bool colpack_hes(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
typedef CPPAD_TESTVECTOR(AD<double>) a_vector;
typedef CPPAD_TESTVECTOR(double) d_vector;
typedef CppAD::vector<size_t> i_vector;
size_t i, j, k, ell;
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 5;
a_vector a_x(n);
for(j = 0; j < n; j++)
a_x[j] = AD<double> (0);
// declare independent variables and starting recording
CppAD::Independent(a_x);
// colpack example case where hessian is a spear head
// i.e, H(i, j) non zero implies i = 0, j = 0, or i = j
AD<double> sum = 0.0;
// partial_0 partial_j = x[j]
// partial_j partial_j = x[0]
for(j = 1; j < n; j++)
sum += a_x[0] * a_x[j] * a_x[j] / 2.0;
//
// partial_i partial_i = 2 * x[i]
for(i = 0; i < n; i++)
sum += a_x[i] * a_x[i] * a_x[i] / 3.0;
// declare dependent variables
size_t m = 1;
a_vector a_y(m);
a_y[0] = sum;
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(a_x, a_y);
// new value for the independent variable vector
d_vector x(n);
for(j = 0; j < n; j++)
x[j] = double(j + 1);
/*
[ 2 2 3 4 5 ]
hes = [ 2 5 0 0 0 ]
[ 3 0 7 0 0 ]
[ 4 0 0 9 0 ]
[ 5 0 0 0 11 ]
*/
d_vector check(n * n);
for(i = 0; i < n; i++)
{ for(j = 0; j < n; j++)
{ size_t index = i * n + j;
check[index] = 0.0;
if( i == 0 && 1 <= j )
check[index] += x[j];
if( 1 <= i && j == 0 )
check[index] += x[i];
if( i == j )
{ check[index] += 2.0 * x[i];
if( i != 0 )
check[index] += x[0];
}
}
}
// Normally one would use f.RevSparseHes to compute
// sparsity pattern, but for this example we extract it from check.
std::vector< std::set<size_t> > p(n);
i_vector row, col;
for(i = 0; i < n; i++)
{ for(j = 0; j < n; j++)
{ ell = i * n + j;
if( check[ell] != 0. )
{ // insert this non-zero entry in sparsity pattern
p[i].insert(j);
// the Hessian is symmetric, so only upper lower triangle
if( j <= i )
{ row.push_back(i);
col.push_back(j);
}
}
}
}
size_t K = row.size();
d_vector hes(K);
// contrast and check results using both cppad and colpack
CppAD::sparse_hessian_work work;
for(size_t i_method = 0; i_method < 3; i_method++)
{ // empty work structure
ok &= work.color_method == "cppad.symmetric";
if( i_method == 2 )
work.color_method = "colpack.star";
// compute Hessian
d_vector w(m);
w[0] = 1.0;
size_t n_sweep = f.SparseHessian(x, w, p, row, col, hes, work);
// check result
for(k = 0; k < K; k++)
{ ell = row[k] * n + col[k];
ok &= NearEqual(check[ell], hes[k], eps, eps);
}
if( work.color_method != "cppad.general" )
ok &= n_sweep == 2;
else
ok &= n_sweep == 5;
//
// check that clear resets color_method to cppad.symmetric
work.clear();
ok &= work.color_method == "cppad.symmetric";
}
return ok;
}
void mexFunction(int nlhs, mxArray *plhs[],int nrhs, const mxArray *prhs[])
{
double *v, *x, sigma, *lambda, *pr;
char *mode; int imode;
//Check Inputs
if(nrhs < 1) {
printInfo();
return;
}
if(mxIsEmpty(prhs[0]) || !mxIsChar(prhs[0])) {
mexErrMsgTxt("The mode must be a string!");
return;
}
//If we have x, check it
if(nrhs > 1) {
if(!mxIsEmpty(prhs[1])) {
