double ls_error(double *xval, double *yval, int cnt, ls_err_t etype)
{
double slope;
double intercept;
ls_stat_t stat;
int i;
double num, denom;
ls_stats(xval, yval, cnt, &stat);
slope = (cnt * stat.sum_xy - stat.sum_x * stat.sum_y)/
(cnt * stat.sum_xx - stat.sum_x*stat.sum_x);
intercept = (stat.sum_xx * stat.sum_y - stat.sum_xy * stat.sum_x)/
(cnt * stat.sum_xx - stat.sum_x*stat.sum_x);
num = denom = 0;
for (i = 0; i < cnt; i++) {
double e = rel_err(xval[i], yval[i], slope, intercept);
switch (etype) {
case LS_AVG:
num += e;
denom++;
break;
case LS_MAX:
if (num < e)
num = e;
denom = 1;
break;
default:
fprintf(stderr, "Invalid error type: %d\n", etype);
exit(1);
break;
}
}
return num/denom;
}
int calculate(double *r, node *A) {
int i, j;
double *r_pre;
double damp_const;
damp_const = (1.0 - DAMPING_FACTOR) / n;
int my_rank, comm_sz, local_n;
double start = 0, end = 0; // for time
MPI_Init(NULL, NULL);
/* Get my process rank */
MPI_Comm_rank(MPI_COMM_WORLD, &my_rank);
/* Find out how many processes are being used */
MPI_Comm_size(MPI_COMM_WORLD, &comm_sz);
r_pre = malloc(n * sizeof(double));
local_n = n / comm_sz;
double still_err = 1;
double *local_r = malloc(local_n * sizeof(double));
if (my_rank == 0) {
GET_TIME(start);
}
while (still_err > EPSILON) {
backup_vec(r, r_pre, n);
for ( i = local_n * my_rank; i < local_n * (my_rank + 1); i++) {
local_r[i - local_n * my_rank] = 0.0;
for ( j = 0; j < A[i].size_Di; ++j) {
local_r[i - local_n * my_rank] += r_pre[A[i].Di[j]] / A[A[i].Di[j]].li;
}
local_r[i - local_n * my_rank] *= DAMPING_FACTOR;
local_r[i - local_n * my_rank] += damp_const;
}
MPI_Gather(local_r, local_n, MPI_DOUBLE, r, local_n, MPI_DOUBLE, 0, MPI_COMM_WORLD);
if (my_rank == 0) {
still_err = rel_err(r, r_pre, n);
}
MPI_Bcast(&still_err, 1, MPI_DOUBLE, 0, MPI_COMM_WORLD);
MPI_Bcast(r, n, MPI_DOUBLE, 0, MPI_COMM_WORLD);
}
if (my_rank == 0) {
GET_TIME(end);
printf("%f\n", end-start);
Lab4_saveoutput(r, n, end-start);
}
free(r_pre);
MPI_Finalize();
return 0;
}
static int hu_moments_test( void )
{
const double success_error_level = 1e-7;
CvSize size = { 512, 512 };
int i;
IplImage* img = atsCreateImage( size.width, size.height, 8, 1, 0 );
CvMoments moments;
CvHuMoments a, b;
AtsRandState rng_state;
int seed = atsGetSeed();
double nu20, nu02, nu11, nu30, nu21, nu12, nu03;
double err = 0;
char buffer[100];
atsRandInit( &rng_state, 0, 255, seed );
atsbRand8u( &rng_state, (uchar*)(img->imageData), size.width * size.height );
cvMoments( img, &moments, 0 );
atsReleaseImage( img );
nu20 = cvGetNormalizedCentralMoment( &moments, 2, 0 );
nu11 = cvGetNormalizedCentralMoment( &moments, 1, 1 );
nu02 = cvGetNormalizedCentralMoment( &moments, 0, 2 );
nu30 = cvGetNormalizedCentralMoment( &moments, 3, 0 );
nu21 = cvGetNormalizedCentralMoment( &moments, 2, 1 );
nu12 = cvGetNormalizedCentralMoment( &moments, 1, 2 );
nu03 = cvGetNormalizedCentralMoment( &moments, 0, 3 );
cvGetHuMoments( &moments, &a );
b.hu1 = nu20 + nu02;
b.hu2 = sqr(nu20 - nu02) + 4*sqr(nu11);
b.hu3 = sqr(nu30 - 3*nu12) + sqr(3*nu21 - nu03);
b.hu4 = sqr(nu30 + nu12) + sqr(nu21 + nu03);
b.hu5 = (nu30 - 3*nu12)*(nu30 + nu12)*(sqr(nu30 + nu12) - 3*sqr(nu21 + nu03)) +
(3*nu21 - nu03)*(nu21 + nu03)*(3*sqr(nu30 + nu12) - sqr(nu21 + nu03));
b.hu6 = (nu20 - nu02)*(sqr(nu30 + nu12) - sqr(nu21 + nu03)) +
4*nu11*(nu30 + nu12)*(nu21 + nu03);
