Пример #1
0
void testCholeskySolve()
{
  dReal A[MSIZE4*MSIZE], L[MSIZE4*MSIZE], b[MSIZE],x[MSIZE],btest[MSIZE],diff;
  HEADER;

  // get A,L = PD matrix
  dMakeRandomMatrix (A,MSIZE,MSIZE,1.0);
  dMultiply2 (L,A,A,MSIZE,MSIZE,MSIZE);
  memcpy (A,L,MSIZE4*MSIZE*sizeof(dReal));

  // get b,x = right hand side
  dMakeRandomMatrix (b,MSIZE,1,1.0);
  memcpy (x,b,MSIZE*sizeof(dReal));

  // factor L
  if (dFactorCholesky (L,MSIZE)) printf ("\tpassed (1)\n");
  else printf ("\tFAILED (1)\n");
  dClearUpperTriangle (L,MSIZE);

  // solve A*x = b
  dSolveCholesky (L,x,MSIZE);

  // compute A*x and compare it with b
  dMultiply2 (btest,A,x,MSIZE,MSIZE,1);
  diff = dMaxDifference(b,btest,MSIZE,1);
  printf ("\tmaximum difference = %.6e - %s (2)\n",diff,
	  diff > tol ? "FAILED" : "passed");
}
Пример #2
0
void testLDLTAddTL()
{
  int i,j;
  dReal A[MSIZE4*MSIZE], L[MSIZE4*MSIZE], d[MSIZE], a[MSIZE],
    DL[MSIZE4*MSIZE], ATEST[MSIZE4*MSIZE], diff;
  HEADER;

  dMakeRandomMatrix (A,MSIZE,MSIZE,1.0);
  dMultiply2 (L,A,A,MSIZE,MSIZE,MSIZE);
  memcpy (A,L,MSIZE4*MSIZE*sizeof(dReal));
  dFactorLDLT (L,d,MSIZE,MSIZE4);

  // delete first row and column of factorization
  for (i=0; i<MSIZE; i++) a[i] = -A[i*MSIZE4];
  a[0] += 1;
  dLDLTAddTL (L,d,a,MSIZE,MSIZE4);
  for (i=1; i<MSIZE; i++) L[i*MSIZE4] = 0;
  d[0] = 1;

  // get modified L*D*L'
  dClearUpperTriangle (L,MSIZE);
  for (i=0; i<MSIZE; i++) L[i*MSIZE4+i] = 1.0;
  dSetZero (DL,MSIZE4*MSIZE);
  for (i=0; i<MSIZE; i++) {
    for (j=0; j<MSIZE; j++) DL[i*MSIZE4+j] = L[i*MSIZE4+j] / d[j];
  }
  dMultiply2 (ATEST,L,DL,MSIZE,MSIZE,MSIZE);

  // compare it to A with its first row/column removed
  for (i=1; i<MSIZE; i++) A[i*MSIZE4] = A[i] = 0;
  A[0] = 1;
  diff = dMaxDifference(A,ATEST,MSIZE,MSIZE);
  printf ("\tmaximum difference = %.6e - %s\n",diff,
	  diff > tol ? "FAILED" : "passed");
}
Пример #3
0
void testCholeskyFactorization()
{
  dReal A[MSIZE4*MSIZE], B[MSIZE4*MSIZE], C[MSIZE4*MSIZE], diff;
  HEADER;
  dMakeRandomMatrix (A,MSIZE,MSIZE,1.0);
  dMultiply2 (B,A,A,MSIZE,MSIZE,MSIZE);
  memcpy (A,B,MSIZE4*MSIZE*sizeof(dReal));
  if (dFactorCholesky (B,MSIZE)) printf ("\tpassed (1)\n");
  else printf ("\tFAILED (1)\n");
  dClearUpperTriangle (B,MSIZE);
  dMultiply2 (C,B,B,MSIZE,MSIZE,MSIZE);
  diff = dMaxDifference(A,C,MSIZE,MSIZE);
  printf ("\tmaximum difference = %.6e - %s (2)\n",diff,
	  diff > tol ? "FAILED" : "passed");
}
Пример #4
0
void testInvertPDMatrix()
{
  int i,j,ok;
  dReal A[MSIZE4*MSIZE], Ainv[MSIZE4*MSIZE], I[MSIZE4*MSIZE];
  HEADER;