if(mxIsClass(prhs[1],"scipvar") || mxIsClass(prhs[1],"barvec")) {
mexErrMsgTxt("SCIP and BARON cannot be used with this callback function - please specify 'mcode' via symbset as the cbmode.");
return;
}
if(!mxIsDouble(prhs[1]) || mxIsComplex(prhs[1]) || mxIsSparse(prhs[1])) {
mexErrMsgTxt("The input vector must be a dense real double vector!");
return;
}
}
else {
mexErrMsgTxt("The input vector must be a dense real double vector!");
return;
}
//Check x input size
if(mxGetNumberOfElements(prhs[1]) != getNoVar()) {
mexErrMsgTxt("The input vector is not the right size!");
}
//Allocate memory, if required
if(xvec.empty())
xvec.resize(getNoVar());
//Get x and copy to xvec
x = mxGetPr(prhs[1]);
memcpy(&xvec[0],x,getNoVar()*sizeof(double));
}
//Determine input mode and setup return variable
mode = mxArrayToString(prhs[0]);
lower(mode);
if(!strcmp(mode,"obj")) {
imode = 0;
plhs[0] = mxCreateDoubleMatrix(1,1, mxREAL);
v = mxGetPr(plhs[0]);
}
else if(!strcmp(mode,"grad")) {
imode = 1;
plhs[0] = mxCreateDoubleMatrix(1,getNoVar(), mxREAL);
v = mxGetPr(plhs[0]);
}
else if(!strcmp(mode,"con")) {
imode = 2;
plhs[0] = mxCreateDoubleMatrix(getNoCon(),1, mxREAL);
v = mxGetPr(plhs[0]);
}
else if(!strcmp(mode,"jac")) {
imode = 3;
//Can't allocate here until we know sparsity pattern
}
else if(!strcmp(mode,"jacstr")) {
imode = 4;
//Can't allocate here until we know sparsity pattern
}
else if(!strcmp(mode,"hess")) {
if(nrhs < 4) {
mexErrMsgTxt("You must supply the callback mode, input vector, sigma and lambda for Hessian Evaluations.");
return;
}
//Check length of Sigma
if(mxIsEmpty(prhs[2]) || !mxIsDouble(prhs[2]) || mxIsComplex(prhs[2]) || mxGetNumberOfElements(prhs[2]) != 1)
mexErrMsgTxt("Sigma must be a real, double scalar.");
//Check length of Lambda
if(!mxIsDouble(prhs[3]) || mxIsComplex(prhs[3]) || mxIsSparse(prhs[3]) || mxGetNumberOfElements(prhs[3]) != getNoCon())
mexErrMsgTxt("Lambda must be a real, double, dense vector with ncon elements.");
//Get Sigma, Lambda
sigma = *mxGetPr(prhs[2]);
lambda = mxGetPr(prhs[3]);
imode = 5;
//Can't allocate here until we know sparsity pattern
}
else if(!strcmp(mode,"hstr")) {
imode = 6;
//Can't allocate here until we know sparsity pattern
}
else
mexErrMsgTxt("Unknown mode - options are 'obj', 'grad', 'con', 'jac', 'jacstr', 'hess' or 'hstr'");
mxFree(mode);
//Ensure we did have x for normal callbacks
if(imode != 4 && imode != 6 && nrhs < 2)
mexErrMsgTxt("You must supply the callback mode and input vector.");
//Call Req Callback
switch(imode)
{
case 0: //objective
*v = objective(xvec);
break;
case 1: //gradient
//Check if we have recorded the objective yet
if(obj.Memory()==0) { //new, tape operations
vector< CppAD::AD<double> > X(getNoVar());
memcpy(&X[0],x,getNoVar()*sizeof(double));
CppAD::Independent(X);
vector< CppAD::AD<double> > Y(1);
Y[0] = objective(X);
obj = CppAD::ADFun<double>(X, Y);
//obj.optimize();
mexAtExit(mexExit); //also register memory clear function
//mexPrintf("Evaluated Tape for Gradient\n");
}
//Evaluate "Jacobian" for gradient
