void test1(){
std::cerr << "-------------------------------------" << std::endl;
std::cerr << "Testing linear search." << std::endl;
int dim=2;
double oLoc[2],oVal;
double grad[2],dir[2];
double nLoc[2],nVal;
int resCode;
double (*func)(double *);
double (*gradFunc)(double *,double *);
func = circ_0_0;
gradFunc = circ_0_0_grad;
oLoc[0] = 0;oLoc[1] = 1.0;
oVal = func(oLoc);
TEST_ASSERT(fabs(oVal-1.0)<1e-4);
gradFunc(oLoc,grad);
dir[0] = 0; dir[1] = -.5;
BFGSOpt::linearSearch(dim,oLoc,oVal,grad,dir,nLoc,nVal,func,0.5,resCode);
TEST_ASSERT(resCode==0);
TEST_ASSERT(fabs(nVal-0.25)<1e-4);
TEST_ASSERT(fabs(nLoc[0])<1e-4);
TEST_ASSERT(fabs(nLoc[1]-0.5)<1e-4);
oLoc[0] = 1.0;oLoc[1] = 1.0;
oVal = func(oLoc);
TEST_ASSERT(fabs(oVal-2.0)<1e-4);
gradFunc(oLoc,grad);
dir[0] = -.5; dir[1] = -.5;
BFGSOpt::linearSearch(dim,oLoc,oVal,grad,dir,nLoc,nVal,func,1.0,resCode);
TEST_ASSERT(resCode==0);
TEST_ASSERT(fabs(nVal-0.5)<1e-4);
TEST_ASSERT(fabs(nLoc[0]-0.5)<1e-4);
TEST_ASSERT(fabs(nLoc[1]-0.5)<1e-4);
// we go hugely too far, but the dir gets cut in half, so we
// immediately hit the minimum
func = circ_0_0;
oLoc[0] = 0;oLoc[1] = 1.0;
oVal = func(oLoc);
TEST_ASSERT(fabs(oVal-1.0)<1e-4);
gradFunc(oLoc,grad);
dir[0] = 0; dir[1] = -2;
BFGSOpt::linearSearch(dim,oLoc,oVal,grad,dir,nLoc,nVal,func,2.0,resCode);
TEST_ASSERT(resCode==0);
TEST_ASSERT(fabs(nVal)<1e-4);
TEST_ASSERT(fabs(nLoc[0])<1e-4);
TEST_ASSERT(fabs(nLoc[1])<1e-4);
std::cerr << " done" << std::endl;
}
// simplified evaluation for interactive render
AColor Gradient::DispEvalFunc(float u, float v)
{
float a = gradFunc(u,v);
if (a<center) {
a = a/center;
return col[2]*(1.0f-a) + col[1]*a;
} else
if (a>center) {
a = (a-center)/(1.0f-center);
return col[1]*(1.0f-a) + col[0]*a;
} else return col[1];
}
Point3 Gradient::EvalNormalPerturb(ShadeContext& sc)
{
Point3 dPdu, dPdv;
if (!sc.doMaps) return Point3(0,0,0);
if (gbufID) sc.SetGBufferID(gbufID);
Point2 dM = uvGen->EvalDeriv(sc,&mysamp);
uvGen->GetBumpDP(sc,dPdu,dPdv);
#if 0
// Blinn's algorithm
Point3 N = sc.Normal();
Point3 uVec = CrossProd(N,dPdv);
Point3 vVec = CrossProd(N,dPdu);
Point3 np = -dM.x*uVec+dM.y*vVec;
#else
// Lazy algorithm
Point3 np = dM.x*dPdu+dM.y*dPdv;
// return texout->Filter(dM.x*dPdu+dM.y*dPdv);
#endif
Texmap* sub[3];
for (int i=0; i<3; i++)
sub[i] = mapOn[i]?subTex[i]:NULL;
if (sub[0]||sub[1]||sub[2]) {
// d((1-k)*a + k*b ) = dk*(b-a) + k*(db-da) + da
float a,b,k;
Point3 da,db;
Point2 UV, dUV;
uvGen->GetUV(sc, UV,dUV);
k = gradFunc(UV.x,UV.y);
if (k<=center) {
k = k/center;
EVALSUBPERTURB(a,da,2);
EVALSUBPERTURB(b,db,1);
}
else {
k = (k-center)/(1.0f-center);
EVALSUBPERTURB(a,da,1);
EVALSUBPERTURB(b,db,0);
}
np = (b-a)*np + k*(db-da) + da;
}
return texout->Filter(np);
}
AColor Gradient::EvalFunction(
ShadeContext& sc, float u, float v, float du, float dv)
{
int n1=0, n2=0;
float a = gradFunc(u,v);
if (a<center) {
a = a/center;
n1 = 2;
n2 = 1;
} else
if (a>center) {
a = (a-center)/(1.0f-center);
n1 = 1;
n2 = 0;
} else {
return (mapOn[1]&&subTex[1]) ? subTex[1]->EvalColor(sc): col[1];
}
Color c1, c2;
c1 = mapOn[n1]&&subTex[n1] ? subTex[n1]->EvalColor(sc): col[n1];
c2 = mapOn[n2]&&subTex[n2] ? subTex[n2]->EvalColor(sc): col[n2];
return c1*(1.0f-a) + c2*a;
}
// Function definitions.
