lovr-ODE/ode/demo/demo_ode.cpp

/*************************************************************************
 *                                                                       *
 * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith.       *
 * All rights reserved.  Email: [email protected]   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 <setjmp.h>
#include <ode/ode.h>

#ifdef _MSC_VER
#pragma warning(disable:4244 4305)  // for VC++, no precision loss complaints
#endif


//****************************************************************************
// matrix accessors

#define _A(i,j) A[(i)*4+(j)]
#define _I(i,j) I[(i)*4+(j)]
#define _R(i,j) R[(i)*4+(j)]

//****************************************************************************
// tolerances

#ifdef dDOUBLE
const double tol = 1e-10;
#endif

#ifdef dSINGLE
const double tol = 1e-5;
#endif

//****************************************************************************
// misc messages and error handling

#ifdef __GNUC__
#define HEADER printf ("%s()\n", __FUNCTION__);
#else
#define HEADER printf ("%s:%d\n",__FILE__,__LINE__);
#endif

static jmp_buf jump_buffer;


void myMessageFunction (int num, const char *msg, va_list ap)
{
  printf ("(Message %d: ",num);
  vprintf (msg,ap);
  printf (")");
  dSetMessageHandler (0);
  longjmp (jump_buffer,1);
}


#define TRAP_MESSAGE(do,ifnomsg,ifmsg) \
  dSetMessageHandler (&myMessageFunction); \
  if (setjmp (jump_buffer)) { \
    dSetMessageHandler (0); \
    ifmsg ; \
  } \
  else { \
    dSetMessageHandler (&myMessageFunction); \
    do ; \
    ifnomsg ; \
  } \
  dSetMessageHandler (0);

//****************************************************************************
// utility stuff

// compare two numbers, within a threshhold, return 1 if approx equal

int cmp (dReal a, dReal b)
{
  return (fabs(a-b) < tol);
}

//****************************************************************************
// matrix utility stuff

// compare a 3x3 matrix with the identity

int cmpIdentityMat3 (dMatrix3 A)
{
  return
    (cmp(_A(0,0),1.0) && cmp(_A(0,1),0.0) && cmp(_A(0,2),0.0) &&
     cmp(_A(1,0),0.0) && cmp(_A(1,1),1.0) && cmp(_A(1,2),0.0) &&
     cmp(_A(2,0),0.0) && cmp(_A(2,1),0.0) && cmp(_A(2,2),1.0));
}


// transpose a 3x3 matrix in-line

void transpose3x3 (dMatrix3 A)
{
  dReal tmp;
  tmp=A[4]; A[4]=A[1]; A[1]=tmp;
  tmp=A[8]; A[8]=A[2]; A[2]=tmp;
  tmp=A[9]; A[9]=A[6]; A[6]=tmp;
}

//****************************************************************************
// test miscellaneous math functions

void testRandomNumberGenerator()
{
  HEADER;
  if (dTestRand()) printf ("\tpassed\n");
  else printf ("\tFAILED\n");
}


void testInfinity()
{
  HEADER;
  if (1e10 < dInfinity && -1e10 > -dInfinity && -dInfinity < dInfinity)
    printf ("\tpassed\n");
  else printf ("\tFAILED\n");
}


void testPad()
{
  HEADER;
  char s[100];
  s[0]=0;
  for (int i=0; i<=16; i++) sprintf (s+strlen(s),"%d ",dPAD(i));
  printf ("\t%s\n", strcmp(s,"0 1 4 4 4 8 8 8 8 12 12 12 12 16 16 16 16 ") ?
	  "FAILED" : "passed");
}


void testCrossProduct()
{
  HEADER;

  dVector3 a1,a2,b,c;
  dMatrix3 B;
  dMakeRandomVector (b,3,1.0);
  dMakeRandomVector (c,3,1.0);

  dCalcVectorCross3(a1,b,c);

  dSetZero (B,12);
  dSetCrossMatrixPlus(B,b,4);
  dMultiply0 (a2,B,c,3,3,1);

  dReal diff = dMaxDifference(a1,a2,3,1);
  printf ("\t%s\n", diff > tol ? "FAILED" : "passed");
}


