// Function definitions.
// -----------------------------------------------------------------
void mexFunction (int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
//Input Args
user_function_data fun;
double *x0, *ydata = NULL, *lb = NULL, *ub = NULL, *A = NULL, *b = NULL, *Aeq = NULL, *beq = NULL;
//Options
int maxIter = 500;
double info[LM_INFO_SZ];
double opts[LM_OPTS_SZ]={J_INIT_MU, J_STOP_THRESH, J_STOP_THRESH, J_STOP_THRESH, LM_DIFF_DELTA};
//Outputs Args
double *x, *fval, *exitflag, *iter, *feval;
double *pcovar = NULL;
//Internal Vars
size_t ndec, ndat;
int i, status, havJac = 0, conMode = 0;
int nineq=0, neq=0;
double *covar = NULL;
double *Apr, *bpr;
double *llb, *lub;
citer = 1;
iterF.enabled = false;
if (nrhs < 1) {
if(nlhs < 1)
printSolverInfo();
else
plhs[0] = mxCreateString(LM_VERSION);
return;
}
//Check user inputs & get constraint information
checkInputs(prhs,nrhs,&conMode);
//Get Sizes
ndec = mxGetNumberOfElements(prhs[2]);
ndat = mxGetNumberOfElements(prhs[3]);
//Get Objective Function Handle
if (mxIsChar(prhs[0])) {
CHECK(mxGetString(prhs[0], fun.f, FLEN) == 0,"error reading objective name string");
fun.nrhs = 1;
fun.xrhs = 0;
} else {
fun.prhs[0] = (mxArray*)prhs[0];
strcpy(fun.f, "feval");
fun.nrhs = 2;
fun.xrhs = 1;
}
fun.prhs[fun.xrhs] = mxCreateDoubleMatrix(ndec, 1, mxREAL); //x0
fun.print = 0;
//Check and Get Gradient Function Handle
if(!mxIsEmpty(prhs[1])) {
havJac = 1;
if (mxIsChar(prhs[1])) {
CHECK(mxGetString(prhs[1], fun.g, FLEN) == 0,"error reading gradient name string");
fun.nrhs_g = 1;
fun.xrhs_g = 0;
} else {
fun.prhs_g[0] = (mxArray*)prhs[1];
strcpy(fun.g, "feval");
fun.nrhs_g = 2;
fun.xrhs_g = 1;
}
fun.prhs_g[fun.xrhs_g] = mxCreateDoubleMatrix(ndec, 1, mxREAL); //x0
}
//Get x0 + data
x0 = mxGetPr(prhs[2]);
ydata = mxGetPr(prhs[3]);
fun.ydata = ydata;
//Get Bounds
if(conMode & 1) {
//LB
if(!mxIsEmpty(prhs[4])){
llb = mxGetPr(prhs[4]);
lb = mxCalloc(ndec,sizeof(double));
memcpy(lb,llb,ndec*sizeof(double));
for(i=0;i<ndec;i++) {
if(mxIsInf(lb[i]))
lb[i] = -DBL_MAX;
}
}
else {
lb = mxCalloc(ndec,sizeof(double));
for(i=0;i<ndec;i++)
lb[i] = -DBL_MAX;
}
//UB
if(nrhs > 5 && !mxIsEmpty(prhs[5])){
lub = mxGetPr(prhs[5]);
ub = mxCalloc(ndec,sizeof(double));
memcpy(ub,lub,ndec*sizeof(double));
for(i=0;i<ndec;i++) {
if(mxIsInf(ub[i]))
ub[i] = DBL_MAX;
}
}
else {
ub = mxCalloc(ndec,sizeof(double));
for(i=0;i<ndec;i++)
ub[i] = DBL_MAX;
}
}
//Get Linear Inequality Constraints
if(conMode & 2) {
nineq = (int)mxGetM(prhs[7]);
Apr = mxGetPr(prhs[6]);
bpr = mxGetPr(prhs[7]);
//Need to flip >= to <=
A = mxCalloc(ndec*nineq,sizeof(double));
b = mxCalloc(nineq,sizeof(double));
for(i=0;i<ndec*nineq;i++)
A[i] = -Apr[i];
for(i=0;i<nineq;i++)
b[i] = -bpr[i];
}
//Get Linear Equality Constraints
if(conMode & 4) {
Aeq = mxGetPr(prhs[8]);
beq = mxGetPr(prhs[9]);
neq = (int)mxGetM(prhs[9]);
}
//Get Options if specified
if(nrhs > 10) {
if(mxGetField(prhs[10],0,"maxiter"))
maxIter = (int)*mxGetPr(mxGetField(prhs[10],0,"maxiter"));
if(mxGetField(prhs[10],0,"display"))
fun.print = (int)*mxGetPr(mxGetField(prhs[10],0,"display"));
if(mxGetField(prhs[10],0,"iterfun") && !mxIsEmpty(mxGetField(prhs[10],0,"iterfun")))
{
iterF.prhs[0] = (mxArray*)mxGetField(prhs[10],0,"iterfun");
strcpy(iterF.f, "feval");
iterF.enabled = true;
iterF.prhs[1] = mxCreateNumericMatrix(1,1,mxINT32_CLASS,mxREAL);
iterF.prhs[2] = mxCreateDoubleMatrix(1,1,mxREAL);
iterF.prhs[3] = mxCreateDoubleMatrix(ndec,1,mxREAL);
}
}
//Create Outputs
plhs[0] = mxCreateDoubleMatrix(ndec,1, mxREAL);
plhs[1] = mxCreateDoubleMatrix(1,1, mxREAL);
plhs[2] = mxCreateDoubleMatrix(1,1, mxREAL);
plhs[3] = mxCreateDoubleMatrix(1,1, mxREAL);
plhs[4] = mxCreateDoubleMatrix(1,1, mxREAL);
x = mxGetPr(plhs[0]);
fval = mxGetPr(plhs[1]);
exitflag = mxGetPr(plhs[2]);
iter = mxGetPr(plhs[3]);
feval = mxGetPr(plhs[4]);
//Copy initial guess to x
memcpy(x,x0,ndec*sizeof(double));
//Create Covariance Matrix if Required
if(nlhs>4)
covar=mxCalloc(ndec*ndec,sizeof(double));
//Print Header
if(fun.print) {
mexPrintf("\n------------------------------------------------------------------\n");
mexPrintf(" This is LEVMAR v2.5\n");
mexPrintf(" Author: Manolis Lourakis\n MEX Interface J. Currie 2011\n\n");
mexPrintf(" Problem Properties:\n");
mexPrintf(" # Decision Variables: %4d\n",ndec);
mexPrintf(" # Data Points: %4d\n",ndat);
mexPrintf("------------------------------------------------------------------\n");
}
//Solve based on constraints
switch(conMode)
{
case MIN_UNCONSTRAINED:
//mexPrintf("Unc Problem\n");
if(havJac)
status = dlevmar_der(func, jac, x, ydata, (int)ndec, (int)ndat, maxIter, opts, info, NULL, covar, &fun);
else
status = dlevmar_dif(func, x, ydata, (int)ndec, (int)ndat, maxIter, opts, info, NULL, covar, &fun);
break;
case MIN_CONSTRAINED_BC:
//mexPrintf("Box Constrained Problem\n");
if(havJac)
status = dlevmar_bc_der(func, jac, x, ydata, (int)ndec, (int)ndat, lb, ub, NULL, maxIter, opts, info, NULL, covar, &fun);
else
status = dlevmar_bc_dif(func, x, ydata, (int)ndec, (int)ndat, lb, ub, NULL, maxIter, opts, info, NULL, covar, &fun);
break;
case MIN_CONSTRAINED_LIC:
//mexPrintf("Linear Inequality Problem\n");
if(havJac)
status = dlevmar_lic_der(func, jac, x, ydata, (int)ndec, (int)ndat, A, b, nineq, maxIter, opts, info, NULL, covar, &fun);
else
status = dlevmar_lic_dif(func, x, ydata, (int)ndec, (int)ndat, A, b, nineq, maxIter, opts, info, NULL, covar, &fun);
break;
case MIN_CONSTRAINED_BLIC:
//mexPrintf("Boxed Linear Inequality Problem\n");
if(havJac)
status = dlevmar_blic_der(func, jac, x, ydata, (int)ndec, (int)ndat, lb, ub, A, b, nineq, maxIter, opts, info, NULL, covar, &fun);
else
status = dlevmar_blic_dif(func, x, ydata, (int)ndec, (int)ndat, lb, ub, A, b, nineq, maxIter, opts, info, NULL, covar, &fun);
break;
case MIN_CONSTRAINED_LEC:
//mexPrintf("Linear Equality Problem\n");
if(havJac)
status = dlevmar_lec_der(func, jac, x, ydata, (int)ndec, (int)ndat, Aeq, beq, neq, maxIter, opts, info, NULL, covar, &fun);
else
status = dlevmar_lec_dif(func, x, ydata, (int)ndec, (int)ndat, Aeq, beq, neq, maxIter, opts, info, NULL, covar, &fun);
break;
case MIN_CONSTRAINED_BLEC:
//mexPrintf("Boxed Linear Equality Problem\n");
if(havJac)
status = dlevmar_blec_der(func, jac, x, ydata, (int)ndec, (int)ndat, lb, ub, Aeq, beq, neq, NULL, maxIter, opts, info, NULL, covar, &fun);
else
status = dlevmar_blec_dif(func, x, ydata, (int)ndec, (int)ndat, lb, ub, Aeq, beq, neq, NULL, maxIter, opts, info, NULL, covar, &fun);
break;
case MIN_CONSTRAINED_LEIC:
//mexPrintf("Linear Inequality + Equality Problem\n");
if(havJac)
status = dlevmar_leic_der(func, jac, x, ydata, (int)ndec, (int)ndat, Aeq, beq, neq, A, b, nineq, maxIter, opts, info, NULL, covar, &fun);
else
status = dlevmar_leic_dif(func, x, ydata, (int)ndec, (int)ndat, Aeq, beq, neq, A, b, nineq, maxIter, opts, info, NULL, covar, &fun);
break;
case MIN_CONSTRAINED_BLEIC:
//mexPrintf("Boxed Linear Inequality + Equality Problem\n");
if(havJac)
status = dlevmar_bleic_der(func, jac, x, ydata, (int)ndec, (int)ndat, lb, ub, Aeq, beq, neq, A, b, nineq, maxIter, opts, info, NULL, covar, &fun);
else
status = dlevmar_bleic_dif(func, x, ydata, (int)ndec, (int)ndat, lb, ub, Aeq, beq, neq, A, b, nineq, maxIter, opts, info, NULL, covar, &fun);
break;
default:
mexErrMsgTxt("Unknown constraint configuration");
}
//Save Status & Iterations
*fval = info[1];
*exitflag = getStatus(info[6]);
*iter = (double)status;
*feval = (double)citer;
//Save Covariance if Required
if(nlhs > 5) {
plhs[5] = mxCreateDoubleMatrix(ndec, ndec, mxREAL);
pcovar = mxGetPr(plhs[5]);
memcpy(pcovar,covar,ndec*ndec*sizeof(double));
}
//Print Header
if(fun.print){
//Termination Detected
if(*exitflag == 1)
mexPrintf("\n *** SUCCESSFUL TERMINATION ***\n");
else if(*exitflag == 0)
mexPrintf("\n *** MAXIMUM ITERATIONS REACHED ***\n");
else if(*exitflag == -1)
mexPrintf("\n *** TERMINATION: TOLERANCE TOO SMALL ***\n");
else if(*exitflag == -2)
mexPrintf("\n *** TERMINATION: ROUTINE ERROR ***\n");
if(*exitflag==1)
mexPrintf(" Final SSE: %12.5g\n In %3.0f iterations\n",*fval,*iter);
mexPrintf("------------------------------------------------------------------\n\n");
}
//Clean Up
if(lb) mxFree(lb);
if(ub) mxFree(ub);
if(covar) mxFree(covar);
if(A) mxFree(A);
if(b) mxFree(b);
}
int main()
{
register int i, j;
int problem, ret;
double p[5], // 5 is max(2, 3, 5)
x[16]; // 16 is max(2, 3, 5, 6, 16)
int m, n;
double opts[LM_OPTS_SZ], info[LM_INFO_SZ];
char *probname[]={
"Rosenbrock function",
"modified Rosenbrock problem",
"Powell's function",
"Wood's function",
"Meyer's (reformulated) problem",
"Osborne's problem",
"helical valley function",
"Boggs & Tolle's problem #3",
"Hock - Schittkowski problem #28",
"Hock - Schittkowski problem #48",
"Hock - Schittkowski problem #51",
"Hock - Schittkowski problem #01",
"Hock - Schittkowski modified problem #21",
"hatfldb problem",
"hatfldc problem",
"equilibrium combustion problem",
"Hock - Schittkowski modified #1 problem #52",
"Schittkowski modified problem #235",
"Boggs & Tolle modified problem #7",
"Hock - Schittkowski modified #2 problem #52",
"Hock - Schittkowski modified problem #76",
};
opts[0]=LM_INIT_MU; opts[1]=1E-15; opts[2]=1E-15; opts[3]=1E-20;
opts[4]= LM_DIFF_DELTA; // relevant only if the Jacobian is approximated using finite differences; specifies forward differencing
//opts[4]=-LM_DIFF_DELTA; // specifies central differencing to approximate Jacobian; more accurate but more expensive to compute!