b.hu7 = (3*nu21 - nu03)*(nu30 + nu12)*(sqr(nu30 + nu12) - 3*sqr(nu21 + nu03)) +
(3*nu12 - nu30)*(nu21 + nu03)*(3*sqr(nu30 + nu12) - sqr(nu21 + nu03));
for( i = 0; i < 7; i++ )
{
double t = rel_err( ((double*)&b)[i], ((double*)&a)[i] );
if( t > err ) err = t;
}
sprintf( buffer, "Accuracy: %.4e", err );
return trsResult( err > success_error_level ? TRS_FAIL : TRS_OK, buffer );
}
/* ///////////////////// moments_test ///////////////////////// */
static int moments_test( void* arg )
{
static double weight[] = {
1e6, 1e6, 1e6, /* m00, m10, m01 */
1e6, 1e6, 1e6, 1, 1, 1, 1, /* m20 - m03 */
1, 1e-4, 1, 1e-5, 1e-5, 1e-5, 1e-5, /* mu20 - mu03 */
1, 1, 1, 1, 1, 1, 1 }; /* nu20 - nu03 */
const double success_error_level = 1e-4;
int param = (int)arg;
int binary = param >= 6;
int depth = (param % 6)/2;
int channels = (param & 1);
int seed = atsGetSeed();
/* position where the maximum error occured */
int merr_w = 0, merr_h = 0, merr_iter = 0, merr_c = 0;
/* test parameters */
int w = 0, h = 0, i = 0, c = 0;
double max_err = 0.;
//int code = TRS_OK;
IplROI roi;
IplImage *img;
AtsRandState rng_state;
atsRandInit( &rng_state, 0, 1, seed );
read_moments_params();
if( !(ATS_RANGE( binary, fn_l, fn_h+1 ) &&
ATS_RANGE( depth, dt_l, dt_h+1 ) &&
ATS_RANGE( channels, ch_l, ch_h+1 ))) return TRS_UNDEF;
depth = depth == 2 ? IPL_DEPTH_32F : depth == 1 ? IPL_DEPTH_8S : IPL_DEPTH_8U;
channels = channels*2 + 1;
img = atsCreateImage( max_img_size, max_img_size, depth, channels, 0 );
roi.coi = 0;
roi.xOffset = roi.yOffset = 0;
img->roi = &roi;
for( h = min_img_size; h <= max_img_size; )
{
for( w = min_img_size; w <= max_img_size; )
{
int denom = (w - min_img_size + 1)*(h - min_img_size + 1)*channels;
int iters = (base_iters*2 + denom)/(2*denom);
roi.width = w;
roi.height = h;
if( iters < 1 ) iters = 1;
for( i = 0; i < iters; i++ )
{
switch( depth )
{
case IPL_DEPTH_8U:
atsRandSetBounds( &rng_state, 0, img8u_range );
break;
case IPL_DEPTH_8S:
atsRandSetBounds( &rng_state, -img8s_range, img8s_range );
break;
case IPL_DEPTH_32F:
atsRandSetBounds( &rng_state, -img32f_range, img32f_range );
if( binary ) atsRandSetFloatBits( &rng_state, img32f_bits );
break;
}
roi.coi = 0;
atsFillRandomImageEx( img, &rng_state );
/*iplSet( img, depth == IPL_DEPTH_8S ? 125 : 251 );*/
for( c = 1; c <= channels; c++ )
{
double err0 = 0;
AtsMomentState astate0, astate1;
CvMoments istate;
double* a0 = (double*)&astate0;
double* a1 = (double*)&astate1;
int j;
roi.coi = c;
/* etalon function */
atsCalcMoments( img, &astate0, binary );
/* cv function */
cvMoments( img, &istate, binary );
atsGetMoments( &istate, &astate1 );
/*iplMoments( img, lstate ); */
/*convert_ipl_to_ats( lstate, &astate1 ); */
for( j = 0; j < sizeof(astate0)/sizeof(double); j++ )
{
double err = rel_err( a0[j], a1[j] )*weight[j];
err0 = MAX( err0, err );
}
if( err0 > max_err )
{
merr_w = w;
merr_h = h;
merr_iter = i;
merr_c = c;
max_err = err0;
if( max_err > success_error_level )
goto test_exit;
}
}
}
ATS_INCREASE( w, img_size_delta_type, img_size_delta );
} /* end of the loop by w */
ATS_INCREASE( h, img_size_delta_type, img_size_delta );
} /* end of the loop by h */
test_exit:
img->roi = 0;
iplDeallocate( img, IPL_IMAGE_ALL );
//if( code == TRS_OK )
{
trsWrite( ATS_LST, "Max err is %g at w = %d, h = %d, "
"iter = %d, c = %d, seed = %08x",
max_err, merr_w, merr_h, merr_iter, merr_c, seed );
return max_err <= success_error_level ?