void testSetZero()
{
  HEADER;
  dReal a[100];
  dMakeRandomVector (a,100,1.0);
  dSetZero (a,100);
  for (int i=0; i<100; i++) if (a[i] != 0.0) {
    printf ("\tFAILED\n");
    return;
  }
  printf ("\tpassed\n");
}


void testNormalize3()
{
  HEADER;
  int i,j,bad=0;
  dVector3 n1,n2;
  for (i=0; i<1000; i++) {
    dMakeRandomVector (n1,3,1.0);
    for (j=0; j<3; j++) n2[j]=n1[j];
    dNormalize3 (n2);
    if (dFabs(dCalcVectorDot3(n2,n2) - 1.0) > tol) bad |= 1;
    if (dFabs(n2[0]/n1[0] - n2[1]/n1[1]) > tol) bad |= 2;
    if (dFabs(n2[0]/n1[0] - n2[2]/n1[2]) > tol) bad |= 4;
    if (dFabs(n2[1]/n1[1] - n2[2]/n1[2]) > tol) bad |= 8;
    if (dFabs(dCalcVectorDot3(n2,n1) - dSqrt(dCalcVectorDot3(n1,n1))) > tol) bad |= 16;
    if (bad) {
      printf ("\tFAILED (code=%x)\n",bad);
      return;
    }
  }
  printf ("\tpassed\n");
}


/*
void testReorthonormalize()
{
  HEADER;
  dMatrix3 R,I;
  dMakeRandomMatrix (R,3,3,1.0);
  for (int i=0; i<30; i++) dReorthonormalize (R);
  dMultiply2 (I,R,R,3,3,3);
  printf ("\t%s\n",cmpIdentityMat3 (I) ? "passed" : "FAILED");
}
*/


void testPlaneSpace()
{
  HEADER;
  dVector3 n,p,q;
  int bad = 0;
  for (int i=0; i<1000; i++) {
    dMakeRandomVector (n,3,1.0);
    dNormalize3 (n);
    dPlaneSpace (n,p,q);
    if (fabs(dCalcVectorDot3(n,p)) > tol) bad = 1;
    if (fabs(dCalcVectorDot3(n,q)) > tol) bad = 1;
    if (fabs(dCalcVectorDot3(p,q)) > tol) bad = 1;
    if (fabs(dCalcVectorDot3(p,p)-1) > tol) bad = 1;
    if (fabs(dCalcVectorDot3(q,q)-1) > tol) bad = 1;
  }
  printf ("\t%s\n", bad ? "FAILED" : "passed");
}

//****************************************************************************
// test matrix functions

#define MSIZE 21
#define MSIZE4 24	// MSIZE rounded up to 4


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");
}


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");
}


void testCholeskyFactorization()
{
  size_t matrixSize = sizeof(dReal) * MSIZE4 * MSIZE;
  dReal *A = (dReal *)dAlloc(matrixSize), *B = (dReal *)dAlloc(matrixSize), *C = (dReal *)dAlloc(matrixSize), 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");

  dFree(C, matrixSize);
  dFree(B, matrixSize);
  dFree(A, matrixSize);
}


void testCholeskySolve()
{
  size_t matrixSize = sizeof(dReal) * MSIZE4 * MSIZE, vectorSize = sizeof(dReal) * MSIZE;
  dReal *A = (dReal *)dAlloc(matrixSize), *L = (dReal *)dAlloc(matrixSize);
  dReal *b = (dReal *)dAlloc(vectorSize), *x = (dReal *)dAlloc(vectorSize), *btest = (dReal *)dAlloc(vectorSize), 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");

  dFree(btest, vectorSize);
  dFree(x, vectorSize);
  dFree(b, vectorSize);
  dFree(L, matrixSize);
  dFree(A, matrixSize);
}


void testInvertPDMatrix()
{
  int i,j,ok;
  size_t matrixSize = sizeof(dReal) * MSIZE4 * MSIZE;
  dReal *A = (dReal *)dAlloc(matrixSize), *Ainv = (dReal *)dAlloc(matrixSize), *I = (dReal *)dAlloc(matrixSize);

  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");

  dFree(I, matrixSize);
  dFree(Ainv, matrixSize);
  dFree(A, matrixSize);
}


void testIsPositiveDefinite()
{
  size_t matrixSize = sizeof(dReal) * MSIZE4 * MSIZE;
  dReal *A = (dReal *)dAlloc(matrixSize), *B = (dReal *)dAlloc(matrixSize);
  
