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smoother.cpp
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smoother.cpp
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/*
* Copyright (C) 2019-2023 The GMGPolar Development Team
*
* Authors: Philippe Leleux, Christina Schwarz, Martin J. Kühn, Carola Kruse, Ulrich Rüde, Ulrich Rüde
*
* Contact:
* Carola Kruse <Carola.Kruse@CERFACS.fr>
* Martin J. Kuehn <Martin.Kuehn@DLR.de>
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/*!
* \file multigrid_iter.cpp
* \brief Implementation of the smoother
* \author M. Kuehn, C. Kruse, P. Leleux, C. Schwarz
* \version 0.0
*/
#include "level.h"
#include <sstream>
/*!
* \brief Returns the index i+1 in (0, ntheta)
*
* Returns (i + 1) % ntheta_int
*
* \param i: theta index
* \param ntheta_int: size of theta
*
* \return (i + 1) % ntheta_int
*
*/
inline int iplus(int i, int ntheta_int)
{
return (i + 1 > ntheta_int - 1) ? 0 : i + 1;
} /* ----- end of inline iplus ----- */
/*!
* \brief Returns the index i-1 in (0, ntheta)
*
* Returns (i + ntheta_int - 1) % ntheta_int
*
* \param i: theta index
* \param ntheta_int: size of theta
*
* \return (i + ntheta_int - 1) % ntheta_int
*
*/
inline int imoins(int i, int ntheta_int)
{
return (i - 1 < 0) ? ntheta_int - 1 : i - 1;
} /* ----- end of inline imoins ----- */
/*!
* \brief Defines the smoother
*
* Defines the smoother
* so far only different types of zebra splittings are implemented
* (basically, two colors, although more can be defined but which might not be used)
*
*/
void level::define_line_splitting()
{
// useless array q
int i;
for (i = 2; i < nr_int - 2; i++) {
// assume that k_ij=theta_{i,j+1}-theta_{i,j} is constant for fixed i and variable j (i.e., constant per circle)
double q = (theta[1] - theta[0]) / (r[i] - r[i - 1]);
if (r[i] > 1 / q)
break;
}
delete_circles = i; // delete_circles = delete_circles(end);
if (gyro::icntl[Param::verbose] > 1)
std::cout << "Shifting from circle to radial at radius " << delete_circles << "\n";
} /* ----- end of destructor level::define_line_splitting ----- */
/*! \brief Applies smoothing
*
* For all lines of the smoother s and the colour c.
* The matrix A_sc is for all lines of points of the smoother s/c.
* The result is in u (or u_previous_cu_previous_r).
*
* if gyro::icntl[Param::smoother]=
* - 3: block Gauss Seidel for all 4 smoothers.
* - 13: block Jacobi between Circle and Radial, and block Gauss Seidel for B/W inside each.
*
* \param smoother: the smoother
*/
void level::multigrid_smoothing(int smoother, int v, std::vector<double>& f_Asc_u, int nblocks, int c, int* dep_Asc_cur,
int* dep_Asc_prev, int* dep_Asc1, int* dep_Asc_ortho_cur)
{
double t, t_smoothing_tmp;
int extrapol = gyro::icntl[Param::extrapolation] == 1 && l == 0;
TIC;
t_smoothing_tmp = t;
if (gyro::icntl[Param::matrix_free] == 1) {
apply_Asc_ortho(f_Asc_u, u, smoother, v, c, dep_Asc_cur, dep_Asc_prev, dep_Asc1, dep_Asc_ortho_cur);
}
else {
/* if (gyro::icntl[Param::openmp] == 1) {
for (auto k = 0; k < A_Zebra_Mix_r[smoother].size(); k++) {
f_Asc_u[A_Zebra_Mix_r[smoother][k]] -= A_Zebra_Mix_v[smoother][k] * u[A_Zebra_Mix_c[smoother][k]];
}
}
else {
*/
if (smoother < 2) {
int start_j = 0;
if (gyro::icntl[Param::DirBC_Interior])
start_j = 1;
int start;
if (smoother == 0)
start = (gyro::icntl[Param::DirBC_Interior]) ? 2 : 0;
else if (smoother == 1)
start = 1;
int shift = 2;
for (int j = start; j < delete_circles; j += shift) {
int odd_j = j % 2;
#pragma omp task shared(u, f_Asc_u) firstprivate(smoother, j, odd_j) depend(in \
: dep_Asc_prev[j - odd_j]), \
depend(in \
: dep_Asc_prev[j + odd_j]), \
depend(out \
: dep_Asc_ortho_cur[j])
{
int smoother_tmp = get_smoother(0, j);
std::vector<int> ptr_vect = get_ptr_sc(j, smoother_tmp, 1);
int ptr_start = ptr_vect[0];