trsResult( TRS_OK, "No errors" ) :
trsResult( TRS_FAIL, "Bad accuracy" );
}
/*else
{
trsWrite( ATS_LST, "Fatal error at w = %d, h = %d, "
"iter = %d, c = %d, seed = %08x",
w, h, i, c, seed );
return trsResult( TRS_FAIL, "Function returns error code" );
}*/
}
int main(int argc, char **argv)
{
try {
const unsigned int d = 2;
const unsigned int pmin = 2;
const unsigned int pmax = 10;
const unsigned int np = pmax-pmin+1;
bool use_pce_quad_points = false;
bool normalize = true;
bool sparse_grid = true;
bool project_integrals = false;
#ifndef HAVE_STOKHOS_DAKOTA
sparse_grid = false;
#endif
Teuchos::Array<double> mean(np), mean_st(np), std_dev(np), std_dev_st(np);
Teuchos::Array<double> pt(np), pt_st(np);
Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<int,double> > > bases(d);
Teuchos::Array<double> eval_pt(d, 0.5);
double pt_true;
// Loop over orders
unsigned int n = 0;
for (unsigned int p=pmin; p<=pmax; p++) {
std::cout << "p = " << p << std::endl;
// Create product basis
for (unsigned int i=0; i<d; i++)
bases[i] = Teuchos::rcp(new basis_type(p));
Teuchos::RCP<const Stokhos::CompletePolynomialBasis<int,double> > basis =
Teuchos::rcp(new Stokhos::CompletePolynomialBasis<int,double>(bases));
// Create approximation
Stokhos::OrthogPolyApprox<int,double> x(basis), u(basis), v(basis),
w(basis), w2(basis);
for (unsigned int i=0; i<d; i++) {
x.term(i, 1) = 1.0;
}
double x_pt = x.evaluate(eval_pt);
pt_true = std::exp(std::sin(x_pt));
// Quadrature
Teuchos::RCP<const Stokhos::Quadrature<int,double> > quad;
#ifdef HAVE_STOKHOS_DAKOTA
if (sparse_grid)
quad =
Teuchos::rcp(new Stokhos::SparseGridQuadrature<int,double>(basis, p));
#endif
if (!sparse_grid)
quad =
Teuchos::rcp(new Stokhos::TensorProductQuadrature<int,double>(basis));
// Triple product tensor
Teuchos::RCP<Stokhos::Sparse3Tensor<int,double> > Cijk =
basis->computeTripleProductTensor(basis->size());
// Quadrature expansion
Stokhos::QuadOrthogPolyExpansion<int,double> quad_exp(basis, Cijk, quad);
// Compute PCE via quadrature expansion
quad_exp.sin(u,x);
//quad_exp.times(u,u,10.0);
quad_exp.exp(w,u);
// Compute Stieltjes basis
Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<int,double> > > st_bases(1);
Teuchos::RCP<const Stokhos::LanczosProjPCEBasis<int,double> > st_1d_basis
= Teuchos::rcp(new Stokhos::LanczosProjPCEBasis<int,double>(
p, Teuchos::rcp(&u,false), Cijk, normalize));
st_bases[0] = st_1d_basis;
Teuchos::RCP<const Stokhos::CompletePolynomialBasis<int,double> >
st_basis =
Teuchos::rcp(new Stokhos::CompletePolynomialBasis<int,double>(st_bases));
//std::cout << *st_basis << std::endl;
Stokhos::OrthogPolyApprox<int,double> u_st(st_basis), w_st(st_basis);
u_st.term(0, 0) = st_1d_basis->getNewCoeffs(0);
u_st.term(0, 1) = st_1d_basis->getNewCoeffs(1);
// Triple product tensor
Teuchos::RCP<Stokhos::Sparse3Tensor<int,double> > st_Cijk =
st_basis->computeTripleProductTensor(st_basis->size());
// Tensor product quadrature
Teuchos::RCP<const Stokhos::Quadrature<int,double> > st_quad;
