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bluecore/ode/src/matrix.cpp

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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. *
* *
*************************************************************************/
#include <ode/common.h>
#include <ode/matrix.h>
// misc defines
#define ALLOCA dALLOCA16
void dSetZero (dReal *a, int n)
{
dAASSERT (a && n >= 0);
while (n > 0) {
*(a++) = 0;
n--;
}
}
void dSetValue (dReal *a, int n, dReal value)
{
dAASSERT (a && n >= 0);
while (n > 0) {
*(a++) = value;
n--;
}
}
void dMultiply0 (dReal *A, const dReal *B, const dReal *C, int p, int q, int r)
{
int i,j,k,qskip,rskip,rpad;
dAASSERT (A && B && C && p>0 && q>0 && r>0);
qskip = dPAD(q);
rskip = dPAD(r);
rpad = rskip - r;
dReal sum;
const dReal *b,*c,*bb;
bb = B;
for (i=p; i; i--) {
for (j=0 ; j<r; j++) {
c = C + j;
b = bb;
sum = 0;
for (k=q; k; k--, c+=rskip) sum += (*(b++))*(*c);
*(A++) = sum;
}
A += rpad;
bb += qskip;
}
}
void dMultiply1 (dReal *A, const dReal *B, const dReal *C, int p, int q, int r)
{
int i,j,k,pskip,rskip;
dReal sum;
dAASSERT (A && B && C && p>0 && q>0 && r>0);
pskip = dPAD(p);
rskip = dPAD(r);
for (i=0; i<p; i++) {
for (j=0; j<r; j++) {
sum = 0;
for (k=0; k<q; k++) sum += B[i+k*pskip] * C[j+k*rskip];
A[i*rskip+j] = sum;
}
}
}
void dMultiply2 (dReal *A, const dReal *B, const dReal *C, int p, int q, int r)
{
int i,j,k,z,rpad,qskip;
dReal sum;
const dReal *bb,*cc;
dAASSERT (A && B && C && p>0 && q>0 && r>0);
rpad = dPAD(r) - r;
qskip = dPAD(q);
bb = B;
for (i=p; i; i--) {
cc = C;
for (j=r; j; j--) {
z = 0;
sum = 0;
for (k=q; k; k--,z++) sum += bb[z] * cc[z];
*(A++) = sum;
cc += qskip;
}
A += rpad;
bb += qskip;
}
}
int dFactorCholesky (dReal *A, int n)
{
int i,j,k,nskip;
dReal sum,*a,*b,*aa,*bb,*cc,*recip;
dAASSERT (n > 0 && A);
nskip = dPAD (n);
recip = (dReal*) ALLOCA (n * sizeof(dReal));
aa = A;
for (i=0; i<n; i++) {
bb = A;
cc = A + i*nskip;
for (j=0; j<i; j++) {
sum = *cc;
a = aa;
b = bb;
for (k=j; k; k--) sum -= (*(a++))*(*(b++));
*cc = sum * recip[j];
bb += nskip;
cc++;
}
sum = *cc;
a = aa;
for (k=i; k; k--, a++) sum -= (*a)*(*a);
if (sum <= REAL(0.0)) return 0;
*cc = dSqrt(sum);
recip[i] = dRecip (*cc);
aa += nskip;
}
return 1;
}
void dSolveCholesky (const dReal *L, dReal *b, int n)
{
int i,k,nskip;
dReal sum,*y;
dAASSERT (n > 0 && L && b);
nskip = dPAD (n);
y = (dReal*) ALLOCA (n*sizeof(dReal));
for (i=0; i<n; i++) {
sum = 0;
for (k=0; k < i; k++) sum += L[i*nskip+k]*y[k];
y[i] = (b[i]-sum)/L[i*nskip+i];
}
for (i=n-1; i >= 0; i--) {
sum = 0;
for (k=i+1; k < n; k++) sum += L[k*nskip+i]*b[k];
b[i] = (y[i]-sum)/L[i*nskip+i];
}
}
int dInvertPDMatrix (const dReal *A, dReal *Ainv, int n)
{
int i,j,nskip;
dReal *L,*x;
dAASSERT (n > 0 && A && Ainv);
nskip = dPAD (n);
L = (dReal*) ALLOCA (nskip*n*sizeof(dReal));
memcpy (L,A,nskip*n*sizeof(dReal));
x = (dReal*) ALLOCA (n*sizeof(dReal));
if (dFactorCholesky (L,n)==0) return 0;
dSetZero (Ainv,n*nskip); // make sure all padding elements set to 0
for (i=0; i<n; i++) {
for (j=0; j<n; j++) x[j] = 0;
x[i] = 1;
dSolveCholesky (L,x,n);
for (j=0; j<n; j++) Ainv[j*nskip+i] = x[j];
}
return 1;
}
int dIsPositiveDefinite (const dReal *A, int n)
{
dReal *Acopy;
dAASSERT (n > 0 && A);
int nskip = dPAD (n);
Acopy = (dReal*) ALLOCA (nskip*n * sizeof(dReal));
memcpy (Acopy,A,nskip*n * sizeof(dReal));
return dFactorCholesky (Acopy,n);
}
/***** this has been replaced by a faster version
void dSolveL1T (const dReal *L, dReal *b, int n, int nskip)
{
int i,j;
dAASSERT (L && b && n >= 0 && nskip >= n);
dReal sum;
for (i=n-2; i>=0; i--) {
sum = 0;
