static double
quadratic_preduction(const gsl_vector * f, const gsl_matrix * J,
const gsl_vector * dx, gsl_vector * work)
{
const size_t n = f->size;
const double normf = gsl_blas_dnrm2(f);
double pred_reduction;
double norm_beta; /* ||J*dx|| / ||f|| */
size_t i;
/* compute beta = J*dx / ||f|| */
gsl_blas_dgemv(CblasNoTrans, 1.0 / normf, J, dx, 0.0, work);
norm_beta = gsl_blas_dnrm2(work);
/* initialize to ( ||J*dx|| / ||f|| )^2 */
pred_reduction = -norm_beta * norm_beta;
/* subtract 2*fhat.beta */
for (i = 0; i < n; ++i)
{
double fi = gsl_vector_get(f, i);
double betai = gsl_vector_get(work, i);
pred_reduction -= 2.0 * (fi / normf) * betai;
}
return pred_reduction;
}
int
test_fdf(const char * desc,
gsl_multimin_function_fdf *f,
initpt_function initpt,
const gsl_multimin_fdfminimizer_type *T)
{
int status;
size_t iter = 0;
double step_size;
gsl_vector *x = gsl_vector_alloc (f->n);
gsl_multimin_fdfminimizer *s;
fcount = 0; gcount = 0;
(*initpt) (x);
step_size = 0.1 * gsl_blas_dnrm2 (x);
s = gsl_multimin_fdfminimizer_alloc(T, f->n);
gsl_multimin_fdfminimizer_set (s, f, x, step_size, 0.1);
#ifdef DEBUG
printf("x "); gsl_vector_fprintf (stdout, s->x, "%g");
printf("g "); gsl_vector_fprintf (stdout, s->gradient, "%g");
#endif
do
{
iter++;
status = gsl_multimin_fdfminimizer_iterate(s);
#ifdef DEBUG
printf("%i: \n",iter);
printf("x "); gsl_vector_fprintf (stdout, s->x, "%g");
printf("g "); gsl_vector_fprintf (stdout, s->gradient, "%g");
printf("f(x) %g\n",s->f);
printf("dx %g\n",gsl_blas_dnrm2(s->dx));
printf("\n");
#endif
status = gsl_multimin_test_gradient(s->gradient,1e-3);
}
while (iter < 5000 && status == GSL_CONTINUE);
status |= (fabs(s->f) > 1e-5);
gsl_test(status, "%s, on %s: %i iters (fn+g=%d+%d), f(x)=%g",
gsl_multimin_fdfminimizer_name(s),desc, iter, fcount, gcount, s->f);
gsl_multimin_fdfminimizer_free(s);
gsl_vector_free(x);
return status;
}
static int
dogleg_preloop(const void * vtrust_state, void * vstate)
{
int status;
const gsl_multifit_nlinear_trust_state *trust_state =
(const gsl_multifit_nlinear_trust_state *) vtrust_state;
dogleg_state_t *state = (dogleg_state_t *) vstate;
const gsl_multifit_nlinear_parameters *params = trust_state->params;
double u;
double alpha; /* ||g||^2 / ||Jg||^2 */
/* initialize linear least squares solver */
status = (params->solver->init)(trust_state, trust_state->solver_state);
if (status)
return status;
/* prepare the linear solver to compute Gauss-Newton step */
status = (params->solver->presolve)(0.0, trust_state, trust_state->solver_state);
if (status)
return status;
/* solve: J dx_gn = -f for Gauss-Newton step */
status = (params->solver->solve)(trust_state->f,
state->dx_gn,
trust_state,
trust_state->solver_state);
if (status)
return status;
/* now calculate the steepest descent step */
/* compute workp = D^{-1} g and its norm */
gsl_vector_memcpy(state->workp, trust_state->g);
gsl_vector_div(state->workp, trust_state->diag);
state->norm_Dinvg = gsl_blas_dnrm2(state->workp);
/* compute workp = D^{-2} g */