  dMakeRandomMatrix (A,MSIZE,MSIZE,1.0);
  dMultiply2 (Ainv,A,A,MSIZE,MSIZE,MSIZE);
  memcpy (A,Ainv,MSIZE4*MSIZE*sizeof(dReal));
  dSetZero (Ainv,MSIZE4*MSIZE);

  if (dInvertPDMatrix (A,Ainv,MSIZE))
    printf ("\tpassed (1)\n"); else printf ("\tFAILED (1)\n");
  dMultiply0 (I,A,Ainv,MSIZE,MSIZE,MSIZE);

  // compare with identity
  ok = 1;
  for (i=0; i<MSIZE; i++) {
    for (j=0; j<MSIZE; j++) {
      if (i != j) if (cmp (I[i*MSIZE4+j],0.0)==0) ok = 0;
    }
  }
  for (i=0; i<MSIZE; i++) {
    if (cmp (I[i*MSIZE4+i],1.0)==0) ok = 0;
  }
  if (ok) printf ("\tpassed (2)\n"); else printf ("\tFAILED (2)\n");
}
Пример #5
0
void testMatrixMultiply()
{
  // A is 2x3, B is 3x4, B2 is B except stored columnwise, C is 2x4
  dReal A[8],B[12],A2[12],B2[16],C[8];
  int i;

  HEADER;
  dSetZero (A,8);
  for (i=0; i<3; i++) A[i] = i+2;
  for (i=0; i<3; i++) A[i+4] = i+3+2;
  for (i=0; i<12; i++) B[i] = i+8;
  dSetZero (A2,12);
  for (i=0; i<6; i++) A2[i+2*(i/2)] = A[i+i/3];
  dSetZero (B2,16);
  for (i=0; i<12; i++) B2[i+i/3] = B[i];

  dMultiply0 (C,A,B,2,3,4);
  if (C[0] != 116 || C[1] != 125 || C[2] != 134 || C[3] != 143 ||
      C[4] != 224 || C[5] != 242 || C[6] != 260 || C[7] != 278)
    printf ("\tFAILED (1)\n"); else printf ("\tpassed (1)\n");

  dMultiply1 (C,A2,B,2,3,4);
  if (C[0] != 160 || C[1] != 172 || C[2] != 184 || C[3] != 196 ||
      C[4] != 196 || C[5] != 211 || C[6] != 226 || C[7] != 241)
    printf ("\tFAILED (2)\n"); else printf ("\tpassed (2)\n");

  dMultiply2 (C,A,B2,2,3,4);
  if (C[0] != 83 || C[1] != 110 || C[2] != 137 || C[3] != 164 ||
      C[4] != 164 || C[5] != 218 || C[6] != 272 || C[7] != 326)
    printf ("\tFAILED (3)\n"); else printf ("\tpassed (3)\n");
}
Пример #6
0
void testIsPositiveDefinite()
{
  dReal A[MSIZE4*MSIZE], B[MSIZE4*MSIZE];
  HEADER;
  dMakeRandomMatrix (A,MSIZE,MSIZE,1.0);
  dMultiply2 (B,A,A,MSIZE,MSIZE,MSIZE);
  printf ("\t%s\n",dIsPositiveDefinite(A,MSIZE) ? "FAILED (1)":"passed (1)");
  printf ("\t%s\n",dIsPositiveDefinite(B,MSIZE) ? "passed (2)":"FAILED (2)");
}
Пример #7
0
void testSolveLDLT()
{
  dReal A[MSIZE4*MSIZE], L[MSIZE4*MSIZE], d[MSIZE], x[MSIZE],
    b[MSIZE], btest[MSIZE], diff;
  HEADER;
  dMakeRandomMatrix (A,MSIZE,MSIZE,1.0);
  dMultiply2 (L,A,A,MSIZE,MSIZE,MSIZE);
  memcpy (A,L,MSIZE4*MSIZE*sizeof(dReal));

  dMakeRandomMatrix (b,MSIZE,1,1.0);
  memcpy (x,b,MSIZE*sizeof(dReal));

