PetscErrorCode MatDuplicate_HT(Mat N, MatDuplicateOption op, Mat* m)
{
Mat_HT *Na = (Mat_HT*)N->data;
PetscErrorCode ierr;
PetscFunctionBegin;
if (op == MAT_COPY_VALUES) {
ierr = MatHermitianTranspose(Na->A,MAT_INITIAL_MATRIX,m);CHKERRQ(ierr);
} else if (op == MAT_DO_NOT_COPY_VALUES) {
ierr = MatDuplicate(Na->A,MAT_DO_NOT_COPY_VALUES,m);CHKERRQ(ierr);
ierr = MatHermitianTranspose(*m,MAT_INPLACE_MATRIX,m);CHKERRQ(ierr);
} else SETERRQ(PetscObjectComm((PetscObject)N),PETSC_ERR_SUP,"MAT_SHARE_NONZERO_PATTERN not supported for this matrix type");
PetscFunctionReturn(0);
}
PetscInt main(PetscInt argc,char **args)
{
Mat A,As;
Vec x,y,ys;
PetscTruth flg,disp_mat=PETSC_FALSE,disp_vec=PETSC_FALSE;
PetscErrorCode ierr;
PetscMPIInt size,rank;
PetscInt m,i,j;
PetscScalar v,sigma2;
PetscRandom rctx;
PetscReal h2,sigma1=100.0,norm;
PetscInt dim,Ii,J,n = 3,use_random,rstart,rend;
PetscInitialize(&argc,&args,(char *)0,help);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(1,"This example requires complex numbers");
#endif
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL, "-display_mat", &disp_mat);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL, "-display_vec", &disp_vec);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
dim = n*n;
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);CHKERRQ(ierr);
ierr = MatSetType(A,MATAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL,"-norandom",&flg);CHKERRQ(ierr);
if (flg) use_random = 0;
else use_random = 1;
if (use_random) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(rctx,0.0,PETSC_i);CHKERRQ(ierr);
ierr = PetscRandomGetValue(rctx,&sigma2);CHKERRQ(ierr); /* RealPart(sigma2) == 0.0 */
} else {
sigma2 = 10.0*PETSC_i;
}
h2 = 1.0/((n+1)*(n+1));
ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
for (Ii=rstart; Ii<rend; Ii++) {
v = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {
J = Ii-n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (i<n-1) {
J = Ii+n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j>0) {
J = Ii-1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j<n-1) {
J = Ii+1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
v = 4.0 - sigma1*h2;
ierr = MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Check whether A is symmetric */
ierr = PetscOptionsHasName(PETSC_NULL, "-check_symmetric", &flg);CHKERRQ(ierr);
if (flg) {
Mat Trans;
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Trans);
ierr = MatEqual(A, Trans, &flg);
if (!flg) SETERRQ(PETSC_ERR_USER,"A is not symmetric");
ierr = MatDestroy(Trans);CHKERRQ(ierr);
}
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
/* make A complex Hermitian */
Ii = 0; J = dim-1;
if (Ii >= rstart && Ii < rend){
v = sigma2*h2; /* RealPart(v) = 0.0 */
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
Ii = dim-2; J = dim-1;
if (Ii >= rstart && Ii < rend){
v = sigma2*h2; /* RealPart(v) = 0.0 */
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Check whether A is Hermitian */
ierr = PetscOptionsHasName(PETSC_NULL, "-check_Hermitian", &flg);CHKERRQ(ierr);
if (flg) {
Mat Hermit;
if (disp_mat){
if (!rank) printf(" A:\n");
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatHermitianTranspose(A,MAT_INITIAL_MATRIX, &Hermit);
if (disp_mat){
if (!rank) printf(" A_Hermitian:\n");
ierr = MatView(Hermit,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatEqual(A, Hermit, &flg);
if (!flg) SETERRQ(PETSC_ERR_USER,"A is not Hermitian");
ierr = MatDestroy(Hermit);CHKERRQ(ierr);
}
ierr = MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);
/* Create a Hermitian matrix As in sbaij format */
ierr = MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&As);CHKERRQ(ierr);
if (disp_mat){
if (!rank) {ierr = PetscPrintf(PETSC_COMM_SELF," As:\n");CHKERRQ(ierr);}
ierr = MatView(As,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,n,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
if (use_random){
