/************************************************************************* * * * 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 __cplusplus extern "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

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