  dFactorLDLT (L,d,MSIZE,MSIZE4);
  dSolveLDLT (L,d,x,MSIZE,MSIZE4);

  dMultiply2 (btest,A,x,MSIZE,MSIZE,1);
  diff = dMaxDifference(b,btest,MSIZE,1);
  printf ("\tmaximum difference = %.6e - %s\n",diff,
	  diff > tol ? "FAILED" : "passed");
}
Пример #8
0
void testRtoQandQtoR()
{
  HEADER;
  dMatrix3 R,I,R2;
  dQuaternion q;
  int i;

  // test makeRandomRotation()
  makeRandomRotation (R);
  dMultiply2 (I,R,R,3,3,3);
  printf ("\tmakeRandomRotation() - %s (1)\n",
	  cmpIdentityMat3(I) ? "passed" : "FAILED");

  // test QtoR() on random normalized quaternions
  int ok = 1;
  for (i=0; i<100; i++) {
    dMakeRandomVector (q,4,1.0);
    dNormalize4 (q);
    dQtoR (q,R);
    dMultiply2 (I,R,R,3,3,3);
    if (cmpIdentityMat3(I)==0) ok = 0;
  }
  printf ("\tQtoR() orthonormality %s (2)\n", ok ? "passed" : "FAILED");

  // test R -> Q -> R works
  dReal maxdiff=0;
  for (i=0; i<100; i++) {
    makeRandomRotation (R);
    dRtoQ (R,q);
    dQtoR (q,R2);
    dReal diff = dMaxDifference (R,R2,3,3);
    if (diff > maxdiff) maxdiff = diff;
  }
  printf ("\tmaximum difference = %e - %s (3)\n",maxdiff,
	  (maxdiff > tol) ? "FAILED" : "passed");
}
Пример #9
0
void testFastLDLTFactorization()
{
  int i,j;
  dReal A[MSIZE4*MSIZE], L[MSIZE4*MSIZE], DL[MSIZE4*MSIZE],
    ATEST[MSIZE4*MSIZE], d[MSIZE], diff;
  HEADER;
  dMakeRandomMatrix (A,MSIZE,MSIZE,1.0);
  dMultiply2 (L,A,A,MSIZE,MSIZE,MSIZE);
  memcpy (A,L,MSIZE4*MSIZE*sizeof(dReal));

  dFactorLDLT (L,d,MSIZE,MSIZE4);
  dClearUpperTriangle (L,MSIZE);
  for (i=0; i<MSIZE; i++) L[i*MSIZE4+i] = 1.0;

  dSetZero (DL,MSIZE4*MSIZE);
  for (i=0; i<MSIZE; i++) {
    for (j=0; j<MSIZE; j++) DL[i*MSIZE4+j] = L[i*MSIZE4+j] / d[j];
  }

  dMultiply2 (ATEST,L,DL,MSIZE,MSIZE,MSIZE);
  diff = dMaxDifference(A,ATEST,MSIZE,MSIZE);
  printf ("\tmaximum difference = %.6e - %s\n",diff,
	  diff > tol ? "FAILED" : "passed");
}
Пример #10
0
void testSmallMatrixMultiply()
{
  dMatrix3 A,B,C,A2;
  dVector3 a,a2,x;

  HEADER;
  dMakeRandomMatrix (A,3,3,1.0);
  dMakeRandomMatrix (B,3,3,1.0);
  dMakeRandomMatrix (C,3,3,1.0);
  dMakeRandomMatrix (x,3,1,1.0);

  // dMultiply0_331()
  dMultiply0_331 (a,B,x);
  dMultiply0 (a2,B,x,3,3,1);
  printf ("\t%s (1)\n",(dMaxDifference (a,a2,3,1) > tol) ? "FAILED" :
	  "passed");

  // dMultiply1_331()
  dMultiply1_331 (a,B,x);
  dMultiply1 (a2,B,x,3,3,1);
  printf ("\t%s (2)\n",(dMaxDifference (a,a2,3,1) > tol) ? "FAILED" :
	  "passed");

