void Stiefel::ObtainPerp(Variable *x) const
{
const double *xM = x->ObtainReadData();
SharedSpace *SharedSpacePerp = new SharedSpace(2, n, n - p);
double *Perp = SharedSpacePerp->ObtainWriteEntireData();
for (integer i = 0; i < n * (n - p); i++)
Perp[i] = genrand_gaussian();
double *temp = new double[p * (n - p)];
char *transn = const_cast<char *> ("n"), *transt = const_cast<char *> ("t");
double one = 1, zero = 0, neg_one = -1;
integer P = p, N = n, NmP = n - p;
// temp = X^T * Perp
dgemm_(transt, transn, &P, &NmP, &N, &one, const_cast<double *> (xM), &N, Perp, &N, &zero, temp, &P);
// Perp = Perp - X * temp
dgemm_(transn, transn, &N, &NmP, &P, &neg_one, const_cast<double *> (xM), &N, temp, &P, &one, Perp, &N);
delete[] temp;
integer *jpvt = new integer[NmP];
integer lwork = 2 * NmP + (1 + NmP) * INITIALBLOCKSIZE, info;
double *tau = new double[NmP + lwork];
double *work = tau + NmP;
for (integer i = 0; i < NmP; i++)
jpvt[i] = 0;
dgeqp3_(&N, &NmP, Perp, &N, jpvt, tau, work, &lwork, &info);
if (info < 0)
Rcpp::Rcout << "Error in qr decomposition!" << std::endl;
dorgqr_(&N, &NmP, &NmP, Perp, &N, tau, work, &lwork, &info);
if (info < 0)
Rcpp::Rcout << "Error in forming Q matrix!" << std::endl;
delete[] jpvt;
delete[] tau;
x->AddToTempData("Perp", SharedSpacePerp);
};
int main(void)
{
init_genrand(0);
// size of the domain
integer dim = 10;
// Generate the matrices in the Euclidean Quadratic problem.
// Use blas to obtain a positive definite matrix by M = Temp * Temp^T
double *M = new double[dim * dim];
double *Temp = new double[dim * dim];
for (integer i = 0; i < dim * dim; i++)
Temp[i] = genrand_gaussian();
char *transn = const_cast<char *> ("n"), *transt = const_cast<char *> ("t");
double one = 1, zero = 0;
integer N = dim;
std::cout << "start" << std::endl;
dgemm_(transn, transt, &N, &N, &N, &one, Temp, &N, Temp, &N, &zero, M, &N);
std::cout << "end" << std::endl;
delete[] Temp;
CheckMemoryDeleted = new std::map<integer *, integer>;
testEucQuadratic(M, dim);
std::map<integer *, integer>::iterator iter = CheckMemoryDeleted->begin();
for (iter = CheckMemoryDeleted->begin(); iter != CheckMemoryDeleted->end(); iter++)
{
if (iter->second != 1)
std::cout << "Global address:" << iter->first << ", sharedtimes:" << iter->second << std::endl;
}
delete CheckMemoryDeleted;
delete[] M;
#ifdef _WIN64
#ifdef _DEBUG
_CrtDumpMemoryLeaks();
#endif
#endif
return 0;
}
int main(void)
{
// choose a random seed
unsigned tt = (unsigned)time(NULL);
init_genrand(tt);
// size of the Stiefel manifold
integer n = 12, p = 8, m = 6, q = 2;
// Generate the matrices in the Brockett problem.
double *B1 = new double[n * n * 2 + p * 2 + m * m + q];
double *B2 = B1 + n * n;
double *B3 = B2 + n * n;
double *D1 = B3 + m * m;
double *D2 = D1 + p;
double *D3 = D2 + p;
for (integer i = 0; i < n; i++)
{
for (integer j = i; j < n; j++)
{
B1[i + j * n] = genrand_gaussian();
B1[j + i * n] = B1[i + j * n];
B2[i + j * n] = genrand_gaussian();
B2[j + i * n] = B2[i + j * n];
}
}
for (integer i = 0; i < m; i++)
{
for (integer j = i; j < m; j++)
{
B3[i + j * m] = genrand_gaussian();
B3[j + i * m] = B3[i + j * m];
}
}
for (integer i = 0; i < p; i++)
{
D1[i] = static_cast<double> (i + 1);
D2[i] = D1[i];
}
for (integer i = 0; i < q; i++)
{
D3[i] = static_cast<double> (i + 1);
}
// number of manifolds in product of manifold
integer numofmanis = 2; // two kinds of manifolds
integer numofmani1 = 2; // the first one has two
integer numofmani2 = 1; // the second one has one
// Obtain an initial iterate
StieVariable StieX1(n, p);
StieVariable StieX2(m, q);
ProductElement ProdX(numofmanis, &StieX1, numofmani1, &StieX2, numofmani2);
ProdX.RandInManifold();
// Define the Stiefel manifold
Stiefel mani1(n, p);
Stiefel mani2(m, q);
ProductManifold Domain(numofmanis, &mani1, numofmani1, &mani2, numofmani2);
// Define the Brockett problem
StieSumBrockett Prob(B1, D1, B2, D2, B3, D3, n, p, m, q);
// Set the domain of the problem to be the Stiefel manifold
Prob.SetDomain(&Domain);
// output the parameters of the manifold of domain
Domain.CheckParams();
//// test RSD
//std::cout << "********************************Check all line search algorithm in RSD*****************************************" << std::endl;
