281 lines
12 KiB
C
281 lines
12 KiB
C
/*************************************************************************
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* *
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* Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
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* All rights reserved. Email: russ@q12.org Web: www.q12.org *
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* *
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* This library is free software; you can redistribute it and/or *
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* modify it under the terms of EITHER: *
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* (1) The GNU Lesser General Public License as published by the Free *
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* Software Foundation; either version 2.1 of the License, or (at *
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* your option) any later version. The text of the GNU Lesser *
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* General Public License is included with this library in the *
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* file LICENSE.TXT. *
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* (2) The BSD-style license that is included with this library in *
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* the file LICENSE-BSD.TXT. *
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* *
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* This library is distributed in the hope that it will be useful, *
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* but WITHOUT ANY WARRANTY; without even the implied warranty of *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files *
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* LICENSE.TXT and LICENSE-BSD.TXT for more details. *
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* *
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*************************************************************************/
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/* optimized and unoptimized vector and matrix functions */
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#ifndef _ODE_MATRIX_H_
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#define _ODE_MATRIX_H_
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#include <ode/common.h>
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#ifdef __cplusplus
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extern "C" {
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#endif
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/* set a vector/matrix of size n to all zeros, or to a specific value. */
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ODE_API void dSetZero (dReal *a, int n);
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ODE_API void dSetValue (dReal *a, int n, dReal value);
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/* get the dot product of two n*1 vectors. if n <= 0 then
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* zero will be returned (in which case a and b need not be valid).
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*/
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ODE_API dReal dDot (const dReal *a, const dReal *b, int n);
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/* get the dot products of (a0,b), (a1,b), etc and return them in outsum.
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* all vectors are n*1. if n <= 0 then zeroes will be returned (in which case
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* the input vectors need not be valid). this function is somewhat faster
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* than calling dDot() for all of the combinations separately.
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*/
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/* NOT INCLUDED in the library for now.
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void dMultidot2 (const dReal *a0, const dReal *a1,
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const dReal *b, dReal *outsum, int n);
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*/
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/* matrix multiplication. all matrices are stored in standard row format.
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* the digit refers to the argument that is transposed:
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* 0: A = B * C (sizes: A:p*r B:p*q C:q*r)
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* 1: A = B' * C (sizes: A:p*r B:q*p C:q*r)
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* 2: A = B * C' (sizes: A:p*r B:p*q C:r*q)
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* case 1,2 are equivalent to saying that the operation is A=B*C but
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* B or C are stored in standard column format.
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*/
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ODE_API void dMultiply0 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
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ODE_API void dMultiply1 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
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ODE_API void dMultiply2 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
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/* do an in-place cholesky decomposition on the lower triangle of the n*n
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* symmetric matrix A (which is stored by rows). the resulting lower triangle
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* will be such that L*L'=A. return 1 on success and 0 on failure (on failure
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* the matrix is not positive definite).
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*/
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ODE_API int dFactorCholesky (dReal *A, int n);
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/* solve for x: L*L'*x = b, and put the result back into x.
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* L is size n*n, b is size n*1. only the lower triangle of L is considered.
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*/
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ODE_API void dSolveCholesky (const dReal *L, dReal *b, int n);
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/* compute the inverse of the n*n positive definite matrix A and put it in
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* Ainv. this is not especially fast. this returns 1 on success (A was
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* positive definite) or 0 on failure (not PD).
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*/
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ODE_API int dInvertPDMatrix (const dReal *A, dReal *Ainv, int n);
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/* check whether an n*n matrix A is positive definite, return 1/0 (yes/no).
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* positive definite means that x'*A*x > 0 for any x. this performs a
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* cholesky decomposition of A. if the decomposition fails then the matrix
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* is not positive definite. A is stored by rows. A is not altered.
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*/
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ODE_API int dIsPositiveDefinite (const dReal *A, int n);
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/* factorize a matrix A into L*D*L', where L is lower triangular with ones on
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* the diagonal, and D is diagonal.
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* A is an n*n matrix stored by rows, with a leading dimension of n rounded
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* up to 4. L is written into the strict lower triangle of A (the ones are not
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* written) and the reciprocal of the diagonal elements of D are written into
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* d.
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*/
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ODE_API void dFactorLDLT (dReal *A, dReal *d, int n, int nskip);
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/* solve L*x=b, where L is n*n lower triangular with ones on the diagonal,
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* and x,b are n*1. b is overwritten with x.
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* the leading dimension of L is `nskip'.