  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)");

  dFree(B, matrixSize);
  dFree(A, matrixSize);
}


void testFastLDLTFactorization()
{
  int i,j;
  size_t matrixSize = sizeof(dReal) * MSIZE4 * MSIZE, vectorSize = sizeof(dReal) * MSIZE;
  dReal *A = (dReal *)dAlloc(matrixSize), *L = (dReal *)dAlloc(matrixSize), *DL = (dReal *)dAlloc(matrixSize),
    *ATEST = (dReal *)dAlloc(matrixSize), *d = (dReal *)dAlloc(vectorSize), 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");

  dFree(d, vectorSize);
  dFree(ATEST, matrixSize);
  dFree(DL, matrixSize);
  dFree(L, matrixSize);
  dFree(A, matrixSize);
}


void testSolveLDLT()
{
  size_t matrixSize = sizeof(dReal) * MSIZE4 * MSIZE, vectorSize = sizeof(dReal) * MSIZE;
  dReal *A = (dReal *)dAlloc(matrixSize), *L = (dReal *)dAlloc(matrixSize), 
      *d = (dReal *)dAlloc(vectorSize), *x = (dReal *)dAlloc(vectorSize), 
      *b = (dReal *)dAlloc(vectorSize), *btest = (dReal *)dAlloc(vectorSize), 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");

  dFree(btest, vectorSize);
  dFree(b, vectorSize);
  dFree(x, vectorSize);
  dFree(d, vectorSize);
  dFree(L, matrixSize);
  dFree(A, matrixSize);
}


void testLDLTAddTL()
{
  int i,j;
  size_t matrixSize = sizeof(dReal) * MSIZE4 * MSIZE, vectorSize = sizeof(dReal) * MSIZE;
  dReal *A = (dReal *)dAlloc(matrixSize), *L = (dReal *)dAlloc(matrixSize), 
      *DL = (dReal *)dAlloc(matrixSize), *ATEST = (dReal *)dAlloc(matrixSize), 
      *d = (dReal *)dAlloc(vectorSize), *a = (dReal *)dAlloc(vectorSize), 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");

  dFree(a, vectorSize);
  dFree(d, vectorSize);
  dFree(ATEST, matrixSize);
  dFree(DL, matrixSize);
  dFree(L, matrixSize);
  dFree(A, matrixSize);
}


void testLDLTRemove()
{
  int i,j,r;
  size_t intVectorSize = sizeof(int) * MSIZE, matrixSize = sizeof(dReal) * MSIZE4 * MSIZE, vectorSize = sizeof(dReal) * MSIZE;
  int *p = (int *)dAlloc(intVectorSize);
  dReal *A = (dReal *)dAlloc(matrixSize), *L = (dReal *)dAlloc(matrixSize), 
      *L2 = (dReal *)dAlloc(matrixSize), *DL2 = (dReal *)dAlloc(matrixSize), 
      *Atest1 = (dReal *)dAlloc(matrixSize), *Atest2 = (dReal *)dAlloc(matrixSize), 
      *d = (dReal *)dAlloc(vectorSize), *d2 = (dReal *)dAlloc(vectorSize), 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");

  dFree(d2, vectorSize);
  dFree(d, vectorSize);
  dFree(Atest2, matrixSize);
  dFree(Atest1, matrixSize);
  dFree(DL2, matrixSize);
  dFree(L2, matrixSize);
  dFree(L, matrixSize);
  dFree(A, matrixSize);
}

//****************************************************************************
// test mass stuff

#define NUMP 10		// number of particles


void printMassParams (dMass *m)
{
  printf ("mass = %.4f\n",m->mass);
  printf ("com  = (%.4f,%.4f,%.4f)\n",m->c[0],m->c[1],m->c[2]);
  printf ("I    = [ %10.4f %10.4f %10.4f ]\n"
	  "       [ %10.4f %10.4f %10.4f ]\n"
	  "       [ %10.4f %10.4f %10.4f ]\n",
	  m->_I(0,0),m->_I(0,1),m->_I(0,2),
	  m->_I(1,0),m->_I(1,1),m->_I(1,2),
	  m->_I(2,0),m->_I(2,1),m->_I(2,2));
}


void compareMassParams (dMass *m1, dMass *m2, const char *msg)
{
  int i,j,ok = 1;
  if (!(cmp(m1->mass,m2->mass) && cmp(m1->c[0],m2->c[0]) &&
	cmp(m1->c[1],m2->c[1]) && cmp(m1->c[2],m2->c[2])))
    ok = 0;
  for (i=0; i<3; i++) for (j=0; j<3; j++)
    if (cmp (m1->_I(i,j),m2->_I(i,j))==0) ok = 0;
  if (ok) printf ("\tpassed (%s)\n",msg); else printf ("\tFAILED (%s)\n",msg);
}