/* uncomment the appropriate line below to select a minimization problem */
problem=
//0; // Rosenbrock function
//1; // modified Rosenbrock problem
//2; // Powell's function
//3; // Wood's function
4; // Meyer's (reformulated) problem
//5; // Osborne's problem
//6; // helical valley function
#ifdef HAVE_LAPACK
//7; // Boggs & Tolle's problem 3
//8; // Hock - Schittkowski problem 28
//9; // Hock - Schittkowski problem 48
//10; // Hock - Schittkowski problem 51
#else // no LAPACK
#ifdef _MSC_VER
#pragma message("LAPACK not available, some test problems cannot be used")
#else
#warning LAPACK not available, some test problems cannot be used
#endif // _MSC_VER
#endif /* HAVE_LAPACK */
//11; // Hock - Schittkowski problem 01
//12; // Hock - Schittkowski modified problem 21
//13; // hatfldb problem
//14; // hatfldc problem
//15; // equilibrium combustion problem
#ifdef HAVE_LAPACK
//16; // Hock - Schittkowski modified #1 problem 52
//17; // Schittkowski modified problem 235
//18; // Boggs & Tolle modified problem #7
//19; // Hock - Schittkowski modified #2 problem 52
//20; // Hock - Schittkowski modified problem #76"
#endif /* HAVE_LAPACK */
switch(problem){
default: fprintf(stderr, "unknown problem specified (#%d)! Note that some minimization problems require LAPACK.\n", problem);
exit(1);
break;
case 0:
/* Rosenbrock function */
m=2; n=2;
p[0]=-1.2; p[1]=1.0;
for(i=0; i<n; i++) x[i]=0.0;
ret=dlevmar_der(ros, jacros, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic Jacobian
//ret=dlevmar_dif(ros, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // no Jacobian
break;
case 1:
/* modified Rosenbrock problem */
m=2; n=3;
p[0]=-1.2; p[1]=1.0;
for(i=0; i<n; i++) x[i]=0.0;
ret=dlevmar_der(modros, jacmodros, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic Jacobian
//ret=dlevmar_dif(modros, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // no Jacobian
break;
case 2:
/* Powell's function */
m=2; n=2;
p[0]=3.0; p[1]=1.0;
for(i=0; i<n; i++) x[i]=0.0;
ret=dlevmar_der(powell, jacpowell, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic Jacobian
//ret=dlevmar_dif(powell, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // no Jacobian
break;
case 3:
/* Wood's function */
m=4; n=6;
p[0]=-3.0; p[1]=-1.0; p[2]=-3.0; p[3]=-1.0;
for(i=0; i<n; i++) x[i]=0.0;
ret=dlevmar_dif(wood, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // no Jacobian
break;
case 4:
/* Meyer's data fitting problem */
m=3; n=16;
p[0]=8.85; p[1]=4.0; p[2]=2.5;
x[0]=34.780; x[1]=28.610; x[2]=23.650; x[3]=19.630;
x[4]=16.370; x[5]=13.720; x[6]=11.540; x[7]=9.744;
x[8]=8.261; x[9]=7.030; x[10]=6.005; x[11]=5.147;
x[12]=4.427; x[13]=3.820; x[14]=3.307; x[15]=2.872;
//ret=dlevmar_der(meyer, jacmeyer, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic Jacobian
{ double *work, *covar;
work=malloc((LM_DIF_WORKSZ(m, n)+m*m)*sizeof(double));
if(!work){
fprintf(stderr, "memory allocation request failed in main()\n");
exit(1);
}
covar=work+LM_DIF_WORKSZ(m, n);
ret=dlevmar_dif(meyer, p, x, m, n, 1000, opts, info, work, covar, NULL); // no Jacobian, caller allocates work memory, covariance estimated
printf("Covariance of the fit:\n");
for(i=0; i<m; ++i){
for(j=0; j<m; ++j)
printf("%g ", covar[i*m+j]);
printf("\n");
}
printf("\n");
free(work);
}
/* uncomment the following block to verify Jacobian */
/*
{
double err[16];
dlevmar_chkjac(meyer, jacmeyer, p, m, n, NULL, err);
for(i=0; i<n; ++i) printf("gradient %d, err %g\n", i, err[i]);
}
*/
break;
case 5:
/* Osborne's data fitting problem */
{
double x33[]={
8.44E-1, 9.08E-1, 9.32E-1, 9.36E-1, 9.25E-1, 9.08E-1, 8.81E-1,
8.5E-1, 8.18E-1, 7.84E-1, 7.51E-1, 7.18E-1, 6.85E-1, 6.58E-1,
6.28E-1, 6.03E-1, 5.8E-1, 5.58E-1, 5.38E-1, 5.22E-1, 5.06E-1,
4.9E-1, 4.78E-1, 4.67E-1, 4.57E-1, 4.48E-1, 4.38E-1, 4.31E-1,
4.24E-1, 4.2E-1, 4.14E-1, 4.11E-1, 4.06E-1};
m=5; n=33;
p[0]=0.5; p[1]=1.5; p[2]=-1.0; p[3]=1.0E-2; p[4]=2.0E-2;
ret=dlevmar_der(osborne, jacosborne, p, x33, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic Jacobian
//ret=dlevmar_dif(osborne, p, x33, m, n, 1000, opts, info, NULL, NULL, NULL); // no Jacobian
}
break;
case 6:
/* helical valley function */
m=3; n=3;
p[0]=-1.0; p[1]=0.0; p[2]=0.0;
for(i=0; i<n; i++) x[i]=0.0;
ret=dlevmar_der(helval, jachelval, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic Jacobian
//ret=dlevmar_dif(helval, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // no Jacobian
break;
#ifdef HAVE_LAPACK
case 7:
/* Boggs-Tolle problem 3 */
m=5; n=5;
p[0]=2.0; p[1]=2.0; p[2]=2.0;
p[3]=2.0; p[4]=2.0;
for(i=0; i<n; i++) x[i]=0.0;
{
double A[3*5]={1.0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0},
b[3]={0.0, 0.0, 0.0};
ret=dlevmar_lec_der(bt3, jacbt3, p, x, m, n, A, b, 3, 1000, opts, info, NULL, NULL, NULL); // lin. constraints, analytic Jacobian
//ret=dlevmar_lec_dif(bt3, p, x, m, n, A, b, 3, 1000, opts, info, NULL, NULL, NULL); // lin. constraints, no Jacobian
}
break;
case 8:
/* Hock - Schittkowski problem 28 */
m=3; n=3;
p[0]=-4.0; p[1]=1.0; p[2]=1.0;
for(i=0; i<n; i++) x[i]=0.0;
{
double A[1*3]={1.0, 2.0, 3.0},
b[1]={1.0};
ret=dlevmar_lec_der(hs28, jachs28, p, x, m, n, A, b, 1, 1000, opts, info, NULL, NULL, NULL); // lin. constraints, analytic Jacobian
//ret=dlevmar_lec_dif(hs28, p, x, m, n, A, b, 1, 1000, opts, info, NULL, NULL, NULL); // lin. constraints, no Jacobian
}
break;
case 9:
/* Hock - Schittkowski problem 48 */
m=5; n=5;
p[0]=3.0; p[1]=5.0; p[2]=-3.0;
p[3]=2.0; p[4]=-2.0;
for(i=0; i<n; i++) x[i]=0.0;
{
double A[2*5]={1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0, -2.0, -2.0},
b[2]={5.0, -3.0};
ret=dlevmar_lec_der(hs48, jachs48, p, x, m, n, A, b, 2, 1000, opts, info, NULL, NULL, NULL); // lin. constraints, analytic Jacobian
//ret=dlevmar_lec_dif(hs48, p, x, m, n, A, b, 2, 1000, opts, info, NULL, NULL, NULL); // lin. constraints, no Jacobian
}
break;
case 10:
/* Hock - Schittkowski problem 51 */
m=5; n=5;
p[0]=2.5; p[1]=0.5; p[2]=2.0;
p[3]=-1.0; p[4]=0.5;
for(i=0; i<n; i++) x[i]=0.0;
{
double A[3*5]={1.0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0},
b[3]={4.0, 0.0, 0.0};
ret=dlevmar_lec_der(hs51, jachs51, p, x, m, n, A, b, 3, 1000, opts, info, NULL, NULL, NULL); // lin. constraints, analytic Jacobian
//ret=dlevmar_lec_dif(hs51, p, x, m, n, A, b, 3, 1000, opts, info, NULL, NULL, NULL); // lin. constraints, no Jacobian
}
break;
#endif /* HAVE_LAPACK */
case 11:
/* Hock - Schittkowski problem 01 */
m=2; n=2;
p[0]=-2.0; p[1]=1.0;
for(i=0; i<n; i++) x[i]=0.0;
//ret=dlevmar_der(hs01, jachs01, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic Jacobian
{
double lb[2], ub[2];
lb[0]=-DBL_MAX; lb[1]=-1.5;
ub[0]=ub[1]=DBL_MAX;