if (!use_pce_quad_points) {
#ifdef HAVE_STOKHOS_DAKOTA
if (sparse_grid)
st_quad = Teuchos::rcp(new Stokhos::SparseGridQuadrature<int,double>(st_basis, p));
#endif
if (!sparse_grid)
st_quad = Teuchos::rcp(new Stokhos::TensorProductQuadrature<int,double>(st_basis));
}
else {
Teuchos::Array<double> st_points_0;
Teuchos::Array<double> st_weights_0;
Teuchos::Array< Teuchos::Array<double> > st_values_0;
st_bases[0]->getQuadPoints(p+1, st_points_0, st_weights_0, st_values_0);
Teuchos::Array<double> st_points_1;
Teuchos::Array<double> st_weights_1;
Teuchos::Array< Teuchos::Array<double> > st_values_1;
st_bases[1]->getQuadPoints(p+1, st_points_1, st_weights_1, st_values_1);
Teuchos::RCP< Teuchos::Array< Teuchos::Array<double> > > st_points =
Teuchos::rcp(new Teuchos::Array< Teuchos::Array<double> >(st_points_0.size()));
for (int i=0; i<st_points_0.size(); i++) {
(*st_points)[i].resize(2);
(*st_points)[i][0] = st_points_0[i];
(*st_points)[i][1] = st_points_1[i];
}
Teuchos::RCP< Teuchos::Array<double> > st_weights =
Teuchos::rcp(new Teuchos::Array<double>(st_weights_0));
Teuchos::RCP< const Stokhos::OrthogPolyBasis<int,double> > st_b =
st_basis;
st_quad =
Teuchos::rcp(new Stokhos::UserDefinedQuadrature<int,double>(st_b,
st_points,
st_weights));
}
// Quadrature expansion
Stokhos::QuadOrthogPolyExpansion<int,double> st_quad_exp(st_basis,
st_Cijk,
st_quad);
// Compute w_st = u_st*v_st in Stieltjes basis
st_quad_exp.exp(w_st, u_st);
// Project w_st back to original basis
pce_quad_func st_func(w_st, *st_basis);
quad_exp.unary_op(st_func, w2, u);
// std::cout.precision(12);
// std::cout << w;
// std::cout << w2;
// std::cout << w_st;
mean[n] = w.mean();
mean_st[n] = w2.mean();
std_dev[n] = w.standard_deviation();
std_dev_st[n] = w2.standard_deviation();
pt[n] = w.evaluate(eval_pt);
pt_st[n] = w2.evaluate(eval_pt);
n++;
}
n = 0;
int wi=10;
std::cout << "Statistical error:" << std::endl;
std::cout << "p "
<< std::setw(wi) << "mean" << " "
<< std::setw(wi) << "mean_st" << " "
<< std::setw(wi) << "std_dev" << " "
<< std::setw(wi) << "std_dev_st" << " "
<< std::setw(wi) << "point" << " "
<< std::setw(wi) << "point_st" << std::endl;
for (unsigned int p=pmin; p<pmax; p++) {
std::cout.precision(3);
std::cout.setf(std::ios::scientific);
std::cout << p << " "
<< std::setw(wi) << rel_err(mean[n], mean[np-1]) << " "
<< std::setw(wi) << rel_err(mean_st[n], mean[np-1]) << " "
<< std::setw(wi) << rel_err(std_dev[n], std_dev[np-1]) << " "
<< std::setw(wi) << rel_err(std_dev_st[n], std_dev[np-1])
<< " "
<< std::setw(wi) << rel_err(pt[n], pt_true) << " "
<< std::setw(wi) << rel_err(pt_st[n], pt_true)
<< std::endl;
n++;
}
}
catch (std::exception& e) {
std::cout << e.what() << std::endl;
}
}
double
estimate_ml_t(log_like_function_t *log_like, const double* t,
size_t n_pts, const double tolerance, bsm_t* model,
bool* success, const double min_t, const double max_t)
{
*success = false;
point_t *starting_pts = malloc(sizeof(point_t) * n_pts);
evaluate_ll(log_like, t, n_pts, starting_pts);