int ptr_end = ptr_start + (ptr_vect[2] - ptr_vect[0]) * ntheta_int / 2;
for (int k = ptr_start; k < ptr_end; k++) {
f_Asc_u[A_Zebra_Mix_r[smoother][k]] -=
A_Zebra_Mix_v[smoother][k] * u[A_Zebra_Mix_c[smoother][k]];
}
dep_Asc_ortho_cur[j] = 1;
}
}
}
else {
std::vector<int> shift_vect, ptr_vect;
if (smoother == 2) {
ptr_vect = ptr_vect_s2;
shift_vect = shift_vect_s2;
}
else {
ptr_vect = ptr_vect_s3;
shift_vect = shift_vect_s3;
}
for (int i = smoother - 2; i < ntheta_int; i += 2) {
int im = imoins(i, ntheta_int);
int ip = iplus(i, ntheta_int);
int odd_d = delete_circles % 2;
int ind_m_odd = i, ind_p_odd = i;
int odd_i = i % 2;
if (odd_i) {
ind_m_odd = im;
ind_p_odd = ip;
}
#pragma omp task shared(u, f_Asc_u) firstprivate(smoother, i, odd_d, ind_m_odd, ind_p_odd) \
depend(in \
: dep_Asc_prev[ind_m_odd]) depend(in \
: dep_Asc_prev[ind_p_odd], dep_Asc1[delete_circles - 1 - odd_d]) \
depend(out \
: dep_Asc_ortho_cur[i])
{
int start_s2_extr = (smoother == 2 && extrapol && delete_circles % 2 == 0) ? 1 : 0;
int shift_s2_extr = (smoother == 2 && extrapol) ? 2 : 1;
for (int j = delete_circles + start_s2_extr; j < nr_int; j += shift_s2_extr) {
for (int k =
ptr_vect[j - delete_circles] + (i - smoother + 2) / 2 * shift_vect[j - delete_circles];
k < ptr_vect[j - delete_circles] +
((i - smoother + 2) / 2 + 1) * shift_vect[j - delete_circles];
k++) {
f_Asc_u[A_Zebra_Mix_r[smoother][k]] -=
A_Zebra_Mix_v[smoother][k] * u[A_Zebra_Mix_c[smoother][k]];
}
}
dep_Asc_ortho_cur[i] = 1;
}
}
}
// }
}
t_Asc_ortho += TOC;
TIC;
/* if (gyro::icntl[Param::openmp] == 1) {
for (int k = 0; k < nblocks; k++) {
int ij_glob = k * 2 + smoother % 2;
int ind = ij_glob, indm = ij_glob - 1, indp = ij_glob + 1;
if (smoother > 1 && gyro::icntl[Param::matrix_free] == 1) {
indm = imoins(ij_glob, ntheta_int);
indp = iplus(ij_glob, ntheta_int);
}
TIC;
// create u_sc, f_sc
std::vector<double> u_sc;
std::vector<double> f_sc(m_sc[smoother]);
std::vector<double> f_total(m_sc[smoother]), f_total2(m_sc[smoother]);
std::vector<double>::const_iterator first = f_Asc_u.begin() + k * m_sc[smoother];
std::vector<double>::const_iterator last = f_Asc_u.begin() + (k + 1) * m_sc[smoother];
f_total = std::vector<double>(first, last);
for (int i = 0; i < m_sc[smoother]; i++)
f_Asc_u[k * m_sc[smoother] + i] = 0;
//compute f_total = f_sc - A_sc_ortho * u
build_fsc(f_sc, fVec, smoother, 0, k * m_sc[smoother], (k + 1) * m_sc[smoother]);
for (int i = 0; i < m_sc[smoother]; i++) {
f_sc[i] += f_total[i];
}
// #pragma omp atomic
t_f_sc += TOC;
TIC;
// Dirichlet or size of system is 1 (diagonal solve)
if ((smoother == 0 && k == 0 && gyro::icntl[Param::DirBC_Interior]) || m_sc[smoother] == 1 ||
(gyro::icntl[Param::extrapolation] && l == 0 && smoother % 2 == 0 &&
!(smoother == 0 && !gyro::icntl[Param::DirBC_Interior] && k == 0))) {
u_sc = solve_diag(A_Zebra_v_LU_row[smoother][k], f_sc);
}
// Circle (not across)
else if (smoother < 2 && !(smoother == 0 && !gyro::icntl[Param::DirBC_Interior] && k == 0)) {
u_sc = solve_circle(A_Zebra_r_LU_row[smoother][k], A_Zebra_c_LU_row[smoother][k],
A_Zebra_v_LU_row[smoother][k], f_sc);
}
// Radial (not across)
else if (smoother > 1) {
u_sc = solve_radial(A_Zebra_r_LU_row[smoother][k], A_Zebra_c_LU_row[smoother][k],
A_Zebra_v_LU_row[smoother][k], f_sc);
}
// Across (direct solver)
else {
#ifdef USE_MUMPS
if (gyro::icntl[Param::optimized] == 0) {
#endif
u_sc = solve_gaussian_elimination(A_Zebra_r_LU_row[smoother][k], A_Zebra_c_LU_row[smoother][k],
A_Zebra_v_LU_row[smoother][k], f_sc);
#ifdef USE_MUMPS
}
else
u_sc = solve_mumps(mumps_across, f_sc);
#endif
}
t_Asc += TOC;
TIC;
build_fsc(u_sc, u, smoother, 1, k * m_sc[smoother], (k + 1) * m_sc[smoother]);
t_f_sc += TOC;
TIC;
}
}
else {
*/
for (int k = 0; k < nblocks; k++) {
int ij_glob = k * 2 + smoother % 2;
int ind = ij_glob, indm = ij_glob - 1, indp = ij_glob + 1;
if (smoother > 1 && gyro::icntl[Param::matrix_free] == 1) {
indm = imoins(ij_glob, ntheta_int);
indp = iplus(ij_glob, ntheta_int);
}
#pragma omp task firstprivate(k, ij_glob, ind, indm, indp, t) shared(f_Asc_u) \
depend(in \
: dep_Asc_ortho_cur[indm], dep_Asc_ortho_cur[ind], dep_Asc_ortho_cur[indp]) depend(out \
: dep_Asc_cur[ind])
{
TIC;
// create u_sc, f_sc
std::vector<double> u_sc;
std::vector<double> f_sc(m_sc[smoother]);
std::vector<double> f_total(m_sc[smoother]), f_total2(m_sc[smoother]);
std::vector<double>::const_iterator first = f_Asc_u.begin() + k * m_sc[smoother];
std::vector<double>::const_iterator last = f_Asc_u.begin() + (k + 1) * m_sc[smoother];
f_total = std::vector<double>(first, last);
for (int i = 0; i < m_sc[smoother]; i++)
f_Asc_u[k * m_sc[smoother] + i] = 0;
//compute f_total = f_sc - A_sc_ortho * u
build_fsc(f_sc, fVec, smoother, 0, k * m_sc[smoother], (k + 1) * m_sc[smoother]);
for (int i = 0; i < m_sc[smoother]; i++) {
f_sc[i] += f_total[i];
}
// #pragma omp atomic
t_f_sc += TOC;
TIC;
// Dirichlet or size of system is 1 (diagonal solve)
if ((smoother == 0 && k == 0 && gyro::icntl[Param::DirBC_Interior]) || m_sc[smoother] == 1 ||
(gyro::icntl[Param::extrapolation] && l == 0 && smoother % 2 == 0 &&
!(smoother == 0 && !gyro::icntl[Param::DirBC_Interior] && k == 0))) {
u_sc = solve_diag(A_Zebra_v_LU_row[smoother][k], f_sc);
}
// Circle (not across)
else if (smoother < 2 && !(smoother == 0 && !gyro::icntl[Param::DirBC_Interior] && k == 0)) {
u_sc = solve_circle(A_Zebra_r_LU_row[smoother][k], A_Zebra_c_LU_row[smoother][k],
A_Zebra_v_LU_row[smoother][k], f_sc);
}
// Radial (not across)
else if (smoother > 1) {
u_sc = solve_radial(A_Zebra_r_LU_row[smoother][k], A_Zebra_c_LU_row[smoother][k],
A_Zebra_v_LU_row[smoother][k], f_sc);
}
// Across (direct solver)
else {
#ifdef USE_MUMPS
if (gyro::icntl[Param::optimized] == 0) {
#endif
u_sc = solve_gaussian_elimination(A_Zebra_r_LU_row[smoother][k], A_Zebra_c_LU_row[smoother][k],
A_Zebra_v_LU_row[smoother][k], f_sc);
#ifdef USE_MUMPS
}
else
u_sc = solve_mumps(mumps_across, f_sc);
#endif
}
#pragma omp atomic
t_Asc += TOC;
TIC;
build_fsc(u_sc, u, smoother, 1, k * m_sc[smoother], (k + 1) * m_sc[smoother]);
#pragma omp atomic
t_f_sc += TOC;
TIC;
dep_Asc_cur[ind] = 1;
}
// }
}
t = t_smoothing_tmp;
t_smoothing += TOC;
} /* ----- end of level::multigrid_smoothing ----- */
/*! \brief Create the RHS part corresponding to Asc_ortho for a smoother (on level l)
*
* Create f_sc, i.e. the RHS part corresponding to Asc_ortho for a smoother (on level l)
*
* \param f_sc: the RHS part (out)
* \param smoother: the smoother
*/
void level::build_fsc(std::vector<double>& f_sc, std::vector<double>& f, int smoother, int loc_to_glob, int start,
int end)
{
std::vector<int> ind = mapping_usc_to_u(start, end, smoother);
if (loc_to_glob) {
//computation of indices in the total vector u corresponding to the indices in u_sc
for (int i = start; i < end; ++i) {
int index = ind[i - start];
f[index] = f_sc[i % m_sc[smoother]];
}
}
else {
//computation of indices in the total vector u corresponding to the indices in u_sc
for (int i = start; i < end; ++i) {
int index = ind[i - start];
f_sc[i % m_sc[smoother]] = f[index];
}
}
} /* ----- end of level::build_fsc ----- */
/*! \brief Build the matrix A_sc explicitely on the level l
*
* Asc corresponds to all lines of a smoother s with colour c
* so we need to build 4 matrices Asc for the 4 smoothers on the level l, all stored in A_Zebra
* 0,1: circular white/black
* 2,3: radial white/black
*
* this function is called only once at the beginning to build the matrices Asc on all levels
* the matrix should contain only the parts corresponding to (s/c),
* thus it is not of size m, but smaller (number of points corresponding to the smoother s/c),
* so we need to treat the indices (!)
