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// Jacobian.cc -- data structures for the Jacobian matrix
// $Id$
//
// Jacobian::Jacobian
//
// print_Jacobian
// print_Jacobians
//
// dense_Jacobian::dense_Jacobian
// dense_Jacobian::~dense_Jacobian
// dense_Jacobian::zero
// dense_Jacobian::zero_row
// dense_Jacobian::solve_linear_system
//
#include <stdio.h>
using std::fopen;
using std::printf;
using std::fprintf;
using std::fclose;
using std::FILE;
#include <assert.h>
#include <math.h>
#include <vector>
#include "util_Table.h"
#include "cctk.h"
#include "cctk_Arguments.h"
#include "stdc.h"
#include "config.hh"
#include "../jtutil/util.hh"
#include "../jtutil/array.hh"
#include "../jtutil/cpm_map.hh"
#include "../jtutil/linear_map.hh"
using jtutil::error_exit;
#include "../util/coords.hh"
#include "../util/grid.hh"
#include "../util/fd_grid.hh"
#include "../util/patch.hh"
#include "../util/patch_edge.hh"
#include "../util/patch_interp.hh"
#include "../util/ghost_zone.hh"
#include "../util/patch_system.hh"
#include "Jacobian.hh"
//#include "lapack.h"
//**************************************
/* lapack.h -- C/C++ prototypes for (some) LAPACK routines */
/* $Id$ */
/*
* prerequisites:
* "cctk.h"
* "config.hh" // for "integer" = Fortran integer
*/
#ifdef __cplusplus
extern "C" {
#endif
void CCTK_FCALL
CCTK_FNAME(sgesv)(const integer* N, const integer* NRHS,
float A[], const int* LDA,
integer IPIV[],
float B[], const integer* LDB, integer* info);
void CCTK_FCALL
CCTK_FNAME(dgesv)(const integer* N, const integer* NRHS,
double A[], const int* LDA,
integer IPIV[],
double B[], const integer* LDB, integer* info);
#ifdef __cplusplus
}; /* extern "C" */
#endif
//**************************************
namespace {
void print_Jacobians_internal(const char file_name[],
const Jacobian& SD_Jac, const Jacobian& NP_Jac,
bool pair_flag);
};
//******************************************************************************
//******************************************************************************
//******************************************************************************
//
// This function constructs a Jacobian object.
//
Jacobian::Jacobian(patch_system& ps)
: ps_(ps),
NN_(ps.N_grid_points())
{ }
//******************************************************************************
//******************************************************************************
//******************************************************************************
//
// This function prints a Jacobian matrix to a named output file.
//
void print_Jacobian(const char file_name[], const Jacobian& Jac)
{
print_Jacobians_internal(file_name, Jac, Jac, false);
}
//******************************************************************************
//
// This function prints a pair of Jacobian matrices (and their difference)
// to a named output file.
//
void print_Jacobians(const char file_name[],
const Jacobian& SD_Jac, const Jacobian& NP_Jac)
{
print_Jacobians_internal(file_name, SD_Jac, NP_Jac, true);
}
//******************************************************************************
//
// If pair_flag = false, this prints SD_Jac.
// If pair_flag = true, this prints both Jacobians, and the error in SD_Jac.