  // dMultiply0_133
  dMultiply0_133 (a,x,B);
  dMultiply0 (a2,x,B,1,3,3);
  printf ("\t%s (3)\n",(dMaxDifference (a,a2,1,3) > tol) ? "FAILED" :
	  "passed");

  // dMultiply0_333()
  dMultiply0_333 (A,B,C);
  dMultiply0 (A2,B,C,3,3,3);
  printf ("\t%s (4)\n",(dMaxDifference (A,A2,3,3) > tol) ? "FAILED" :
	  "passed");

  // dMultiply1_333()
  dMultiply1_333 (A,B,C);
  dMultiply1 (A2,B,C,3,3,3);
  printf ("\t%s (5)\n",(dMaxDifference (A,A2,3,3) > tol) ? "FAILED" :
	  "passed");

  // dMultiply2_333()
  dMultiply2_333 (A,B,C);
  dMultiply2 (A2,B,C,3,3,3);
  printf ("\t%s (6)\n",(dMaxDifference (A,A2,3,3) > tol) ? "FAILED" :
	  "passed");
}
Пример #11
0
void testQuaternionMultiply()
{
  HEADER;
  dMatrix3 RA,RB,RC,Rtest;
  dQuaternion qa,qb,qc;
  dReal diff,maxdiff=0;

  for (int i=0; i<100; i++) {
    makeRandomRotation (RB);
    makeRandomRotation (RC);
    dRtoQ (RB,qb);
    dRtoQ (RC,qc);

    dMultiply0 (RA,RB,RC,3,3,3);
    dQMultiply0 (qa,qb,qc);
    dQtoR (qa,Rtest);
    diff = dMaxDifference (Rtest,RA,3,3);
    if (diff > maxdiff) maxdiff = diff;

    dMultiply1 (RA,RB,RC,3,3,3);
    dQMultiply1 (qa,qb,qc);
    dQtoR (qa,Rtest);
    diff = dMaxDifference (Rtest,RA,3,3);
    if (diff > maxdiff) maxdiff = diff;

    dMultiply2 (RA,RB,RC,3,3,3);
    dQMultiply2 (qa,qb,qc);
    dQtoR (qa,Rtest);
    diff = dMaxDifference (Rtest,RA,3,3);
    if (diff > maxdiff) maxdiff = diff;

    dMultiply0 (RA,RC,RB,3,3,3);
    transpose3x3 (RA);
    dQMultiply3 (qa,qb,qc);
    dQtoR (qa,Rtest);
    diff = dMaxDifference (Rtest,RA,3,3);
    if (diff > maxdiff) maxdiff = diff;
  }
  printf ("\tmaximum difference = %e - %s\n",maxdiff,
	  (maxdiff > tol) ? "FAILED" : "passed");
}
Пример #12
0
extern "C" ODE_API int dTestSolveLCP()
{
  const int n = 100;

  //size_t memreq = EstimateTestSolveLCPMemoryReq(n);
  //dxWorldProcessMemArena *arena = dxAllocateTemporaryWorldProcessMemArena(memreq, nullptr, nullptr);
  //if (arena == nullptr) {
  //  return 0;
  //}

  //int i,nskip = dPAD(n);
  int i;
  int nskip = n;
#ifdef dDOUBLE
  const dReal tol = REAL(1e-9);
#endif
#ifdef dSINGLE
  const dReal tol = REAL(1e-4);
#endif
  printf ("dTestSolveLCP()\n");

  dReal *A = new dReal[n*nskip];
  dReal *x = new dReal[n];
  dReal *b = new dReal[n];
  dReal *w = new dReal[n];
  dReal *lo = new dReal[n];
  dReal *hi = new dReal[n];
  
  dReal *A2 = new dReal[n*nskip];
  dReal *b2 = new dReal[n];
  dReal *lo2 = new dReal[n];
  dReal *hi2 = new dReal[n];
  
  dReal *tmp1 = new dReal[n];
  dReal *tmp2 = new dReal[n];

  // double total_time = 0;
  for (int count=0; count < 1000; count++) {

      // form (A,b) = a random positive definite LCP problem
      dMakeRandomMatrix (A2,n,n,1.0);
      dMultiply2 (A,A2,A2,n,n,n);
      dMakeRandomMatrix (x,n,1,1.0);
      dMultiply0 (b,A,x,n,n,1);
      for (i=0; i<n; i++) b[i] += (dRandReal()*REAL(0.2))-REAL(0.1);