*/
void level::build_Asc()
{
int extrapol = gyro::icntl[Param::extrapolation] == 1 && l == 0;
int shift_ij = extrapol ? 1 : 0;
int smoother_prev, smoother_cur, smoother_next, smoother;
int start_j, start_loop, shift_loop, ip, im, ptr, row, col;
double coeff, coeff2, coeff3, kt, ktmin1, hs, hsmin1, beta_val;
std::vector<int> smoother23(ntheta_int);
std::vector<int> row_vect_prev, row_vect, row_vect_next;
std::vector<int> ptr_vect_prev, ptr_vect, ptr_vect_next;
std::vector<int> stencil_prev, stencil_cur, stencil_next, stencil;
std::vector<double> arr_vect, arr_vect2, att_vect, art_vect;
std::vector<std::vector<int>> stencil23_prev(2), stencil23_cur(2), stencil23_next(2);
for (int i = 0; i < ntheta_int; i += 2) {
smoother23[i] = 2;
smoother23[i + 1] = 3;
}
/* !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
* !!!!!!!!!!!!!!!!!!!!!!! Circle Smoother !!!!!!!!!!!!!!!!!!!!!!!
* !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
*/
// Take boundary condition into account: Dirichlet-RB
smoother = 0;
if (gyro::icntl[Param::DirBC_Interior]) { // (r[0],0) is on Dirichlet boundary
for (int i = 0; i < ntheta_int / (shift_ij + 1); i++) {
A_Zebra_r_row[smoother][0][i] = i;
A_Zebra_c_row[smoother][0][i] = i;
A_Zebra_v_row[smoother][0][i] = 1.0;
}
start_j = 1;
}
else { // (r[0],0) is not on Dirichlet boundary
start_j = 0;
}
for (int j = start_j; j < delete_circles; j++) {
/* Initialize moother, row_vect, ptr, and stencil */
if (j > start_j) {
smoother_prev = smoother_cur;
smoother_cur = smoother_next;
row_vect_prev = row_vect;
row_vect = row_vect_next;
ptr_vect_prev = ptr_vect;
ptr_vect = ptr_vect_next;
stencil_prev = stencil_cur;
stencil_cur = stencil_next;
}
else {
smoother_cur = j;
row_vect = get_row(j, smoother_cur, extrapol, 1, 1);
ptr_vect = get_ptr_sc(j, smoother_cur, 0);
stencil_cur = get_stencil_sc(j, smoother_cur, 0);
}
if (j < delete_circles - 1)
smoother_next = get_smoother(0, j + 1);
else
smoother_next = 2;
row_vect_next = get_row(j + 1, smoother_next, extrapol, 1, 1);
ptr_vect_next = get_ptr_sc(j + 1, smoother_next, 0);
if (j < delete_circles - 1)
stencil_next = get_stencil_sc(j + 1, smoother_next, 0);
else {
stencil23_next[0] = get_stencil_sc(j + 1, 2, 0);
stencil23_next[1] = get_stencil_sc(j + 1, 3, 0);
}
hs = hplus[j];
gyro::arr_att_art(r[j], theta, sin_theta, cos_theta, ntheta_int, arr_vect, att_vect, art_vect, 0);
/* Update (j-1, i) */
if (j > start_j) {
hsmin1 = hplus[j - 1];
smoother = smoother_prev;
if (extrapol && smoother == 0) {
start_loop = 1;
shift_loop = 2;
}
else {
start_loop = 0;
shift_loop = 1;
}
for (int i = start_loop; i < ntheta_int; i += shift_loop) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
// Update (j-1, i)
ptr = ptr_vect_prev[i];
stencil = stencil_prev;
coeff = 0.5 * (kt + ktmin1) * arr_vect[i] / hsmin1;
col = row_vect_prev[i];
A_Zebra_v_row[smoother][(j - 1) / 2][ptr + stencil[Param::middle]] += coeff;
}
}
else {
smoother = smoother_cur;
stencil = stencil_cur;
// Across: bottom update
if (!gyro::icntl[Param::DirBC_Interior]) {
hsmin1 = 2 * r[0];
arr_vect2 = gyro::arr(r[j], theta_PI, sin_theta_PI, cos_theta_PI, ntheta_int, 0);
for (int i = shift_ij; i < ntheta_int; i += shift_ij + 1) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
ptr = ptr_vect[i];
row = row_vect[i];
col = row_vect[(i + ntheta_int / 2) % ntheta_int];
A_Zebra_r_row[smoother][j / 2][ptr + stencil[Param::bottom]] = row;
A_Zebra_c_row[smoother][j / 2][ptr + stencil[Param::bottom]] = col;