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*/
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ODE_API void dSolveL1 (const dReal *L, dReal *b, int n, int nskip);
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/* solve L'*x=b, where L is n*n lower triangular with ones on the diagonal,
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* and x,b are n*1. b is overwritten with x.
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* the leading dimension of L is `nskip'.
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*/
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ODE_API void dSolveL1T (const dReal *L, dReal *b, int n, int nskip);
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/* in matlab syntax: a(1:n) = a(1:n) .* d(1:n) */
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ODE_API void dVectorScale (dReal *a, const dReal *d, int n);
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/* given `L', a n*n lower triangular matrix with ones on the diagonal,
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* and `d', a n*1 vector of the reciprocal diagonal elements of an n*n matrix
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* D, solve L*D*L'*x=b where x,b are n*1. x overwrites b.
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* the leading dimension of L is `nskip'.
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*/
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ODE_API void dSolveLDLT (const dReal *L, const dReal *d, dReal *b, int n, int nskip);
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/* given an L*D*L' factorization of an n*n matrix A, return the updated
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* factorization L2*D2*L2' of A plus the following "top left" matrix:
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*
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* [ b a' ] <-- b is a[0]
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* [ a 0 ] <-- a is a[1..n-1]
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*
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* - L has size n*n, its leading dimension is nskip. L is lower triangular
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* with ones on the diagonal. only the lower triangle of L is referenced.
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* - d has size n. d contains the reciprocal diagonal elements of D.
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* - a has size n.
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* the result is written into L, except that the left column of L and d[0]
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* are not actually modified. see ldltaddTL.m for further comments.
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*/
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ODE_API void dLDLTAddTL (dReal *L, dReal *d, const dReal *a, int n, int nskip);
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/* given an L*D*L' factorization of a permuted matrix A, produce a new
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* factorization for row and column `r' removed.
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* - A has size n1*n1, its leading dimension in nskip. A is symmetric and
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* positive definite. only the lower triangle of A is referenced.
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* A itself may actually be an array of row pointers.
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* - L has size n2*n2, its leading dimension in nskip. L is lower triangular
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* with ones on the diagonal. only the lower triangle of L is referenced.
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* - d has size n2. d contains the reciprocal diagonal elements of D.
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* - p is a permutation vector. it contains n2 indexes into A. each index
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* must be in the range 0..n1-1.
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* - r is the row/column of L to remove.
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* the new L will be written within the old L, i.e. will have the same leading
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* dimension. the last row and column of L, and the last element of d, are
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* undefined on exit.
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*
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* a fast O(n^2) algorithm is used. see ldltremove.m for further comments.
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*/
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ODE_API void dLDLTRemove (dReal **A, const int *p, dReal *L, dReal *d,
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int n1, int n2, int r, int nskip);
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/* given an n*n matrix A (with leading dimension nskip), remove the r'th row
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* and column by moving elements. the new matrix will have the same leading
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* dimension. the last row and column of A are untouched on exit.
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*/
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ODE_API void dRemoveRowCol (dReal *A, int n, int nskip, int r);
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#if defined(__ODE__)
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void _dSetZero (dReal *a, int n);
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void _dSetValue (dReal *a, int n, dReal value);
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dReal _dDot (const dReal *a, const dReal *b, int n);
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void _dMultiply0 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
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void _dMultiply1 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
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void _dMultiply2 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
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int _dFactorCholesky (dReal *A, int n, void *tmpbuf);
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void _dSolveCholesky (const dReal *L, dReal *b, int n, void *tmpbuf);
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int _dInvertPDMatrix (const dReal *A, dReal *Ainv, int n, void *tmpbuf);
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int _dIsPositiveDefinite (const dReal *A, int n, void *tmpbuf);
