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/*************************************************************************
* *
* 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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