// compute the mass parameters of a particle set

void computeMassParams (dMass *m, dReal q[NUMP][3], dReal pm[NUMP])
{
  int i,j;
  dMassSetZero (m);
  for (i=0; i<NUMP; i++) {
    m->mass += pm[i];
    for (j=0; j<3; j++) m->c[j] += pm[i]*q[i][j];
    m->_I(0,0) += pm[i]*(q[i][1]*q[i][1] + q[i][2]*q[i][2]);
    m->_I(1,1) += pm[i]*(q[i][0]*q[i][0] + q[i][2]*q[i][2]);
    m->_I(2,2) += pm[i]*(q[i][0]*q[i][0] + q[i][1]*q[i][1]);
    m->_I(0,1) -= pm[i]*(q[i][0]*q[i][1]);
    m->_I(0,2) -= pm[i]*(q[i][0]*q[i][2]);
    m->_I(1,2) -= pm[i]*(q[i][1]*q[i][2]);
  }
  for (j=0; j<3; j++) m->c[j] /= m->mass;
  m->_I(1,0) = m->_I(0,1);
  m->_I(2,0) = m->_I(0,2);
  m->_I(2,1) = m->_I(1,2);
}


void testMassFunctions()
{
  dMass m;
  int i,j;
  dReal q[NUMP][3];		// particle positions
  dReal pm[NUMP];		// particle masses
  dMass m1,m2;
  dMatrix3 R;

  HEADER;

  printf ("\t");
  dMassSetZero (&m);
  TRAP_MESSAGE (dMassSetParameters (&m,10, 0,0,0, 1,2,3, 4,5,6),
		printf (" FAILED (1)\n"), printf (" passed (1)\n"));

  printf ("\t");
  dMassSetZero (&m);
  TRAP_MESSAGE (dMassSetParameters (&m,10, 0.1,0.2,0.15, 3,5,14, 3.1,3.2,4),
		printf ("passed (2)\n") , printf (" FAILED (2)\n"));
  if (m.mass==10 && m.c[0]==REAL(0.1) && m.c[1]==REAL(0.2) &&
      m.c[2]==REAL(0.15) && m._I(0,0)==3 && m._I(1,1)==5 && m._I(2,2)==14 &&
      m._I(0,1)==REAL(3.1) && m._I(0,2)==REAL(3.2) && m._I(1,2)==4 &&
      m._I(1,0)==REAL(3.1) && m._I(2,0)==REAL(3.2) && m._I(2,1)==4)
    printf ("\tpassed (3)\n"); else printf ("\tFAILED (3)\n");

  dMassSetZero (&m);
  dMassSetSphere (&m,1.4, 0.86);
  if (cmp(m.mass,3.73002719949386) && m.c[0]==0 && m.c[1]==0 && m.c[2]==0 &&
      cmp(m._I(0,0),1.10349124669826) &&
      cmp(m._I(1,1),1.10349124669826) &&
      cmp(m._I(2,2),1.10349124669826) &&
      m._I(0,1)==0 && m._I(0,2)==0 && m._I(1,2)==0 &&
      m._I(1,0)==0 && m._I(2,0)==0 && m._I(2,1)==0)
    printf ("\tpassed (4)\n"); else printf ("\tFAILED (4)\n");

  dMassSetZero (&m);
  dMassSetCapsule (&m,1.3,1,0.76,1.53);
  if (cmp(m.mass,5.99961928996029) && m.c[0]==0 && m.c[1]==0 && m.c[2]==0 &&
      cmp(m._I(0,0),1.59461986077384) &&
      cmp(m._I(1,1),4.21878433864904) &&
      cmp(m._I(2,2),4.21878433864904) &&
      m._I(0,1)==0 && m._I(0,2)==0 && m._I(1,2)==0 &&
      m._I(1,0)==0 && m._I(2,0)==0 && m._I(2,1)==0)
    printf ("\tpassed (5)\n"); else printf ("\tFAILED (5)\n");