      // choose `nub' in the range 0..n-1
      int nub = 50; //dRandInt (n);

      // make limits
      for (i=0; i<nub; i++) lo[i] = -dInfinity;
      for (i=0; i<nub; i++) hi[i] = dInfinity;
      //for (i=nub; i<n; i++) lo[i] = 0;
      //for (i=nub; i<n; i++) hi[i] = dInfinity;
      //for (i=nub; i<n; i++) lo[i] = -dInfinity;
      //for (i=nub; i<n; i++) hi[i] = 0;
      for (i=nub; i<n; i++) lo[i] = -(dRandReal()*REAL(1.0))-REAL(0.01);
      for (i=nub; i<n; i++) hi[i] =  (dRandReal()*REAL(1.0))+REAL(0.01);

      // set a few limits to lo=hi=0
      /*
      for (i=0; i<10; i++) {
      int j = dRandInt (n-nub) + nub;
      lo[j] = 0;
      hi[j] = 0;
      }
      */

      // solve the LCP. we must make copy of A,b,lo,hi (A2,b2,lo2,hi2) for
      // SolveLCP() to permute. also, we'll clear the upper triangle of A2 to
      // ensure that it doesn't get referenced (if it does, the answer will be
      // wrong).

      memcpy (A2,A,n*nskip*sizeof(dReal));
      dClearUpperTriangle (A2,n);
      memcpy (b2,b,n*sizeof(dReal));
      memcpy (lo2,lo,n*sizeof(dReal));
      memcpy (hi2,hi,n*sizeof(dReal));
      dSetZero (x,n);
      dSetZero (w,n);

 
      dSolveLCP (n,A2,x,b2,w,nub,lo2,hi2,0);

      // check the solution

      dMultiply0 (tmp1,A,x,n,n,1);
      for (i=0; i<n; i++) tmp2[i] = b[i] + w[i];
      dReal diff = dMaxDifference (tmp1,tmp2,n,1);
      // printf ("\tA*x = b+w, maximum difference = %.6e - %s (1)\n",diff,
      //	    diff > tol ? "FAILED" : "passed");
      if (diff > tol) dDebug (0,"A*x = b+w, maximum difference = %.6e",diff);
      int n1=0,n2=0,n3=0;
      for (i=0; i<n; i++) {
        if (x[i]==lo[i] && w[i] >= 0) {
          n1++;	// ok
        }
        else if (x[i]==hi[i] && w[i] <= 0) {
          n2++;	// ok
        }
        else if (x[i] >= lo[i] && x[i] <= hi[i] && w[i] == 0) {
          n3++;	// ok
        }
        else {
          dDebug (0,"FAILED: i=%d x=%.4e w=%.4e lo=%.4e hi=%.4e",i,
            x[i],w[i],lo[i],hi[i]);
        }
      }

      // pacifier
      printf ("passed: NL=%3d NH=%3d C=%3d   ",n1,n2,n3);
  }
 
  delete[] A;
  delete[] x;
  delete[] b;
  delete[] w;
  delete[] lo ;
  delete[] hi ;

  delete[] A2 ;
  delete[] b2 ;
  delete[] lo2;
  delete[] hi2;
  
  delete[] tmp1;
  delete[] tmp2;

  return 1;
}
Пример #13
0
extern "C" ODE_API int dTestSolveLCP()
{
  const int n = 100;

  size_t memreq = EstimateTestSolveLCPMemoryReq(n);
  dxWorldProcessMemArena *arena = dxAllocateTemporaryWorldProcessMemArena(memreq, NULL, NULL);
  if (arena == NULL) {
    return 0;
  }

  int i,nskip = dPAD(n);
#ifdef dDOUBLE
  const dReal tol = REAL(1e-9);
#endif
#ifdef dSINGLE
  const dReal tol = REAL(1e-4);
#endif
  printf ("dTestSolveLCP()\n");