ret=dlevmar_bc_der(hs01, jachs01, p, x, m, n, lb, ub, 1000, opts, info, NULL, NULL, NULL); // with analytic Jacobian
}
break;
case 12:
/* Hock - Schittkowski (modified) problem 21 */
m=2; n=2;
p[0]=-1.0; p[1]=-1.0;
for(i=0; i<n; i++) x[i]=0.0;
//ret=dlevmar_der(hs21, jachs21, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic Jacobian
{
double lb[2], ub[2];
lb[0]=2.0; lb[1]=-50.0;
ub[0]=50.0; ub[1]=50.0;
ret=dlevmar_bc_der(hs21, jachs21, p, x, m, n, lb, ub, 1000, opts, info, NULL, NULL, NULL); // with analytic Jacobian
}
break;
case 13:
/* hatfldb problem */
m=4; n=4;
p[0]=p[1]=p[2]=p[3]=0.1;
for(i=0; i<n; i++) x[i]=0.0;
//ret=dlevmar_der(hatfldb, jachatfldb, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic Jacobian
{
double lb[4], ub[4];
lb[0]=lb[1]=lb[2]=lb[3]=0.0;
ub[0]=ub[2]=ub[3]=DBL_MAX;
ub[1]=0.8;
ret=dlevmar_bc_der(hatfldb, jachatfldb, p, x, m, n, lb, ub, 1000, opts, info, NULL, NULL, NULL); // with analytic Jacobian
}
break;
case 14:
/* hatfldc problem */
m=4; n=4;
p[0]=p[1]=p[2]=p[3]=0.9;
for(i=0; i<n; i++) x[i]=0.0;
//ret=dlevmar_der(hatfldc, jachatfldc, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic Jacobian
{
double lb[4], ub[4];
lb[0]=lb[1]=lb[2]=lb[3]=0.0;
ub[0]=ub[1]=ub[2]=ub[3]=10.0;
ret=dlevmar_bc_der(hatfldc, jachatfldc, p, x, m, n, lb, ub, 1000, opts, info, NULL, NULL, NULL); // with analytic Jacobian
}
break;
case 15:
/* equilibrium combustion problem */
m=5; n=5;
p[0]=p[1]=p[2]=p[3]=p[4]=0.0001;
for(i=0; i<n; i++) x[i]=0.0;
//ret=dlevmar_der(combust, jaccombust, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic Jacobian
{
double lb[5], ub[5];
lb[0]=lb[1]=lb[2]=lb[3]=lb[4]=0.0001;
ub[0]=ub[1]=ub[2]=ub[3]=ub[4]=100.0;
ret=dlevmar_bc_der(combust, jaccombust, p, x, m, n, lb, ub, 5000, opts, info, NULL, NULL, NULL); // with analytic Jacobian
}
break;
#ifdef HAVE_LAPACK
case 16:
/* Hock - Schittkowski modified #1 problem 52 */
m=5; n=4;
p[0]=2.0; p[1]=2.0; p[2]=2.0;
p[3]=2.0; p[4]=2.0;
for(i=0; i<n; i++) x[i]=0.0;
{
double A[3*5]={1.0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, -2.0, 0.0, 1.0, 0.0, 0.0, -1.0},
b[3]={0.0, 0.0, 0.0};
double lb[5], ub[5];
double weights[5]={2000.0, 2000.0, 2000.0, 2000.0, 2000.0}; // penalty terms weights
lb[0]=-0.09; lb[1]=0.0; lb[2]=-DBL_MAX; lb[3]=-0.2; lb[4]=0.0;
ub[0]=DBL_MAX; ub[1]=0.3; ub[2]=0.25; ub[3]=0.3; ub[4]=0.3;
ret=dlevmar_blec_der(mod1hs52, jacmod1hs52, p, x, m, n, lb, ub, A, b, 3, weights, 1000, opts, info, NULL, NULL, NULL); // box & lin. constraints, analytic Jacobian
//ret=dlevmar_blec_dif(mod1hs52, p, x, m, n, lb, ub, A, b, 3, weights, 1000, opts, info, NULL, NULL, NULL); // box & lin. constraints, no Jacobian
}
break;
case 17:
/* Schittkowski modified problem 235 */
m=3; n=2;
p[0]=-2.0; p[1]=3.0; p[2]=1.0;
for(i=0; i<n; i++) x[i]=0.0;
{
double A[2*3]={1.0, 0.0, 1.0, 0.0, 1.0, -4.0},
b[2]={-1.0, 0.0};
double lb[3], ub[3];
lb[0]=-DBL_MAX; lb[1]=0.1; lb[2]=0.7;
ub[0]=DBL_MAX; ub[1]=2.9; ub[2]=DBL_MAX;
ret=dlevmar_blec_der(mods235, jacmods235, p, x, m, n, lb, ub, A, b, 2, NULL, 1000, opts, info, NULL, NULL, NULL); // box & lin. constraints, analytic Jacobian
//ret=dlevmar_blec_dif(mods235, p, x, m, n, lb, ub, A, b, 2, NULL, 1000, opts, info, NULL, NULL, NULL); // box & lin. constraints, no Jacobian
}
break;
case 18:
/* Boggs & Tolle modified problem 7 */
m=5; n=5;
p[0]=-2.0; p[1]=1.0; p[2]=1.0; p[3]=1.0; p[4]=1.0;
for(i=0; i<n; i++) x[i]=0.0;
{
double A[3*5]={1.0, 1.0, -1.0, 0.0, 0.0, 1.0, 1.0, 0.0, -1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0},
b[3]={1.0, 0.0, 0.5};
double lb[5], ub[5];
lb[0]=-DBL_MAX; lb[1]=-DBL_MAX; lb[2]=-DBL_MAX; lb[3]=-DBL_MAX; lb[4]=-0.3;
ub[0]=0.7; ub[1]= DBL_MAX; ub[2]= DBL_MAX; ub[3]= DBL_MAX; ub[4]=DBL_MAX;
ret=dlevmar_blec_der(modbt7, jacmodbt7, p, x, m, n, lb, ub, A, b, 3, NULL, 1000, opts, info, NULL, NULL, NULL); // box & lin. constraints, analytic Jacobian
//ret=dlevmar_blec_dif(modbt7, p, x, m, n, lb, ub, A, b, 3, NULL, 10000, opts, info, NULL, NULL, NULL); // box & lin. constraints, no Jacobian
}
break;
case 19:
/* Hock - Schittkowski modified #2 problem 52 */
m=5; n=5;
p[0]=2.0; p[1]=2.0; p[2]=2.0;
p[3]=2.0; p[4]=2.0;
for(i=0; i<n; i++) x[i]=0.0;
{
double C[3*5]={1.0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, -2.0, 0.0, -1.0, 0.0, 0.0, 1.0},
d[3]={-1.0, -2.0, -7.0};
ret=dlevmar_bleic_der(mod2hs52, jacmod2hs52, p, x, m, n, NULL, NULL, NULL, NULL, 0, C, d, 3, 1000, opts, info, NULL, NULL, NULL); // lin. ineq. constraints, analytic Jacobian
//ret=dlevmar_bleic_dif(mod2hs52, p, x, m, n, NULL, NULL, NULL, NULL, 0, C, d, 3, 1000, opts, info, NULL, NULL, NULL); // lin. ineq. constraints, no Jacobian
}
break;
case 20:
/* Hock - Schittkowski modified problem 76 */
m=4; n=4;
p[0]=0.5; p[1]=0.5; p[2]=0.5; p[3]=0.5;
for(i=0; i<n; i++) x[i]=0.0;
{
double A[1*4]={0.0, 1.0, 4.0, 0.0},
b[1]={1.5};
double C[2*4]={-1.0, -2.0, -1.0, -1.0, -3.0, -1.0, -2.0, 1.0},
d[2]={-5.0, -0.4};
double lb[4]={0.0, 0.0, 0.0, 0.0};
ret=dlevmar_bleic_der(modhs76, jacmodhs76, p, x, m, n, lb, NULL, A, b, 1, C, d, 2, 1000, opts, info, NULL, NULL, NULL); // lin. ineq. constraints, analytic Jacobian
//ret=dlevmar_bleic_dif(modhs76, p, x, m, n, lb, NULL, A, b, 1, C, d, 2, 1000, opts, info, NULL, NULL, NULL); // lin. ineq. constraints, no Jacobian
/* variations:
* if no lb is used, the minimizer is (-0.1135922 0.1330097 0.3417476 0.07572816)
* if the rhs of constr2 is 4.0, the minimizer is (0.0, 0.166667, 0.333333, 0.0)
*/
}
break;
#endif /* HAVE_LAPACK */
} /* switch */
printf("Results for %s:\n", probname[problem]);
printf("Levenberg-Marquardt returned %d in %g iter, reason %g\nSolution: ", ret, info[5], info[6]);
for(i=0; i<m; ++i)
printf("%.7g ", p[i]);
printf("\n\nMinimization info:\n");
for(i=0; i<LM_INFO_SZ; ++i)
printf("%g ", info[i]);
printf("\n");
return 0;
}
static PyObject *
_pylm_dlevmar_generic(PyObject *mod, PyObject *args, PyObject *kwds,
char *argstring, char *kwlist[],
int jacobian, int bounds) {
PyObject *func = NULL;
PyObject *jacf = NULL;
PyObject *initial = NULL, *initial_npy = NULL;
PyObject *measurements = NULL, *measurements_npy = NULL;
PyObject *lower = NULL, *lower_npy = NULL;
PyObject *upper = NULL, *upper_npy = NULL;
PyObject *opts = NULL, *opts_npy = NULL;
PyObject *covar = NULL;
PyObject *retval = NULL;
PyObject *info = NULL;
pylm_callback_data *pydata = NULL;
double *c_initial = NULL;
double *c_measurements = NULL;
double *c_opts = NULL;
double *c_lower = NULL;
double *c_upper = NULL;
double *c_covar = NULL;
int max_iter = 0;
int run_iter = 0;
int m = 0, n = 0;
double c_info[LM_INFO_SZ];
int nopts;
// If finite-difference approximate Jacobians are used, we
// need 5 optional params; otherwise 4.