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void _dFactorLDLT (dReal *A, dReal *d, int n, int nskip);
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void _dSolveL1 (const dReal *L, dReal *b, int n, int nskip);
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void _dSolveL1T (const dReal *L, dReal *b, int n, int nskip);
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void _dVectorScale (dReal *a, const dReal *d, int n);
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void _dSolveLDLT (const dReal *L, const dReal *d, dReal *b, int n, int nskip);
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void _dLDLTAddTL (dReal *L, dReal *d, const dReal *a, int n, int nskip, void *tmpbuf);
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void _dLDLTRemove (dReal **A, const int *p, dReal *L, dReal *d, int n1, int n2, int r, int nskip, void *tmpbuf);
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void _dRemoveRowCol (dReal *A, int n, int nskip, int r);
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PURE_INLINE size_t _dEstimateFactorCholeskyTmpbufSize(int n)
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{
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return dPAD(n) * sizeof(dReal);
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}
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PURE_INLINE size_t _dEstimateSolveCholeskyTmpbufSize(int n)
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{
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return dPAD(n) * sizeof(dReal);
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}
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PURE_INLINE size_t _dEstimateInvertPDMatrixTmpbufSize(int n)
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{
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size_t FactorCholesky_size = _dEstimateFactorCholeskyTmpbufSize(n);
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size_t SolveCholesky_size = _dEstimateSolveCholeskyTmpbufSize(n);
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size_t MaxCholesky_size = FactorCholesky_size > SolveCholesky_size ? FactorCholesky_size : SolveCholesky_size;
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return dPAD(n) * (n + 1) * sizeof(dReal) + MaxCholesky_size;
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}
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PURE_INLINE size_t _dEstimateIsPositiveDefiniteTmpbufSize(int n)
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{
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return dPAD(n) * n * sizeof(dReal) + _dEstimateFactorCholeskyTmpbufSize(n);
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}
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PURE_INLINE size_t _dEstimateLDLTAddTLTmpbufSize(int nskip)
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{
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return nskip * 2 * sizeof(dReal);
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}
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PURE_INLINE size_t _dEstimateLDLTRemoveTmpbufSize(int n2, int nskip)
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{
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return n2 * sizeof(dReal) + _dEstimateLDLTAddTLTmpbufSize(nskip);
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}
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/* For internal use*/
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#define dSetZero(a, n) _dSetZero(a, n)
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#define dSetValue(a, n, value) _dSetValue(a, n, value)
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#define dDot(a, b, n) _dDot(a, b, n)
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#define dMultiply0(A, B, C, p, q, r) _dMultiply0(A, B, C, p, q, r)
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#define dMultiply1(A, B, C, p, q, r) _dMultiply1(A, B, C, p, q, r)
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#define dMultiply2(A, B, C, p, q, r) _dMultiply2(A, B, C, p, q, r)
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#define dFactorCholesky(A, n, tmpbuf) _dFactorCholesky(A, n, tmpbuf)
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#define dSolveCholesky(L, b, n, tmpbuf) _dSolveCholesky(L, b, n, tmpbuf)
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#define dInvertPDMatrix(A, Ainv, n, tmpbuf) _dInvertPDMatrix(A, Ainv, n, tmpbuf)
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#define dIsPositiveDefinite(A, n, tmpbuf) _dIsPositiveDefinite(A, n, tmpbuf)
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#define dFactorLDLT(A, d, n, nskip) _dFactorLDLT(A, d, n, nskip)
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#define dSolveL1(L, b, n, nskip) _dSolveL1(L, b, n, nskip)
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#define dSolveL1T(L, b, n, nskip) _dSolveL1T(L, b, n, nskip)
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#define dVectorScale(a, d, n) _dVectorScale(a, d, n)
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#define dSolveLDLT(L, d, b, n, nskip) _dSolveLDLT(L, d, b, n, nskip)
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#define dLDLTAddTL(L, d, a, n, nskip, tmpbuf) _dLDLTAddTL(L, d, a, n, nskip, tmpbuf)
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#define dLDLTRemove(A, p, L, d, n1, n2, r, nskip, tmpbuf) _dLDLTRemove(A, p, L, d, n1, n2, r, nskip, tmpbuf)
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#define dRemoveRowCol(A, n, nskip, r) _dRemoveRowCol(A, n, nskip, r)
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#define dEstimateFactorCholeskyTmpbufSize(n) _dEstimateFactorCholeskyTmpbufSize(n)
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#define dEstimateSolveCholeskyTmpbufSize(n) _dEstimateSolveCholeskyTmpbufSize(n)
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#define dEstimateInvertPDMatrixTmpbufSize(n) _dEstimateInvertPDMatrixTmpbufSize(n)
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#define dEstimateIsPositiveDefiniteTmpbufSize(n) _dEstimateIsPositiveDefiniteTmpbufSize(n)
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#define dEstimateLDLTAddTLTmpbufSize(nskip) _dEstimateLDLTAddTLTmpbufSize(nskip)
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#define dEstimateLDLTRemoveTmpbufSize(n2, nskip) _dEstimateLDLTRemoveTmpbufSize(n2, nskip)
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#endif /* defined(__ODE__)*/
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#ifdef __cplusplus
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}
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#endif
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#endif
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