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algebra.cpp
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algebra.cpp
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// ----------------------------------------------------------------//
// Filename : algebra.cpp
// Author : Xiao Zigang <zxiao2@illinois.edu>
//
// linear algebra library
// ----------------------------------------------------------------//
// - Zigang Xiao - Wed Jan 26 18:15:02 CST 2011
// * algebra::solve
#include "cholmod.h"
#include <cassert>
#include <ctype.h>
#include "global.h"
#include "util.h"
#include "vec.h"
#include "umfpack.h"
#include "algebra.h"
// solve x for linear system Ax=b
// NOTE: UF_long and size_t must have the same size!
void Algebra::solve(const Matrix & A, const Vec & b, Vec & x){
assert(x.size() == b.size());
assert(sizeof(UF_long) == sizeof(size_t));
clock_t t1,t2;
size_t n = b.size();
//Vec x(n);
double * _x = x.val;
double * _b = b.val;
size_t n_row = n;
size_t n_col = n;
size_t nz = A.size();
// NOTE: DO NOT MODIFY. size must be n_col+1, see UMFPACK manual
UF_long * Ti = new UF_long[nz];
UF_long * Tj = new UF_long[nz];
double * Tx = new double[nz];
A.to_arrays((size_t*)Ti,(size_t*)Tj,Tx);
UF_long * Ap = new UF_long[n_col+1];
UF_long * Ai = new UF_long[nz];
double *Ax = new double [nz];
int status;
double Control [UMFPACK_CONTROL];
umfpack_dl_defaults (Control) ;
status = umfpack_dl_triplet_to_col(n_row, n_col, nz, Ti, Tj, Tx,
Ap, Ai, Ax, (UF_long *) NULL);
if( status < 0 ) {
umfpack_dl_report_status (Control, status) ;
report_exit("umfpack_zi_triplet_to_col failed\n") ;
}
double *null = (double *) NULL;
void *Symbolic, *Numeric;
t1=clock();
status = umfpack_dl_symbolic(n, n, Ap, Ai, Ax,
&Symbolic, Control, null);
t2=clock();
clog<<"Symbolic time = "<<1.0*(t2-t1)/CLOCKS_PER_SEC<<endl;
if( status < 0 ){
umfpack_dl_report_status (Control, status) ;
report_exit("umfpack_dl_symbolic failed\n") ;
}
t1=clock();
status = umfpack_dl_numeric(Ap, Ai, Ax, Symbolic,
&Numeric, Control, null) ;
t2=clock();
clog<<"Numeric time = "<<1.0*(t2-t1)/CLOCKS_PER_SEC<<endl;
if( status < 0 ){
umfpack_dl_report_status (Control, status) ;
report_exit("umfpack_dl_numeric failed\n") ;
}
umfpack_dl_free_symbolic (&Symbolic) ;
t1=clock();
status = umfpack_dl_solve(UMFPACK_A, Ap, Ai, Ax, _x, _b,
Numeric, Control, null) ;
t2=clock();
clog<<"Solve time = "<<1.0*(t2-t1)/CLOCKS_PER_SEC<<endl;
if( status < 0 ){
umfpack_dl_report_status (Control, status) ;
report_exit("umfpack_dl_solve failed\n") ;
}
umfpack_dl_free_numeric (&Numeric) ;
delete [] Ti;
delete [] Tj;
delete [] Tx;
delete [] Ax;
delete [] Ai;
delete [] Ap;
//return x;
}
// deliver the address of x
void Algebra::solve_CK(Matrix & A, cholmod_dense *&x, cholmod_dense *b, cholmod_common *cm, size_t &peak_mem, size_t &CK_mem){
cholmod_factor *L;
cm->final_ll = true; // stay in LL' format
clock_t t1, t2;
t1 = clock();
CK_decomp(A, L, cm, peak_mem, CK_mem);
t2 = clock();
clog<<"decomp time for CK is: "<<1.0*(t2-t1) / CLOCKS_PER_SEC<<endl;
// then solve
t1 = clock();
x = cholmod_solve(CHOLMOD_A, L, b, cm);
t2 = clock();
clog<<"solve time is: "<<1.0*(t2-t1)/ CLOCKS_PER_SEC<<endl;
//cholmod_print_dense(x, "x", cm);
//cholmod_print_dense(b, "b", cm);
//cholmod_print_factor(L, "L", cm);
cholmod_free_factor(&L, cm);
}
// Given column compressed form of matrix A
// perform LU decomposition and store the result in Numeric
// n is the dimension of matrix A
void Algebra::LU_decomposition(int n, UF_long * Ap, UF_long * Ai, double * Ax,
void ** p_Numeric){
int status;
double Control [UMFPACK_CONTROL];
umfpack_dl_defaults (Control) ;
double *null = (double *) NULL;
void * Symbolic;
// perform ordering
status = umfpack_dl_symbolic(n, n, Ap, Ai, Ax,
&Symbolic, Control, null);
if( status < 0 ){
umfpack_dl_report_status (Control, status) ;
report_exit("umfpack_dl_symbolic failed\n") ;
}
// LU decomposition
status = umfpack_dl_numeric(Ap, Ai, Ax, Symbolic,
p_Numeric, Control, null) ;
if( status < 0 ){
umfpack_dl_report_status (Control, status) ;
report_exit("umfpack_dl_numeric failed\n") ;
}
umfpack_dl_free_symbolic (&Symbolic) ;
}
// doing cholesky decomposition
void Algebra::CK_decomp(Matrix &A, cholmod_factor *&L, cholmod_common *cm, size_t &peak_mem, size_t & CK_mem){
// doing factorization first
cholmod_triplet * T;
size_t n_row = A.get_row();
size_t n_col = A.get_row();
size_t nnz = A.size();
int *Ti;
int *Tj;
double *Tx;
int stype = -1;// lower triangular storage
T = cholmod_allocate_triplet(n_row, n_col, nnz, stype,
CHOLMOD_REAL, cm);
Ti = static_cast<int *>(T->i);
Tj = static_cast<int *>(T->j);
Tx = static_cast<double *>(T->x);
// copy data into T
for(size_t k=0;k<nnz;k++){
Ti[k] = A.Ti[k];
Tj[k] = A.Tj[k];
Tx[k] = A.Tx[k];
}
T->nnz = nnz;
A.Ti.clear();
A.Tj.clear();
A.Tx.clear();
cholmod_sparse * A_cholmod;
A_cholmod = cholmod_triplet_to_sparse(T, nnz, cm);
// free the triplet pointer
cholmod_free_triplet(&T, cm);
//cm->supernodal = -1;
L = cholmod_analyze(A_cholmod, cm);
//L->ordering = CHOLMOD_NATURAL;
cholmod_factorize(A_cholmod, L, cm);
//cholmod_print_factor(L, "L", cm);
//if(peak_mem < cm->memory_usage)
//peak_mem = cm->memory_usage;
//CK_mem += cm->lnz;
cholmod_free_sparse(&A_cholmod, cm);
}