if (jacobian){
nopts = 4;
} else {
nopts = 5;
}
// parse arguments
if (!bounds) {
if (jacobian) {
if (!PyArg_ParseTupleAndKeywords(args, kwds, argstring, kwlist,
&func, &jacf, &initial,
&measurements, &max_iter,
&opts, &covar)){
return NULL;
}
} else {
if (!PyArg_ParseTupleAndKeywords(args, kwds, argstring, kwlist,
&func, &initial,
&measurements, &max_iter,
&opts, &covar)){
return NULL;
}
}
} else {
if (jacobian) {
if (!PyArg_ParseTupleAndKeywords(args, kwds, argstring, kwlist,
&func, &jacf, &initial,
&measurements, &lower, &upper, &max_iter,
&opts, &covar)){
return NULL;
}
} else {
if (!PyArg_ParseTupleAndKeywords(args, kwds, argstring, kwlist,
&func, &initial,
&measurements, &lower, &upper, &max_iter,
&opts, &covar)){
return NULL;
}
}
}
// Check each variable type
if (!PyCallable_Check(func)) {
PyErr_SetString(PyExc_TypeError, "func must be a callable object");
return NULL;
}
if (!PyArray_Check(initial)) {
PyErr_SetString(PyExc_TypeError, "initial must be a numpy array");
return NULL;
}
if (!PyArray_Check(measurements)) {
PyErr_SetString(PyExc_TypeError, "measurements must be a numpy array");
return NULL;
}
if (jacobian && !PyCallable_Check(jacf)) {
PyErr_SetString(PyExc_TypeError, "jacf must be a callable object");
return NULL;
}
if (lower && !PyArray_Check(lower)) {
PyErr_SetString(PyExc_TypeError, "lower bounds must be a numpy array");
return NULL;
}
if (upper && !PyArray_Check(upper)) {
PyErr_SetString(PyExc_TypeError, "upper bounds must be a numpy array");
return NULL;
}
if (opts && !PyArray_Check(opts) && (PyArray_Size(opts) != nopts)) {
if (nopts == 4){
PyErr_SetString(PyExc_TypeError,
"opts must be a numpy vector of length 4.");
} else {
PyErr_SetString(PyExc_TypeError,
"opts must be a numpy vector of length 5.");
}
return NULL;
}
// convert python types into C
pydata = PyMem_Malloc(sizeof(pydata));
if(!pydata){
PyErr_SetString(PyExc_RuntimeError,
"Error in allocating memory for data.");
return NULL;
}
pydata->func = func;
pydata->jacf = jacf;
initial_npy = PyArray_FROMANY(initial, NPY_DOUBLE, 0, 0, NPY_INOUT_ARRAY);
measurements_npy = PyArray_FROMANY(measurements, NPY_DOUBLE, 0, 0, NPY_IN_ARRAY);
if(!initial_npy || !measurements_npy){
// Cannot create array
PyErr_SetString(PyExc_RuntimeError,
"Error in creating arrays from input data.");
//Py_XDECREF(initial_npy);
//Py_XDECREF(measurements_npy);
return NULL;
}
c_initial = (double *)PyArray_DATA(initial_npy);
c_measurements = (double *)PyArray_DATA(measurements_npy);
m = PyArray_SIZE(initial_npy);
n = PyArray_SIZE(measurements_npy);
npy_intp dims[2] = {m, m};
covar = PyArray_SimpleNew(2, dims, NPY_DOUBLE);
c_covar = PyArray_DATA(covar);
if (lower){
lower_npy = PyArray_FROMANY(lower, PyArray_DOUBLE, 0, 0, NPY_IN_ARRAY);
c_lower = PyArray_DATA(lower_npy);
// TODO check dims
}
if (upper){
upper_npy = PyArray_FROMANY(upper, PyArray_DOUBLE, 0, 0, NPY_IN_ARRAY);
c_upper = PyArray_DATA(upper_npy);
// TODO check dims
}
if (opts) {
opts_npy = PyArray_FROMANY(opts, PyArray_DOUBLE, 0, 0, NPY_IN_ARRAY);
c_opts = PyArray_DATA(opts_npy);
// TODO check dims
}
// call function to do the fitting
if (!bounds) {
if (jacobian) {
run_iter = dlevmar_der(_pylm_func_callback, _pylm_jacf_callback,
c_initial, c_measurements, m, n,
max_iter, c_opts, c_info, NULL, c_covar, pydata);
} else {
run_iter = dlevmar_dif(_pylm_func_callback, c_initial, c_measurements,
m, n, max_iter, c_opts, c_info, NULL, c_covar, pydata);
}
} else {
if (jacobian) {
run_iter = dlevmar_bc_der(_pylm_func_callback, _pylm_jacf_callback,
c_initial, c_measurements, m, n,
c_lower, c_upper,
max_iter, c_opts, c_info, NULL, c_covar, pydata);
} else {
run_iter = dlevmar_bc_dif(_pylm_func_callback, c_initial, c_measurements,
m, n, c_lower, c_upper,
max_iter, c_opts, c_info, NULL, c_covar, pydata);
}
}
// convert results back into python
if (run_iter > 0) {
npy_intp dims[1] = {m};
retval = PyArray_SimpleNewFromData(1, dims, PyArray_DOUBLE, c_initial);
} else {
retval = Py_None;
Py_INCREF(Py_None);
}
if (pydata) {
PyMem_Free(pydata);
}
// convert additional information into python
info = Py_BuildValue("{s:d,s:d,s:d,s:d,s:d,s:d,s:d,s:d,s:d}",
"initial_e2", c_info[0],
"estimate_e2", c_info[1],
"estimate_Jt", c_info[2],
"estimate_Dp2", c_info[3],
"estimate_mu", c_info[4],
"iterations", c_info[5],
"termination", c_info[6],
"function_evaluations", c_info[7],
"jacobian_evaluations", c_info[8]);
//Py_XDECREF(measurements_npy);
//Py_XDECREF(initial_npy);
//Py_XDECREF(lower_npy);
//Py_XDECREF(upper_npy);
//Py_XDECREF(opts_npy);
return Py_BuildValue("(OOiO)", retval, covar, run_iter, info, NULL);
}
bool SQ_fitter_b<PointT>::minimize( const int &_type,
const PointCloudPtr &_cloud,
const SQ_parameters &_in,
SQ_parameters &_out,
double &_error ) {
// Parameters initially _in:
_out = _in;
// Set necessary parameters
int n = _cloud->points.size();
int m = 13;
double p[m]; // Parameters of SQ
double y[n]; // Values we want to achieve
double opts[LM_OPTS_SZ];
double info[LM_INFO_SZ];
opts[0] = LM_INIT_MU;
opts[1] = 1E-15;
opts[2] = 1E-15;
opts[3] = 1E-20;
opts[4] = LM_DIFF_DELTA;
struct levmar_data data;
data.x = new double[n];
data.y = new double[n];
data.z = new double[n];
data.num = n;
int i; int ret;
typename pcl::PointCloud<PointT>::iterator pit;
for( pit = _cloud->begin(), i = 0; pit != _cloud->end(); ++pit, ++i ) {
data.x[i] = (*pit).x;
data.y[i] = (*pit).y;
data.z[i] = (*pit).z;
}
// Set minimizer value to zero (could be 1, depending of what equation you are minimizing)
for( i = 0; i < n; ++i ) { y[i] = 0.0; }
// Initialize values for parameters p
for( i = 0; i < 3; ++i ) { p[i] = _in.dim[i]; }
for( i = 0; i < 2; ++i ) { p[i+3] = _in.e[i]; }
for( i = 0; i < 3; ++i ) { p[i+5] = _in.trans[i]; }
for( i = 0; i < 3; ++i ) { p[i+8] = _in.rot[i]; }
p[11] = _in.alpha;
p[12] = _in.k;
printf("Initial p: %f %f %f %f %f %f %f %f %f %f %f alpha: %f k: %f \n",
p[0], p[1], p[2], p[3], p[4], p[5], p[6], p[7], p[8], p[9], p[10], p[11], p[12] );
// Set limits
double ub[m], lb[m];
for( i = 0; i < 3; ++i ) { lb[i] = this->mLowerLim_dim[i]; ub[i] = this->mUpperLim_dim[i]; }
for( i = 0; i < 2; ++i ) { lb[i+3] = this->mLowerLim_e; ub[i+3] = this->mUpperLim_e; }
for( i = 0; i < 3; ++i ) { lb[i+5] = this->mLowerLim_trans[i]; ub[i+5] = this->mUpperLim_trans[i]; }
for( i = 0; i < 3; ++i ) { lb[i+8] = this->mLowerLim_rot[i]; ub[i+8] = this->mUpperLim_rot[i]; }
lb[11] = mLowerLim_alpha; ub[11] = mUpperLim_alpha;
lb[12] = mLowerLim_k; ub[12] = mUpperLim_k;
switch( _type ) {
case SQ_FX_RADIAL: {
ret = dlevmar_bc_der( fr_add_b,
Jr_add_b,
p, y, m, n,
lb, ub,
NULL,
5000,
opts, info,
NULL, NULL, (void*)&data );
} break;
case SQ_FX_ICHIM: {
ret = dlevmar_bc_der( fi_add_b,
Ji_add_b,
p, y, m, n,
lb, ub,
NULL,
1000,
opts, info,
NULL, NULL, (void*)&data );
} break;
case SQ_FX_SOLINA: {
ret = dlevmar_bc_der( fs_add_b,
Js_add_b,
p, y, m, n,
lb, ub,
NULL,
1000,
opts, info,
NULL, NULL, (void*)&data );
} break;
case SQ_FX_CHEVALIER: {
ret = dlevmar_bc_der( fc_add_b,
Jc_add_b,
p, y, m, n,
lb, ub,
NULL,
1000,
opts, info,
NULL, NULL, (void*)&data );
} break;
case SQ_FX_5: {
ret = dlevmar_bc_der( f5_add_b,
J5_add_b,
p, y, m, n,
lb, ub,
NULL,
1000,
opts, info,
NULL, NULL, (void*)&data );
} break;
case SQ_FX_6: {
ret = dlevmar_bc_der( f6_add_b,
J6_add_b,
p, y, m, n,
lb, ub,
NULL,
1000,
opts, info,
NULL, NULL, (void*)&data );
} break;
} // end switch
// Fill _out
for( i = 0; i < 3; ++i ) { _out.dim[i] = p[i]; }
for( i = 0; i < 2; ++i ) { _out.e[i] = p[i+3]; }
for( i = 0; i < 3; ++i ) { _out.trans[i] = p[i+5]; }
for( i = 0; i < 3; ++i ) { _out.rot[i] = p[i+8]; }
_out.alpha = p[11];
_out.k = p[12];
_out.type = BENT;
// Return status and error
double eg, er;
get_error( _out, this->cloud_, eg, er, _error );
// If stopped by invalid (TODO: Add other reasons)
if( info[6] == 7 ) {
return false;
} else {
return true;