ierr = VecSetRandom(x,rctx);CHKERRQ(ierr);
} else {
ierr = VecSet(x,1.0);CHKERRQ(ierr);
}
/* Create vectors */
ierr = VecCreate(PETSC_COMM_WORLD,&y);CHKERRQ(ierr);
ierr = VecSetSizes(y,m,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(y);CHKERRQ(ierr);
ierr = VecDuplicate(y,&ys);CHKERRQ(ierr);
/* Test MatMult */
ierr = MatMult(A,x,y);CHKERRQ(ierr);
ierr = MatMult(As,x,ys);CHKERRQ(ierr);
if (disp_vec){
printf("y = A*x:\n");
ierr = VecView(y,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"ys = As*x:\n");
ierr = VecView(ys,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = VecAXPY(y,-1.0,ys);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_INFINITY,&norm);CHKERRQ(ierr);
if (norm > 1.e-12 || disp_vec){
printf("|| A*x - As*x || = %G\n",norm);
}
/* Free spaces */
if (use_random) {ierr = PetscRandomDestroy(rctx);CHKERRQ(ierr);}
ierr = MatDestroy(A);CHKERRQ(ierr);
ierr = MatDestroy(As);CHKERRQ(ierr);
ierr = VecDestroy(x);CHKERRQ(ierr);
ierr = VecDestroy(y);CHKERRQ(ierr);
ierr = VecDestroy(ys);CHKERRQ(ierr);
ierr = PetscFinalize();CHKERRQ(ierr);
return 0;
}
PetscInt main(PetscInt argc,char **args)
{
Mat A,As;
PetscBool flg,disp_mat=PETSC_FALSE;
PetscErrorCode ierr;
PetscMPIInt size,rank;
PetscInt i,j;
PetscScalar v,sigma2;
PetscRandom rctx;
PetscReal h2,sigma1=100.0;
PetscInt dim,Ii,J,n = 3,use_random,rstart,rend;
KSP ksp;
PC pc;
Mat F;
PetscInt nneg, nzero, npos;
PetscInitialize(&argc,&args,(char *)0,help);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,1,"This example requires complex numbers");
#endif
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL, "-display_mat", &disp_mat);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
dim = n*n;
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);CHKERRQ(ierr);
ierr = MatSetType(A,MATAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL,"-norandom",&flg);CHKERRQ(ierr);
if (flg) use_random = 0;
else use_random = 1;
if (use_random) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(rctx,0.0,PETSC_i);CHKERRQ(ierr);
ierr = PetscRandomGetValue(rctx,&sigma2);CHKERRQ(ierr); /* RealPart(sigma2) == 0.0 */
} else {
sigma2 = 10.0*PETSC_i;
}
h2 = 1.0/((n+1)*(n+1));
ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
for (Ii=rstart; Ii<rend; Ii++) {
v = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {
J = Ii-n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (i<n-1) {
J = Ii+n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j>0) {
J = Ii-1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
if (j<n-1) {
J = Ii+1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);}
v = 4.0 - sigma1*h2;
ierr = MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Check whether A is symmetric */
ierr = PetscOptionsHasName(PETSC_NULL, "-check_symmetric", &flg);CHKERRQ(ierr);
if (flg) {
Mat Trans;
ierr = MatTranspose(A,MAT_INITIAL_MATRIX, &Trans);
ierr = MatEqual(A, Trans, &flg);
if (!flg) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_USER,"A is not symmetric");
ierr = MatDestroy(&Trans);CHKERRQ(ierr);
}
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
/* make A complex Hermitian */
Ii = 0; J = dim-1;
if (Ii >= rstart && Ii < rend){
v = sigma2*h2; /* RealPart(v) = 0.0 */
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
Ii = dim-2; J = dim-1;
if (Ii >= rstart && Ii < rend){
v = sigma2*h2; /* RealPart(v) = 0.0 */
ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
v = -sigma2*h2;
ierr = MatSetValues(A,1,&J,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Check whether A is Hermitian */
ierr = PetscOptionsHasName(PETSC_NULL, "-check_Hermitian", &flg);CHKERRQ(ierr);
if (flg) {
Mat Hermit;
if (disp_mat){
if (!rank) printf(" A:\n");
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatHermitianTranspose(A,MAT_INITIAL_MATRIX, &Hermit);
if (disp_mat){
if (!rank) printf(" A_Hermitian:\n");
ierr = MatView(Hermit,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatEqual(A, Hermit, &flg);