gsl_vector_div(state->workp, trust_state->diag);
/* compute: workn = J D^{-2} g */
gsl_blas_dgemv(CblasNoTrans, 1.0, trust_state->J, state->workp, 0.0, state->workn);
state->norm_JDinv2g = gsl_blas_dnrm2(state->workn);
u = state->norm_Dinvg / state->norm_JDinv2g;
alpha = u * u;
/* dx_sd = -alpha D^{-2} g */
gsl_vector_memcpy(state->dx_sd, state->workp);
gsl_vector_scale(state->dx_sd, -alpha);
state->norm_Dgn = scaled_enorm(trust_state->diag, state->dx_gn);
state->norm_Dsd = scaled_enorm(trust_state->diag, state->dx_sd);
return GSL_SUCCESS;
}
bool SphereConNet2D::is_floater(int i) {
bool fltr = false; int n = con.at(i).size();
if(n==0||n==1) fltr = true;//always a floater when 0 or 1 contacts
else if(n==2){//check if the two are antiparallel
double normprod = gsl_blas_dnrm2(rs[i][0])*gsl_blas_dnrm2(rs[i][1]);
double * dotprod; gsl_blas_ddot(rs[i][0],rs[i][1],dotprod);
double prodsum = normprod+*dotprod;//if small->antiparallel
//if not small->not antiparallel->is floater
if(prodsum>std::pow(10,-14)) fltr = true;
}
return fltr;
}
static void
test_random(const size_t N, const gsl_rng *r, const int compress)
{
const gsl_splinalg_itersolve_type *T = gsl_splinalg_itersolve_gmres;
const double tol = 1.0e-8;
int status;
gsl_spmatrix *A = create_random_sparse(N, N, 0.3, r);
gsl_spmatrix *B;
gsl_vector *b = gsl_vector_alloc(N);
gsl_vector *x = gsl_vector_calloc(N);
/* these random matrices require all N iterations to converge */
gsl_splinalg_itersolve *w = gsl_splinalg_itersolve_alloc(T, N, N);
const char *desc = gsl_splinalg_itersolve_name(w);
create_random_vector(b, r);
if (compress)
B = gsl_spmatrix_compcol(A);
else
B = A;
status = gsl_splinalg_itersolve_iterate(B, b, tol, x, w);
gsl_test(status, "%s random status s=%d N=%zu", desc, status, N);
/* check that the residual satisfies ||r|| <= tol*||b|| */
{
gsl_vector *res = gsl_vector_alloc(N);
double normr, normb;
gsl_vector_memcpy(res, b);
gsl_spblas_dgemv(CblasNoTrans, -1.0, A, x, 1.0, res);
normr = gsl_blas_dnrm2(res);
normb = gsl_blas_dnrm2(b);
status = (normr <= tol*normb) != 1;
gsl_test(status, "%s random residual N=%zu normr=%.12e normb=%.12e",
desc, N, normr, normb);
gsl_vector_free(res);
}
gsl_spmatrix_free(A);
gsl_vector_free(b);
gsl_vector_free(x);
gsl_splinalg_itersolve_free(w);
if (compress)
gsl_spmatrix_free(B);
} /* test_random() */
int NonLinearLSQ::curvefit() {
size_t n(nSize());
size_t p(nParms());
// Initialize the solver function information
_nlsqPointer d = { this };
gsl_multifit_function_fdf mf;
mf.f = &f;
mf.df = &df;
mf.fdf = &fdf;
mf.n = n;
mf.p = p;
mf.params = &d;
const gsl_multifit_fdfsolver_type *T = gsl_multifit_fdfsolver_lmsder;
gsl_multifit_fdfsolver *s = gsl_multifit_fdfsolver_alloc(T, n, p);
_fitParms = guess();
gsl_vector *x = NlsqTogsl(_fitParms);
gsl_matrix *covar = gsl_matrix_alloc(p, p);
gsl_multifit_fdfsolver_set(s, &mf, x);
_nIters = 0;
checkIteration(_nIters, gslToNlsq(s->x), NLVector(p,999.0),
gsl_blas_dnrm2(s->f), GSL_CONTINUE);
do {
_nIters++;
_status = gsl_multifit_fdfsolver_iterate(s);
_fitParms = gslToNlsq(s->x);
gsl_multifit_covar(s->J, 0.0, covar);
_uncert = getUncertainty(covar);
_status = checkIteration(_nIters, _fitParms, _uncert, gsl_blas_dnrm2(s->f),
_status);
if ( _status ) { break; }
if(!doContinue()) { break; }
_status = gsl_multifit_test_delta(s->dx, s->x, absErr(), relErr());
} while ((_status == GSL_CONTINUE) && (_nIters < _maxIters));
// Clean up
gsl_multifit_fdfsolver_free(s);
gsl_matrix_free(covar);
return (_status);
}
int
lls_lcurve(gsl_vector *reg_param, gsl_vector *rho, gsl_vector *eta,
lls_workspace *w)
{
const size_t N = rho->size; /* number of points on L-curve */
if (N != reg_param->size)
{
GSL_ERROR("size of reg_param and rho do not match", GSL_EBADLEN);
}
else if (N != eta->size)
{
GSL_ERROR("size of eta and rho do not match", GSL_EBADLEN);
}
else
{
int s;
double smax, smin;
size_t i;
/* compute eigenvalues of A^T W A */
gsl_matrix_transpose_memcpy(w->work_A, w->ATA);
s = gsl_eigen_symm(w->work_A, w->eval, w->eigen_p);
if (s)
return s;
/* find largest and smallest eigenvalues */
gsl_vector_minmax(w->eval, &smin, &smax);
/* singular values are square roots of eigenvalues */
smax = sqrt(smax);
if (smin > GSL_DBL_EPSILON)
smin = sqrt(fabs(smin));
gsl_multifit_linear_lreg(smin, smax, reg_param);
for (i = 0; i < N; ++i)
{
double r2;
double lambda = gsl_vector_get(reg_param, i);
lls_solve(lambda, w->c, w);
/* store ||c|| */
gsl_vector_set(eta, i, gsl_blas_dnrm2(w->c));
/* compute: A^T A c - 2 A^T y */
gsl_vector_memcpy(w->work_b, w->ATb);
gsl_blas_dsymv(CblasUpper, 1.0, w->ATA, w->c, -2.0, w->work_b);
/* compute: c^T A^T A c - 2 c^T A^T y */
gsl_blas_ddot(w->c, w->work_b, &r2);
r2 += w->bTb;
gsl_vector_set(rho, i, sqrt(r2));
}
return GSL_SUCCESS;
}
} /* lls_lcurve() */
static double
cod_householder_transform(double *alpha, gsl_vector * v)
{
double beta, tau;
double xnorm = gsl_blas_dnrm2(v);
if (xnorm == 0)
{
return 0.0; /* tau = 0 */
}
beta = - (*alpha >= 0.0 ? +1.0 : -1.0) * gsl_hypot(*alpha, xnorm);
tau = (beta - *alpha) / beta;
{
double s = (*alpha - beta);
if (fabs(s) > GSL_DBL_MIN)
{
gsl_blas_dscal (1.0 / s, v);
}
else
{
gsl_blas_dscal (GSL_DBL_EPSILON / s, v);
gsl_blas_dscal (1.0 / GSL_DBL_EPSILON, v);
}
*alpha = beta;
}
return tau;
}
double MLFitterGSL::iteration(){
//do one itteration
//lock the model so user can not add or remove components during itteration
modelptr->setlocked(true);
//if the model has changed (a new or removed component eg.) create a new solver
if (modelptr->has_changed()){
createmodelinfo(); //this automaticaly calls initfitter() via created_modelinfo()
}
//do an itteration step
try{
const int status=gsl_multifit_fdfsolver_iterate(solver);
#ifdef FITTER_DEBUG
std::cout <<"solver status: "<<gsl_strerror(status)<<"\n";
std::cout <<"chi square/dof: "<<gsl_blas_dnrm2(solver->f)<<"\n";
#endif
this->setstatus(gsl_strerror(status)); //update status info of fitter
convertxtoparam(solver->x);
}
catch(...){
Saysomething mysay(0,"Error","Problem with call to gsl_multifit_fdfsolver_iterate, exit MLFitterGSL",true);