const size_t orig_n_pts = n_pts;
point_t* points = select_points(log_like, starting_pts, &n_pts,
DEFAULT_MAX_POINTS, min_t, max_t);
free(starting_pts);
if (points == NULL) {
fprintf(stderr, "ERROR: select_points returned NULL\n");
*success = false;
return NAN;
}
curve_type_t curvature = classify_curve(points, n_pts);
if (!(curvature == CRV_ENC_MAXIMA || curvature == CRV_MONO_DEC)) {
fprintf(stderr, "ERROR: "
"points don't enclose a maximum and aren't decreasing\n");
free(points);
*success = false;
return NAN;
}
/* From here on, curvature is CRV_ENC_MAXIMA or CRV_MONO_DEC, and
* thus ml_t is zero or positive (but not infinite). */
assert(n_pts >= orig_n_pts);
if (n_pts > orig_n_pts) {
/* Subset to top orig_n_pts */
subset_points(points, n_pts, orig_n_pts);
n_pts = orig_n_pts;
}
assert(points[0].t >= min_t);
assert(points[n_pts - 1].t <= max_t);
#ifdef LCFIT_AUTO_VERBOSE
fprintf(stderr, "starting iterative fit\n");
fprintf(stderr, "starting points: ");
print_points(stderr, points, n_pts);
fprintf(stderr, "\n");
#endif /* LCFIT_AUTO_VERBOSE */
/* Allocate an extra point for scratch */
points = realloc(points, sizeof(point_t) * (n_pts + 1));
size_t iter = 0;
const point_t* max_pt = NULL;
double ml_t = 0.0;
double prev_t = 0.0;
for (iter = 0; iter < MAX_ITERS; iter++) {
max_pt = max_point(points, n_pts);
/* Re-fit */
lcfit_bsm_rescale(max_pt->t, max_pt->ll, model);
double* tbuf = malloc(sizeof(double) * n_pts);
double* lbuf = malloc(sizeof(double) * n_pts);
blit_points_to_arrays(points, n_pts, tbuf, lbuf);
double* wbuf = malloc(sizeof(double) * n_pts);
double alpha = (double) iter / (MAX_ITERS - 1);
for (size_t i = 0; i < n_pts; ++i) {
wbuf[i] = exp(alpha * (lbuf[i] - max_pt->ll));
}
#ifdef LCFIT_AUTO_VERBOSE
fprintf(stderr, "weights: ");
for (size_t i = 0; i < n_pts; ++i) {
fprintf(stderr, "%g ", wbuf[i]);
}
fprintf(stderr, "\n");
#endif /* LCFIT_AUTO_VERBOSE */
lcfit_fit_bsm_weight(n_pts, tbuf, lbuf, wbuf, model, 250);
free(tbuf);
free(lbuf);
free(wbuf);
ml_t = lcfit_bsm_ml_t(model);
if (isnan(ml_t)) {
fprintf(stderr, "ERROR: "
"lcfit_bsm_ml_t returned NaN"
", model = { %.3f, %.3f, %.6f, %.6f }\n",
model->c, model->m, model->r, model->b);
*success = false;
break;
}
if (curvature == CRV_ENC_MAXIMA) {
/* Stop if the modeled maximum likelihood branch length is
* within tolerance of the empirical maximum. */
if (rel_err(max_pt->t, ml_t) <= tolerance) {
*success = true;
break;
}
}
double next_t = bound_point(ml_t, points, n_pts, min_t, max_t);
/* Stop if the next sample point is within tolerance of the
* previous sample point. */
if (rel_err(prev_t, next_t) <= tolerance) {
*success = true;
break;
}
points[n_pts].t = next_t;
points[n_pts].ll = log_like->fn(next_t, log_like->args);
prev_t = next_t;
sort_by_t(points, n_pts + 1);
curvature = classify_curve(points, n_pts + 1);
if (!(curvature == CRV_ENC_MAXIMA || curvature == CRV_MONO_DEC)) {
fprintf(stderr, "ERROR: "
"after iteration points don't enclose a maximum "
"and aren't decreasing\n");
*success = false;
