static PetscErrorCode PCSetup_ICC(PC pc)
{
PC_ICC *icc = (PC_ICC*)pc->data;
IS perm,cperm;
PetscErrorCode ierr;
MatInfo info;
PetscFunctionBegin;
ierr = MatGetOrdering(pc->pmat, ((PC_Factor*)icc)->ordering,&perm,&cperm);CHKERRQ(ierr);
if (!pc->setupcalled) {
if (!((PC_Factor*)icc)->fact) {
ierr = MatGetFactor(pc->pmat,((PC_Factor*)icc)->solvertype,MAT_FACTOR_ICC,&((PC_Factor*)icc)->fact);CHKERRQ(ierr);
}
ierr = MatICCFactorSymbolic(((PC_Factor*)icc)->fact,pc->pmat,perm,&((PC_Factor*)icc)->info);CHKERRQ(ierr);
} else if (pc->flag != SAME_NONZERO_PATTERN) {
ierr = MatDestroy(&((PC_Factor*)icc)->fact);CHKERRQ(ierr);
ierr = MatGetFactor(pc->pmat,((PC_Factor*)icc)->solvertype,MAT_FACTOR_ICC,&((PC_Factor*)icc)->fact);CHKERRQ(ierr);
ierr = MatICCFactorSymbolic(((PC_Factor*)icc)->fact,pc->pmat,perm,&((PC_Factor*)icc)->info);CHKERRQ(ierr);
}
ierr = MatGetInfo(((PC_Factor*)icc)->fact,MAT_LOCAL,&info);CHKERRQ(ierr);
icc->actualfill = info.fill_ratio_needed;
ierr = ISDestroy(&cperm);CHKERRQ(ierr);
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = MatCholeskyFactorNumeric(((PC_Factor*)icc)->fact,pc->pmat,&((PC_Factor*)icc)->info);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **args)
{
PetscMPIInt size;
PetscErrorCode ierr;
Vec x,y,b,s1,s2;
Mat A; /* linear system matrix */
Mat sA,sB,sC; /* symmetric part of the matrices */
PetscInt n,mbs=16,bs=1,nz=3,prob=1,i,j,k1,k2,col[3],lf,block, row,Ii,J,n1,inc;
PetscReal norm1,norm2,rnorm,tol=PETSC_SMALL;
PetscScalar neg_one = -1.0,four=4.0,value[3];
IS perm, iscol;
PetscRandom rdm;
PetscBool doIcc=PETSC_TRUE,equal;
MatInfo minfo1,minfo2;
MatFactorInfo factinfo;
MatType type;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This is a uniprocessor example only!");
ierr = PetscOptionsGetInt(NULL,"-bs",&bs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-mbs",&mbs,NULL);CHKERRQ(ierr);
n = mbs*bs;
ierr = MatCreate(PETSC_COMM_SELF,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetType(A,MATSEQBAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSeqBAIJSetPreallocation(A,bs,nz,NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_SELF,&sA);CHKERRQ(ierr);
ierr = MatSetSizes(sA,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetType(sA,MATSEQSBAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(sA);CHKERRQ(ierr);
ierr = MatGetType(sA,&type);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)sA,MATSEQSBAIJ,&doIcc);CHKERRQ(ierr);
ierr = MatSeqSBAIJSetPreallocation(sA,bs,nz,NULL);CHKERRQ(ierr);
ierr = MatSetOption(sA,MAT_IGNORE_LOWER_TRIANGULAR,PETSC_TRUE);CHKERRQ(ierr);
/* Test MatGetOwnershipRange() */
ierr = MatGetOwnershipRange(A,&Ii,&J);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(sA,&i,&j);CHKERRQ(ierr);
if (i-Ii || j-J) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetOwnershipRange() in MatSBAIJ format\n");CHKERRQ(ierr);
}
/* Assemble matrix */
if (bs == 1) {
ierr = PetscOptionsGetInt(NULL,"-test_problem",&prob,NULL);CHKERRQ(ierr);
if (prob == 1) { /* tridiagonal matrix */
value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
for (i=1; i<n-1; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = n - 1; col[0]=0; col[1] = n - 2; col[2] = n - 1;
value[0]= 0.1; value[1]=-1; value[2]=2;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0;
col[0] = n-1; col[1] = 1; col[2] = 0;
value[0] = 0.1; value[1] = -1.0; value[2] = 2;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
} else if (prob ==2) { /* matrix for the five point stencil */
n1 = (PetscInt) (PetscSqrtReal((PetscReal)n) + 0.001);
if (n1*n1 - n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"sqrt(n) must be a positive interger!");
for (i=0; i<n1; i++) {
for (j=0; j<n1; j++) {
Ii = j + n1*i;
if (i>0) {
J = Ii - n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (i<n1-1) {
J = Ii + n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j>0) {
J = Ii - 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j<n1-1) {
J = Ii + 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatSetValues(A,1,&Ii,1,&Ii,&four,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&Ii,&four,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
} else { /* bs > 1 */