delete(this);
}
//unlock the model so user can add or remove components
modelptr->setlocked(false);
//put the goodness in the goodnessqueue to check for convergence
const double newgoodness= goodness_of_fit();
addgoodness(newgoodness);
return newgoodness;
}
static double
nmsimplex_size (nmsimplex_state_t * state)
{
/* calculates simplex size as average sum of length of vectors
from simplex center to corner points:
( sum ( || y - y_middlepoint || ) ) / n
*/
gsl_vector *s = state->ws1;
gsl_vector *mp = state->ws2;
gsl_matrix *x1 = state->x1;
size_t i;
double ss = 0.0;
/* Calculate middle point */
nmsimplex_calc_center (state, mp);
for (i = 0; i < x1->size1; i++)
{
gsl_matrix_get_row (s, x1, i);
gsl_blas_daxpy (-1.0, mp, s);
ss += gsl_blas_dnrm2 (s);
}
return ss / (double) (x1->size1);
}
void update_unit(unit *u, camera *cam, PLAYERS *players) {
if(is_unit_dead(u)) {
if(u->state != NULL)
unit_dead(u);
return;
}
// set the velocity to 0
gsl_vector_scale(u->velocity, 0);
if(!((state *) u->state->value)->update(players, cam, u)) {
pop_unit_state(u);
}
double norm = gsl_blas_dnrm2(u->velocity);
if(norm > 0) {
gsl_vector_scale(u->velocity, 1 / norm);
gsl_vector_memcpy(u->heading, u->velocity);
gsl_vector_scale(u->velocity, u->attributes.speed);
gsl_vector_add(u->position, u->velocity);
gsl_vector_set(u->side, 0, -y(u->heading));
gsl_vector_set(u->side, 1, x(u->heading));
}
}
int lsQRPT(gsl_matrix * A, gsl_vector * b, gsl_vector * x, double * sigma)
{
int i;
gsl_vector *tau, *res;
gsl_permutation *p;
gsl_vector_view norm;
if (A->size1 < A->size2) return -1;
if (A->size1 != b->size) return -1;
if (A->size2 != x->size) return -1;
tau = gsl_vector_alloc(x->size);
res = gsl_vector_alloc(b->size);
p = gsl_permutation_alloc(x->size);
norm = gsl_vector_subvector(res, 0, x->size);
gsl_linalg_QRPT_decomp(A, tau, p, &i, &norm.vector);
gsl_linalg_QR_lssolve(A, tau, b, x, res);
gsl_permute_vector_inverse(p, x);
*sigma = gsl_blas_dnrm2(res);
gsl_vector_free(tau);
gsl_vector_free(res);
gsl_permutation_free(p);
return 0;
}
int
main (void)
{
size_t i,j;
gsl_matrix *m = gsl_matrix_alloc (10, 10);
for (i = 0; i < 10; i++)
for (j = 0; j < 10; j++)
gsl_matrix_set (m, i, j, sin (i) + cos (j));
for (j = 0; j < 10; j++)
{
gsl_vector_view column = gsl_matrix_column (m, j);
double d;
d = gsl_blas_dnrm2 (&column.vector);
printf ("matrix column %d, norm = %g\n", j, d);
}
gsl_matrix_free (m);
return 0;
}
/** Rotates point b around point a using the rotation matrix R. */
void rotate(bool transpose, const gsl_matrix *R, const gsl_vector *a, gsl_vector *b)
{
declare_stack_allocated_vector(v, 3);
gsl_vector_memcpy(v, b);
gsl_vector_sub(v, a);
/* Rotate end vector. */
declare_stack_allocated_vector(w, 3);
gsl_blas_dgemv(transpose == false ? CblasNoTrans : CblasTrans, 1.0, R, v, 0.0, w);
/* Update position. */
gsl_vector_memcpy(b, a);
gsl_vector_add(b, w);
assert(gsl_fcmp(gsl_blas_dnrm2(v), gsl_blas_dnrm2(w), 1e-15) == 0);
}
static int