  dMassSetZero (&m);
  dMassSetBox (&m,0.27,3,4,5);
  if (cmp(m.mass,16.2) && m.c[0]==0 && m.c[1]==0 && m.c[2]==0 &&
      cmp(m._I(0,0),55.35) && cmp(m._I(1,1),45.9) && cmp(m._I(2,2),33.75) &&
      m._I(0,1)==0 && m._I(0,2)==0 && m._I(1,2)==0 &&
      m._I(1,0)==0 && m._I(2,0)==0 && m._I(2,1)==0)
    printf ("\tpassed (6)\n"); else printf ("\tFAILED (6)\n");

  // test dMassAdjust?

  // make random particles and compute the mass, COM and inertia, then
  // translate and repeat.
  for (i=0; i<NUMP; i++) {
    pm[i] = dRandReal()+0.5;
    for (j=0; j<3; j++) {
      q[i][j] = 2.0*(dRandReal()-0.5);
    }
  }
  computeMassParams (&m1,q,pm);
  memcpy (&m2,&m1,sizeof(dMass));
  dMassTranslate (&m2,1,2,-3);
  for (i=0; i<NUMP; i++) {
    q[i][0] += 1;
    q[i][1] += 2;
    q[i][2] -= 3;
  }
  computeMassParams (&m1,q,pm);
  compareMassParams (&m1,&m2,"7");

  // rotate the masses
  _R(0,0) = -0.87919618797635;
  _R(0,1) = 0.15278881840384;
  _R(0,2) = -0.45129772879842;
  _R(1,0) = -0.47307856232664;
  _R(1,1) = -0.39258064912909;
  _R(1,2) = 0.78871864932708;
  _R(2,0) = -0.05666336483842;
  _R(2,1) = 0.90693771059546;
  _R(2,2) = 0.41743652473765;
  dMassRotate (&m2,R);
  for (i=0; i<NUMP; i++) {
    dReal a[3];
    dMultiply0 (a,&_R(0,0),&q[i][0],3,3,1);
    q[i][0] = a[0];
    q[i][1] = a[1];
    q[i][2] = a[2];
  }
  computeMassParams (&m1,q,pm);
  compareMassParams (&m1,&m2,"8");
}

//****************************************************************************
// test rotation stuff

void makeRandomRotation (dMatrix3 R)
{
  dReal *u1 = R, *u2=R+4, *u3=R+8;
  dMakeRandomVector (u1,3,1.0);
  dNormalize3 (u1);
  dMakeRandomVector (u2,3,1.0);
  dReal d = dCalcVectorDot3(u1,u2);
  u2[0] -= d*u1[0];
  u2[1] -= d*u1[1];
  u2[2] -= d*u1[2];
  dNormalize3(u2);
  dCalcVectorCross3(u3,u1,u2);
}


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");
}


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");
}


void testRotationFunctions()
{
  dMatrix3 R1;
  HEADER;

  printf ("\tdRSetIdentity - ");
  dMakeRandomMatrix (R1,3,3,1.0);
  dRSetIdentity (R1);
  if (cmpIdentityMat3(R1)) printf ("passed\n"); else printf ("FAILED\n");

  printf ("\tdRFromAxisAndAngle - ");

  printf ("\n");
  printf ("\tdRFromEulerAngles - ");

  printf ("\n");
  printf ("\tdRFrom2Axes - ");

  printf ("\n");
}

//****************************************************************************

#include <assert.h>

template<class T>
class simplevector
{
private:
  int n;
  int max;
  T* data;

public:
  simplevector() { initialize(); }
  ~simplevector() { finalize(); }
  T& operator[](int i) { assert(i>=0 && i<n); return data[i]; }
  const T& operator[](int i) const { assert(i>=0 && i<n); return data[i]; }
  void push_back(const T& elem)
  {
    if (n == max)
    {
      max *= 2;
      T* newdata = new T[max];
      memcpy(newdata, data, sizeof(T)*n);
      delete[] data;
      data = newdata;
    }
    data[n++] = elem;
  }
  int size() const { return n; }
  void clear() { finalize(); initialize(); }

private:
  void finalize() { delete[] data; }
  void initialize() { data = new T[32]; max = 32; n = 0; }
};

