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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. */
+
+ODE_API void dSetZero (dReal *a, int n);
+ODE_API 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).
+ */
+
+ODE_API 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.
+ */
+
+ODE_API void dMultiply0 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
+ODE_API void dMultiply1 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
+ODE_API 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).
+ */
+
+ODE_API 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.
+ */
+
+ODE_API 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).
+ */
+
+ODE_API 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.
+ */
+
+ODE_API 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.
+ */
+ODE_API 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'.
+ */
+ODE_API 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'.
+ */
+ODE_API void dSolveL1T (const dReal *L, dReal *b, int n, int nskip);
+
+
+/* in matlab syntax: a(1:n) = a(1:n) .* d(1:n) */
+
+ODE_API 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'.
+ */
+
+ODE_API 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. 
+ */
+ODE_API 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.
+ */
+ODE_API 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.
+ */
+ODE_API void dRemoveRowCol (dReal *A, int n, int nskip, int r);
+
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif