int
zpcgr (
int n_matrixSize,
int type,
int symmetryflag,
InpMtx *mtxA,
FrontMtx *Precond,
DenseMtx *mtxX,
DenseMtx *mtxB,
int itermax,
double convergetol,
int msglvl,
FILE *msgFile
)
{
Chv *chv, *rootchv ;
ChvManager *chvmanager ;
DenseMtx *mtxZ ;
DenseMtx *vecP, *vecR, *vecQ ;
DenseMtx *vecX, *vecZ ;
double Alpha[2], Beta[2], Rho[2], Rho0[2], Rtmp[2];
double Init_norm, ratio, Res_norm ;
double t1, t2, cpus[9] ;
double one[2] = {1.0, 0.0}, zero[2] = {0.0, 0.0} ;
double Tiny[2] = {0.1e-28, 0.0};
int Iter, neqns;
int stats[6] ;
if (symmetryflag != SPOOLES_HERMITIAN){
fprintf(msgFile, "\n\n Fatal Error, \n"
" Matrix is not Hermitian in ZPCGR !!") ;
spoolesFatal();
};
neqns = n_matrixSize;
/*
--------------------
init the vectors in ZPCGR
--------------------
*/
vecP = DenseMtx_new() ;
DenseMtx_init(vecP, type, 0, 0, neqns, 1, 1, neqns) ;
vecR = DenseMtx_new() ;
DenseMtx_init(vecR, type, 0, 0, neqns, 1, 1, neqns) ;
vecX = DenseMtx_new() ;
DenseMtx_init(vecX, type, 0, 0, neqns, 1, 1, neqns) ;
vecQ = DenseMtx_new() ;
DenseMtx_init(vecQ, type, 0, 0, neqns, 1, 1, neqns) ;
vecZ = DenseMtx_new() ;
DenseMtx_init(vecZ, type, 0, 0, neqns, 1, 1, neqns) ;
/*
--------------------------
Initialize the iterations
--------------------------
*/
Init_norm = DenseMtx_twoNormOfColumn (mtxB, 0);
if ( Init_norm == 0.0 ){
Init_norm = 1.0; };
ratio = 1.0;
DenseMtx_zero(vecX) ;
DenseMtx_colCopy (vecR, 0, mtxB, 0);
MARKTIME(t1) ;
Iter = 0;
/*
------------------------------
Main Loop of the iterations
------------------------------
*/
while ( ratio > convergetol && Iter <= itermax )
{
Iter++;
/* */
FrontMtx_solve(Precond, vecZ, vecR, Precond->manager,
cpus, msglvl, msgFile) ;
DenseMtx_colDotProduct(vecR, 0, vecZ, 0, Rho);
if ( Rho[0] == 0.0 & Rho[1] == 0.0){
fprintf(stderr, "\n breakdown in ZPCGR !! "
"\n Fatal error \n");
spoolesFatal();
}
/* */
if ( Iter == 1 ) {
DenseMtx_colCopy (vecP, 0, vecZ, 0);
} else {
zdiv(Rho, Rho0, Beta);
DenseMtx_colGenAxpy (Beta, vecP, 0, one, vecZ, 0);
};
InpMtx_herm_gmmm(mtxA, zero, vecQ, one, vecP) ;
DenseMtx_colDotProduct (vecP, 0, vecQ,0, Rtmp);
zdiv(Rho, Rtmp, Alpha);
DenseMtx_colGenAxpy (one, vecX, 0, Alpha, vecP, 0);
Rtmp[0] = -Alpha[0];
Rtmp[1] = -Alpha[1];
DenseMtx_colGenAxpy (one, vecR, 0, Rtmp, vecQ, 0);
Rho0[0] = Rho[0];
Rho0[1] = Rho[1];
/* */
Res_norm = DenseMtx_twoNormOfColumn (vecR, 0);
ratio = Res_norm/Init_norm;
fprintf(msgFile, "\n\n At iteration %d"
" the convergence ratio is %12.4e",
Iter, ratio) ;
}
/* End of while loop */
MARKTIME(t2) ;
fprintf(msgFile, "\n CPU : Converges in time: %8.3f ", t2 - t1) ;
fprintf(msgFile, "\n # iterations = %d", Iter) ;
fprintf(msgFile, "\n\n after ZPCGR") ;
DenseMtx_colCopy (mtxX, 0, vecX, 0);
/*
------------------------
free the working storage
------------------------
*/
DenseMtx_free(vecP) ;
DenseMtx_free(vecR) ;
DenseMtx_free(vecX) ;
DenseMtx_free(vecQ) ;
DenseMtx_free(vecZ) ;
fprintf(msgFile, "\n") ;
return(1) ; }
int
tfqmrl (
int n_matrixSize,
int type,
int symmetryflag,
InpMtx *mtxA,
FrontMtx *Precond,
DenseMtx *mtxX,
DenseMtx *mtxB,
int itermax,
double convergetol,
int msglvl,
FILE *msgFile
)
{
Chv *chv, *rootchv ;
ChvManager *chvmanager ;
DenseMtx *vecD, *vecR, *vecT, *vecU1, *vecU2, *vecV, *vecW;
DenseMtx *vecX, *vecY1, *vecY2 ;
double Alpha, Beta, Cee, Eta, Rho, Rho_new ;
double Sigma, Tau, Theta;
double Init_norm, ratio, Res_norm;
double error_trol, m, Rtmp;
double t1, t2, cpus[9] ;
double one[2] = {1.0, 0.0}, zero[2] ={0.0, 0.0} ;
double Tiny = 0.1e-28;
int Iter, Imv, neqns;
int stats[6] ;
neqns = n_matrixSize;
/*
--------------------
init the vectors in TFQMRL
--------------------
*/
vecD = DenseMtx_new() ;
DenseMtx_init(vecD, type, 0, 0, neqns, 1, 1, neqns) ;
vecR = DenseMtx_new() ;
DenseMtx_init(vecR, type, 0, 0, neqns, 1, 1, neqns) ;
vecT = DenseMtx_new() ;
DenseMtx_init(vecT, type, 0, 0, neqns, 1, 1, neqns) ;
vecU1 = DenseMtx_new() ;
DenseMtx_init(vecU1, type, 0, 0, neqns, 1, 1, neqns) ;
vecU2 = DenseMtx_new() ;
DenseMtx_init(vecU2, type, 0, 0, neqns, 1, 1, neqns) ;
vecV = DenseMtx_new() ;
DenseMtx_init(vecV, type, 0, 0, neqns, 1, 1, neqns) ;
vecW = DenseMtx_new() ;
DenseMtx_init(vecW, type, 0, 0, neqns, 1, 1, neqns) ;
vecX = DenseMtx_new() ;
DenseMtx_init(vecX, type, 0, 0, neqns, 1, 1, neqns) ;
vecY1 = DenseMtx_new() ;
DenseMtx_init(vecY1, type, 0, 0, neqns, 1, 1, neqns) ;
vecY2 = DenseMtx_new() ;
DenseMtx_init(vecY2, type, 0, 0, neqns, 1, 1, neqns) ;
/*
--------------------------
Initialize the iterations
--------------------------
*/
/* ---- Set initial guess as zero ---- */
DenseMtx_zero(vecX) ;
DenseMtx_colCopy(vecT, 0, mtxB, 0);
/* */
FrontMtx_solve(Precond, vecR, vecT, Precond->manager,
cpus, msglvl, msgFile) ;
/* */
Init_norm = DenseMtx_twoNormOfColumn(vecR,0);
if ( Init_norm == 0.0 ){
Init_norm = 1.0;
};
error_trol = Init_norm * convergetol ;