memcpy(v,&(obj.Jacobian(xvec)[0]),getNoVar()*sizeof(double));
break;
case 2: //constraints
//Check if we have constraint memory yet
if(cvec.empty())
cvec.resize(getNoCon()); //allocate it
//Evaluate Constraints
constraints(xvec,cvec);
//Copy Out
memcpy(v,&cvec[0],getNoCon()*sizeof(double));
break;
case 3: //jacobian
case 4: //jacobian structure
//Check if we have recorded the constraints yet
if(con.Memory()==0){ //new, tape operations
vector< CppAD::AD<double> > X(getNoVar());
memcpy(&X[0],x,getNoVar()*sizeof(double));
CppAD::Independent(X);
vector< CppAD::AD<double> > Y(getNoCon());
constraints(X,Y);
con = CppAD::ADFun<double>(X, Y);
//con.optimize();
mexAtExit(mexExit); //also register memory clear function
//mexPrintf("Evaluated Tape for Jacobian\n");
}
//Check if we have the sparsity pattern yet
if(jstr.empty()) {
vector<set<size_t>> r(getNoVar());
for(size_t i = 0; i < getNoVar(); i++)
r[i].insert(i); //identity matrix
jstr.resize(getNoCon());
jstr = con.ForSparseJac(getNoVar(),r,true); //note transpose
//Determine nnzs
for(int i = 0; i < jstr.size(); i++)
nnzJac += jstr[i].size();
//Save ir, jc for jac
jir = (mwIndex*)mxCalloc(nnzJac,sizeof(mwIndex));
jjc = (mwIndex*)mxCalloc(getNoVar()+1,sizeof(mwIndex));
mexMakeMemoryPersistent(jir);
mexMakeMemoryPersistent(jjc);
jwork.clear(); //reset jacobian calculations
//Col starts
jjc[0] = 0;
for(int i = 1; i <= getNoVar(); i++)
jjc[i] = (mwIndex)(jjc[i-1] + jstr[i-1].size());
//Rows
size_t idx = 0;
for(int i = 0; i < jstr.size(); i++)
for (set<size_t>::iterator it=jstr[i].begin(); it!=jstr[i].end(); ++it)
jir[idx++] = (mwIndex)*it;
//Build missing triple so we can eval just sparse elements of Jac
jrow.resize(nnzJac);
jcol.resize(nnzJac);
idx = 0;
for(size_t i = 0; i < nnzJac; i++)
jrow[i] = jir[i];
for(size_t i = 0; i < getNoVar();i++)
for(size_t j = jjc[i]; j < jjc[i+1]; j++)
jcol[idx++] = i;
//Re-do with no transpose... (bad really...)
jstr = con.ForSparseJac(getNoVar(),r,false);
//mexPrintf("Determined Jac Sparsity Structure (%d nzs)\n",nnzJac);
}
//Create Sparse Return Matrix
plhs[0] = mxCreateSparse(getNoCon(),getNoVar(),nnzJac,mxREAL);
pr = mxGetPr(plhs[0]);
memcpy(mxGetIr(plhs[0]),jir,nnzJac*sizeof(mwIndex));
memcpy(mxGetJc(plhs[0]),jjc,(getNoVar()+1)*sizeof(mwIndex));
//If we want the sparsity pattern only, fill in return matrix with 1s
if(imode==4) {
for(int i = 0; i < nnzJac; i++)
pr[i] = 1.0;
}
//Else, evaluate sparse jacobian and return as sparse matrix
else {
//Check if we have jacobian memory yet
if(jac.empty())
jac.resize(nnzJac); //allocate it
//If ndec > ncon, use reverse mode
if(getNoVar() > getNoCon())
con.SparseJacobianReverse(xvec,jstr,jrow,jcol,jac,jwork);
//else use forward
else
con.SparseJacobianForward(xvec,jstr,jrow,jcol,jac,jwork);
//Copy out
memcpy(pr,&jac[0],nnzJac*sizeof(double));
}
break;
case 5: //hessian of the lagrangian
case 6: //hessian structure
//Check if we have recorded the objective+constraints yet
//Not sure if we can reuse ones we have done above??
if(lag.Memory()==0){ //new, tape operations
vector< CppAD::AD<double> > X(getNoVar());
memcpy(&X[0],x,getNoVar()*sizeof(double));
CppAD::Independent(X);
//Output Array
vector< CppAD::AD<double> > Y(1);
vector< CppAD::AD<double> > Yc(getNoCon());
Y[0] = objective(X); //eval objective
if(getNoCon() > 0)
constraints(X,Yc); //eval constraints
Yc.insert(Yc.begin(),Y.begin(),Y.end());
//Create ADFun
lag.Dependent(Yc);
//lag.optimize();
mexAtExit(mexExit); //also register memory clear function
//mexPrintf("Evaluated Tape for Hessian\n");
}
//Check if we have the sparsity pattern yet
if(hstr.empty()) {
//First eval jac structure (not sure why)
vector< std::set<size_t> > r(getNoVar());
for(size_t i = 0; i < getNoVar(); i++)
r[i].insert(i);
lag.ForSparseJac(getNoVar(), r);
//Now do Hessian structure
vector<set<size_t>> s(1);
for(size_t i = 0; i < getNoCon()+1; i++)
s[0].insert(i); //identity matrix
hstr.resize(getNoVar());
hstr = lag.RevSparseHes(getNoVar(),s);
//Determine total nnzs
for(int i = 0; i < hstr.size(); i++)
nnzHess += hstr[i].size();
//Determine nnzs in lower tri
for(int i = 0; i < hstr.size(); i++)
for (set<size_t>::iterator it=hstr[i].begin(); it!=hstr[i].end(); ++it)
if(*it >= i)
nnzHessLT++;
//Save ir, jc for jac
hir = (mwIndex*)mxCalloc(nnzHessLT,sizeof(mwIndex));
hjc = (mwIndex*)mxCalloc(getNoVar()+1,sizeof(mwIndex));
mexMakeMemoryPersistent(hir);
mexMakeMemoryPersistent(hjc);
hwork.clear(); //reset hessian calculations
//Col & Row Starts
size_t idx = 0;
for(int i = 0; i < hstr.size(); i++) {
hjc[i] = idx;
for (set<size_t>::iterator it=hstr[i].begin(); it!=hstr[i].end(); ++it)
if(*it >= i)
hir[idx++] = (mwIndex)*it;
}
hjc[getNoVar()] = nnzHessLT;
//Build missing triple so we can eval just sparse elements of Jac
hrow.resize(nnzHessLT);
hcol.resize(nnzHessLT);
idx = 0;
for(size_t i = 0; i < nnzHessLT; i++)
hrow[i] = hir[i];
for(size_t i = 0; i < getNoVar();i++)
for(size_t j = hjc[i]; j < hjc[i+1]; j++)
hcol[idx++] = i;
//mexPrintf("Determined Hess Sparsity Structure (%d nzs in tril)\n",nnzHessLT);
}
//Create Sparse Return Matrix
plhs[0] = mxCreateSparse(getNoVar(),getNoVar(),nnzHessLT,mxREAL);
pr = mxGetPr(plhs[0]);
memcpy(mxGetIr(plhs[0]),hir,nnzHessLT*sizeof(mwIndex));
memcpy(mxGetJc(plhs[0]),hjc,(getNoVar()+1)*sizeof(mwIndex));
//If we want the sparsity pattern only, fill in return matrix with 1s
if(imode==6) {
for(int i = 0; i < nnzHessLT; i++)
pr[i] = 1.0;
}
//Else, evaluate sparse hessian and return as sparse matrix
else {
//Check if we have hessian memory yet
if(hes.empty())
hes.resize(nnzHessLT); //allocate it
if(w.empty())
w.resize(1+getNoCon()); //allocate it
//Copy in Weights
w[0] = sigma;
for(int i = 0; i < getNoCon(); i++)
w[i+1] = lambda[i];
//If ndec > ncon, use reverse mode
lag.SparseHessian(xvec,w,hstr,hrow,hcol,hes,hwork);
//Copy out elements
memcpy(pr,&hes[0],nnzHessLT*sizeof(double));
}
break;
}
}