
180 int n1, int n2, int r, int nskip);
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.
187 ODE_API void dRemoveRowCol (dReal *A, int n, int nskip, int r);
192 void _dSetZero (dReal *a, size_t n);
193 void _dSetValue (dReal *a, size_t n, dReal value);
194 dReal _dDot (const dReal *a, const dReal *b, int n);
195 void _dMultiply0 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
196 void _dMultiply1 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
197 void _dMultiply2 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
198 int _dFactorCholesky (dReal *A, int n, void *tmpbuf);
199 void _dSolveCholesky (const dReal *L, dReal *b, int n, void *tmpbuf);
200 int _dInvertPDMatrix (const dReal *A, dReal *Ainv, int n, void *tmpbuf);
201 int _dIsPositiveDefinite (const dReal *A, int n, void *tmpbuf);
202 void _dFactorLDLT (dReal *A, dReal *d, int n, int nskip);
203 void _dSolveL1 (const dReal *L, dReal *b, int n, int nskip);
204 void _dSolveL1T (const dReal *L, dReal *b, int n, int nskip);
205 void _dVectorScale (dReal *a, const dReal *d, int n);
206 void _dSolveLDLT (const dReal *L, const dReal *d, dReal *b, int n, int nskip);
207 void _dLDLTAddTL (dReal *L, dReal *d, const dReal *a, int n, int nskip, void *tmpbuf);
208 void _dLDLTRemove (dReal **A, const int *p, dReal *L, dReal *d, int n1, int n2, int r, int nskip, void *tmpbuf);
209 void _dRemoveRowCol (dReal *A, int n, int nskip, int r);
211 PURE_INLINE size_t _dEstimateFactorCholeskyTmpbufSize(int n)
213 return dPAD(n) * sizeof(dReal);
216 PURE_INLINE size_t _dEstimateSolveCholeskyTmpbufSize(int n)
218 return dPAD(n) * sizeof(dReal);
221 PURE_INLINE size_t _dEstimateInvertPDMatrixTmpbufSize(int n)
223 size_t FactorCholesky_size = _dEstimateFactorCholeskyTmpbufSize(n);
224 size_t SolveCholesky_size = _dEstimateSolveCholeskyTmpbufSize(n);
225 size_t MaxCholesky_size = FactorCholesky_size > SolveCholesky_size ? FactorCholesky_size : SolveCholesky_size;
226 return dPAD(n) * (n + 1) * sizeof(dReal) + MaxCholesky_size;
229 PURE_INLINE size_t _dEstimateIsPositiveDefiniteTmpbufSize(int n)
231 return dPAD(n) * n * sizeof(dReal) + _dEstimateFactorCholeskyTmpbufSize(n);
234 PURE_INLINE size_t _dEstimateLDLTAddTLTmpbufSize(int nskip)
236 return nskip * 2 * sizeof(dReal);
239 PURE_INLINE size_t _dEstimateLDLTRemoveTmpbufSize(int n2, int nskip)
241 return n2 * sizeof(dReal) + _dEstimateLDLTAddTLTmpbufSize(nskip);
245 #define dSetZero(a, n) _dSetZero(a, n)
246 #define dSetValue(a, n, value) _dSetValue(a, n, value)
247 #define dDot(a, b, n) _dDot(a, b, n)
248 #define dMultiply0(A, B, C, p, q, r) _dMultiply0(A, B, C, p, q, r)
249 #define dMultiply1(A, B, C, p, q, r) _dMultiply1(A, B, C, p, q, r)
250 #define dMultiply2(A, B, C, p, q, r) _dMultiply2(A, B, C, p, q, r)
251 #define dFactorCholesky(A, n, tmpbuf) _dFactorCholesky(A, n, tmpbuf)
252 #define dSolveCholesky(L, b, n, tmpbuf) _dSolveCholesky(L, b, n, tmpbuf)
253 #define dInvertPDMatrix(A, Ainv, n, tmpbuf) _dInvertPDMatrix(A, Ainv, n, tmpbuf)
254 #define dIsPositiveDefinite(A, n, tmpbuf) _dIsPositiveDefinite(A, n, tmpbuf)
255 #define dFactorLDLT(A, d, n, nskip) _dFactorLDLT(A, d, n, nskip)
256 #define dSolveL1(L, b, n, nskip) _dSolveL1(L, b, n, nskip)
257 #define dSolveL1T(L, b, n, nskip) _dSolveL1T(L, b, n, nskip)
258 #define dVectorScale(a, d, n) _dVectorScale(a, d, n)
259 #define dSolveLDLT(L, d, b, n, nskip) _dSolveLDLT(L, d, b, n, nskip)
260 #define dLDLTAddTL(L, d, a, n, nskip, tmpbuf) _dLDLTAddTL(L, d, a, n, nskip, tmpbuf)
261 #define dLDLTRemove(A, p, L, d, n1, n2, r, nskip, tmpbuf) _dLDLTRemove(A, p, L, d, n1, n2, r, nskip, tmpbuf)
262 #define dRemoveRowCol(A, n, nskip, r) _dRemoveRowCol(A, n, nskip, r)
265 #define dEstimateFactorCholeskyTmpbufSize(n) _dEstimateFactorCholeskyTmpbufSize(n)
266 #define dEstimateSolveCholeskyTmpbufSize(n) _dEstimateSolveCholeskyTmpbufSize(n)
267 #define dEstimateInvertPDMatrixTmpbufSize(n) _dEstimateInvertPDMatrixTmpbufSize(n)
268 #define dEstimateIsPositiveDefiniteTmpbufSize(n) _dEstimateIsPositiveDefiniteTmpbufSize(n)
269 #define dEstimateLDLTAddTLTmpbufSize(nskip) _dEstimateLDLTAddTLTmpbufSize(nskip)
270 #define dEstimateLDLTRemoveTmpbufSize(n2, nskip) _dEstimateLDLTRemoveTmpbufSize(n2, nskip)
273 #endif // defined(__ODE__)