coeff = 0.5 * (kt + ktmin1) * arr_vect2[i] / hsmin1;
coeff2 = 0.5 * (kt + ktmin1) * arr_vect[i] / hsmin1;
A_Zebra_v_row[smoother][j / 2][ptr + stencil[Param::bottom]] += -coeff - coeff2;
A_Zebra_v_row[smoother][j / 2][ptr + stencil[Param::middle]] += coeff;
}
}
// Dirichlet
else {
hsmin1 = hplus[j - 1];
// DB contribution arr (r(0))
arr_vect2 = gyro::arr(r[j - 1], theta, sin_theta, cos_theta, ntheta_int, 0);
for (int i = 0; i < ntheta_int; i++) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
ptr = ptr_vect[i];
row = row_vect[i];
coeff = 0.5 * (kt + ktmin1) * arr_vect2[i] / hsmin1;
A_Zebra_v_row[smoother][j / 2][ptr + stencil[Param::middle]] += coeff;
}
}
}
/* Update (j, x) */
smoother = smoother_cur;
if (!extrapol || smoother == 1) {
for (int i = 0; i < ntheta_int; i++) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
stencil = stencil_cur;
ip = iplus(i, ntheta_int);
im = imoins(i, ntheta_int);
// Update (j, i)
ptr = ptr_vect[i];
row = row_vect[i];
A_Zebra_r_row[smoother][j / 2][ptr + stencil[Param::middle]] = row;
A_Zebra_c_row[smoother][j / 2][ptr + stencil[Param::middle]] = row;
coeff = 0.5 * (kt + ktmin1) * arr_vect[i];
coeff2 = 0.5 * (hs + hsmin1) * att_vect[i];
col = row_vect[im];
A_Zebra_v_row[smoother][j / 2][ptr + stencil[Param::left]] += -coeff2 / ktmin1;
col = row_vect[ip];
A_Zebra_v_row[smoother][j / 2][ptr + stencil[Param::right]] += -coeff2 / kt;
A_Zebra_v_row[smoother][j / 2][ptr + stencil[Param::middle]] +=
coeff / hs + coeff / hsmin1 + coeff2 / ktmin1 + coeff2 / kt;
// Beta coefficient
beta_val = betaVec[j * ntheta_int + i];
A_Zebra_v_row[smoother][j / 2][ptr + stencil[Param::middle]] += beta_val;
// Update (j, i+1)
ptr = ptr_vect[ip];
row = row_vect[ip];
col = row_vect[i];
coeff = 0.5 * (hs + hsmin1) * att_vect[i] / kt;
A_Zebra_r_row[smoother][j / 2][ptr + stencil[Param::left]] = row;
A_Zebra_c_row[smoother][j / 2][ptr + stencil[Param::left]] = col;
A_Zebra_v_row[smoother][j / 2][ptr + stencil[Param::left]] += -coeff;
A_Zebra_v_row[smoother][j / 2][ptr + stencil[Param::middle]] += coeff;
// Update (j, i-1)
ptr = ptr_vect[im];
row = row_vect[im];
col = row_vect[i];
coeff = 0.5 * (hs + hsmin1) * att_vect[i] / ktmin1;
A_Zebra_r_row[smoother][j / 2][ptr + stencil[Param::right]] = row;
A_Zebra_c_row[smoother][j / 2][ptr + stencil[Param::right]] = col;
A_Zebra_v_row[smoother][j / 2][ptr + stencil[Param::right]] += -coeff;
A_Zebra_v_row[smoother][j / 2][ptr + stencil[Param::middle]] += coeff;
}
}
if (extrapol && smoother == 0) {
start_loop = 0;
shift_loop = 2;
for (int i = start_loop; i < ntheta_int; i += shift_loop) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
stencil = stencil_cur;
ip = iplus(i, ntheta_int);
im = imoins(i, ntheta_int);
col = row_vect[i];
// Update (j, i+1)
ptr = ptr_vect[iplus(i, ntheta_int)];
coeff = 0.5 * (hs + hsmin1) * att_vect[i] / kt;
row = row_vect[ip];
A_Zebra_v_row[smoother][j / 2][ptr + stencil[Param::middle]] += coeff;
// Update (j, i-1)
ptr = ptr_vect[imoins(i, ntheta_int)];
coeff = 0.5 * (hs + hsmin1) * att_vect[i] / ktmin1;
row = row_vect[im];
A_Zebra_v_row[smoother][j / 2][ptr + stencil[Param::middle]] += coeff;
// Update (j, i) [for i+1]
kt = thetaplus_per[i + 2];
ktmin1 = thetaplus_per[i + 1];
ptr = ptr_vect[i + 1];
coeff = 0.5 * (kt + ktmin1) * arr_vect[i + 1];
coeff2 = 0.5 * (hs + hsmin1) * att_vect[i + 1];
row = row_vect[i + 1];
A_Zebra_r_row[smoother][j / 2][ptr + stencil[Param::middle]] = row;
A_Zebra_c_row[smoother][j / 2][ptr + stencil[Param::middle]] = row;