// -----------------------------------------------------------------
void mexFunction (int nlhs, mxArray *plhs[],
int nrhs, const mxArray *prhs[])
try {
// Check to see if we have the correct number of input and output
// arguments.
if (nrhs < minNumInputArgs)
throw MatlabException("Incorrect number of input arguments");
// Get the starting point for the variables. This is specified in
// the first input argument. The variables must be either a single
// matrix or a cell array of matrices.
int k = 0; // The index of the current input argument.
ArrayOfMatrices x0(prhs[k++]);
// Create the output, which stores the solution obtained from
// running IPOPT. There should be as many output arguments as cell
// entries in X.
if (nlhs != x0.length())
throw MatlabException("Incorrect number of output arguments");
ArrayOfMatrices x(plhs,x0);
// Load the lower and upper bounds on the variables as
// ArrayOfMatrices objects. They should have the same structure as
// the ArrayOfMatrices object "x".
ArrayOfMatrices lb(prhs[k++]);
ArrayOfMatrices ub(prhs[k++]);
// Check to make sure the bounds make sense.
if (lb != x || ub != x)
throw MatlabException("Input arguments LB and UB must have the same \
structure as X");
// Get the Matlab callback functions.
MatlabString objFunc(prhs[k++]);
MatlabString gradFunc(prhs[k++]);
// Get the auxiliary data.
const mxArray* auxData;
const mxArray* ptr = prhs[k++];
if (nrhs > 5) {
if (mxIsEmpty(ptr))
auxData = 0;
else
auxData = ptr;
}
else
auxData = 0;
// Get the intermediate callback function.
MatlabString* iterFunc;
ptr = prhs[k++];
if (nrhs > 6) {
if (mxIsEmpty(ptr))
iterFunc = 0;
else
iterFunc = new MatlabString(ptr);
}
else
iterFunc = 0;
// Set the options for the L-BFGS algorithm to their defaults.
int maxiter = defaultmaxiter;
int m = defaultm;
double factr = defaultfactr;
double pgtol = defaultpgtol;
// Process the remaining input arguments, which set options for
// the IPOPT algorithm.
while (k < nrhs) {
// Get the option label from the Matlab input argument.
MatlabString optionLabel(prhs[k++]);
if (k < nrhs) {
// Get the option value from the Matlab input argument.
MatlabScalar optionValue(prhs[k++]);
double value = optionValue;
if (!strcmp(optionLabel,"maxiter"))
maxiter = (int) value;
else if (!strcmp(optionLabel,"m"))
m = (int) value;
else if (!strcmp(optionLabel,"factr"))
factr = value / mxGetEps();
else if (!strcmp(optionLabel,"pgtol"))
pgtol = value;
else {
if (iterFunc) delete iterFunc;
throw MatlabException("Nonexistent option");
}
}
}
// Create a new instance of the optimization problem.
x = x0;
MatlabProgram program(x,lb,ub,&objFunc,&gradFunc,iterFunc,
(mxArray*) auxData,m,maxiter,factr,pgtol);
// Run the L-BFGS-B solver.
SolverExitStatus exitStatus = program.runSolver();
if (exitStatus == abnormalTermination) {
if (iterFunc) delete iterFunc;
throw MatlabException("Solver unable to satisfy convergence \
criteria due to abnormal termination");
}
else if (exitStatus == errorOnInput) {