if (!flg) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_USER,"A is not Hermitian");
ierr = MatDestroy(&Hermit);CHKERRQ(ierr);
}
ierr = MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);
/* Create a Hermitian matrix As in sbaij format */
ierr = MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&As);CHKERRQ(ierr);
if (disp_mat){
if (!rank) {ierr = PetscPrintf(PETSC_COMM_SELF," As:\n");CHKERRQ(ierr);}
ierr = MatView(As,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* Test MatGetInertia() */
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetType(ksp,KSPPREONLY);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,As,As,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCSetType(pc,PCCHOLESKY);CHKERRQ(ierr);
ierr = PCSetFromOptions(pc);CHKERRQ(ierr);
ierr = PCSetUp(pc);CHKERRQ(ierr);
ierr = PCFactorGetMatrix(pc,&F);CHKERRQ(ierr);
ierr = MatGetInertia(F,&nneg,&nzero,&npos);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
if (!rank){
ierr = PetscPrintf(PETSC_COMM_SELF," MatInertia: nneg: %D, nzero: %D, npos: %D\n",nneg,nzero,npos);CHKERRQ(ierr);
}
/* Free spaces */
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
if (use_random) {ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);}
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&As);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **argv)
{
Mat A,F,B,X,C,Aher,G;
Vec b,x,c,d,e;
PetscErrorCode ierr;
PetscInt m = 5,n,p,i,j,nrows,ncols;
PetscScalar *v,*barray,rval;
PetscReal norm,tol=1.e-12;
PetscMPIInt size,rank;
PetscRandom rand;
const PetscInt *rows,*cols;
IS isrows,iscols;
PetscBool mats_view=PETSC_FALSE;
MatFactorInfo finfo;
PetscInitialize(&argc,&argv,(char*) 0,help);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rand);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rand);CHKERRQ(ierr);
/* Get local dimensions of matrices */
ierr = PetscOptionsGetInt(NULL,"-m",&m,NULL);CHKERRQ(ierr);
n = m;
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
p = m/2;
ierr = PetscOptionsGetInt(NULL,"-p",&p,NULL);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,"-mats_view",&mats_view);CHKERRQ(ierr);
/* Create matrix A */
ierr = PetscPrintf(PETSC_COMM_WORLD," Create Elemental matrix A\n");CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,m,n,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
ierr = MatSetType(A,MATELEMENTAL);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
/* Set local matrix entries */
ierr = MatGetOwnershipIS(A,&isrows,&iscols);CHKERRQ(ierr);
ierr = ISGetLocalSize(isrows,&nrows);CHKERRQ(ierr);
ierr = ISGetIndices(isrows,&rows);CHKERRQ(ierr);
ierr = ISGetLocalSize(iscols,&ncols);CHKERRQ(ierr);
ierr = ISGetIndices(iscols,&cols);CHKERRQ(ierr);
ierr = PetscMalloc1(nrows*ncols,&v);CHKERRQ(ierr);
for (i=0; i<nrows; i++) {
for (j=0; j<ncols; j++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
v[i*ncols+j] = rval;
}
}
ierr = MatSetValues(A,nrows,rows,ncols,cols,v,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = ISRestoreIndices(isrows,&rows);CHKERRQ(ierr);
ierr = ISRestoreIndices(iscols,&cols);CHKERRQ(ierr);
ierr = ISDestroy(&isrows);CHKERRQ(ierr);
ierr = ISDestroy(&iscols);CHKERRQ(ierr);
ierr = PetscFree(v);CHKERRQ(ierr);
if (mats_view) {
ierr = PetscPrintf(PETSC_COMM_WORLD, "A: nrows %d, m %d; ncols %d, n %d\n",nrows,m,ncols,n);CHKERRQ(ierr);
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* Create rhs matrix B */
ierr = PetscPrintf(PETSC_COMM_WORLD," Create rhs matrix B\n");CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&B);CHKERRQ(ierr);
ierr = MatSetSizes(B,m,p,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
ierr = MatSetType(B,MATELEMENTAL);CHKERRQ(ierr);
ierr = MatSetFromOptions(B);CHKERRQ(ierr);
ierr = MatSetUp(B);CHKERRQ(ierr);
ierr = MatGetOwnershipIS(B,&isrows,&iscols);CHKERRQ(ierr);
ierr = ISGetLocalSize(isrows,&nrows);CHKERRQ(ierr);
ierr = ISGetIndices(isrows,&rows);CHKERRQ(ierr);