}
}
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *Prhs[])
{
register int i;
register double *pdbl;
mxArray **prhs=(mxArray **)&Prhs[0], *At, *Ct;
struct mexdata mdata;
int len, status;
double *p, *p0, *ret, *x;
int m, n, havejac, Arows, Crows, itmax, nopts, mintype, nextra;
double opts[LM_OPTS_SZ]={LM_INIT_MU, LM_STOP_THRESH, LM_STOP_THRESH, LM_STOP_THRESH, LM_DIFF_DELTA};
double info[LM_INFO_SZ];
double *lb=NULL, *ub=NULL, *A=NULL, *b=NULL, *wghts=NULL, *C=NULL, *d=NULL, *covar=NULL;
/* parse input args; start by checking their number */
if((nrhs<5))
matlabFmtdErrMsgTxt("levmar: at least 5 input arguments required (got %d).", nrhs);
if(nlhs>4)
matlabFmtdErrMsgTxt("levmar: too many output arguments (max. 4, got %d).", nlhs);
else if(nlhs<2)
matlabFmtdErrMsgTxt("levmar: too few output arguments (min. 2, got %d).", nlhs);
/* note that in order to accommodate optional args, prhs & nrhs are adjusted accordingly below */
/** func **/
/* first argument must be a string , i.e. a char row vector */
if(mxIsChar(prhs[0])!=1)
mexErrMsgTxt("levmar: first argument must be a string.");
if(mxGetM(prhs[0])!=1)
mexErrMsgTxt("levmar: first argument must be a string (i.e. char row vector).");
/* store supplied name */
len=mxGetN(prhs[0])+1;
mdata.fname=mxCalloc(len, sizeof(char));
status=mxGetString(prhs[0], mdata.fname, len);
if(status!=0)
mexErrMsgTxt("levmar: not enough space. String is truncated.");
/** jac (optional) **/
/* check whether second argument is a string */
if(mxIsChar(prhs[1])==1){
if(mxGetM(prhs[1])!=1)
mexErrMsgTxt("levmar: second argument must be a string (i.e. row vector).");
/* store supplied name */
len=mxGetN(prhs[1])+1;
mdata.jacname=mxCalloc(len, sizeof(char));
status=mxGetString(prhs[1], mdata.jacname, len);
if(status!=0)
mexErrMsgTxt("levmar: not enough space. String is truncated.");
havejac=1;
++prhs;
--nrhs;
}
else{
mdata.jacname=NULL;
havejac=0;
}
#ifdef DEBUG
fflush(stderr);
fprintf(stderr, "LEVMAR: %s analytic Jacobian\n", havejac? "with" : "no");
#endif /* DEBUG */
/* CHECK
if(!mxIsDouble(prhs[1]) || mxIsComplex(prhs[1]) || !(mxGetM(prhs[1])==1 && mxGetN(prhs[1])==1))
*/
/** p0 **/
/* the second required argument must be a real row or column vector */
if(!mxIsDouble(prhs[1]) || mxIsComplex(prhs[1]) || !(mxGetM(prhs[1])==1 || mxGetN(prhs[1])==1))
mexErrMsgTxt("levmar: p0 must be a real vector.");
p0=mxGetPr(prhs[1]);
/* determine if we have a row or column vector and retrieve its
* size, i.e. the number of parameters
*/
if(mxGetM(prhs[1])==1){
m=mxGetN(prhs[1]);
mdata.isrow_p0=1;
}
else{
m=mxGetM(prhs[1]);
mdata.isrow_p0=0;
}
/* copy input parameter vector to avoid destroying it */
p=mxMalloc(m*sizeof(double));
for(i=0; i<m; ++i)
p[i]=p0[i];
/** x **/
/* the third required argument must be a real row or column vector */
if(!mxIsDouble(prhs[2]) || mxIsComplex(prhs[2]) || !(mxGetM(prhs[2])==1 || mxGetN(prhs[2])==1))
mexErrMsgTxt("levmar: x must be a real vector.");
x=mxGetPr(prhs[2]);
n=__MAX__(mxGetM(prhs[2]), mxGetN(prhs[2]));
/** itmax **/
/* the fourth required argument must be a scalar */
if(!mxIsDouble(prhs[3]) || mxIsComplex(prhs[3]) || mxGetM(prhs[3])!=1 || mxGetN(prhs[3])!=1)
mexErrMsgTxt("levmar: itmax must be a scalar.");
itmax=(int)mxGetScalar(prhs[3]);
/** opts **/
/* the fifth required argument must be a real row or column vector */
if(!mxIsDouble(prhs[4]) || mxIsComplex(prhs[4]) || (!(mxGetM(prhs[4])==1 || mxGetN(prhs[4])==1) &&
!(mxGetM(prhs[4])==0 && mxGetN(prhs[4])==0)))
mexErrMsgTxt("levmar: opts must be a real vector.");
pdbl=mxGetPr(prhs[4]);
nopts=__MAX__(mxGetM(prhs[4]), mxGetN(prhs[4]));
if(nopts!=0){ /* if opts==[], nothing needs to be done and the defaults are used */
if(nopts>LM_OPTS_SZ)
matlabFmtdErrMsgTxt("levmar: opts must have at most %d elements, got %d.", LM_OPTS_SZ, nopts);
else if(nopts<((havejac)? LM_OPTS_SZ-1 : LM_OPTS_SZ))
matlabFmtdWarnMsgTxt("levmar: only the %d first elements of opts specified, remaining set to defaults.", nopts);
for(i=0; i<nopts; ++i)
opts[i]=pdbl[i];
}
#ifdef DEBUG
else{
fflush(stderr);
fprintf(stderr, "LEVMAR: empty options vector, using defaults\n");
}
#endif /* DEBUG */
/** mintype (optional) **/
/* check whether sixth argument is a string */
if(nrhs>=6 && mxIsChar(prhs[5])==1 && mxGetM(prhs[5])==1){
char *minhowto;
/* examine supplied name */
len=mxGetN(prhs[5])+1;
minhowto=mxCalloc(len, sizeof(char));
status=mxGetString(prhs[5], minhowto, len);
if(status!=0)
mexErrMsgTxt("levmar: not enough space. String is truncated.");
for(i=0; minhowto[i]; ++i)
minhowto[i]=tolower(minhowto[i]);
if(!strncmp(minhowto, "unc", 3)) mintype=MIN_UNCONSTRAINED;
else if(!strncmp(minhowto, "bc", 2)) mintype=MIN_CONSTRAINED_BC;
else if(!strncmp(minhowto, "lec", 3)) mintype=MIN_CONSTRAINED_LEC;
else if(!strncmp(minhowto, "blec", 4)) mintype=MIN_CONSTRAINED_BLEC;
else if(!strncmp(minhowto, "bleic", 5)) mintype=MIN_CONSTRAINED_BLEIC;
else if(!strncmp(minhowto, "blic", 4)) mintype=MIN_CONSTRAINED_BLIC;
else if(!strncmp(minhowto, "leic", 4)) mintype=MIN_CONSTRAINED_LEIC;
else if(!strncmp(minhowto, "lic", 3)) mintype=MIN_CONSTRAINED_BLIC;
else matlabFmtdErrMsgTxt("levmar: unknown minimization type '%s'.", minhowto);
mxFree(minhowto);
++prhs;
--nrhs;
}
else
mintype=MIN_UNCONSTRAINED;
if(mintype==MIN_UNCONSTRAINED) goto extraargs;
/* arguments below this point are optional and their presence depends
* upon the minimization type determined above
*/
/** lb, ub **/
if(nrhs>=7 && (mintype==MIN_CONSTRAINED_BC || mintype==MIN_CONSTRAINED_BLEC || mintype==MIN_CONSTRAINED_BLIC || mintype==MIN_CONSTRAINED_BLEIC)){
/* check if the next two arguments are real row or column vectors */
if(mxIsDouble(prhs[5]) && !mxIsComplex(prhs[5]) && (mxGetM(prhs[5])==1 || mxGetN(prhs[5])==1)){
if(mxIsDouble(prhs[6]) && !mxIsComplex(prhs[6]) && (mxGetM(prhs[6])==1 || mxGetN(prhs[6])==1)){
if((i=__MAX__(mxGetM(prhs[5]), mxGetN(prhs[5])))!=m)
matlabFmtdErrMsgTxt("levmar: lb must have %d elements, got %d.", m, i);
if((i=__MAX__(mxGetM(prhs[6]), mxGetN(prhs[6])))!=m)
matlabFmtdErrMsgTxt("levmar: ub must have %d elements, got %d.", m, i);
lb=mxGetPr(prhs[5]);
ub=mxGetPr(prhs[6]);
prhs+=2;
nrhs-=2;
}
}
}
/** A, b **/
if(nrhs>=7 && (mintype==MIN_CONSTRAINED_LEC || mintype==MIN_CONSTRAINED_BLEC || mintype==MIN_CONSTRAINED_LEIC || mintype==MIN_CONSTRAINED_BLEIC)){
/* check if the next two arguments are a real matrix and a real row or column vector */
if(mxIsDouble(prhs[5]) && !mxIsComplex(prhs[5]) && mxGetM(prhs[5])>=1 && mxGetN(prhs[5])>=1){
if(mxIsDouble(prhs[6]) && !mxIsComplex(prhs[6]) && (mxGetM(prhs[6])==1 || mxGetN(prhs[6])==1)){
if((i=mxGetN(prhs[5]))!=m)
matlabFmtdErrMsgTxt("levmar: A must have %d columns, got %d.", m, i);
if((i=__MAX__(mxGetM(prhs[6]), mxGetN(prhs[6])))!=(Arows=mxGetM(prhs[5])))
matlabFmtdErrMsgTxt("levmar: b must have %d elements, got %d.", Arows, i);
At=prhs[5];
b=mxGetPr(prhs[6]);
A=getTranspose(At);
prhs+=2;
nrhs-=2;
}
}
}
/* wghts */
/* check if we have a weights vector */
if(nrhs>=6 && mintype==MIN_CONSTRAINED_BLEC){ /* only check if we have seen both box & linear constraints */
if(mxIsDouble(prhs[5]) && !mxIsComplex(prhs[5]) && (mxGetM(prhs[5])==1 || mxGetN(prhs[5])==1)){
if(__MAX__(mxGetM(prhs[5]), mxGetN(prhs[5]))==m){
wghts=mxGetPr(prhs[5]);
++prhs;
--nrhs;
}
}
}
/** C, d **/
if(nrhs>=7 && (mintype==MIN_CONSTRAINED_BLEIC || mintype==MIN_CONSTRAINED_BLIC || mintype==MIN_CONSTRAINED_LEIC || mintype==MIN_CONSTRAINED_LIC)){
/* check if the next two arguments are a real matrix and a real row or column vector */
if(mxIsDouble(prhs[5]) && !mxIsComplex(prhs[5]) && mxGetM(prhs[5])>=1 && mxGetN(prhs[5])>=1){
if(mxIsDouble(prhs[6]) && !mxIsComplex(prhs[6]) && (mxGetM(prhs[6])==1 || mxGetN(prhs[6])==1)){
if((i=mxGetN(prhs[5]))!=m)
matlabFmtdErrMsgTxt("levmar: C must have %d columns, got %d.", m, i);