fprintf(msgFile, "\n TFQMRL Initial norml: %6.2e ", Init_norm ) ;
fprintf(msgFile, "\n TFQMRL Conveg. Control: %7.3e ", convergetol ) ;
fprintf(msgFile, "\n TFQMRL Convergen Control: %7.3e ",error_trol ) ;
DenseMtx_zero(vecD) ;
DenseMtx_zero(vecU1) ;
DenseMtx_zero(vecU2) ;
DenseMtx_zero(vecY2) ;
/* DenseMtx_copy(vecR, mtxB); */
DenseMtx_colCopy(vecW, 0, vecR, 0);
DenseMtx_colCopy(vecY1, 0, vecR, 0);
Iter = 0;
Imv = 0;
switch ( symmetryflag ) {
case SPOOLES_SYMMETRIC :
InpMtx_sym_gmmm(mtxA, zero, vecT, one, vecY1) ;
break ;
case SPOOLES_HERMITIAN :
fprintf(msgFile, "\n TFQMRL Matrix type wrong");
fprintf(msgFile, "\n Fatal error");
goto end;
case SPOOLES_NONSYMMETRIC :
InpMtx_nonsym_gmmm(mtxA, zero, vecT, one, vecY1) ;
break ;
default :
fprintf(msgFile, "\n TFQMRL Matrix type wrong");
fprintf(msgFile, "\n Fatal error");
goto end;
}
/* */
FrontMtx_solve(Precond, vecV, vecT, Precond->manager,
cpus, msglvl, msgFile) ;
/* */
Imv++;
DenseMtx_colCopy(vecU1, 0, vecV, 0);
/*
*/
Theta = 0.0;
Eta = 0.0;
Tau = Init_norm ;
Rho = Tau * Tau ;
/*
------------------------------
TFQMRL Iteration start
------------------------------
*/
MARKTIME(t1) ;
while ( Iter <= itermax )
{
Iter++;
DenseMtx_colDotProduct(vecV, 0, vecR, 0, &Sigma);
if (Sigma == 0){
fprintf(msgFile, "\n\n Fatal Error, \n"
" TFQMRL Breakdown, Sigma = 0 !!") ;
Imv = -1;
goto end;
};
Alpha = Rho/Sigma;
/*
----------------
Odd step
---------------
*/
m = 2 * Iter - 1;
Rtmp=-Alpha;
DenseMtx_colGenAxpy(one, vecW, 0, &Rtmp, vecU1, 0);
Rtmp = Theta * Theta * Eta / Alpha ;
DenseMtx_colGenAxpy(&Rtmp, vecD, 0, one, vecY1, 0);
Theta = DenseMtx_twoNormOfColumn(vecW,0)/Tau;
Cee = 1.0/sqrt(1.0 + Theta*Theta);
Tau = Tau * Theta * Cee ;
Eta = Cee * Cee * Alpha ;
DenseMtx_colGenAxpy(one, vecX, 0, &Eta, vecD, 0);
fprintf(msgFile, "\n\n Odd step at %d", Imv);
fprintf(msgFile, " \n Tau is : %7.3e", Tau) ;
/*
Debug purpose: Check the convergence history
for the true residual norm
*/
/*
DenseMtx_zero(vecT) ;
InpMtx_nonsym_mmm(mtxA, vecT, one, vecX) ;
DenseMtx_sub(vecT, mtxB) ;
Rtmp = DenseMtx_twoNormOfColumn(vecT,0);
fprintf(msgFile, "\n TFQMRL Residual norm: %6.2e ", Rtmp) ;
*/
/*
----------------
Convergence Test
---------------
*/
if (Tau * sqrt(m + 1) <= error_trol ) {
/* */
DenseMtx_colCopy(mtxX, 0, vecX, 0);
/*
DenseMtx_zero(vecT) ;
InpMtx_nonsym_mmm(mtxA, vecT, one, mtxX) ;
*/
switch ( symmetryflag ) {
case SPOOLES_SYMMETRIC :
InpMtx_sym_gmmm(mtxA, zero, vecT, one, mtxX) ;
break ;
case SPOOLES_HERMITIAN :
fprintf(msgFile, "\n TFQMRL Matrix type wrong");
fprintf(msgFile, "\n Fatal error");
goto end;
case SPOOLES_NONSYMMETRIC :
InpMtx_nonsym_gmmm(mtxA, zero, vecT, one, mtxX) ;
break ;
default :
fprintf(msgFile, "\n TFQMRL Matrix type wrong");
fprintf(msgFile, "\n Fatal error");
goto end;
}
DenseMtx_sub(vecT, mtxB) ;
Rtmp = DenseMtx_twoNormOfColumn(vecT,0);
fprintf(msgFile, "\n TFQMRL Residual norm: %6.2e ", Rtmp) ;
MARKTIME(t2) ;
fprintf(msgFile, "\n CPU : Converges in time: %8.3f ", t2 - t1) ;
fprintf(msgFile, "\n # iterations = %d", Imv) ;
fprintf(msgFile, "\n\n after TFQMRL") ;
goto end;
};
/*
----------------
Even step
---------------
*/
DenseMtx_colCopy(vecY2, 0, vecY1, 0);
Rtmp=-Alpha;
DenseMtx_colGenAxpy(one, vecY2, 0, &Rtmp, vecV, 0);
/*
DenseMtx_zero(vecT) ;
InpMtx_nonsym_mmm(mtxA, vecT, one, vecY2) ;
*/
switch ( symmetryflag ) {
case SPOOLES_SYMMETRIC :
InpMtx_sym_gmmm(mtxA, zero, vecT, one, vecY2) ;
break ;
case SPOOLES_HERMITIAN :
fprintf(msgFile, "\n TFQMRL Matrix type wrong");
fprintf(msgFile, "\n Fatal error");
goto end;
case SPOOLES_NONSYMMETRIC :
InpMtx_nonsym_gmmm(mtxA, zero, vecT, one, vecY2) ;
break ;
default :
fprintf(msgFile, "\n TFQMRL Matrix type wrong");
fprintf(msgFile, "\n Fatal error");
goto end;
}
FrontMtx_solve(Precond, vecU2, vecT, Precond->manager,
cpus, msglvl, msgFile) ;
Imv++;
m = 2 * Iter ;
Rtmp = -Alpha;
DenseMtx_colGenAxpy(one, vecW, 0, &Rtmp, vecU2, 0);
Rtmp = Theta * Theta * Eta / Alpha ;
DenseMtx_colGenAxpy(&Rtmp, vecD, 0, one, vecY2, 0);
Theta = DenseMtx_twoNormOfColumn(vecW,0)/Tau;
Cee = 1.0/sqrt(1.0 + Theta*Theta);
Tau = Tau * Theta * Cee ;
Eta = Cee * Cee * Alpha ;
DenseMtx_colGenAxpy(one, vecX, 0, &Eta, vecD, 0);
fprintf(msgFile, "\n\n Even step at %d", Imv) ;
/*
----------------
Convergence Test for even step
---------------
*/
if (Tau * sqrt(m + 1) <= error_trol ) {
DenseMtx_colCopy(mtxX, 0, vecX, 0);
/*
DenseMtx_zero(vecT) ;
InpMtx_nonsym_mmm(mtxA, vecT, one, mtxX) ;
*/
switch ( symmetryflag ) {
case SPOOLES_SYMMETRIC :
InpMtx_sym_gmmm(mtxA, zero, vecT, one, mtxX) ;
break ;
case SPOOLES_HERMITIAN :
fprintf(msgFile, "\n TFQMRL Matrix type wrong");
fprintf(msgFile, "\n Fatal error");
goto end;
case SPOOLES_NONSYMMETRIC :
InpMtx_nonsym_gmmm(mtxA, zero, vecT, one, mtxX) ;
break ;
default :
fprintf(msgFile, "\n TFQMRL Matrix type wrong");
