/************************************************************************* *                                                                       * * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith.       * * All rights reserved.  Email: russ@q12.org   Web: www.q12.org          * *                                                                       * * This library is free software; you can redistribute it and/or         * * modify it under the terms of EITHER:                                  * *   (1) The GNU Lesser General Public License as published by the Free  * *       Software Foundation; either version 2.1 of the License, or (at  * *       your option) any later version. The text of the GNU Lesser      * *       General Public License is included with this library in the     * *       file LICENSE.TXT.                                               * *   (2) The BSD-style license that is included with this library in     * *       the file LICENSE-BSD.TXT.                                       * *                                                                       * * This library is distributed in the hope that it will be useful,       * * but WITHOUT ANY WARRANTY; without even the implied warranty of        * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files    * * LICENSE.TXT and LICENSE-BSD.TXT for more details.                     * *                                                                       * *************************************************************************//* optimized and unoptimized vector and matrix functions */#ifndef _ODE_MATRIX_H_#define _ODE_MATRIX_H_#include <ode/common.h>#ifdef __cplusplusextern "C" {#endif/* set a vector/matrix of size n to all zeros, or to a specific value. */void dSetZero (dReal *a, int n);void dSetValue (dReal *a, int n, dReal value);/* get the dot product of two n*1 vectors. if n <= 0 then * zero will be returned (in which case a and b need not be valid). */dReal dDot (const dReal *a, const dReal *b, int n);/* get the dot products of (a0,b), (a1,b), etc and return them in outsum. * all vectors are n*1. if n <= 0 then zeroes will be returned (in which case * the input vectors need not be valid). this function is somewhat faster * than calling dDot() for all of the combinations separately. *//* NOT INCLUDED in the library for now.void dMultidot2 (const dReal *a0, const dReal *a1,		 const dReal *b, dReal *outsum, int n);*//* matrix multiplication. all matrices are stored in standard row format. * the digit refers to the argument that is transposed: *   0:   A = B  * C   (sizes: A:p*r B:p*q C:q*r) *   1:   A = B' * C   (sizes: A:p*r B:q*p C:q*r) *   2:   A = B  * C'  (sizes: A:p*r B:p*q C:r*q) * case 1,2 are equivalent to saying that the operation is A=B*C but * B or C are stored in standard column format. */void dMultiply0 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);void dMultiply1 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);void dMultiply2 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);/* do an in-place cholesky decomposition on the lower triangle of the n*n * symmetric matrix A (which is stored by rows). the resulting lower triangle * will be such that L*L'=A. return 1 on success and 0 on failure (on failure * the matrix is not positive definite). */int dFactorCholesky (dReal *A, int n);/* solve for x: L*L'*x = b, and put the result back into x. * L is size n*n, b is size n*1. only the lower triangle of L is considered. */void dSolveCholesky (const dReal *L, dReal *b, int n);/* compute the inverse of the n*n positive definite matrix A and put it in * Ainv. this is not especially fast. this returns 1 on success (A was * positive definite) or 0 on failure (not PD). */int dInvertPDMatrix (const dReal *A, dReal *Ainv, int n);/* check whether an n*n matrix A is positive definite, return 1/0 (yes/no). * positive definite means that x'*A*x > 0 for any x. this performs a * cholesky decomposition of A. if the decomposition fails then the matrix * is not positive definite. A is stored by rows. A is not altered. */int dIsPositiveDefinite (const dReal *A, int n);/* factorize a matrix A into L*D*L', where L is lower triangular with ones on * the diagonal, and D is diagonal. * A is an n*n matrix stored by rows, with a leading dimension of n rounded * up to 4. L is written into the strict lower triangle of A (the ones are not * written) and the reciprocal of the diagonal elements of D are written into * d. */void dFactorLDLT (dReal *A, dReal *d, int n, int nskip);/* solve L*x=b, where L is n*n lower triangular with ones on the diagonal, * and x,b are n*1. b is overwritten with x. * the leading dimension of L is `nskip'. */void dSolveL1 (const dReal *L, dReal *b, int n, int nskip);/* solve L'*x=b, where L is n*n lower triangular with ones on the diagonal, * and x,b are n*1. b is overwritten with x. * the leading dimension of L is `nskip'. */void dSolveL1T (const dReal *L, dReal *b, int n, int nskip);/* in matlab syntax: a(1:n) = a(1:n) .* d(1:n) */void dVectorScale (dReal *a, const dReal *d, int n);/* given `L', a n*n lower triangular matrix with ones on the diagonal, * and `d', a n*1 vector of the reciprocal diagonal elements of an n*n matrix * D, solve L*D*L'*x=b where x,b are n*1. x overwrites b. * the leading dimension of L is `nskip'. */void dSolveLDLT (const dReal *L, const dReal *d, dReal *b, int n, int nskip);/* given an L*D*L' factorization of an n*n matrix A, return the updated * factorization L2*D2*L2' of A plus the following "top left" matrix: * *    [ b a' ]     <-- b is a[0] *    [ a 0  ]     <-- a is a[1..n-1] * *   - L has size n*n, its leading dimension is nskip. L is lower triangular *     with ones on the diagonal. only the lower triangle of L is referenced. *   - d has size n. d contains the reciprocal diagonal elements of D. *   - a has size n. * the result is written into L, except that the left column of L and d[0] * are not actually modified. see ldltaddTL.m for further comments.  */void dLDLTAddTL (dReal *L, dReal *d, const dReal *a, int n, int nskip);/* given an L*D*L' factorization of a permuted matrix A, produce a new * factorization for row and column `r' removed. *   - A has size n1*n1, its leading dimension in nskip. A is symmetric and *     positive definite. only the lower triangle of A is referenced. *     A itself may actually be an array of row pointers. *   - L has size n2*n2, its leading dimension in nskip. L is lower triangular *     with ones on the diagonal. only the lower triangle of L is referenced. *   - d has size n2. d contains the reciprocal diagonal elements of D. *   - p is a permutation vector. it contains n2 indexes into A. each index *     must be in the range 0..n1-1. *   - r is the row/column of L to remove. * the new L will be written within the old L, i.e. will have the same leading * dimension. the last row and column of L, and the last element of d, are * undefined on exit. * * a fast O(n^2) algorithm is used. see ldltremove.m for further comments. */void dLDLTRemove (dReal **A, const int *p, dReal *L, dReal *d,		  int n1, int n2, int r, int nskip);/* given an n*n matrix A (with leading dimension nskip), remove the r'th row * and column by moving elements. the new matrix will have the same leading * dimension. the last row and column of A are untouched on exit. */void dRemoveRowCol (dReal *A, int n, int nskip, int r);#ifdef __cplusplus}#endif#endif