//
namespace {
void print_Jacobians_internal(const char file_name[],
const Jacobian& SD_Jac, const Jacobian& NP_Jac,
bool pair_flag)
{
const patch_system& ps = SD_Jac.my_patch_system();
FILE *fileptr = fopen(file_name, "w");
if (fileptr == NULL)
then error_exit(ERROR_EXIT,
"***** dense_Jacobian::print(): can't open output file \"%s\"!",
file_name); /*NOTREACHED*/
fprintf(fileptr, "# column 1 = x II\n");
fprintf(fileptr, "# column 2 = x patch number\n");
fprintf(fileptr, "# column 3 = x irho\n");
fprintf(fileptr, "# column 4 = x isigma\n");
fprintf(fileptr, "# column 5 = y JJ\n");
fprintf(fileptr, "# column 6 = y patch number\n");
fprintf(fileptr, "# column 7 = y irho\n");
fprintf(fileptr, "# column 8 = y isigma\n");
if (pair_flag)
then {
fprintf(fileptr, "# column 9 = SD_Jac(II,JJ)\n");
fprintf(fileptr, "# column 10 = NP_Jac(II,JJ)\n");
fprintf(fileptr, "# column 11 = abs error\n");
fprintf(fileptr, "# column 12 = rel error\n");
}
else fprintf(fileptr, "# column 9 = Jac(II,JJ)\n");
for (int xpn = 0 ; xpn < ps.N_patches() ; ++xpn)
{
patch& xp = ps.ith_patch(xpn);
for (int x_irho = xp.min_irho() ; x_irho <= xp.max_irho() ; ++x_irho)
{
for (int x_isigma = xp.min_isigma() ;
x_isigma <= xp.max_isigma() ;
++x_isigma)
{
const int II = ps.gpn_of_patch_irho_isigma(xp, x_irho,x_isigma);
for (int ypn = 0 ; ypn < ps.N_patches() ; ++ypn)
{
patch& yp = ps.ith_patch(ypn);
for (int y_irho = yp.min_irho() ;
y_irho <= yp.max_irho() ;
++y_irho)
{
for (int y_isigma = yp.min_isigma() ;
y_isigma <= yp.max_isigma() ;
++y_isigma)
{
const int JJ = ps.gpn_of_patch_irho_isigma(yp, y_irho,y_isigma);
if (! SD_Jac.is_explicitly_stored(II,JJ))
then continue; // skip sparse points
const fp SD = SD_Jac(II,JJ);
const fp NP = NP_Jac(II,JJ);
const fp abs_error = SD - NP;
if (pair_flag ? ((SD == 0.0) && (NP == 0.0))
: (SD == 0.0))
then continue; // skip zero values (if == )
const fp abs_SD = jtutil::abs(SD);
const fp abs_NP = jtutil::abs(NP);
const fp rel_error = abs_error / jtutil::max(abs_SD, abs_NP);
fprintf(fileptr,
"%d %d %d %d\t%d %d %d %d\t",
II, xpn, x_irho, x_isigma,
JJ, ypn, y_irho, y_isigma);
if (pair_flag)
then fprintf(fileptr,
"%.10g\t%.10g\t%e\t%e\n",
double(SD), double(NP),
double(abs_error), double(rel_error));
else fprintf(fileptr,
"%.10g\n",
double(SD));
}
}
}
}
}
}
fclose(fileptr);
}
};
//******************************************************************************
//******************************************************************************
//******************************************************************************
//
// This function constructs a dense_Jacobian object.
//
dense_Jacobian::dense_Jacobian(patch_system& ps)
: Jacobian(ps),
matrix_(0,NN()-1, 0,NN()-1),
pivot_(new integer[NN()])
{ }
//******************************************************************************
//
// THis function destroys a dense_Jacobian object.
//
dense_Jacobian::~dense_Jacobian()
{
delete[] pivot_;
}
//******************************************************************************
//
// This function zeros a dense_Jacobian object.
//
void dense_Jacobian::zero()
{
jtutil::array_zero(matrix_.N_array(), matrix_.data_array());
}
//******************************************************************************
//
// This function zeros a single row of a dense_Jacobian object.
//
void dense_Jacobian::zero_row(int II)
{
for (int JJ = 0 ; JJ < NN() ; ++JJ)
{
matrix_(JJ,II) = 0.0;
}
}
//******************************************************************************
//
// This function solves the linear system J.x = rhs, with rhs and x
// being nominal-grid gridfns. The computation is done using the LAPACK
// [sd]gesv() subroutines; which modify the Jacobian matrix J in-place
// for the LU decomposition.
//
void dense_Jacobian::solve_linear_system(int rhs_gfn, int x_gfn)
{
const fp *rhs = my_patch_system().gridfn_data(rhs_gfn);
fp *x = my_patch_system().gridfn_data(x_gfn);
//
// [sd]gesv() use an "in out" design, where the same argument is used for
// both rhs and x ==> first copy rhs to x so we can pass that to [sd]gesv()
//
jtutil::array_copy(NN(), rhs, x);
integer N = NN();
integer NRHS = 1;
integer info;
#ifdef FP_IS_FLOAT
CCTK_FNAME(sgesv)(&N, &NRHS, matrix_.data_array(), &N, pivot_, x, &N, &info);
#endif
#ifdef FP_IS_DOUBLE
CCTK_FNAME(dgesv)(&N, &NRHS, matrix_.data_array(), &N, pivot_, x, &N, &info);
#endif
if (info != 0)
then error_exit(ERROR_EXIT,
"\n"
"***** dense_Jacobian::solve_linear_system(rhs_gfn=%d, x_gfn=%d):\n"
" error return info=%d from [sd]gesv() LAPACK routine!\n"
,
rhs_gfn, x_gfn,
int(info)); /*NOTREACHED*/
}
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