fprintf(msgFile, "\n Fatal error");
goto end;
}
DenseMtx_sub(vecT, mtxB) ;
Rtmp = DenseMtx_twoNormOfColumn(vecT,0);
fprintf(msgFile, "\n TFQMRL Residual norm: %6.2e ", Rtmp) ;
MARKTIME(t2) ;
fprintf(msgFile, "\n CPU : Converges in time: %8.3f ", t2 - t1) ;
fprintf(msgFile, "\n # iterations = %d", Imv) ;
fprintf(msgFile, "\n\n after TFQMRL") ;
goto end;
};
if (Rho == 0){
fprintf(msgFile, "\n\n Fatal Error, \n"
" TFQMRL Breakdown, Rho = 0 !!") ;
Imv = -1;
goto end;
};
DenseMtx_colDotProduct(vecW, 0, vecR, 0, &Rho_new);
Beta = Rho_new / Rho;
Rho = Rho_new ;
DenseMtx_colCopy(vecY1, 0, vecY2, 0);
DenseMtx_colGenAxpy(&Beta, vecY1, 0, one, vecW, 0);
/*
DenseMtx_zero(vecT) ;
InpMtx_nonsym_mmm(mtxA, vecT, one, vecY1) ;
*/
switch ( symmetryflag ) {
case SPOOLES_SYMMETRIC :
InpMtx_sym_gmmm(mtxA, zero, vecT, one, vecY1) ;
break ;
case SPOOLES_HERMITIAN :
fprintf(msgFile, "\n TFQMRL Matrix type wrong");
fprintf(msgFile, "\n Fatal error");
goto end;
case SPOOLES_NONSYMMETRIC :
InpMtx_nonsym_gmmm(mtxA, zero, vecT, one, vecY1) ;
break ;
default :
fprintf(msgFile, "\n TFQMRL Matrix type wrong");
fprintf(msgFile, "\n Fatal error");
goto end;
}
FrontMtx_solve(Precond, vecU1, vecT, Precond->manager,
cpus, msglvl, msgFile) ;
Imv++;
/* */
DenseMtx_colCopy(vecT, 0, vecU2, 0);
DenseMtx_colGenAxpy(one, vecT, 0, &Beta, vecV, 0);
DenseMtx_colCopy(vecV, 0, vecT, 0);
DenseMtx_colGenAxpy(&Beta, vecV, 0, one, vecU1, 0);
Rtmp = Tau*sqrt(m + 1)/Init_norm ;
fprintf(msgFile, "\n\n At iteration %d"
" the convergence ratio is %12.4e",
Imv, Rtmp) ;
}
/* End of while loop */
MARKTIME(t2) ;
fprintf(msgFile, "\n CPU : Total iteration time is : %8.3f ", t2 - t1) ;
fprintf(msgFile, "\n # iterations = %d", Imv) ;
fprintf(msgFile, "\n\n TFQMRL did not Converge !") ;
fprintf(msgFile, "\n\n after TFQMRL") ;
DenseMtx_colCopy(mtxX, 0, vecX, 0);
/*
------------------------
free the working storage
------------------------
*/
end:
DenseMtx_free(vecD) ;
DenseMtx_free(vecR) ;
DenseMtx_free(vecT) ;
DenseMtx_free(vecU1) ;
DenseMtx_free(vecU2) ;
DenseMtx_free(vecV) ;
DenseMtx_free(vecW) ;
DenseMtx_free(vecX) ;
DenseMtx_free(vecY1) ;
DenseMtx_free(vecY2) ;
fprintf(msgFile, "\n") ;
return(Imv) ; }
/*--------------------------------------------------------------------*/
int
main ( int argc, char *argv[] )
/*
-----------------------------------------------
test the DenseMtx_twoNormOfColumn routine.