A_Zebra_v_row[smoother][j / 2][ptr + stencil[Param::middle]] +=
coeff / hs + coeff / hsmin1 + coeff2 / ktmin1 + coeff2 / kt;
// Beta coefficient
beta_val = betaVec[j * ntheta_int + ip];
A_Zebra_v_row[smoother][j / 2][ptr + stencil[Param::middle]] += beta_val;
}
}
/* Update (j+1, i) */
if (j < delete_circles - 1) {
smoother = smoother_next;
if (extrapol && smoother == 0) {
start_loop = 1;
shift_loop = 2;
}
else {
start_loop = 0;
shift_loop = 1;
}
for (int i = start_loop; i < ntheta_int; i += shift_loop) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
ptr = ptr_vect_next[i];
stencil = stencil_next;
coeff = 0.5 * (kt + ktmin1) * arr_vect[i] / hs;
row = row_vect_next[i];
A_Zebra_v_row[smoother][(j + 1) / 2][ptr + stencil[Param::middle]] += coeff;
}
}
else if (j == delete_circles - 1) {
if (extrapol && (j + 1) % 2 == 0) {
start_loop = 1;
shift_loop = 2;
}
else {
start_loop = 0;
shift_loop = 1;
}
for (int i = start_loop; i < ntheta_int; i += shift_loop) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
ptr = ptr_vect_next[i];
smoother = smoother23[i];
stencil = stencil23_next[smoother - 2];
coeff = 0.5 * (kt + ktmin1) * arr_vect[i] / hs;
row = row_vect_next[i];
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::middle]] += coeff;
}
}
}
/* !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
* !!!!!!!!!!!!!!!!!!!!!!! Radial Smoother !!!!!!!!!!!!!!!!!!!!!!!
* !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
*/
for (int j = delete_circles; j < nr_int; j++) {
/* Initialize moother, row_vect, ptr, and stencil */
if (j == delete_circles) {
smoother_prev = get_smoother(0, j - 1);
stencil_prev = get_stencil_sc(j - 1, smoother_prev, 0);
row_vect_prev = get_row(j - 1, smoother_prev, extrapol, 1, 1);
ptr_vect_prev = get_ptr_sc(j - 1, smoother_prev, 0);
}
else {
stencil23_prev[0] = get_stencil_sc(j - 1, 2, 0);
stencil23_prev[1] = get_stencil_sc(j - 1, 3, 0);
row_vect_prev = get_row(j - 1, 2, extrapol, 1, 1);
ptr_vect_prev = get_ptr_sc(j - 1, 2, 0);
}
row_vect = row_vect_next;
ptr_vect = ptr_vect_next;
stencil23_cur[0] = get_stencil_sc(j, 2, 0);
stencil23_cur[1] = get_stencil_sc(j, 3, 0);
if (j < nr_int - 1) {
row_vect_next = get_row(j + 1, 2, extrapol, 1, 1);
ptr_vect_next = get_ptr_sc(j + 1, 2, 0);
stencil23_next[0] = get_stencil_sc(j + 1, 2, 0);
stencil23_next[1] = get_stencil_sc(j + 1, 3, 0);
}
hs = hplus[j];
hsmin1 = hplus[j - 1];
gyro::arr_att_art(r[j], theta, sin_theta, cos_theta, ntheta_int, arr_vect, att_vect, art_vect, 0);
if (j == nr_int - 1)
arr_vect2 = gyro::arr(r[j + 1], theta, sin_theta, cos_theta, ntheta_int, 0);
/* Update (j-1, i) */
if (j == delete_circles) {
smoother = smoother_prev;
stencil = stencil_prev;
if (extrapol && smoother == 0) {
start_loop = 1;
shift_loop = 2;
}
else {
start_loop = 0;
shift_loop = 1;
}
for (int i = start_loop; i < ntheta_int; i += shift_loop) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
ptr = ptr_vect_prev[i];
coeff = 0.5 * (kt + ktmin1) * arr_vect[i] / hsmin1;
row = row_vect_prev[i];
A_Zebra_v_row[smoother][(j - 1) / 2][ptr + stencil[Param::middle]] += coeff;
}
}
else {
if (extrapol) {
start_loop = 1;
shift_loop = 2;
}
else {
start_loop = 0;
shift_loop = 1;
}
for (int i = start_loop; i < ntheta_int; i += shift_loop) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
smoother = smoother23[i];
ptr = ptr_vect_prev[i];
stencil = stencil23_prev[smoother - 2];
coeff = 0.5 * (kt + ktmin1) * arr_vect[i] / hsmin1;
row = row_vect_prev[i];
