1 files changed, 358 insertions, 0 deletions

diff --git a/libraries/ode-0.9/ode/src/matrix.cpp b/libraries/ode-0.9/ode/src/matrix.cpp
new file mode 100644
index 0000000..16afe91
--- /dev/null
+++ b/libraries/ode-0.9/ode/src/matrix.cpp
@@ -0,0 +1,358 @@
+/*************************************************************************
+ *                                                                       *
+ * 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));
+}