break;
}
++n_pts;
points = realloc(points, sizeof(point_t) * (n_pts + 1));
#ifdef LCFIT_AUTO_VERBOSE
fprintf(stderr, "current points: ");
print_points(stderr, points, n_pts);
fprintf(stderr, "\n");
#endif /* LCFIT_AUTO_VERBOSE */
}
if (iter == MAX_ITERS) {
fprintf(stderr, "WARNING: maximum number of iterations reached\n");
}
free(points);
#ifdef LCFIT_AUTO_VERBOSE
fprintf(stderr, "ending iterative fit after %zu iteration(s)\n", iter);
#endif /* LCFIT_AUTO_VERBOSE */
if (ml_t < min_t) {
ml_t = min_t;
} else if (ml_t > max_t) {
ml_t = max_t;
}
return ml_t;
}
int main(int argc, char **argv)
{
try {
const int d = 5;
const int pmin = 1;
const int pmax = 10;
const int np = pmax-pmin+1;
const double a = 1.5;
bool use_pce_quad_points = false;
bool normalize = false;
bool project_integrals = false;
bool lanczos = true;
bool sparse_grid = true;
#ifndef HAVE_STOKHOS_DAKOTA
sparse_grid = false;
#endif
Teuchos::Array<double> mean(np), mean_st(np), std_dev(np), std_dev_st(np);
Teuchos::Array<double> pt(np), pt_st(np);
Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<int,double> > > bases(d);
Teuchos::Array<double> eval_pt(d, 0.56789);
double pt_true;
// Loop over orders
int n = 0;
for (int p=pmin; p<=pmax; p++) {
std::cout << "p = " << p << std::endl;
// Create product basis
for (int i=0; i<d; i++)
bases[i] = Teuchos::rcp(new basis_type(p));
Teuchos::RCP<const Stokhos::CompletePolynomialBasis<int,double> > basis =
Teuchos::rcp(new Stokhos::CompletePolynomialBasis<int,double>(bases));
// Create approximation
Stokhos::OrthogPolyApprox<int,double> s(basis), t1(basis), t2(basis);
Teuchos::Array< Stokhos::OrthogPolyApprox<int,double>* > xi(d);
for (int i=0; i<d; i++) {
xi[i] = new Stokhos::OrthogPolyApprox<int,double>(basis);
xi[i]->term(i, 1) = 1.0;
}
// Quadrature
Teuchos::RCP<const Stokhos::Quadrature<int,double> > quad;
#ifdef HAVE_STOKHOS_DAKOTA
if (sparse_grid)
quad =
Teuchos::rcp(new Stokhos::SparseGridQuadrature<int,double>(basis, p));
#endif
if (!sparse_grid)
quad =
Teuchos::rcp(new Stokhos::TensorProductQuadrature<int,double>(basis));
// Triple product tensor
Teuchos::RCP<Stokhos::Sparse3Tensor<int,double> > Cijk =
basis->computeTripleProductTensor();
// Quadrature expansion
Stokhos::QuadOrthogPolyExpansion<int,double> quad_exp(basis, Cijk, quad);
// Compute PCE via quadrature expansion
s_quad_func<d> s_func(a);
const Stokhos::OrthogPolyApprox<int,double> **xip =
new const Stokhos::OrthogPolyApprox<int,double>*[d];
for (int i=0; i<d; i++)
xip[i] = xi[i];
quad_exp.nary_op(s_func,s,xip);
quad_exp.divide(t1,1.0,s);
delete [] xip;
// compute true point
Teuchos::Array<double> xx(d);
for (int i=0; i<d; i++)
xx[i] = xi[i]->evaluate(eval_pt);
pt_true = s_func(&(xx[0]));
pt_true = 1.0/pt_true;
// Compute Stieltjes basis
Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<int,double> > > st_bases(1);
Teuchos::RCP< Stokhos::LanczosProjPCEBasis<int,double> > stp_basis_s;
Teuchos::RCP< Stokhos::LanczosPCEBasis<int,double> > st_basis_s;
if (lanczos) {