  dReal *A = arena->AllocateArray<dReal> (n*nskip);
  dReal *x = arena->AllocateArray<dReal> (n);
  dReal *b = arena->AllocateArray<dReal> (n);
  dReal *w = arena->AllocateArray<dReal> (n);
  dReal *lo = arena->AllocateArray<dReal> (n);
  dReal *hi = arena->AllocateArray<dReal> (n);
  
  dReal *A2 = arena->AllocateArray<dReal> (n*nskip);
  dReal *b2 = arena->AllocateArray<dReal> (n);
  dReal *lo2 = arena->AllocateArray<dReal> (n);
  dReal *hi2 = arena->AllocateArray<dReal> (n);
  
  dReal *tmp1 = arena->AllocateArray<dReal> (n);
  dReal *tmp2 = arena->AllocateArray<dReal> (n);

  double total_time = 0;
  for (int count=0; count < 1000; count++) {
    BEGIN_STATE_SAVE(arena, saveInner) {

      // form (A,b) = a random positive definite LCP problem
      dMakeRandomMatrix (A2,n,n,1.0);
      dMultiply2 (A,A2,A2,n,n,n);
      dMakeRandomMatrix (x,n,1,1.0);
      dMultiply0 (b,A,x,n,n,1);
      for (i=0; i<n; i++) b[i] += (dRandReal()*REAL(0.2))-REAL(0.1);

      // choose `nub' in the range 0..n-1
      int nub = 50; //dRandInt (n);

      // make limits
      for (i=0; i<nub; i++) lo[i] = -dInfinity;
      for (i=0; i<nub; i++) hi[i] = dInfinity;
      //for (i=nub; i<n; i++) lo[i] = 0;
      //for (i=nub; i<n; i++) hi[i] = dInfinity;
      //for (i=nub; i<n; i++) lo[i] = -dInfinity;
      //for (i=nub; i<n; i++) hi[i] = 0;
      for (i=nub; i<n; i++) lo[i] = -(dRandReal()*REAL(1.0))-REAL(0.01);
      for (i=nub; i<n; i++) hi[i] =  (dRandReal()*REAL(1.0))+REAL(0.01);

      // set a few limits to lo=hi=0
      /*
      for (i=0; i<10; i++) {
      int j = dRandInt (n-nub) + nub;
      lo[j] = 0;
      hi[j] = 0;
      }
      */

      // solve the LCP. we must make copy of A,b,lo,hi (A2,b2,lo2,hi2) for
      // SolveLCP() to permute. also, we'll clear the upper triangle of A2 to
      // ensure that it doesn't get referenced (if it does, the answer will be
      // wrong).

      memcpy (A2,A,n*nskip*sizeof(dReal));
      dClearUpperTriangle (A2,n);
      memcpy (b2,b,n*sizeof(dReal));
      memcpy (lo2,lo,n*sizeof(dReal));
      memcpy (hi2,hi,n*sizeof(dReal));
      dSetZero (x,n);
      dSetZero (w,n);

      dStopwatch sw;
      dStopwatchReset (&sw);
      dStopwatchStart (&sw);

      dSolveLCP (arena,n,A2,x,b2,w,nub,lo2,hi2,0);

      dStopwatchStop (&sw);
      double time = dStopwatchTime(&sw);
      total_time += time;
      double average = total_time / double(count+1) * 1000.0;

      // check the solution

      dMultiply0 (tmp1,A,x,n,n,1);
      for (i=0; i<n; i++) tmp2[i] = b[i] + w[i];
      dReal diff = dMaxDifference (tmp1,tmp2,n,1);
      // printf ("\tA*x = b+w, maximum difference = %.6e - %s (1)\n",diff,
      //	    diff > tol ? "FAILED" : "passed");
      if (diff > tol) dDebug (0,"A*x = b+w, maximum difference = %.6e",diff);
      int n1=0,n2=0,n3=0;
      for (i=0; i<n; i++) {
        if (x[i]==lo[i] && w[i] >= 0) {
          n1++;	// ok
        }
        else if (x[i]==hi[i] && w[i] <= 0) {
          n2++;	// ok
        }
        else if (x[i] >= lo[i] && x[i] <= hi[i] && w[i] == 0) {
          n3++;	// ok
        }
        else {
          dDebug (0,"FAILED: i=%d x=%.4e w=%.4e lo=%.4e hi=%.4e",i,
            x[i],w[i],lo[i],hi[i]);
        }
      }