ierr = ISGetLocalSize(iscols,&ncols);CHKERRQ(ierr);
ierr = ISGetIndices(iscols,&cols);CHKERRQ(ierr);
ierr = PetscMalloc1(nrows*ncols,&v);CHKERRQ(ierr);
for (i=0; i<nrows; i++) {
for (j=0; j<ncols; j++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
v[i*ncols+j] = rval;
}
}
ierr = MatSetValues(B,nrows,rows,ncols,cols,v,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = ISRestoreIndices(isrows,&rows);CHKERRQ(ierr);
ierr = ISRestoreIndices(iscols,&cols);CHKERRQ(ierr);
ierr = ISDestroy(&isrows);CHKERRQ(ierr);
ierr = ISDestroy(&iscols);CHKERRQ(ierr);
ierr = PetscFree(v);CHKERRQ(ierr);
if (mats_view) {
ierr = PetscPrintf(PETSC_COMM_WORLD, "B: nrows %d, m %d; ncols %d, p %d\n",nrows,m,ncols,p);CHKERRQ(ierr);
ierr = MatView(B,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* Create rhs vector b and solution x (same size as b) */
ierr = VecCreate(PETSC_COMM_WORLD,&b);CHKERRQ(ierr);
ierr = VecSetSizes(b,m,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(b);CHKERRQ(ierr);
ierr = VecGetArray(b,&barray);CHKERRQ(ierr);
for (j=0; j<m; j++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
barray[j] = rval;
}
ierr = VecRestoreArray(b,&barray);CHKERRQ(ierr);
ierr = VecAssemblyBegin(b);CHKERRQ(ierr);
ierr = VecAssemblyEnd(b);CHKERRQ(ierr);
if (mats_view) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD, "[%d] b: m %d\n",rank,m);CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);CHKERRQ(ierr);
ierr = VecView(b,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = VecDuplicate(b,&x);CHKERRQ(ierr);
/* Create matrix X - same size as B */
ierr = PetscPrintf(PETSC_COMM_WORLD," Create solution matrix X\n");CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&X);CHKERRQ(ierr);
ierr = MatSetSizes(X,m,p,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
ierr = MatSetType(X,MATELEMENTAL);CHKERRQ(ierr);
ierr = MatSetFromOptions(X);CHKERRQ(ierr);
ierr = MatSetUp(X);CHKERRQ(ierr);
ierr = MatAssemblyBegin(X,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(X,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Cholesky factorization */
/*------------------------*/
ierr = PetscPrintf(PETSC_COMM_WORLD," Create Elemental matrix Aher\n");CHKERRQ(ierr);
ierr = MatHermitianTranspose(A,MAT_INITIAL_MATRIX,&Aher);CHKERRQ(ierr);
ierr = MatAXPY(Aher,1.0,A,SAME_NONZERO_PATTERN);CHKERRQ(ierr); /* Aher = A + A^T */
if (!rank) { /* add 100.0 to diagonals of Aher to make it spd */
PetscInt M,N;
ierr = MatGetSize(Aher,&M,&N);CHKERRQ(ierr);
for (i=0; i<M; i++) {
rval = 100.0;
ierr = MatSetValues(Aher,1,&i,1,&i,&rval,ADD_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(Aher,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Aher,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (mats_view) {
ierr = PetscPrintf(PETSC_COMM_WORLD, "Aher:\n");CHKERRQ(ierr);
ierr = MatView(Aher,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* Cholesky factorization */
/*------------------------*/
ierr = PetscPrintf(PETSC_COMM_WORLD," Test Cholesky Solver \n");CHKERRQ(ierr);
/* In-place Cholesky */
/* Create matrix factor G, then copy Aher to G */
ierr = MatCreate(PETSC_COMM_WORLD,&G);CHKERRQ(ierr);
ierr = MatSetSizes(G,m,n,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
ierr = MatSetType(G,MATELEMENTAL);CHKERRQ(ierr);
ierr = MatSetFromOptions(G);CHKERRQ(ierr);
ierr = MatSetUp(G);CHKERRQ(ierr);
ierr = MatAssemblyBegin(G,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(G,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatCopy(Aher,G,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
/* Only G = U^T * U is implemented for now */
ierr = MatCholeskyFactor(G,0,0);CHKERRQ(ierr);
if (mats_view) {
ierr = PetscPrintf(PETSC_COMM_WORLD, "Cholesky Factor G:\n");CHKERRQ(ierr);
ierr = MatView(G,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* Solve U^T * U x = b and U^T * U X = B */
ierr = MatSolve(G,b,x);CHKERRQ(ierr);
ierr = MatMatSolve(G,B,X);CHKERRQ(ierr);