if (project_integrals) {
stp_basis_s =
Teuchos::rcp(new Stokhos::LanczosProjPCEBasis<int,double>(
p, Teuchos::rcp(&s,false), Cijk, normalize, true));
st_bases[0] = stp_basis_s;
}
else {
st_basis_s =
Teuchos::rcp(new Stokhos::LanczosPCEBasis<int,double>(
p, Teuchos::rcp(&s,false), quad, normalize, true));
st_bases[0] = st_basis_s;
}
}
else {
st_bases[0] =
Teuchos::rcp(new Stokhos::StieltjesPCEBasis<int,double>(
p, Teuchos::rcp(&s,false), quad, use_pce_quad_points,
normalize, project_integrals, Cijk));
}
Teuchos::RCP<const Stokhos::CompletePolynomialBasis<int,double> >
st_basis =
Teuchos::rcp(new Stokhos::CompletePolynomialBasis<int,double>(st_bases));
//std::cout << *st_basis << std::endl;
Stokhos::OrthogPolyApprox<int,double> s_st(st_basis), t_st(st_basis);
if (lanczos) {
if (project_integrals) {
s_st.term(0, 0) = stp_basis_s->getNewCoeffs(0);
s_st.term(0, 1) = stp_basis_s->getNewCoeffs(1);
}
else {
s_st.term(0, 0) = st_basis_s->getNewCoeffs(0);
s_st.term(0, 1) = st_basis_s->getNewCoeffs(1);
}
}
else {
s_st.term(0, 0) = s.mean();
s_st.term(0, 1) = 1.0;
}
// Triple product tensor
Teuchos::RCP<Stokhos::Sparse3Tensor<int,double> > st_Cijk =
st_basis->computeTripleProductTensor();
// Tensor product quadrature
Teuchos::RCP<const Stokhos::Quadrature<int,double> > st_quad;
#ifdef HAVE_STOKHOS_DAKOTA
if (sparse_grid)
st_quad = Teuchos::rcp(new Stokhos::SparseGridQuadrature<int,double>(st_basis, p));
#endif
if (!sparse_grid)
st_quad = Teuchos::rcp(new Stokhos::TensorProductQuadrature<int,double>(st_basis));
// Quadrature expansion
Stokhos::QuadOrthogPolyExpansion<int,double> st_quad_exp(st_basis,
st_Cijk,
st_quad);
// Compute t_st = 1/s_st in Stieltjes basis
st_quad_exp.divide(t_st, 1.0, s_st);
// Project t_st back to original basis
pce_quad_func st_func(t_st, *st_basis);
quad_exp.unary_op(st_func, t2, s);
// std::cout.precision(12);
// std::cout << w;
// std::cout << w2;
// std::cout << w_st;
mean[n] = t1.mean();
mean_st[n] = t2.mean();
std_dev[n] = t1.standard_deviation();
std_dev_st[n] = t2.standard_deviation();
pt[n] = t1.evaluate(eval_pt);
pt_st[n] = t2.evaluate(eval_pt);
n++;
for (int i=0; i<d; i++)
delete xi[i];
}
n = 0;
int wi=10;
std::cout << "Statistical error:" << std::endl;
std::cout << "p "
<< std::setw(wi) << "mean" << " "
<< std::setw(wi) << "mean_st" << " "
<< std::setw(wi) << "std_dev" << " "
<< std::setw(wi) << "std_dev_st" << " "
<< std::setw(wi) << "point" << " "
<< std::setw(wi) << "point_st" << std::endl;
for (int p=pmin; p<pmax; p++) {
std::cout.precision(3);
std::cout.setf(std::ios::scientific);
std::cout << p << " "
<< std::setw(wi) << rel_err(mean[n], mean[np-1]) << " "
<< std::setw(wi) << rel_err(mean_st[n], mean[np-1]) << " "
<< std::setw(wi) << rel_err(std_dev[n], std_dev[np-1]) << " "
<< std::setw(wi) << rel_err(std_dev_st[n], std_dev[np-1])
<< " "
<< std::setw(wi) << rel_err(pt[n], pt_true) << " "
<< std::setw(wi) << rel_err(pt_st[n], pt_true)
<< std::endl;
n++;
}
}
catch (std::exception& e) {
std::cout << e.what() << std::endl;
}
}