      // pacifier
      printf ("passed: NL=%3d NH=%3d C=%3d   ",n1,n2,n3);
      printf ("time=%10.3f ms  avg=%10.4f\n",time * 1000.0,average);
    
    } END_STATE_SAVE(arena, saveInner);
  }
Пример #14
0
void testLDLTRemove()
{
  int i,j,r,p[MSIZE];
  dReal A[MSIZE4*MSIZE], L[MSIZE4*MSIZE], d[MSIZE],
    L2[MSIZE4*MSIZE], d2[MSIZE], DL2[MSIZE4*MSIZE],
    Atest1[MSIZE4*MSIZE], Atest2[MSIZE4*MSIZE], diff, maxdiff;
  HEADER;

  // make array of A row pointers
  dReal *Arows[MSIZE];
  for (i=0; i<MSIZE; i++) Arows[i] = A+i*MSIZE4;

  // fill permutation vector
  for (i=0; i<MSIZE; i++) p[i]=i;

  dMakeRandomMatrix (A,MSIZE,MSIZE,1.0);
  dMultiply2 (L,A,A,MSIZE,MSIZE,MSIZE);
  memcpy (A,L,MSIZE4*MSIZE*sizeof(dReal));
  dFactorLDLT (L,d,MSIZE,MSIZE4);

  maxdiff = 1e10;
  for (r=0; r<MSIZE; r++) {
    // get Atest1 = A with row/column r removed
    memcpy (Atest1,A,MSIZE4*MSIZE*sizeof(dReal));
    dRemoveRowCol (Atest1,MSIZE,MSIZE4,r);

    // test that the row/column removal worked
    int bad = 0;
    for (i=0; i<MSIZE; i++) {
      for (j=0; j<MSIZE; j++) {
	if (i != r && j != r) {
	  int ii = i;
	  int jj = j;
	  if (ii >= r) ii--;
	  if (jj >= r) jj--;
	  if (A[i*MSIZE4+j] != Atest1[ii*MSIZE4+jj]) bad = 1;
	}
      }
    }
    if (bad) printf ("\trow/col removal FAILED for row %d\n",r);

    // zero out last row/column of Atest1
    for (i=0; i<MSIZE; i++) {
      Atest1[(MSIZE-1)*MSIZE4+i] = 0;
      Atest1[i*MSIZE4+MSIZE-1] = 0;
    }    

    // get L2*D2*L2' = adjusted factorization to remove that row
    memcpy (L2,L,MSIZE4*MSIZE*sizeof(dReal));
    memcpy (d2,d,MSIZE*sizeof(dReal));
    dLDLTRemove (/*A*/ Arows,p,L2,d2,MSIZE,MSIZE,r,MSIZE4);

    // get Atest2 = L2*D2*L2'
    dClearUpperTriangle (L2,MSIZE);
    for (i=0; i<(MSIZE-1); i++) L2[i*MSIZE4+i] = 1.0;
    for (i=0; i<MSIZE; i++) L2[(MSIZE-1)*MSIZE4+i] = 0;
    d2[MSIZE-1] = 1;
    dSetZero (DL2,MSIZE4*MSIZE);
    for (i=0; i<(MSIZE-1); i++) {
      for (j=0; j<MSIZE-1; j++) DL2[i*MSIZE4+j] = L2[i*MSIZE4+j] / d2[j];
    }

    dMultiply2 (Atest2,L2,DL2,MSIZE,MSIZE,MSIZE);

    diff = dMaxDifference(Atest1,Atest2,MSIZE,MSIZE);
    if (diff < maxdiff) maxdiff = diff;

    /*
    dPrintMatrix (Atest1,MSIZE,MSIZE);
    printf ("\n");
    dPrintMatrix (Atest2,MSIZE,MSIZE);
    printf ("\n");
    */
  }
  printf ("\tmaximum difference = %.6e - %s\n",maxdiff,
	  maxdiff > tol ? "FAILED" : "passed");
}