conjugate_fr_set (void *vstate, gsl_multimin_function_fdf * fdf,
const gsl_vector * x, double *f, gsl_vector * gradient,
double step_size, double tol)
{
conjugate_fr_state_t *state = (conjugate_fr_state_t *) vstate;
state->iter = 0;
state->step = step_size;
state->max_step = step_size;
state->tol = tol;
GSL_MULTIMIN_FN_EVAL_F_DF (fdf, x, f, gradient);
/* Use the gradient as the initial direction */
gsl_vector_memcpy (state->p, gradient);
gsl_vector_memcpy (state->g0, gradient);
{
double gnorm = gsl_blas_dnrm2 (gradient);
state->pnorm = gnorm;
state->g0norm = gnorm;
}
return GSL_SUCCESS;
}
static void normalizeJacobian( gsl_matrix *jac, gsl_vector *scaling ) {
for (int i = 0; i < jac->size2; i++) {
gsl_vector jac_col = gsl_matrix_column(jac, i).vector;
gsl_vector_set(scaling, i, 1 / gsl_blas_dnrm2(&jac_col));
gsl_vector_scale(&jac_col, gsl_vector_get(scaling, i));
}
}
static inline double l2norm(const mtrx* in, int n){
double out = 0.0;
for(int i = 0; i< in->size1; i++){
gsl_vector_view v1 = gsl_vector_view_array(in->data+i*in->tda,n);
out += gsl_blas_dnrm2(&v1.vector);
}
return out/(in->size1);
}
/*
% project v in direction of u
function p=project_vec(v,u)
p = (dot(v,u)/norm(u)^2)*u;
*/
void project_vector(gsl_vector *v, gsl_vector *u, gsl_vector *p){
double dot_product_val, vec_norm, scalar_val;
gsl_blas_ddot(v, u, &dot_product_val);
vec_norm = gsl_blas_dnrm2(u);
scalar_val = dot_product_val/(vec_norm*vec_norm);
gsl_vector_memcpy(p, u);
gsl_vector_scale (p, scalar_val);
}
static VALUE rb_gsl_blas_dnrm(int argc, VALUE *argv, VALUE obj)
{
gsl_vector *x = NULL;
double a;
get_vector1(argc, argv, obj, &x);
a = gsl_blas_dnrm2(x);
return rb_float_new(a*a);
}
void GammaDistributionFitter::printState_(size_t iter, gsl_multifit_fdfsolver * s)
{
printf("iter: %3u x = % 15.8f % 15.8f "
"|f(x)| = %g\n",
(unsigned int)iter,
gsl_vector_get(s->x, 0),
gsl_vector_get(s->x, 1),
gsl_blas_dnrm2(s->f));
}
void
test_lmder (gsl_multifit_function_fdf * f, double x0[],
double * X, double F[], double * cov)
{
const gsl_multifit_fdfsolver_type *T;
gsl_multifit_fdfsolver *s;
const size_t n = f->n;
const size_t p = f->p;
int status;
size_t iter = 0, i;
gsl_vector_view x = gsl_vector_view_array (x0, p);
T = gsl_multifit_fdfsolver_lmsder;
s = gsl_multifit_fdfsolver_alloc (T, n, p);
gsl_multifit_fdfsolver_set (s, f, &x.vector);
do
{
status = gsl_multifit_fdfsolver_iterate (s);
for (i = 0 ; i < p; i++)
{
gsl_test_rel (gsl_vector_get (s->x, i), X[p*iter+i], 1e-5,
"lmsder, iter=%u, x%u", iter, i);
}
gsl_test_rel (gsl_blas_dnrm2 (s->f), F[iter], 1e-5,
"lmsder, iter=%u, f", iter);
iter++;
}
while (iter < 20);
{
size_t i, j;
gsl_matrix * covar = gsl_matrix_alloc (4, 4);
gsl_multifit_covar (s->J, 0.0, covar);
for (i = 0; i < 4; i++)
{
for (j = 0; j < 4; j++)
{
gsl_test_rel (gsl_matrix_get(covar,i,j), cov[i*p + j], 1e-7,
"gsl_multifit_covar cov(%d,%d)", i, j) ;
}
}
gsl_matrix_free (covar);
}
gsl_multifit_fdfsolver_free (s);
}
static void
test_scale_x0(gsl_vector *x0, const double scale)
{
double nx = gsl_blas_dnrm2(x0);