// matrix header on the stack

class dMatrixComparison {
  struct dMatInfo;
  simplevector<dMatInfo*> mat;
  int afterfirst,index;

public:
  dMatrixComparison();
  ~dMatrixComparison();

  dReal nextMatrix (dReal *A, int n, int m, int lower_tri, const char *name, ...);
  // add a new n*m matrix A to the sequence. the name of the matrix is given
  // by the printf-style arguments (name,...). if this is the first sequence
  // then this object will simply record the matrices and return 0.
  // if this the second or subsequent sequence then this object will compare
  // the matrices with the first sequence, and report any differences.
  // the matrix error will be returned. if `lower_tri' is 1 then only the
  // lower triangle of the matrix (including the diagonal) will be compared
  // (the matrix must be square).

  void end();
  // end a sequence.

  void reset();
  // restarts the object, so the next sequence will be the first sequence.

  void dump();
  // print out info about all the matrices in the sequence
};

struct dMatrixComparison::dMatInfo {
  int n,m;		// size of matrix
  char name[128];	// name of the matrix
  dReal *data;		// matrix data
  int size;		// size of `data'
};



dMatrixComparison::dMatrixComparison()
{
  afterfirst = 0;
  index = 0;
}


dMatrixComparison::~dMatrixComparison()
{
  reset();
}


dReal dMatrixComparison::nextMatrix (dReal *A, int n, int m, int lower_tri,
				     const char *name, ...)
{
  if (A==0 || n < 1 || m < 1 || name==0) dDebug (0,"bad args to nextMatrix");
  int num = n*dPAD(m);

  if (afterfirst==0) {
    dMatInfo *mi = (dMatInfo*) dAlloc (sizeof(dMatInfo));
    mi->n = n;
    mi->m = m;
    mi->size = num * sizeof(dReal);
    mi->data = (dReal*) dAlloc (mi->size);
    memcpy (mi->data,A,mi->size);

    va_list ap;
    va_start (ap,name);
    vsprintf (mi->name,name,ap);
    va_end (ap);
    if (strlen(mi->name) >= sizeof (mi->name)) dDebug (0,"name too long");

    mat.push_back(mi);
    return 0;
  }
  else {
    if (lower_tri && n != m)
      dDebug (0,"dMatrixComparison, lower triangular matrix must be square");
    if (index >= mat.size()) dDebug (0,"dMatrixComparison, too many matrices");
    dMatInfo *mp = mat[index];
    index++;

    dMatInfo mi;
    va_list ap;
    va_start (ap,name);
    vsprintf (mi.name,name,ap);
    va_end (ap);
    if (strlen(mi.name) >= sizeof (mi.name)) dDebug (0,"name too long");

    if (strcmp(mp->name,mi.name) != 0)
      dDebug (0,"dMatrixComparison, name mismatch (\"%s\" and \"%s\")",
	      mp->name,mi.name);
    if (mp->n != n || mp->m != m)
      dDebug (0,"dMatrixComparison, size mismatch (%dx%d and %dx%d)",
	      mp->n,mp->m,n,m);

    dReal maxdiff;
    if (lower_tri) {
      maxdiff = dMaxDifferenceLowerTriangle (A,mp->data,n);
    }
    else {
      maxdiff = dMaxDifference (A,mp->data,n,m);
    }
    if (maxdiff > tol)
      dDebug (0,"dMatrixComparison, matrix error (size=%dx%d, name=\"%s\", "
	      "error=%.4e)",n,m,mi.name,maxdiff);
    return maxdiff;
  }
}


void dMatrixComparison::end()
{
  if (mat.size() <= 0) dDebug (0,"no matrices in sequence");
  afterfirst = 1;
  index = 0;
}


void dMatrixComparison::reset()
{
  for (int i=0; i<mat.size(); i++) {
    dFree (mat[i]->data,mat[i]->size);
    dFree (mat[i],sizeof(dMatInfo));
  }
  mat.clear();
  afterfirst = 0;
  index = 0;
}


void dMatrixComparison::dump()
{
  for (int i=0; i<mat.size(); i++)
    printf ("%d: %s (%dx%d)\n",i,mat[i]->name,mat[i]->n,mat[i]->m);
}

