/**
* Copy the parameter values to a GSLVector.
* @param params :: A vector to copy the parameters to
*/
void CostFuncLeastSquares::getParameters(GSLVector ¶ms) const {
if (params.size() != nParams()) {
params.resize(nParams());
}
for (size_t i = 0; i < nParams(); ++i) {
params.set(i, getParameter(i));
}
}
/// Calculate the eigensystem of a symmetric matrix
/// @param eigenValues :: Output variable that receives the eigenvalues of this
/// matrix.
/// @param eigenVectors :: Output variable that receives the eigenvectors of
/// this matrix.
void GSLMatrix::eigenSystem(GSLVector &eigenValues, GSLMatrix &eigenVectors) {
size_t n = size1();
if (n != size2()) {
throw std::runtime_error("Matrix eigenSystem: the matrix must be square.");
}
eigenValues.resize(n);
eigenVectors.resize(n, n);
auto workspace = gsl_eigen_symmv_alloc(n);
gsl_eigen_symmv(gsl(), eigenValues.gsl(), eigenVectors.gsl(), workspace);
gsl_eigen_symmv_free(workspace);
}
/**
* Improve the solution by using obtained functions as a basis for diagonalization.
*
* @param hamiltonian :: The Hamiltonian.
* @param basis :: The basis functions.
* @param n :: The size of the basis to use.
* @param eigv :: Output eigenvalues.
* @param eigf :: Output eigenvectors (functions). This method creates a new ChebfunVector instance and returns it.
*/
void Schrodinger1D::improve(ChebOperator *hamiltonian, ChebfunVector *basis, GSLVector &eigv, ChebfunVector **eigf) const
{
size_t n = basis->size();
GSLMatrix H(n,n);
for(size_t i = 0; i < n; ++i)
{
const chebfun &f1 = basis->cfun(i).cfun(0).getUnscaled();
chebfun d1(f1);
hamiltonian->apply(f1, d1);
chebfun dd = d1;
dd *= f1;
double me = dd.integr();
H.set( i, i, me );
//std::cerr << "e=" << me << std::endl;
for(size_t j = i+1; j < n; ++j)
{
const chebfun &f2 = basis->cfun(j).cfun(0).getUnscaled();
chebfun d2(f2);
hamiltonian->apply(f2, d2);
d2 *= f1;
double me = d2.integr();
//std::cerr << "o=" << me << std::endl;
H.set( i, j, me );
H.set( j, i, me );
}
}
//std::cerr << H << std::endl;
GSLVector en;
GSLMatrix v;
H.diag(en,v);
std::vector<size_t> indx;
getSortedIndex( en, indx );
if ( indx.empty() )
{
throw std::runtime_error("Schrodinger1D failed to find solution.");
}
eigv.resize( indx.size() );
*eigf = new ChebfunVector;
ChebfunVector &funs = **eigf;
funs.fromLinearCombinations( *basis, v );
funs.sort( indx );
for(size_t i = 0; i < indx.size(); ++i)
{
std::cerr << i << ' ' << en[indx[i]] << std::endl;
eigv.set( i, en[indx[i]] );
}
}
/// Solve system of linear equations M*x == rhs, M is this matrix
/// This matrix is destroyed.
/// @param rhs :: The right-hand-side vector
/// @param x :: The solution vector
void GSLMatrix::solve(const GSLVector &rhs, GSLVector &x) {
if (size1() != size2()) {
throw std::runtime_error(
"System of linear equations: the matrix must be square.");
}
size_t n = size1();
if (rhs.size() != n) {
throw std::runtime_error(
"System of linear equations: right-hand side vector has wrong size.");
}
x.resize(n);
int s;
gsl_permutation *p = gsl_permutation_alloc(n);
gsl_linalg_LU_decomp(gsl(), p, &s); // matrix is modified at this moment
gsl_linalg_LU_solve(gsl(), p, rhs.gsl(), x.gsl());
gsl_permutation_free(p);
}
/// Solve system of linear equations M*x == rhs, M is this matrix
/// This matrix is destroyed.
/// @param rhs :: The right-hand-side vector
/// @param x :: The solution vector
/// @throws std::invalid_argument if the input vectors have wrong sizes.
/// @throws std::runtime_error if the GSL fails to solve the equations.
void GSLMatrix::solve(const GSLVector &rhs, GSLVector &x) {
if (size1() != size2()) {
throw std::invalid_argument(
"System of linear equations: the matrix must be square.");
}
size_t n = size1();
if (rhs.size() != n) {
throw std::invalid_argument(
"System of linear equations: right-hand side vector has wrong size.");
}
x.resize(n);
int s;
gsl_permutation *p = gsl_permutation_alloc(n);
gsl_linalg_LU_decomp(gsl(), p, &s); // matrix is modified at this moment
int res = gsl_linalg_LU_solve(gsl(), p, rhs.gsl(), x.gsl());
gsl_permutation_free(p);
if (res != GSL_SUCCESS) {
std::string message = "Failed to solve system of linear equations.\n"
"Error message returned by the GSL:\n" +
std::string(gsl_strerror(res));
throw std::runtime_error(message);
}
}