if((i=__MAX__(mxGetM(prhs[6]), mxGetN(prhs[6])))!=(Crows=mxGetM(prhs[5])))
matlabFmtdErrMsgTxt("levmar: d must have %d elements, got %d.", Crows, i);
Ct=prhs[5];
d=mxGetPr(prhs[6]);
C=getTranspose(Ct);
prhs+=2;
nrhs-=2;
}
}
}
/* arguments below this point are assumed to be extra arguments passed
* to every invocation of the fitting function and its Jacobian
*/
extraargs:
/* handle any extra args and allocate memory for
* passing the current parameter estimate to matlab
*/
nextra=nrhs-5;
mdata.nrhs=nextra+1;
mdata.rhs=(mxArray **)mxMalloc(mdata.nrhs*sizeof(mxArray *));
for(i=0; i<nextra; ++i)
mdata.rhs[i+1]=(mxArray *)prhs[nrhs-nextra+i]; /* discard 'const' modifier */
#ifdef DEBUG
fflush(stderr);
fprintf(stderr, "LEVMAR: %d extra args\n", nextra);
#endif /* DEBUG */
if(mdata.isrow_p0){ /* row vector */
mdata.rhs[0]=mxCreateDoubleMatrix(1, m, mxREAL);
/*
mxSetM(mdata.rhs[0], 1);
mxSetN(mdata.rhs[0], m);
*/
}
else{ /* column vector */
mdata.rhs[0]=mxCreateDoubleMatrix(m, 1, mxREAL);
/*
mxSetM(mdata.rhs[0], m);
mxSetN(mdata.rhs[0], 1);
*/
}
/* ensure that the supplied function & Jacobian are as expected */
if(checkFuncAndJacobian(p, m, n, havejac, &mdata)){
status=LM_ERROR;
goto cleanup;
}
if(nlhs>3) /* covariance output required */
covar=mxMalloc(m*m*sizeof(double));
/* invoke levmar */
switch(mintype){
case MIN_UNCONSTRAINED: /* no constraints */
if(havejac)
status=dlevmar_der(func, jacfunc, p, x, m, n, itmax, opts, info, NULL, covar, (void *)&mdata);
else
status=dlevmar_dif(func, p, x, m, n, itmax, opts, info, NULL, covar, (void *)&mdata);
#ifdef DEBUG
fflush(stderr);
fprintf(stderr, "LEVMAR: calling dlevmar_der()/dlevmar_dif()\n");
#endif /* DEBUG */
break;
case MIN_CONSTRAINED_BC: /* box constraints */
if(havejac)
status=dlevmar_bc_der(func, jacfunc, p, x, m, n, lb, ub, itmax, opts, info, NULL, covar, (void *)&mdata);
else
status=dlevmar_bc_dif(func, p, x, m, n, lb, ub, itmax, opts, info, NULL, covar, (void *)&mdata);
#ifdef DEBUG
fflush(stderr);
fprintf(stderr, "LEVMAR: calling dlevmar_bc_der()/dlevmar_bc_dif()\n");
#endif /* DEBUG */
break;
case MIN_CONSTRAINED_LEC: /* linear equation constraints */
#ifdef HAVE_LAPACK
if(havejac)
status=dlevmar_lec_der(func, jacfunc, p, x, m, n, A, b, Arows, itmax, opts, info, NULL, covar, (void *)&mdata);
else
status=dlevmar_lec_dif(func, p, x, m, n, A, b, Arows, itmax, opts, info, NULL, covar, (void *)&mdata);
#else
mexErrMsgTxt("levmar: no linear constraints support, HAVE_LAPACK was not defined during MEX-file compilation.");
#endif /* HAVE_LAPACK */
#ifdef DEBUG
fflush(stderr);
fprintf(stderr, "LEVMAR: calling dlevmar_lec_der()/dlevmar_lec_dif()\n");
#endif /* DEBUG */
break;
case MIN_CONSTRAINED_BLEC: /* box & linear equation constraints */
#ifdef HAVE_LAPACK
if(havejac)
status=dlevmar_blec_der(func, jacfunc, p, x, m, n, lb, ub, A, b, Arows, wghts, itmax, opts, info, NULL, covar, (void *)&mdata);
else
status=dlevmar_blec_dif(func, p, x, m, n, lb, ub, A, b, Arows, wghts, itmax, opts, info, NULL, covar, (void *)&mdata);
#else
mexErrMsgTxt("levmar: no box & linear constraints support, HAVE_LAPACK was not defined during MEX-file compilation.");
#endif /* HAVE_LAPACK */
#ifdef DEBUG
fflush(stderr);
fprintf(stderr, "LEVMAR: calling dlevmar_blec_der()/dlevmar_blec_dif()\n");
#endif /* DEBUG */
break;
case MIN_CONSTRAINED_BLEIC: /* box, linear equation & inequalities constraints */
#ifdef HAVE_LAPACK
if(havejac)
status=dlevmar_bleic_der(func, jacfunc, p, x, m, n, lb, ub, A, b, Arows, C, d, Crows, itmax, opts, info, NULL, covar, (void *)&mdata);
else
status=dlevmar_bleic_dif(func, p, x, m, n, lb, ub, A, b, Arows, C, d, Crows, itmax, opts, info, NULL, covar, (void *)&mdata);
#else
mexErrMsgTxt("levmar: no box, linear equation & inequality constraints support, HAVE_LAPACK was not defined during MEX-file compilation.");
#endif /* HAVE_LAPACK */
#ifdef DEBUG
fflush(stderr);
fprintf(stderr, "LEVMAR: calling dlevmar_bleic_der()/dlevmar_bleic_dif()\n");
#endif /* DEBUG */
break;
case MIN_CONSTRAINED_BLIC: /* box, linear inequalities constraints */
#ifdef HAVE_LAPACK
if(havejac)
status=dlevmar_bleic_der(func, jacfunc, p, x, m, n, lb, ub, NULL, NULL, 0, C, d, Crows, itmax, opts, info, NULL, covar, (void *)&mdata);
else
status=dlevmar_bleic_dif(func, p, x, m, n, lb, ub, NULL, NULL, 0, C, d, Crows, itmax, opts, info, NULL, covar, (void *)&mdata);
#else
mexErrMsgTxt("levmar: no box & linear inequality constraints support, HAVE_LAPACK was not defined during MEX-file compilation.");
#endif /* HAVE_LAPACK */
#ifdef DEBUG
fflush(stderr);
fprintf(stderr, "LEVMAR: calling dlevmar_blic_der()/dlevmar_blic_dif()\n");
#endif /* DEBUG */
break;
case MIN_CONSTRAINED_LEIC: /* linear equation & inequalities constraints */
#ifdef HAVE_LAPACK
if(havejac)
status=dlevmar_bleic_der(func, jacfunc, p, x, m, n, NULL, NULL, A, b, Arows, C, d, Crows, itmax, opts, info, NULL, covar, (void *)&mdata);
else
status=dlevmar_bleic_dif(func, p, x, m, n, NULL, NULL, A, b, Arows, C, d, Crows, itmax, opts, info, NULL, covar, (void *)&mdata);
#else
mexErrMsgTxt("levmar: no linear equation & inequality constraints support, HAVE_LAPACK was not defined during MEX-file compilation.");
#endif /* HAVE_LAPACK */
#ifdef DEBUG
fflush(stderr);
fprintf(stderr, "LEVMAR: calling dlevmar_leic_der()/dlevmar_leic_dif()\n");
#endif /* DEBUG */
break;
case MIN_CONSTRAINED_LIC: /* linear inequalities constraints */
#ifdef HAVE_LAPACK
if(havejac)
status=dlevmar_bleic_der(func, jacfunc, p, x, m, n, NULL, NULL, NULL, NULL, 0, C, d, Crows, itmax, opts, info, NULL, covar, (void *)&mdata);
else
status=dlevmar_bleic_dif(func, p, x, m, n, NULL, NULL, NULL, NULL, 0, C, d, Crows, itmax, opts, info, NULL, covar, (void *)&mdata);
#else
mexErrMsgTxt("levmar: no linear equation & inequality constraints support, HAVE_LAPACK was not defined during MEX-file compilation.");
#endif /* HAVE_LAPACK */
#ifdef DEBUG
fflush(stderr);
fprintf(stderr, "LEVMAR: calling dlevmar_lic_der()/dlevmar_lic_dif()\n");
#endif /* DEBUG */
break;
default:
mexErrMsgTxt("levmar: unexpected internal error.");
}
#ifdef DEBUG
fflush(stderr);
printf("LEVMAR: minimization returned %d in %g iter, reason %g\n\tSolution: ", status, info[5], info[6]);
for(i=0; i<m; ++i)
printf("%.7g ", p[i]);
printf("\n\n\tMinimization info:\n\t");
for(i=0; i<LM_INFO_SZ; ++i)
printf("%g ", info[i]);
printf("\n");
#endif /* DEBUG */
/* copy back return results */
/** ret **/
plhs[0]=mxCreateDoubleMatrix(1, 1, mxREAL);
ret=mxGetPr(plhs[0]);
ret[0]=(double)status;
/** popt **/
plhs[1]=(mdata.isrow_p0==1)? mxCreateDoubleMatrix(1, m, mxREAL) : mxCreateDoubleMatrix(m, 1, mxREAL);
pdbl=mxGetPr(plhs[1]);
for(i=0; i<m; ++i)
pdbl[i]=p[i];
/** info **/
if(nlhs>2){
plhs[2]=mxCreateDoubleMatrix(1, LM_INFO_SZ, mxREAL);
pdbl=mxGetPr(plhs[2]);
for(i=0; i<LM_INFO_SZ; ++i)
pdbl[i]=info[i];
}
/** covar **/
if(nlhs>3){
plhs[3]=mxCreateDoubleMatrix(m, m, mxREAL);
pdbl=mxGetPr(plhs[3]);
for(i=0; i<m*m; ++i) /* covariance matrices are symmetric, thus no need to transpose! */
pdbl[i]=covar[i];
}
cleanup:
/* cleanup */
mxDestroyArray(mdata.rhs[0]);
if(A) mxFree(A);
if(C) mxFree(C);
mxFree(mdata.fname);
if(havejac) mxFree(mdata.jacname);
mxFree(p);
mxFree(mdata.rhs);
if(covar) mxFree(covar);
if(status==LM_ERROR)
mexWarnMsgTxt("levmar: optimization returned with an error!");
}
double stfnum::lmFit( const Vector_double& data, double dt,
const stfnum::storedFunc& fitFunc, const Vector_double& opts,
bool use_scaling,
Vector_double& p, std::string& info, int& warning )
{
// Basic range checking:
if (fitFunc.pInfo.size()!=p.size()) {
std::string msg("Error in stfnum::lmFit()\n"
"function parameters (p_fit) and parameters entered (p) have different sizes");
throw std::runtime_error(msg);
}
if ( opts.size() != 6 ) {
std::string msg("Error in stfnum::lmFit()\n"