//****************************************************************************
// unit test

#include <setjmp.h>

// static jmp_buf jump_buffer;

static void myDebug (int /*num*/, const char* /*msg*/, va_list /*ap*/)
{
  // printf ("(Error %d: ",num);
  // vprintf (msg,ap);
  // printf (")\n");
  longjmp (jump_buffer,1);
}


extern "C" void dTestMatrixComparison()
{
  volatile int i;
  printf ("dTestMatrixComparison()\n");
  dMessageFunction *orig_debug = dGetDebugHandler();

  dMatrixComparison mc;
  dReal A[50*50];

  // make first sequence
  unsigned long seed = dRandGetSeed();
  for (i=1; i<49; i++) {
    dMakeRandomMatrix (A,i,i+1,1.0);
    mc.nextMatrix (A,i,i+1,0,"A%d",i);
  }
  mc.end();

  //mc.dump();

  // test identical sequence
  dSetDebugHandler (&myDebug);
  dRandSetSeed (seed);
  if (setjmp (jump_buffer)) {
    printf ("\tFAILED (1)\n");
  }
  else {
    for (i=1; i<49; i++) {
      dMakeRandomMatrix (A,i,i+1,1.0);
      mc.nextMatrix (A,i,i+1,0,"A%d",i);
    }
    mc.end();
    printf ("\tpassed (1)\n");
  }
  dSetDebugHandler (orig_debug);

  // test broken sequences (with matrix error)
  dRandSetSeed (seed);
  volatile int passcount = 0;
  for (i=1; i<49; i++) {
    if (setjmp (jump_buffer)) {
      passcount++;
    }
    else {
      dSetDebugHandler (&myDebug);
      dMakeRandomMatrix (A,i,i+1,1.0);
      A[(i-1)*dPAD(i+1)+i] += REAL(0.01);
      mc.nextMatrix (A,i,i+1,0,"A%d",i);
      dSetDebugHandler (orig_debug);
    }
  }
  mc.end();
  printf ("\t%s (2)\n",(passcount == 48) ? "passed" : "FAILED");

  // test broken sequences (with name error)
  dRandSetSeed (seed);
  passcount = 0;
  for (i=1; i<49; i++) {
    if (setjmp (jump_buffer)) {
      passcount++;
    }
    else {
      dSetDebugHandler (&myDebug);
      dMakeRandomMatrix (A,i,i+1,1.0);
      mc.nextMatrix (A,i,i+1,0,"B%d",i);
      dSetDebugHandler (orig_debug);
    }
  }
  mc.end();
  printf ("\t%s (3)\n",(passcount == 48) ? "passed" : "FAILED");

  // test identical sequence again
  dSetDebugHandler (&myDebug);
  dRandSetSeed (seed);
  if (setjmp (jump_buffer)) {
    printf ("\tFAILED (4)\n");
  }
  else {
    for (i=1; i<49; i++) {
      dMakeRandomMatrix (A,i,i+1,1.0);
      mc.nextMatrix (A,i,i+1,0,"A%d",i);
    }
    mc.end();
    printf ("\tpassed (4)\n");
  }
  dSetDebugHandler (orig_debug);
}

//****************************************************************************

// internal unit tests
extern "C" void dTestDataStructures();
extern "C" void dTestMatrixComparison();
extern "C" int dTestSolveLCP();


int main()
{
  dInitODE();
  testRandomNumberGenerator();
  testInfinity();
  testPad();
  testCrossProduct();
  testSetZero();
  testNormalize3();
  //testReorthonormalize();     ... not any more
  testPlaneSpace();
  testMatrixMultiply();
  testSmallMatrixMultiply();
  testCholeskyFactorization();
  testCholeskySolve();
  testInvertPDMatrix();
  testIsPositiveDefinite();
  testFastLDLTFactorization();
  testSolveLDLT();
  testLDLTAddTL();
  testLDLTRemove();
  testMassFunctions();
  testRtoQandQtoR();
  testQuaternionMultiply();
  testRotationFunctions();
  dTestMatrixComparison();
  dTestSolveLCP();
  // dTestDataStructures();
  dCloseODE();
  return 0;
}