text: /*************************************************************************
   *                                                                       *
   * Open Dynamics Engine, Copyright (C) 2001 Russell L. Smith.            *
   *   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 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.    *
   *                                                                       *
   * 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 GNU      *
   * Lesser General Public License for more details.                       *
   *                                                                       *
   * You should have received a copy of the GNU Lesser General Public      *
   * License along with this library (see the file LICENSE.TXT); if not,   *
   * write to the Free Software Foundation, Inc., 59 Temple Place,         *
   * Suite 330, Boston, MA 02111-1307 USA.                                 *
   *                                                                       *
   *************************************************************************/
  
  #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));
  }
  