"wrong number of options");
throw std::runtime_error(msg);
}
bool constrained = false;
std::vector< double > constrains_lm_lb( fitFunc.pInfo.size() );
std::vector< double > constrains_lm_ub( fitFunc.pInfo.size() );
bool can_scale = use_scaling;
for ( unsigned n_p=0; n_p < fitFunc.pInfo.size(); ++n_p ) {
if ( fitFunc.pInfo[n_p].constrained ) {
constrained = true;
constrains_lm_lb[n_p] = fitFunc.pInfo[n_p].constr_lb;
constrains_lm_ub[n_p] = fitFunc.pInfo[n_p].constr_ub;
} else {
constrains_lm_lb[n_p] = -DBL_MAX;
constrains_lm_ub[n_p] = DBL_MAX;
}
if ( can_scale ) {
if (fitFunc.pInfo[n_p].scale == stfnum::noscale) {
can_scale = false;
}
}
}
// Store the functions at global scope:
saveFunc(fitFunc.func);
saveJac(fitFunc.jac);
double info_id[LM_INFO_SZ];
Vector_double data_ptr(data);
Vector_double xyscale(4);
if (can_scale) {
xyscale = get_scale(data_ptr, dt);
}
// The parameters need to be separated into two parts:
// Those that are to be fitted and those that the client wants
// to keep constant. Since there is no native support to
// do so in Lourakis' routines, the workaround is a little
// tricky, making (ab)use of the *void pointer:
// number of parameters that need to be fitted:
int n_fitted=0;
for ( unsigned n_p=0; n_p < fitFunc.pInfo.size(); ++n_p ) {
n_fitted += fitFunc.pInfo[n_p].toFit;
}
// parameters that need to be fitted:
Vector_double p_toFit(n_fitted);
std::deque<bool> p_fit_bool( fitFunc.pInfo.size() );
// parameters that are held constant:
Vector_double p_const( fitFunc.pInfo.size()-n_fitted );
for ( unsigned n_p=0, n_c=0, n_f=0; n_p < fitFunc.pInfo.size(); ++n_p ) {
if (fitFunc.pInfo[n_p].toFit) {
p_toFit[n_f++] = p[n_p];
if (can_scale) {
p_toFit[n_f-1] = fitFunc.pInfo[n_p].scale(p_toFit[n_f-1], xyscale[0],
xyscale[1], xyscale[2], xyscale[3]);
}
} else {
p_const[n_c++] = p[n_p];
if (can_scale) {
p_const[n_c-1] = fitFunc.pInfo[n_p].scale(p_const[n_c-1], xyscale[0],
xyscale[1], xyscale[2], xyscale[3]);
}
}
p_fit_bool[n_p] = fitFunc.pInfo[n_p].toFit;
}
// size * dt_new = 1 -> dt_new = 1.0/size
double dt_finfo = dt;
if (can_scale)
dt_finfo = 1.0/data_ptr.size();
fitInfo fInfo( p_fit_bool, p_const, dt_finfo );
// make l-value of opts:
Vector_double opts_l(5);
for (std::size_t n=0; n < 4; ++n) opts_l[n] = opts[n];
opts_l[4] = -1e-6;
int it = 0;
if (p_toFit.size()!=0 && data_ptr.size()!=0) {
double old_info_id[LM_INFO_SZ];
// initialize with initial parameter guess:
Vector_double old_p_toFit(p_toFit);
#ifdef _DEBUG
std::ostringstream optsMsg;
optsMsg << "\nopts: ";
for (std::size_t n_p=0; n_p < opts.size(); ++n_p)
optsMsg << opts[n_p] << "\t";
optsMsg << "\n" << "data_ptr[" << data_ptr.size()-1 << "]=" << data_ptr[data_ptr.size()-1] << "\n";
optsMsg << "constrains_lm_lb: ";
for (std::size_t n_p=0; n_p < constrains_lm_lb.size(); ++n_p)
optsMsg << constrains_lm_lb[n_p] << "\t";
optsMsg << "\n" << "constrains_lm_ub: ";
for (std::size_t n_p=0; n_p < constrains_lm_ub.size(); ++n_p)
optsMsg << constrains_lm_ub[n_p] << "\t";
optsMsg << "\n\n";
std::cout << optsMsg;
#endif
while ( 1 ) {
#ifdef _DEBUG
std::ostringstream paramMsg;
paramMsg << "Pass: "******"\t";
paramMsg << "p_toFit: ";
for (std::size_t n_p=0; n_p < p_toFit.size(); ++n_p)
paramMsg << p_toFit[n_p] << "\t";
paramMsg << "\n";
std::cout << paramMsg.str().c_str();
#endif
if ( !fitFunc.hasJac ) {
if ( !constrained ) {
dlevmar_dif( c_func_lour, &p_toFit[0], &data_ptr[0], n_fitted,
(int)data.size(), (int)opts[4], &opts_l[0], info_id,
NULL, NULL, &fInfo );
} else {
dlevmar_bc_dif( c_func_lour, &p_toFit[0], &data_ptr[0], n_fitted,
(int)data.size(), &constrains_lm_lb[0], &constrains_lm_ub[0], NULL,
(int)opts[4], &opts_l[0], info_id, NULL, NULL, &fInfo );
}
} else {
if ( !constrained ) {
dlevmar_der( c_func_lour, c_jac_lour, &p_toFit[0], &data_ptr[0],
n_fitted, (int)data.size(), (int)opts[4], &opts_l[0], info_id,
NULL, NULL, &fInfo );
} else {
dlevmar_bc_der( c_func_lour, c_jac_lour, &p_toFit[0],
&data_ptr[0], n_fitted, (int)data.size(), &constrains_lm_lb[0],
&constrains_lm_ub[0], NULL, (int)opts[4], &opts_l[0], info_id,
NULL, NULL, &fInfo );
}
}
it++;
if ( info_id[1] != info_id[1] ) {
// restore previous parameters if new chisqr is NaN:
p_toFit = old_p_toFit;
} else {
double dchisqr = (info_id[0] - info_id[1]) / info_id[1]; // (old chisqr - new chisqr) / new_chisqr
if ( dchisqr < 0 ) {
// restore previous results and exit if new chisqr is larger:
for ( int n_i = 0; n_i < LM_INFO_SZ; ++n_i ) info_id[n_i] = old_info_id[n_i];
p_toFit = old_p_toFit;
break;
}
if ( dchisqr < 1e-5 ) {
// Keep current results and exit if change in chisqr is below threshold
break;
}
// otherwise, store results and continue iterating:
for ( int n_i = 0; n_i < LM_INFO_SZ; ++n_i ) old_info_id[n_i] = info_id[n_i];
old_p_toFit = p_toFit;
}
if ( it >= opts[5] )
// Exit if maximal number of iterations is reached
break;
// decrease initial step size for next iteration:
opts_l[0] *= 1e-4;
}
} else {
std::runtime_error e("Array of size zero in lmFit");
throw e;
}
// copy back the fitted parameters to p:
for ( unsigned n_p=0, n_f=0, n_c=0; n_p<fitFunc.pInfo.size(); ++n_p ) {
if (fitFunc.pInfo[n_p].toFit) {
p[n_p] = p_toFit[n_f++];
} else {
p[n_p] = p_const[n_c++];
}
if (can_scale) {
p[n_p] = fitFunc.pInfo[n_p].unscale(p[n_p], xyscale[0],
xyscale[1], xyscale[2], xyscale[3]);
}
}
std::ostringstream str_info;
str_info << "Passes: " << it;
str_info << "\nIterations during last pass: "******"\nStopping reason during last pass:"******"\nStopped by small gradient of squared error.";
warning = 0;
break;
case 2:
str_info << "\nStopped by small rel. parameter change.";
warning = 0;
break;
case 3:
str_info << "\nReached max. number of iterations. Restart\n"
<< "with smarter initial parameters and / or with\n"
<< "increased initial scaling factor and / or with\n"
<< "increased max. number of iterations.";
warning = 3;
break;
case 4:
str_info << "\nSingular matrix. Restart from current parameters\n"
<< "with increased initial scaling factor.";
warning = 4;
break;
case 5:
str_info << "\nNo further error reduction is possible.\n"
<< "Restart with increased initial scaling factor.";
warning = 5;
break;
case 6:
str_info << "\nStopped by small squared error.";
warning = 0;
break;
case 7:
str_info << "\nStopped by invalid (i.e. NaN or Inf) \"func\" values.\n";
str_info << "This is a user error.";
warning = 7;
break;
default:
str_info << "\nUnknown reason for stopping the fit.";
warning = -1;
}
if (use_scaling && !can_scale) {
str_info << "\nCouldn't use scaling because one or more "
<< "of the parameters don't allow it.";
}
info=str_info.str();
return info_id[1];
}
void gaussfit_main (int nlhs, mxArray *plhs[],int nrhs, const mxArray *prhs[], char* variant, char* model, const int m, const int background_int,
void(*fit_model)(double *p, double *x, int m, int n, void *data ), void(*fit_jacobian)(double *p, double *jac, int m, int n, void *data),
const int numEqualityConstraints, const int numBounds, const int numInputs, const int numDataEntries)
{
//gets the dimensions of the input data (window size)
int sizex = mxGetN(prhs[0]);
int sizey = mxGetM(prhs[0]);
//checks that input frame is square
if( sizex != sizey)
{
mexErrMsgTxt("Input data is not a square matrix.");
}
//===================================
//Read in data from MATLAB
//===================================
int n = sizex*sizey; //number of pixels in data
//here we create a dynamic array of size N to hold the data
double* x;
x = new double[n];
//Read in data to x from MATLAB
double *datapoint = mxGetPr(prhs[0]);
for(int j = 0; j < sizey; j++)
{
for(int i = 0; i < sizex; i++)
{
x[(i * sizex) + j] = datapoint[i + (j*sizey)];
}
}
//Because of the way MATLAB reads mxArrays (down each column)
//important to account for this because of having fixed positions etc
//or fixed elliptical width.