when msglvl > 1, the output of this program
can be fed into Matlab to check for errors
created -- 98dec03, ycp
-----------------------------------------------
*/
{
DenseMtx *A ;
double t1, t2, value ;
Drand *drand ;
FILE *msgFile ;
int inc1, inc2, jcol, msglvl, nrow, ncol, seed, type ;
if ( argc != 10 ) {
fprintf(stdout,
"\n\n usage : %s msglvl msgFile type nrow ncol inc1 inc2 "
"\n , jcol, seed "
"\n msglvl -- message level"
"\n msgFile -- message file"
"\n type -- entries type"
"\n 1 -- real"
"\n 2 -- complex"
"\n nrow -- # of rows "
"\n ncol -- # of columns "
"\n inc1 -- row increment "
"\n inc2 -- column increment "
"\n jcol -- vector x: j-th column of A "
"\n seed -- random number seed"
"\n", argv[0]) ;
return(0) ;
}
if ( (msglvl = atoi(argv[1])) < 0 ) {
fprintf(stderr, "\n message level must be positive\n") ;
exit(-1) ;
}
if ( strcmp(argv[2], "stdout") == 0 ) {
msgFile = stdout ;
} else if ( (msgFile = fopen(argv[2], "a")) == NULL ) {
fprintf(stderr, "\n unable to open file %s\n", argv[2]) ;
return(-1) ;
}
type = atoi(argv[3]) ;
nrow = atoi(argv[4]) ;
ncol = atoi(argv[5]) ;
inc1 = atoi(argv[6]) ;
inc2 = atoi(argv[7]) ;
if ( type < 1 || type > 2 || nrow < 0 || ncol < 0
|| inc1 < 1 || inc2 < 1 ) {
fprintf(stderr,
"\n fatal error, type %d, nrow %d, ncol %d, inc1 %d, inc2 %d",
type, nrow, ncol, inc1, inc2) ;
exit(-1) ;
}
jcol = atoi(argv[8]) ;
seed = atoi(argv[9]) ;
fprintf(msgFile, "\n\n %% %s :"
"\n %% msglvl = %d"
"\n %% msgFile = %s"
"\n %% type = %d"
"\n %% nrow = %d"
"\n %% ncol = %d"
"\n %% inc1 = %d"
"\n %% inc2 = %d"
"\n %% jcol = %d"
"\n %% seed = %d"
"\n",
argv[0], msglvl, argv[2], type, nrow, ncol, inc1, inc2, jcol, seed) ;
/*
----------------------------
initialize the matrix object
----------------------------
*/
MARKTIME(t1) ;
A = DenseMtx_new() ;
DenseMtx_init(A, type, 0, 0, nrow, ncol, inc1, inc2) ;
MARKTIME(t2) ;
fprintf(msgFile, "\n %% CPU : %.3f to initialize matrix object",
t2 - t1) ;
MARKTIME(t1) ;
drand = Drand_new() ;
Drand_setSeed(drand, seed) ;
seed++ ;
Drand_setUniform(drand, -1.0, 1.0) ;
DenseMtx_fillRandomEntries(A, drand) ;
MARKTIME(t2) ;
fprintf(msgFile,
"\n %% CPU : %.3f to fill matrix with random numbers", t2 - t1) ;
if ( msglvl > 3 ) {
fprintf(msgFile, "\n matrix A") ;
DenseMtx_writeForHumanEye(A, msgFile) ;
}
if ( msglvl > 1 ) {
fprintf(msgFile, "\n %% matrix A") ;
fprintf(msgFile, "\n nrow = %d ;", nrow) ;
fprintf(msgFile, "\n ncol = %d ;", ncol) ;
fprintf(msgFile, "\n");
DenseMtx_writeForMatlab(A, "A", msgFile) ;
}
/*
--------------------------
compute the frobenius norm
--------------------------
*/
value = DenseMtx_twoNormOfColumn(A,jcol);
if ( msglvl > 1 ) {
fprintf(msgFile, "\n %% Two Norm = %e", value) ;
fprintf(msgFile, "\n");
fflush(msgFile) ;
}
/*
------------------------
free the working storage
------------------------
*/
DenseMtx_free(A) ;
Drand_free(drand) ;
return(1) ; }