col = row_vect[i];
A_Zebra_r_row[smoother][i / 2][ptr + stencil[Param::top]] = row;
A_Zebra_c_row[smoother][i / 2][ptr + stencil[Param::top]] = col;
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::top]] += -coeff;
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::middle]] += coeff;
}
start_loop = 0;
shift_loop = 2;
if (extrapol && j % 2 == 0) {
for (int i = start_loop; i < ntheta_int; i += shift_loop) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
smoother = smoother23[i];
ptr = ptr_vect_prev[i];
stencil = stencil23_prev[smoother - 2];
coeff = 0.5 * (kt + ktmin1) * arr_vect[i] / hsmin1;
row = row_vect_prev[i];
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::middle]] += coeff;
}
}
}
/* Update (j, x) */
if (extrapol) {
start_loop = 1;
shift_loop = 2;
}
else {
start_loop = 0;
shift_loop = 1;
}
if (j == delete_circles) {
for (int i = start_loop; i < ntheta_int; i += shift_loop) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
smoother = smoother23[i];
// Update (j, i)
ptr = ptr_vect[i];
stencil = stencil23_cur[smoother - 2];
coeff = 0.5 * (kt + ktmin1) * arr_vect[i];
coeff2 = 0.5 * (hs + hsmin1) * att_vect[i];
row = row_vect[i];
A_Zebra_r_row[smoother][i / 2][ptr + stencil[Param::middle]] = row;
A_Zebra_c_row[smoother][i / 2][ptr + stencil[Param::middle]] = row;
col = row_vect_prev[i];
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::top]] += -coeff / hs;
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::middle]] +=
coeff / hs + coeff / hsmin1 + coeff2 / ktmin1 + coeff2 / kt;
// Beta coefficient
beta_val = betaVec[j * ntheta_int + i];
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::middle]] += beta_val;
}
}
else if (j == nr_int - 1) {
for (int i = start_loop; i < ntheta_int; i += shift_loop) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
smoother = smoother23[i];
// Update (j, i)
ptr = ptr_vect[i];
stencil = stencil23_cur[smoother - 2];
coeff = 0.5 * (kt + ktmin1) * arr_vect[i];
// Contribution to middle (top) from DB
coeff3 = 0.5 * (kt + ktmin1) * arr_vect2[i] / hs;
coeff2 = 0.5 * (hs + hsmin1) * att_vect[i];
row = row_vect[i];
A_Zebra_r_row[smoother][i / 2][ptr + stencil[Param::middle]] = row;
A_Zebra_c_row[smoother][i / 2][ptr + stencil[Param::middle]] = row;
col = row_vect_next[i];
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::bottom]] += -coeff / hsmin1;
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::middle]] +=
coeff / hsmin1 + coeff / hs + coeff3 + coeff2 / ktmin1 + coeff2 / kt;
// Beta coefficient
beta_val = betaVec[j * ntheta_int + i];
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::middle]] += beta_val;
}
}
else {
for (int i = start_loop; i < ntheta_int; i += shift_loop) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
smoother = smoother23[i];
// Update (j, i)
ptr = ptr_vect[i];
stencil = stencil23_cur[smoother - 2];
coeff = 0.5 * (kt + ktmin1) * arr_vect[i];
coeff2 = 0.5 * (hs + hsmin1) * att_vect[i];
row = row_vect[i];
A_Zebra_r_row[smoother][i / 2][ptr + stencil[Param::middle]] = row;
A_Zebra_c_row[smoother][i / 2][ptr + stencil[Param::middle]] = row;
col = row_vect_next[i];
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::top]] += -coeff / hs;
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::middle]] +=
coeff / hs + coeff / hsmin1 + coeff2 / ktmin1 + coeff2 / kt;
col = row_vect_prev[i];
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::bottom]] += -coeff / hsmin1;
// Beta coefficient