if (nx == 0.0)
gsl_vector_set_all(x0, scale);
else
gsl_vector_scale(x0, scale);
} /* test_scale_x0() */
static double
cgst_calc_tau(const gsl_vector * p, const gsl_vector * d,
const double delta)
{
double norm_p, norm_d, u;
double t1, t2, tau;
norm_p = gsl_blas_dnrm2(p);
norm_d = gsl_blas_dnrm2(d);
/* compute (p, d) */
gsl_blas_ddot(p, d, &u);
t1 = u / (norm_d * norm_d);
t2 = t1*u + (delta + norm_p) * (delta - norm_p);
tau = -t1 + sqrt(t2) / norm_d;
return tau;
}
int
lls_fold(gsl_matrix *A, gsl_vector *b,
gsl_vector *wts, lls_workspace *w)
{
const size_t n = A->size1;
if (A->size2 != w->p)
{
GSL_ERROR("A has wrong size2", GSL_EBADLEN);
}
else if (n != b->size)
{
GSL_ERROR("b has wrong size", GSL_EBADLEN);
}
else if (n != wts->size)
{
GSL_ERROR("wts has wrong size", GSL_EBADLEN);
}
else
{
int s = 0;
size_t i;
double bnorm;
for (i = 0; i < n; ++i)
{
gsl_vector_view rv = gsl_matrix_row(A, i);
double *bi = gsl_vector_ptr(b, i);
double wi = gsl_vector_get(wts, i);
double swi = sqrt(wi);
/* A <- sqrt(W) A */
gsl_vector_scale(&rv.vector, swi);
/* b <- sqrt(W) b */
*bi *= swi;
}
/* ATA += A^T W A, using only the upper half of the matrix */
s = gsl_blas_dsyrk(CblasUpper, CblasTrans, 1.0, A, 1.0, w->ATA);
if (s)
return s;
/* ATb += A^T W b */
s = gsl_blas_dgemv(CblasTrans, 1.0, A, b, 1.0, w->ATb);
if (s)
return s;
/* bTb += b^T W b */
bnorm = gsl_blas_dnrm2(b);
w->bTb += bnorm * bnorm;
return s;
}
} /* lls_fold() */
static int vector_bfgs3_set(void *vstate, gsl_multimin_function_fdf * fdf, const gsl_vector * x, double *f, gsl_vector * gradient, double step_size, double tol)
{
vector_bfgs3_state_t *state = (vector_bfgs3_state_t *) vstate;
state->iter = 0;
state->step = step_size;
state->delta_f = 0;
GSL_MULTIMIN_FN_EVAL_F_DF(fdf, x, f, gradient);
/*
* Use the gradient as the initial direction
*/
gsl_vector_memcpy(state->x0, x);
gsl_vector_memcpy(state->g0, gradient);
state->g0norm = gsl_blas_dnrm2(state->g0);
gsl_vector_memcpy(state->p, gradient);
gsl_blas_dscal(-1 / state->g0norm, state->p);
state->pnorm = gsl_blas_dnrm2(state->p); /* should be 1 */
state->fp0 = -state->g0norm;
/*
* Prepare the wrapper
*/
prepare_wrapper(&state->wrap, fdf, state->x0, *f, state->g0, state->p, state->x_alpha, state->g_alpha);
/*
* Prepare 1d minimisation parameters
*/
state->rho = 0.01;
state->sigma = tol;
state->tau1 = 9;
state->tau2 = 0.05;
state->tau3 = 0.5;
state->order = 3; /* use cubic interpolation where possible */
return GSL_SUCCESS;
}
double shapeAlign::cosineSim(const gsl_matrix* X, const gsl_matrix *Y)
{
double cosSim = 0;
double denomX = 0, denomY = 0;
for (size_t i = 0; i < X->size1; i++){
double dot = 0;
// Get vector views of rows
gsl_vector_const_view Xrow = gsl_matrix_const_row(X,i);
gsl_vector_const_view Yrow = gsl_matrix_const_row(Y,i);
// Compute dot product
gsl_blas_ddot(&Xrow.vector,&Yrow.vector,&dot);
cosSim +=dot;
denomX += pow(gsl_blas_dnrm2(&Xrow.vector),2.0);
denomY += pow(gsl_blas_dnrm2(&Yrow.vector),2.0);
}
cosSim = cosSim / (sqrt(denomX * denomY));
