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tr_optim.cpp
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#include <gsl/gsl_vector_double.h>
#include "tr_optim.h"
using namespace std;
double quadratic_eval(gsl_matrix *M, gsl_vector *g, gsl_vector *x) {
int dim = x->size;
int i, j;
double result = 0.0;
for (i = 0; i < dim; i++) {
result += g->data[i] * x->data[i];
for (j = 0; j < dim; j++)
result += 0.5 * x->data[i] * M->data[i * dim + j] * x->data[j];
}
return result;
}
double *trust_region_optimization(void (*function)(double *, double *, double *, double *), int dim, double *xx0,
double step_size, double step_limit, int max_iterations) {
cout << setprecision(15);
gsl_vector *xx = gsl_vector_alloc((const size_t) dim);
gsl_vector *yy = gsl_vector_alloc((const size_t) 1);
gsl_vector *grad = gsl_vector_alloc((const size_t) dim);
gsl_matrix *hess = gsl_matrix_alloc((const size_t) dim, (const size_t) dim);
gsl_vector *xx_new = gsl_vector_alloc((const size_t) dim);
gsl_vector *yy_new = gsl_vector_alloc((const size_t) 1);
gsl_vector *grad_new = gsl_vector_alloc((const size_t) dim);
gsl_matrix *hess_new = gsl_matrix_alloc((const size_t) dim, (const size_t) dim);
gsl_vector_view xx0V = gsl_vector_view_array(xx0, (size_t) dim);
gsl_vector_memcpy(xx, &xx0V.vector);
function(xx->data, yy->data, grad->data, hess->data);
gsl_vector *result = rec_trust_region_optimization(function, xx, yy, grad, hess,
xx_new, yy_new, grad_new, hess_new,
0, step_size, step_limit,
max_iterations);
double *result_copy = (double *) malloc(sizeof(double) * dim);
int i;
for (i = 0; i < dim; i++)
result_copy[i] = result->data[i];
gsl_vector_free(xx);
gsl_vector_free(yy);
gsl_vector_free(grad);
gsl_matrix_free(hess);
gsl_vector_free(xx_new);
gsl_vector_free(yy_new);
gsl_vector_free(grad_new);
gsl_matrix_free(hess_new);
return result_copy;
}
gsl_vector *rec_trust_region_optimization(
void (*function)(double *, double *, double *, double *),
gsl_vector *xx, gsl_vector *yy, gsl_vector *grad, gsl_matrix *hess,
gsl_vector *xx_new, gsl_vector *yy_new, gsl_vector *grad_new, gsl_matrix *hess_new,
int iteration, double step_size, double step_limit, int max_iterations) {
trust_region_step(grad, hess, xx_new, step_size);
double cc = max(gsl_vector_max(xx_new), -gsl_vector_min(xx_new));
bool stop_criterion = iteration >= (max_iterations - 1) || cc < step_limit;
if (stop_criterion) {
double moved = gsl_blas_dnrm2(xx_new);
gsl_vector_add(xx_new, xx);
cout << iteration << "\t" << step_size << "\t" << moved << "\t" << yy << "\t" << xx_new << endl;
return xx_new;
} else {
double pred = quadratic_eval(hess, grad, xx_new);
double moved = gsl_blas_dnrm2(xx_new);
double was_newton = moved < step_size * 0.9;
gsl_vector_add(xx_new, xx);
function(xx_new->data, yy_new->data, grad_new->data, hess_new->data);
double actual = yy_new->data[0] - yy->data[0];
// Test if predicted function value is close enough to yyNew. Reduce step size if not.
bool approximation_was_good = actual < 0 && pred < actual * 0.8 && pred > actual * 1.2;
if (approximation_was_good) {
cout << iteration << "\t" << step_size << "\t" << moved << "\t" << yy << "\t" << xx << endl;
double step_size_new = was_newton ? step_size : step_size * 2.0;
return rec_trust_region_optimization(function, xx_new, yy_new, grad_new, hess_new, xx, yy, grad, hess,
iteration + 1, step_size_new, step_limit, max_iterations);
} else {
double step_size_new = step_size / 4.0;
return rec_trust_region_optimization(function, xx, yy, grad, hess, xx_new, yy_new, grad_new, hess_new,
iteration, step_size_new, step_limit, max_iterations);
}
}
}
bool vector_too_small(gsl_vector *vec, double tol = 1e-7) {
double vmin, vmax;
gsl_vector_minmax(vec, &vmin, &vmax);
return vmin > -tol && vmax < tol;
}
bool hard_case(gsl_vector *vec, gsl_vector *lam, double tol = 1e-7) {
double lambda_one = gsl_vector_min(lam);
if (lambda_one <= 0) {
int i;
for (i = 0; i < vec->size; i++) if (fabs(vec->data[i]) < tol && lam->data[i] == lambda_one) return true;
}
return false;
}
void trust_region_step(gsl_vector *grad,
gsl_matrix *hess,
gsl_vector *xxStep,
double rho) {
const size_t dim = hess->size1;
gsl_vector *eval = gsl_vector_alloc(dim);
gsl_matrix *evec = gsl_matrix_alloc(dim, dim);
gsl_eigen_symmv_workspace *w = gsl_eigen_symmv_alloc(dim);
gsl_eigen_symmv(hess, eval, evec, w);
if (vector_too_small(eval)) {
double gradient_norm = gsl_blas_dnrm2(grad);
if (vector_too_small(grad)) {
// Handle creep case where both gradient and Hessian are zero.
gsl_vector_view firstev = gsl_matrix_row(evec, 0);
gsl_vector_memcpy(xxStep, &(firstev.vector));
gsl_vector_scale(xxStep, rho);
} else {
// Flat function with gradient, just follow the gradient.
gsl_vector_memcpy(xxStep, grad);
gsl_vector_scale(xxStep, rho / gradient_norm);
}
} else {
gsl_vector *alpha = gsl_vector_alloc(dim);
gsl_vector *beta = gsl_vector_alloc(dim);
gsl_blas_dgemv(CblasTrans, 1.0, evec, grad, 0.0, alpha);
bool fork_inside_region = false;
double beta_norm = 0.0;
if (hard_case(alpha, eval)) {
double min_eval = gsl_vector_min(eval);
int i;
for (i = 0; i < dim; i++)
beta->data[i] = (eval->data[i] > min_eval) ? alpha->data[i] / (eval->data[i] - min_eval) : 0;
beta_norm = gsl_blas_dnrm2(beta);
fork_inside_region = beta_norm <= rho;
}
if (fork_inside_region) {
gsl_vector_view mv = gsl_matrix_column(evec, gsl_vector_min_index(eval));
gsl_vector_memcpy(xxStep, &mv.vector);
gsl_blas_dgemv(CblasNoTrans, 1.0, evec, beta, sqrt(rho * rho - beta_norm * beta_norm), xxStep);
} else {
double nu_opt = *(find_root(dim, alpha->data, eval->data, rho, 1e-5));
gsl_vector_memcpy(beta, alpha);
gsl_vector_scale(beta, 1.0);
gsl_vector_add_constant(eval, nu_opt);
gsl_vector_div(beta, eval);
gsl_blas_dgemv(CblasNoTrans, 1.0, evec, beta, 0.0, xxStep);
}
gsl_vector_free(alpha);
gsl_vector_free(beta);
}
gsl_vector_scale(xxStep, -1.0);
gsl_eigen_symmv_free(w);
gsl_vector_free(eval);
gsl_matrix_free(evec);
}
ostream &operator<<(ostream &os, const gsl_vector *vec) {
int i;
cout << vec->data[0];
for (i = 1; i < vec->size; i++) cout << "\t" << vec->data[i];
return os;
}