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// Jacobian.cc -- data structures for the Jacobian matrix
// $Id$
//
// Jacobian::Jacobian
//
// dense_Jacobian::dense_Jacobian
// dense_Jacobian::~dense_Jacobian
// dense_Jacobian::zero_matrix
// dense_Jacobian::zero_row
// dense_Jacobian::solve_linear_system
//
// new_Jacobian
//
#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) BLAS+LAPACK+wrapper routines */
/* $Id$ */
/*
* prerequisites:
* "cctk.h"
* "config.hh" // for "integer" = Fortran integer
*/
#ifdef __cplusplus
extern "C" {
#endif
/*
* ***** BLAS *****
*/
integer CCTK_FCALL
CCTK_FNAME(isamax)(const integer* N, const float SX[], const integer* incx);
integer CCTK_FCALL
CCTK_FNAME(idamax)(const integer* N, const double DX[], const integer* incx);
/*
* ***** LAPACK *****
*/
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);
/*
* ***** wrappers (for passing character-string args) *****
*/
/* norm_int = 0 for infinity-norm, 1 for 1-norm */
void CCTK_FCALL
CCTK_FNAME(sgecon_wrapper)(const integer* norm_int,
const integer* N,
float A[], const integer* LDA,
const float* anorm, float* rcond,
float WORK[], integer IWORK[],
integer* info);
void CCTK_FCALL
CCTK_FNAME(dgecon_wrapper)(const integer* norm_int,
const integer* N,
double A[], const integer* LDA,
const double* anorm, double* rcond,
double WORK[], integer IWORK[],
integer* info);
#ifdef __cplusplus
}; /* extern "C" */
#endif
//**************************************
//******************************************************************************
//******************************************************************************
//******************************************************************************
//
// This function constructs a Jacobian object.
//
Jacobian::Jacobian(patch_system& ps)
: ps_(ps),
NN_(ps.N_grid_points())
{ }
//******************************************************************************
//******************************************************************************
//******************************************************************************
//
// 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()]),
iwork_(new integer[NN()]),
rwork_(new fp[4*NN()]) // no comma
{ }
//******************************************************************************
//
// THis function destroys a dense_Jacobian object.
//
dense_Jacobian::~dense_Jacobian()
{
delete[] iwork_;
delete[] rwork_;
delete[] pivot_;
}
//******************************************************************************
//
// This function zeros a dense_Jacobian object.
//
void dense_Jacobian::zero_matrix()
{
for (int JJ = 0 ; JJ < NN() ; ++JJ)
{
for (int II = 0 ; II < NN() ; ++II)
{
matrix_(JJ,II) = 0.0;
}
}
}
//******************************************************************************
//
// 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, using LU decomposition. It returns the
// estimated infinity-norm condition number of the linear system, or
// 0.0 if the matrix is numerically singular
//
fp 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);
fp *A = matrix_.data_array();
const integer zero = 0;
const integer one = 1;
const integer NRHS = 1;
const integer N = NN();
const integer N2 = NN() * NN();
integer info;
// compute the infinity-norm of the matrix A
// ... posn = 1-origin index of A[] element with max absolute value
#if defined(FP_IS_FLOAT)
const integer posn = CCTK_FNAME(isamax)(&N2, A, &one);
#elif defined(FP_IS_DOUBLE)
const integer posn = CCTK_FNAME(idamax)(&N2, A, &one);
#else
#error "don't know fp datatype!"
#endif
const fp A_infnorm = A[posn-1];
// LU decompose and solve the linear system
//
// ... [sd]gesv() use an "in out" design, where the same argument
// is used for both rhs and x ==> we must first copy rhs to x
//
for (int II = 0 ; II < NN() ; ++II)
{
x[II] = rhs[II];
}
#if defined(FP_IS_FLOAT)
CCTK_FNAME(sgesv)(&N, &NRHS, A, &N, pivot_, x, &N, &info);
#elif defined(FP_IS_DOUBLE)
CCTK_FNAME(dgesv)(&N, &NRHS, A, &N, pivot_, x, &N, &info);
#else
#error "don't know fp datatype!"
#endif
if (info < 0)
then error_exit(ERROR_EXIT,
"\n"
"***** dense_Jacobian::solve_linear_system(rhs_gfn=%d, x_gfn=%d):\n"
" error return (bad argument) info=%d from [sd]gesv() LAPACK routine!\n"
,
rhs_gfn, x_gfn,
int(info)); /*NOTREACHED*/
if (info > 0)
then return 0.0; // *** ERROR RETURN ***
// *** (singular matrix)
// estimate infinity-norm condition number
fp rcond;
#if defined(FP_IS_FLOAT)
CCTK_FNAME(sgecon_wrapper)(&zero, &N, A, &N, &A_infnorm, &rcond,
rwork_, iwork_, &info);
#elif defined(FP_IS_DOUBLE)
CCTK_FNAME(dgecon_wrapper)(&zero, &N, A, &N, &A_infnorm, &rcond,
rwork_, iwork_, &info);
#else
#error "don't know fp datatype!"
#endif
if (rcond == 0.0)
then return 0.0; // *** ERROR RETURN ***
// *** (singular matrix)
return 1.0/rcond;
}
//******************************************************************************
//******************************************************************************
//******************************************************************************
//
// This function is an "object factory" for Jacobians: it constructs
// and returns a new-allocated Jacobian object of a specified type.
//
// FIXME: the patch system shouldn't really have to be non-const, but
// the Jacobian constructors all require this to allow the
// linear solvers to directly update gridfns
//
Jacobian& new_Jacobian(patch_system& ps,
const char Jacobian_type[])
{
if (STRING_EQUAL(Jacobian_type, "dense matrix"))
then return *new dense_Jacobian(ps);
else CCTK_VWarn(-1, __LINE__, __FILE__, CCTK_THORNSTRING,
"unknown Jacobian_type=\"%s\"!",
Jacobian_type); /*NOTREACHED*/
}
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