return cosSim;
}
void
test_eigen_gensymm_results (const gsl_matrix * A,
const gsl_matrix * B,
const gsl_vector * eval,
const gsl_matrix * evec,
size_t count,
const char * desc,
const char * desc2)
{
const size_t N = A->size1;
size_t i, j;
gsl_vector * x = gsl_vector_alloc(N);
gsl_vector * y = gsl_vector_alloc(N);
gsl_vector * z = gsl_vector_alloc(N);
/* check A v = lambda B v */
for (i = 0; i < N; i++)
{
double ei = gsl_vector_get (eval, i);
gsl_vector_const_view vi = gsl_matrix_const_column(evec, i);
double norm = gsl_blas_dnrm2(&vi.vector);
/* check that eigenvector is normalized */
gsl_test_rel(norm, 1.0, N * GSL_DBL_EPSILON,
"gensymm(N=%u,cnt=%u), %s, normalized(%d), %s", N, count,
desc, i, desc2);
gsl_vector_memcpy(z, &vi.vector);
/* compute y = A z */
gsl_blas_dgemv (CblasNoTrans, 1.0, A, z, 0.0, y);
/* compute x = B z */
gsl_blas_dgemv (CblasNoTrans, 1.0, B, z, 0.0, x);
/* compute x = lambda B z */
gsl_blas_dscal(ei, x);
/* now test if y = x */
for (j = 0; j < N; j++)
{
double xj = gsl_vector_get (x, j);
double yj = gsl_vector_get (y, j);
gsl_test_rel(yj, xj, 1e9 * GSL_DBL_EPSILON,
"gensymm(N=%u,cnt=%u), %s, eigenvalue(%d,%d), real, %s", N, count, desc, i, j, desc2);
}
}
gsl_vector_free(x);
gsl_vector_free(y);
gsl_vector_free(z);
}
void
print_state (size_t iter, gsl_multifit_fdfsolver * s)
{
printf ("iter: %3u x = % 15.8f % 15.8f % 15.8f "
"|f(x)| = %g\n",
iter,
gsl_vector_get (s->x, 0),
gsl_vector_get (s->x, 1),
gsl_vector_get (s->x, 2),
gsl_blas_dnrm2 (s->f));
}
/* ----------- evaluate the objective function --------------*/
double objective(gsl_vector *x, double lambda, gsl_vector *z, int N) {
double obj = 0;
double temp =0.0;
temp = gsl_blas_dnrm2(z);
temp = temp*temp/(double)(2.0*N);
double foo;
foo = gsl_blas_dasum(x);
// double recv;
// MPI_Allreduce(&foo, &recv, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
obj = lambda*foo + temp;
return obj;
}
static double
trust_calc_rho(const gsl_multilarge_nlinear_trust_state * trust_state,
const gsl_vector * f_trial, const gsl_vector * dx,
trust_state_t * state)
{
int status;
const gsl_multilarge_nlinear_parameters *params = &(state->params);
const gsl_multilarge_nlinear_trs *trs = params->trs;
const gsl_vector * f = trust_state->f;
const double normf = gsl_blas_dnrm2(f);
const double normf_trial = gsl_blas_dnrm2(f_trial);
double rho;
double actual_reduction;
double pred_reduction;
double u;
/* if ||f(x+dx)|| > ||f(x)|| reject step immediately */
if (normf_trial >= normf)
return -1.0;
/* compute numerator of rho (actual reduction) */
u = normf_trial / normf;
actual_reduction = 1.0 - u*u;
/*
* compute denominator of rho (predicted reduction); this is calculated
* inside each trust region subproblem, since it depends on the local
* model used, which can vary according to each TRS
*/
status = (trs->preduction)(trust_state, dx, &pred_reduction, state->trs_state);
if (status)
return -1.0;
if (pred_reduction > 0.0)
rho = actual_reduction / pred_reduction;
else
rho = -1.0;
return rho;
}