//so read the MATLAB array consecutively for speed and then the first element (1,1) goes to
//position (1,1) [element 0], then the second element (1,2) goes to position (2,1) [element 1*sizex] etc
//so we fill x[] down the "columns" in the array
//eg for a 3x3 matrix we read in elements[0 - 8] from MATLAB and input them in array element order
//[0], [3], [6] (first column done), [1],[4],[7] (second), [2], [5], [8] - all done
double* constraints_pointer;
double *data; //read in data from MATLAB input, if required
if(numDataEntries == 0)
{
data = NULL;
}
else
{
data = new double[numDataEntries];
for(int i = 0; i < numDataEntries; i++)
{
constraints_pointer = mxGetPr(prhs[i+1]); //+1 because array of intensity data is indexed at [0]
data[i] = constraints_pointer[0];
}
}
//data contains any constants we need to pass to the constraints functions
//data contains any constants we need to pass to the constraints functions
//Read in bounding condition data from MATLAB to pass to constraints function
//Matlab input convention - data first, then all fixed parameters, then all bounded parameters in order -
//lower bound first, then upper bound, with standard variable sequence A, sigma, b, Xo, Yo, then extra options. So bound indices for
// prhs[] start at numEqualityConstraints + 1 ([0] is always the data)
//===================================
//Sets up initial guess and boundaries for solver
//===================================
double* p;
p = new double[m];
double back_p[1];
void initialfit (char *variant, double p[], double data_array[], int n, double *data); //define initial fit function
//if flag in input is set to true, use supplied guess, otherwise run initial fit routine
bool* use_initial_fit_guess = mxGetLogicals(prhs[numInputs-3] );
if (use_initial_fit_guess[0] == true) //then use the guess given in input
{
double* init_guess_pointer = mxGetPr(prhs[numEqualityConstraints + numBounds + 2]); //gets pointer to guess
for(int i = 0; i < m; i++)
{
p[i] = init_guess_pointer[i];
} //transfer guess from input argument
}
else //run the initial fits program to generate the initial guess
{initialfit(variant, p, x, n, data);}
//sets the initial value for the background to be used by the background only solver
back_p[0] = p[background_int - 1];
//initialise boundary and penalty weighting arrays
//which will be taken as the arguments for constraint calculating
//and solver functions - constraints() and dlevmar_etc()
double* lb;
double* ub;
lb = new double[m];
ub = new double[m];
//lower and upper boundary arrays
double* weights;
weights = new double[m]; //Not actually used but if we want to define weighting for penalty function
//for use in the boundary conditions, this is here
double info[LM_INFO_SZ];
//Read in search stopping parameters from input array from Matlab
double* options_pointer = mxGetPr(prhs[numEqualityConstraints+numBounds+3]);
double searchstopParams[4] = {options_pointer[1], options_pointer[2], options_pointer[3]};
int numIterations = options_pointer[4];
//this array controls parameters epsilon 1,2 and 3 as described in http://www.ics.forth.gr/~lourakis/levmar/levmar.pdf
//the purpose of them is to stop the solver before it has reached its maximum number of iterations if the solution has
//already sufficiently converged
//for data with reasonable signal to noise, sufficient convergence should only take ~10 iterations, so these conditions
//are important
//searchstopParams[0] is epsilon1, the gradient of chi squared, 10^-2 or -3 seems to work well
//searchstopParams[1] is epsilon2, the gradient of the change in best fit parameters, relative to the values of those parameters
//this is generally the condition that will determine the speed/accuracy/precision of the output and is worth playing around with
//higher values generally slow down the routine, but increase the accuracy, especially for badly scaled conditions (eg. background
//several orders of magnitude higher than peak amplitude) good values seem to be in the range 10^-3 (for well scaled conditions) to
//10^-5
//searchstopParams[2] is epsilon3, the absolute value of chi squared. For a well solved gaussian with low noise
//this will still be a large number so this is essentially ignored
double opts[LM_OPTS_SZ] = {LM_INIT_MU, searchstopParams[0],searchstopParams[1],searchstopParams[2], LM_DIFF_DELTA};
//opts[0] is initial mu value - controls the damping in the LM algorithm - using default
//opts[1] is stopping threshold on gradient of chi square
//opts[2] is stopping threshold on relative change of parameter magnitudes
//opts[3] is stopping threshold on value of chi squared
//opts[4] is irrelevant if analytic jacobian used, so use default
//===================================
//define constraint setting function
void constraints(char *variant, double *lb, double *ub, double *constraintMatrix, double *constraintRHS,
int numBounds, int numEqualityConstraints, double *weights, int m, int framesize, double *data);
int ret;
//We will always have box (inequality constraints) eg. amplitude must be positive
//However, in some cases we will have linear (equality) constraints and will need to use dlevmar_blec_der
//But, if we have no equality constraints we should use dlevmar_bc_der which uses box constraints only
//So use an if-else condition on numEqualityConstraints to decide which to us
if(numEqualityConstraints > 0) //then we need box and linear constraints
{
double *ConstraintMatrix = new double[numEqualityConstraints * m];
double *ConstraintRHS = new double[numEqualityConstraints];
///constraints function
constraints(variant, lb, ub, ConstraintMatrix, ConstraintRHS, numBounds, numEqualityConstraints, weights, m, sizex, data);
///main solver function if you need equality constraints
ret = dlevmar_blec_der
///basics
(fit_model, //pointer to the function that calculates the model values at each datapoint given parameters p
fit_jacobian, //pointer to the function that calculates the analytic jacobian dxi/dpj at each datapoint
p, //current best guess parameters as an array of size m
x, //data to be fitted to the model, array of size n
m, //number of free parameters
n, //number of datapoints
///constraints
lb, //array of m elements setting lower bounds on each parameter (p[i] >= lb[i])
ub, //array of m elements setting upper bounds on each parameter (p[i] <= ub[i])
ConstraintMatrix, //matrix of equality constraint values, numEqualityconstraints = number of rows
//m is number of columns
ConstraintRHS, //RHS of constraint equation ConstraintMatrix * p = ConstraintRHS
numEqualityConstraints, //how many constraints you have
NULL, //penalty weighting array, set to NULL to use defaults, otherwise fill and use weights[m]
///solver stop procedure and debugging
numIterations, //max no. of iterations the solver will run for, 50 to 100 seems about right
opts, //5 element array, described above
info, //from source code of levmar library:
/* info: information regarding the minimization. Used to find the lsq minimisation value at output
* info[0]= ||e||_2 at initial p.
* info[1-4]=[ ||e||_2, ||J^T e||_inf, ||Dp||_2, mu/max[J^T J]_ii ], all computed at estimated p.
* info[5]= # iterations,
* info[6]=reason for terminating: 1 - stopped by small gradient J^T e
* 2 - stopped by small Dp
* 3 - stopped by itmax
* 4 - singular matrix. Restart from current p with increased mu
* 5 - no further error reduction is possible. Restart with increased mu
* 6 - stopped by small ||e||_2
* 7 - stopped by invalid (i.e. NaN or Inf) "func" values. This is a user error
* info[7]= # function evaluations
* info[8]= # Jacobian evaluations
* info[9]= # linear systems solved, i.e. # attempts for reducing error
*/
NULL, // working memory at least LM_BLEC_DER_WORKSZ() reals large, allocated if NULL
NULL, //Covariance matrix corresponding to LS solution; mxm. Set to NULL if not needed.
data); // pointer to additional data passed to function and jacobian calculator - fixed constants etc
delete [] ConstraintMatrix;
delete [] ConstraintRHS;
}
///main solver function if you only need inequality constraints - see above for arg details
else if(numEqualityConstraints == 0) //we only need box constraints
{
///constraints function, inequality constraints only
constraints(variant, lb, ub, NULL, NULL, numBounds, numEqualityConstraints, weights, m, sizex, data);
///main solver, see above for arg descriptions
ret = dlevmar_bc_der
(fit_model, fit_jacobian, p, x, m, n,
lb, ub, NULL,
numIterations, opts, info, NULL, NULL, data); // with analytic Jacobian
}
else { mexErrMsgTxt("Number of equality constraints not set properly, should be an integer >= 0"); }
///OUTPUT
//output brightness, final fit parameters and normalised least squares value to matlab
double brightness, lsq_normalised;
const double pi = 3.14159265358979323846; //easier to do this than require a library Pi function
bool got_signal = true; //assume signal as default
if ( model == "circular" )
{brightness = 2.0*pi*p[0]*pow(p[1],2);}
else if (model == "elliptical")
{
brightness = 2.0*pi*p[0]*p[1]*p[2];
}
else
{mexErrMsgTxt("Error, model not set.");}
//if elliptical model transform the paramaters st. s_y is semimajor axis, and 0<theta<pi
if(model == "elliptical")
{
double s_x,s_y,theta;
s_x = p[1];
s_y = p[2];
theta = p[6];
if (s_x > s_y) //ie if the fit has got the axes the wrong way around
{
p[1] = s_y;//swap the two values
p[2] = s_x;
theta = theta + pi/2; //rotate the axes 90deg
}
//transform theta st. its 0<theta<pi ie
//ie, mod(theta,pi) = theta - floor(theta/pi) * pi;
theta = theta - floor(theta/pi) * pi;
p[6] = theta;
}
lsq_normalised = info[1]/n;
plhs[0] = mxCreateDoubleScalar(brightness); //send brightness as output to MATLAB
plhs[1] = mxCreateDoubleMatrix(1, m, mxREAL);
//need to do this next bit because can only pass an array back to Matlab as a matrix if array is
//in dynamic memory via mxCalloc command
void* final_fit_alloc = mxCalloc(m, sizeof(double));
double* final_fit = (double *) final_fit_alloc;
for (int i = 0; i < m; i++)
{
final_fit[i] = p[i];
}
mxFree(mxGetPr(plhs[1])); //mxSetPr will not deallocate memory allocated to plhs[1], so do it manually or get a leak
mxSetPr(plhs[1],final_fit); //fit parameters are now ready to be passed to Matlab
plhs[2] = mxCreateDoubleScalar(lsq_normalised);
if (options_pointer[0] == true) //then display the output, otherwise just forward it to MATLAB
{
if (model == "circular")
{
mexPrintf("\nBrightness is %f.\n", brightness);
mexPrintf("Fit parameters are: A = %f, sigma = %f, b = %f, Xo = %f, Yo = %f. \n", p[0],p[1],p[2],p[3],p[4]);
mexPrintf("Normalised lsq is %f.\n", lsq_normalised);
}
if (model == "elliptical") //then display the output, otherwise just forward it to MATLAB
{
mexPrintf("\nBrightness is %f.\n", brightness);
mexPrintf("Fit parameters are: A = %f, sigma = %f, %f, b = %f, Xo = %f, Yo = %f. Theta = %f. \n", p[0],p[1],p[2],p[3],p[4],p[5],p[6]);
mexPrintf("Normalised lsq is %f.\n", lsq_normalised);
}
//******************Uncomment for extra information***************************************
mexPrintf("Levenberg-Marquardt returned in %g iter, reason %g, sumsq %g [%g]\n", info[5], info[6], info[1], info[0]);
// Debugging - info[0] returns lsq at start of fit,info[1] returns lsq at end of fit,
//******************Uncomment for extra information***************************************
}
//freeup memory allocated for dynamic arrays
delete [] x;
delete [] p;
delete [] data;
delete [] lb;
delete [] ub;
delete [] weights;
return;
}