beta_val = betaVec[j * ntheta_int + i];
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::middle]] += beta_val;
}
}
start_loop = 0;
shift_loop = 2;
if (extrapol && j % 2 == 1) {
if (j == nr_int - 1) {
for (int i = start_loop; i < ntheta_int; i += shift_loop) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
// Update (j, i)
smoother = smoother23[i];
stencil = stencil23_cur[smoother - 2];
ptr = ptr_vect[i];
coeff = 0.5 * (kt + ktmin1) * arr_vect[i];
// Contribution to middle (top) from DB
coeff3 = 0.5 * (kt + ktmin1) * arr_vect2[i] / hs;
coeff2 = 0.5 * (hs + hsmin1) * att_vect[i];
row = row_vect[i];
A_Zebra_r_row[smoother][i / 2][ptr + stencil[Param::middle]] = row;
A_Zebra_c_row[smoother][i / 2][ptr + stencil[Param::middle]] = row;
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::middle]] +=
coeff / hsmin1 + coeff / hs + coeff3 + coeff2 / ktmin1 + coeff2 / kt;
// Beta coefficient
beta_val = betaVec[j * ntheta_int + i];
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::middle]] += beta_val;
}
}
else {
for (int i = start_loop; i < ntheta_int; i += shift_loop) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
// Update (j, i)
smoother = smoother23[i];
stencil = stencil23_cur[smoother - 2];
ptr = ptr_vect[i];
coeff = 0.5 * (kt + ktmin1) * arr_vect[i];
coeff2 = 0.5 * (hs + hsmin1) * att_vect[i];
row = row_vect[i];
A_Zebra_r_row[smoother][i / 2][ptr + stencil[Param::middle]] = row;
A_Zebra_c_row[smoother][i / 2][ptr + stencil[Param::middle]] = row;
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::middle]] +=
coeff / hs + coeff / hsmin1 + coeff2 / ktmin1 + coeff2 / kt;
// Beta coefficient
beta_val = betaVec[j * ntheta_int + i];
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::middle]] += beta_val;
}
}
}
if (extrapol && j % 2 == 0) {
start_loop = 0;
shift_loop = 2;
}
else {
start_loop = 0;
shift_loop = 1;
}
for (int i = start_loop; i < ntheta_int; i += shift_loop) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
ip = iplus(i, ntheta_int);
im = imoins(i, ntheta_int);
smoother = smoother23[ip];
stencil = stencil23_cur[smoother - 2];
// Update (j, i+1)
ptr = ptr_vect[ip];
coeff = 0.5 * (hs + hsmin1) * att_vect[i] / kt;
row = row_vect[ip];
A_Zebra_v_row[smoother][ip / 2][ptr + stencil[Param::middle]] += coeff;
// Update (j, i-1)
smoother = smoother23[im];
ptr = ptr_vect[im];
coeff = 0.5 * (hs + hsmin1) * att_vect[i] / ktmin1;
row = row_vect[im];
A_Zebra_v_row[smoother][im / 2][ptr + stencil[Param::middle]] += coeff;
}
/* Update (j+1, i) */
if (j < nr_int - 1) {
if (extrapol) {
start_loop = 1;
shift_loop = 2;
}
else {
start_loop = 0;
shift_loop = 1;
}
for (int i = start_loop; i < ntheta_int; i += shift_loop) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
smoother = smoother23[i];
ptr = ptr_vect_next[i];
stencil = stencil23_next[smoother - 2];
coeff = 0.5 * (kt + ktmin1) * arr_vect[i] / hs;
row = row_vect_next[i];
col = row_vect[i];
A_Zebra_r_row[smoother][i / 2][ptr + stencil[Param::bottom]] = row;
A_Zebra_c_row[smoother][i / 2][ptr + stencil[Param::bottom]] = col;
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::bottom]] += -coeff;
A_Zebra_v_row[smoother][i / 2][ptr + stencil[Param::middle]] += coeff;
}
start_loop = 0;
shift_loop = 2;
if (extrapol && j % 2 == 0) {
for (int i = start_loop; i < ntheta_int; i += shift_loop) {
kt = thetaplus_per[i + 1];
ktmin1 = thetaplus_per[i];
smoother = smoother23[i];
ptr = ptr_vect_next[i];
stencil = stencil23_next[smoother - 2];