//for (integer i = 0; i < LSALGOLENGTH; i++)
//{
// RSD *RSDsolver = new RSD(&Prob, &ProdX);
// RSDsolver->LineSearch_LS = static_cast<LSAlgo> (i);
// RSDsolver->DEBUG = FINALRESULT;
// RSDsolver->CheckParams();
// RSDsolver->Run();
// delete RSDsolver;
//}
//// test RNewton
//std::cout << "********************************Check all line search algorithm in RNewton*************************************" << std::endl;
//for (integer i = 0; i < LSALGOLENGTH; i++)
//{
// RNewton *RNewtonsolver = new RNewton(&Prob, &ProdX);
// RNewtonsolver->LineSearch_LS = static_cast<LSAlgo> (i);
// RNewtonsolver->DEBUG = FINALRESULT;
// RNewtonsolver->CheckParams();
// RNewtonsolver->Run();
// delete RNewtonsolver;
//}
//// test RCG
//std::cout << "********************************Check all Formulas in RCG*************************************" << std::endl;
//for (integer i = 0; i < RCGMETHODSLENGTH; i++)
//{
// RCG *RCGsolver = new RCG(&Prob, &ProdX);
// RCGsolver->RCGmethod = static_cast<RCGmethods> (i);
// RCGsolver->LineSearch_LS = STRONGWOLFE;
// RCGsolver->LS_beta = 0.1;
// RCGsolver->DEBUG = FINALRESULT;
// RCGsolver->CheckParams();
// RCGsolver->Run();
// delete RCGsolver;
//}
//// test RBroydenFamily
//std::cout << "********************************Check all line search algorithm in RBroydenFamily*************************************" << std::endl;
//for (integer i = 0; i < LSALGOLENGTH; i++)
//{
// RBroydenFamily *RBroydenFamilysolver = new RBroydenFamily(&Prob, &ProdX);
// RBroydenFamilysolver->LineSearch_LS = static_cast<LSAlgo> (i);
// RBroydenFamilysolver->DEBUG = FINALRESULT;
// RBroydenFamilysolver->CheckParams();
// RBroydenFamilysolver->Run();
// delete RBroydenFamilysolver;
//}
//// test RWRBFGS
//std::cout << "********************************Check all line search algorithm in RWRBFGS*************************************" << std::endl;
//for (integer i = 0; i < LSALGOLENGTH; i++)
//{
// RWRBFGS *RWRBFGSsolver = new RWRBFGS(&Prob, &ProdX);
// RWRBFGSsolver->LineSearch_LS = static_cast<LSAlgo> (i);
// RWRBFGSsolver->DEBUG = FINALRESULT; //ITERRESULT;//
// RWRBFGSsolver->CheckParams();
// RWRBFGSsolver->Run();
// delete RWRBFGSsolver;
//}
//// test RBFGS
//std::cout << "********************************Check all line search algorithm in RBFGS*************************************" << std::endl;
//for (integer i = 0; i < LSALGOLENGTH; i++)
//{
// RBFGS *RBFGSsolver = new RBFGS(&Prob, &ProdX);
// RBFGSsolver->LineSearch_LS = static_cast<LSAlgo> (i);
// RBFGSsolver->DEBUG = FINALRESULT;
// RBFGSsolver->CheckParams();
// RBFGSsolver->Run();
// delete RBFGSsolver;
//}
//// test LRBFGS
//std::cout << "********************************Check all line search algorithm in LRBFGS*************************************" << std::endl;
//for (integer i = 0; i < 1; i++)//LSALGOLENGTH
//{
// LRBFGS *LRBFGSsolver = new LRBFGS(&Prob, &ProdX);
// LRBFGSsolver->LineSearch_LS = static_cast<LSAlgo> (i);
// LRBFGSsolver->DEBUG = FINALRESULT; //ITERRESULT;//
// LRBFGSsolver->CheckParams();
// LRBFGSsolver->Run();
// delete LRBFGSsolver;
//}
//// test RTRSD
//std::cout << "********************************Check RTRSD*************************************" << std::endl;
//RTRSD RTRSDsolver(&Prob, &ProdX);
//RTRSDsolver.DEBUG = FINALRESULT;
//RTRSDsolver.CheckParams();
//RTRSDsolver.Run();
// test RTRNewton
std::cout << "********************************Check RTRNewton*************************************" << std::endl;
RTRNewton RTRNewtonsolver(&Prob, &ProdX);
RTRNewtonsolver.DEBUG = FINALRESULT;
RTRNewtonsolver.CheckParams();
RTRNewtonsolver.Run();
//// test RTRSR1
//std::cout << "********************************Check RTRSR1*************************************" << std::endl;
//RTRSR1 RTRSR1solver(&Prob, &ProdX);
//RTRSR1solver.DEBUG = FINALRESULT;
//RTRSR1solver.CheckParams();
//RTRSR1solver.Run();
//// test LRTRSR1
//std::cout << "********************************Check LRTRSR1*************************************" << std::endl;
//LRTRSR1 LRTRSR1solver(&Prob, &ProdX);
//LRTRSR1solver.DEBUG = FINALRESULT;
//LRTRSR1solver.CheckParams();
//LRTRSR1solver.Run();
// Check gradient and Hessian
Prob.CheckGradHessian(&ProdX);
const Variable *xopt = RTRNewtonsolver.GetXopt();
Prob.CheckGradHessian(xopt);
delete[] B1;
return 0;
}