ierr = MatDestroy(&G);CHKERRQ(ierr);
/* Out-place Cholesky */
ierr = MatGetFactor(Aher,MATSOLVERELEMENTAL,MAT_FACTOR_CHOLESKY,&G);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(G,Aher,0,&finfo);CHKERRQ(ierr);
ierr = MatCholeskyFactorNumeric(G,Aher,&finfo);CHKERRQ(ierr);
if (mats_view) {
ierr = MatView(G,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatSolve(G,b,x);CHKERRQ(ierr);
ierr = MatMatSolve(G,B,X);CHKERRQ(ierr);
ierr = MatDestroy(&G);CHKERRQ(ierr);
/* Check norm(Aher*x - b) */
ierr = VecCreate(PETSC_COMM_WORLD,&c);CHKERRQ(ierr);
ierr = VecSetSizes(c,m,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(c);CHKERRQ(ierr);
ierr = MatMult(Aher,x,c);CHKERRQ(ierr);
ierr = VecAXPY(c,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(c,NORM_1,&norm);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Warning: |Aher*x - b| for Cholesky %g\n",(double)norm);CHKERRQ(ierr);
}
/* Check norm(Aher*X - B) */
ierr = MatMatMult(Aher,X,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&C);CHKERRQ(ierr);
ierr = MatAXPY(C,-1.0,B,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatNorm(C,NORM_1,&norm);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Warning: |Aher*X - B| for Cholesky %g\n",(double)norm);CHKERRQ(ierr);
}
/* LU factorization */
/*------------------*/
ierr = PetscPrintf(PETSC_COMM_WORLD," Test LU Solver \n");CHKERRQ(ierr);
/* In-place LU */
/* Create matrix factor F, then copy A to F */
ierr = MatCreate(PETSC_COMM_WORLD,&F);CHKERRQ(ierr);
ierr = MatSetSizes(F,m,n,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
ierr = MatSetType(F,MATELEMENTAL);CHKERRQ(ierr);
ierr = MatSetFromOptions(F);CHKERRQ(ierr);
ierr = MatSetUp(F);CHKERRQ(ierr);
ierr = MatAssemblyBegin(F,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(F,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatCopy(A,F,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
/* Create vector d to test MatSolveAdd() */
ierr = VecDuplicate(x,&d);CHKERRQ(ierr);
ierr = VecCopy(x,d);CHKERRQ(ierr);
/* PF=LU or F=LU factorization - perms is ignored by Elemental;
set finfo.dtcol !0 or 0 to enable/disable partial pivoting */
finfo.dtcol = 0.1;
ierr = MatLUFactor(F,0,0,&finfo);CHKERRQ(ierr);
/* Solve LUX = PB or LUX = B */
ierr = MatSolveAdd(F,b,d,x);CHKERRQ(ierr);
ierr = MatMatSolve(F,B,X);CHKERRQ(ierr);
ierr = MatDestroy(&F);CHKERRQ(ierr);
/* Check norm(A*X - B) */
ierr = VecCreate(PETSC_COMM_WORLD,&e);CHKERRQ(ierr);
ierr = VecSetSizes(e,m,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(e);CHKERRQ(ierr);
ierr = MatMult(A,x,c);CHKERRQ(ierr);
ierr = MatMult(A,d,e);CHKERRQ(ierr);
ierr = VecAXPY(c,-1.0,e);CHKERRQ(ierr);
ierr = VecAXPY(c,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(c,NORM_1,&norm);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Warning: |A*x - b| for LU %g\n",(double)norm);CHKERRQ(ierr);
}
ierr = MatMatMult(A,X,MAT_REUSE_MATRIX,PETSC_DEFAULT,&C);CHKERRQ(ierr);
ierr = MatAXPY(C,-1.0,B,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatNorm(C,NORM_1,&norm);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Warning: |A*X - B| for LU %g\n",(double)norm);CHKERRQ(ierr);
}
/* Out-place LU */
ierr = MatGetFactor(A,MATSOLVERELEMENTAL,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
ierr = MatLUFactorSymbolic(F,A,0,0,&finfo);CHKERRQ(ierr);
ierr = MatLUFactorNumeric(F,A,&finfo);CHKERRQ(ierr);
if (mats_view) {
ierr = MatView(F,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
ierr = MatSolve(F,b,x);CHKERRQ(ierr);
ierr = MatMatSolve(F,B,X);CHKERRQ(ierr);
ierr = MatDestroy(&F);CHKERRQ(ierr);
/* Free space */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&Aher);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&X);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = VecDestroy(&c);CHKERRQ(ierr);
ierr = VecDestroy(&d);CHKERRQ(ierr);
ierr = VecDestroy(&e);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