for (j=i+1; j<n; j++) sum += L[j*nskip+i]*b[j];
b[i] -= sum;
}
}
*/
void dVectorScale (dReal *a, const dReal *d, int n)
{
dAASSERT (a && d && n >= 0);
for (int i=0; i<n; i++) a[i] *= d[i];
}
void dSolveLDLT (const dReal *L, const dReal *d, dReal *b, int n, int nskip)
{
dAASSERT (L && d && b && n > 0 && nskip >= n);
dSolveL1 (L,b,n,nskip);
dVectorScale (b,d,n);
dSolveL1T (L,b,n,nskip);
}
void dLDLTAddTL (dReal *L, dReal *d, const dReal *a, int n, int nskip)
{
int j,p;
dReal *W1,*W2,W11,W21,alpha1,alpha2,alphanew,gamma1,gamma2,k1,k2,Wp,ell,dee;
dAASSERT (L && d && a && n > 0 && nskip >= n);
if (n < 2) return;
W1 = (dReal*) ALLOCA (n*sizeof(dReal));
W2 = (dReal*) ALLOCA (n*sizeof(dReal));
W1[0] = 0;
W2[0] = 0;
for (j=1; j<n; j++) W1[j] = W2[j] = a[j] * M_SQRT1_2;
W11 = (REAL(0.5)*a[0]+1)*M_SQRT1_2;
W21 = (REAL(0.5)*a[0]-1)*M_SQRT1_2;
alpha1=1;
alpha2=1;
dee = d[0];
alphanew = alpha1 + (W11*W11)*dee;
dee /= alphanew;
gamma1 = W11 * dee;
dee *= alpha1;
alpha1 = alphanew;
alphanew = alpha2 - (W21*W21)*dee;
dee /= alphanew;
gamma2 = W21 * dee;
alpha2 = alphanew;
k1 = REAL(1.0) - W21*gamma1;
k2 = W21*gamma1*W11 - W21;
for (p=1; p<n; p++) {
Wp = W1[p];
ell = L[p*nskip];
W1[p] = Wp - W11*ell;
W2[p] = k1*Wp + k2*ell;
}
for (j=1; j<n; j++) {
dee = d[j];
alphanew = alpha1 + (W1[j]*W1[j])*dee;
dee /= alphanew;
gamma1 = W1[j] * dee;
dee *= alpha1;
alpha1 = alphanew;
alphanew = alpha2 - (W2[j]*W2[j])*dee;
dee /= alphanew;
gamma2 = W2[j] * dee;
dee *= alpha2;
d[j] = dee;
alpha2 = alphanew;
k1 = W1[j];
k2 = W2[j];
for (p=j+1; p<n; p++) {
ell = L[p*nskip+j];
Wp = W1[p] - k1 * ell;
ell += gamma1 * Wp;
W1[p] = Wp;
Wp = W2[p] - k2 * ell;
ell -= gamma2 * Wp;
W2[p] = Wp;
L[p*nskip+j] = ell;
}
}
}
// macros for dLDLTRemove() for accessing A - either access the matrix
// directly or access it via row pointers. we are only supposed to reference
// the lower triangle of A (it is symmetric), but indexes i and j come from
// permutation vectors so they are not predictable. so do a test on the
// indexes - this should not slow things down too much, as we don't do this
// in an inner loop.
#define _GETA(i,j) (A[i][j])
//#define _GETA(i,j) (A[(i)*nskip+(j)])
#define GETA(i,j) ((i > j) ? _GETA(i,j) : _GETA(j,i))
void dLDLTRemove (dReal **A, const int *p, dReal *L, dReal *d,
int n1, int n2, int r, int nskip)
{
int i;
dAASSERT(A && p && L && d && n1 > 0 && n2 > 0 && r >= 0 && r < n2 &&
n1 >= n2 && nskip >= n1);
#ifndef dNODEBUG
for (i=0; i<n2; i++) dIASSERT(p[i] >= 0 && p[i] < n1);
#endif
if (r==n2-1) {
return; // deleting last row/col is easy
}
else if (r==0) {
dReal *a = (dReal*) ALLOCA (n2 * sizeof(dReal));
for (i=0; i<n2; i++) a[i] = -GETA(p[i],p[0]);
a[0] += REAL(1.0);
dLDLTAddTL (L,d,a,n2,nskip);
}
else {
dReal *t = (dReal*) ALLOCA (r * sizeof(dReal));
dReal *a = (dReal*) ALLOCA ((n2-r) * sizeof(dReal));
for (i=0; i<r; i++) t[i] = L[r*nskip+i] / d[i];
for (i=0; i<(n2-r); i++)
a[i] = dDot(L+(r+i)*nskip,t,r) - GETA(p[r+i],p[r]);
a[0] += REAL(1.0);
dLDLTAddTL (L + r*nskip+r, d+r, a, n2-r, nskip);
}
// snip out row/column r from L and d
dRemoveRowCol (L,n2,nskip,r);
if (r < (n2-1)) memmove (d+r,d+r+1,(n2-r-1)*sizeof(dReal));
}
void dRemoveRowCol (dReal *A, int n, int nskip, int r)
{
int i;
dAASSERT(A && n > 0 && nskip >= n && r >= 0 && r < n);
if (r >= n-1) return;
if (r > 0) {
for (i=0; i<r; i++)
memmove (A+i*nskip+r,A+i*nskip+r+1,(n-r-1)*sizeof(dReal));
for (i=r; i<(n-1); i++)
memcpy (A+i*nskip,A+i*nskip+nskip,r*sizeof(dReal));
}
for (i=r; i<(n-1); i++)
memcpy (A+i*nskip+r,A+i*nskip+nskip+r+1,(n-r-1)*sizeof(dReal));
}
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