for (block=0; block<n/bs; block++) {
/* diagonal blocks */
value[0] = -1.0; value[1] = 4.0; value[2] = -1.0;
for (i=1+block*bs; i<bs-1+block*bs; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = bs - 1+block*bs; col[0] = bs - 2+block*bs; col[1] = bs - 1+block*bs;
value[0]=-1.0; value[1]=4.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0+block*bs; col[0] = 0+block*bs; col[1] = 1+block*bs;
value[0]=4.0; value[1] = -1.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
/* off-diagonal blocks */
value[0]=-1.0;
for (i=0; i<(n/bs-1)*bs; i++) {
col[0]=i+bs;
ierr = MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
col[0]=i; row=i+bs;
ierr = MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Test MatGetInfo() of A and sA */
ierr = MatGetInfo(A,MAT_LOCAL,&minfo1);CHKERRQ(ierr);
ierr = MatGetInfo(sA,MAT_LOCAL,&minfo2);CHKERRQ(ierr);
/*
printf("A matrix nonzeros (BAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo1.nz_used,(int)minfo1.nz_allocated);
printf("sA matrix nonzeros(SBAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo2.nz_used,(int)minfo2.nz_allocated);
*/
i = (int) (minfo1.nz_used - minfo2.nz_used);
j = (int) (minfo1.nz_allocated - minfo2.nz_allocated);
k1 = (int) (minfo1.nz_allocated - minfo1.nz_used);
k2 = (int) (minfo2.nz_allocated - minfo2.nz_used);
if (i < 0 || j < 0 || k1 < 0 || k2 < 0) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error (compare A and sA): MatGetInfo()\n");CHKERRQ(ierr);
}
/* Test MatDuplicate() */
ierr = MatNorm(A,NORM_FROBENIUS,&norm1);CHKERRQ(ierr);
ierr = MatDuplicate(sA,MAT_COPY_VALUES,&sB);CHKERRQ(ierr);
ierr = MatEqual(sA,sB,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"Error in MatDuplicate()");
/* Test MatNorm() */
ierr = MatNorm(A,NORM_FROBENIUS,&norm1);CHKERRQ(ierr);
ierr = MatNorm(sB,NORM_FROBENIUS,&norm2);CHKERRQ(ierr);
rnorm = PetscAbsReal(norm1-norm2)/norm2;
if (rnorm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_FROBENIUS, NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_INFINITY,&norm1);CHKERRQ(ierr);
ierr = MatNorm(sB,NORM_INFINITY,&norm2);CHKERRQ(ierr);
rnorm = PetscAbsReal(norm1-norm2)/norm2;
if (rnorm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_INFINITY(), NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_1,&norm1);CHKERRQ(ierr);
ierr = MatNorm(sB,NORM_1,&norm2);CHKERRQ(ierr);
rnorm = PetscAbsReal(norm1-norm2)/norm2;
if (rnorm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_INFINITY(), NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
}
/* Test MatGetInfo(), MatGetSize(), MatGetBlockSize() */
ierr = MatGetInfo(A,MAT_LOCAL,&minfo1);CHKERRQ(ierr);
ierr = MatGetInfo(sB,MAT_LOCAL,&minfo2);CHKERRQ(ierr);
/*
printf("matrix nonzeros (BAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo1.nz_used,(int)minfo1.nz_allocated);
printf("matrix nonzeros(SBAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo2.nz_used,(int)minfo2.nz_allocated);
*/
i = (int) (minfo1.nz_used - minfo2.nz_used);
j = (int) (minfo1.nz_allocated - minfo2.nz_allocated);
k1 = (int) (minfo1.nz_allocated - minfo1.nz_used);
k2 = (int) (minfo2.nz_allocated - minfo2.nz_used);
if (i < 0 || j < 0 || k1 < 0 || k2 < 0) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error(compare A and sB): MatGetInfo()\n");CHKERRQ(ierr);
}
ierr = MatGetSize(A,&Ii,&J);CHKERRQ(ierr);
ierr = MatGetSize(sB,&i,&j);CHKERRQ(ierr);
if (i-Ii || j-J) {
PetscPrintf(PETSC_COMM_SELF,"Error: MatGetSize()\n");CHKERRQ(ierr);
}
ierr = MatGetBlockSize(A, &Ii);CHKERRQ(ierr);
ierr = MatGetBlockSize(sB, &i);CHKERRQ(ierr);
if (i-Ii) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetBlockSize()\n");CHKERRQ(ierr);
}
ierr = PetscRandomCreate(PETSC_COMM_SELF,&rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,n,&x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&s1);CHKERRQ(ierr);
ierr = VecDuplicate(x,&s2);CHKERRQ(ierr);
ierr = VecDuplicate(x,&y);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
/* Test MatDiagonalScale(), MatGetDiagonal(), MatScale() */
#if !defined(PETSC_USE_COMPLEX)
/* Scaling matrix with complex numbers results non-spd matrix,
causing crash of MatForwardSolve() and MatBackwardSolve() */
ierr = MatDiagonalScale(A,x,x);CHKERRQ(ierr);
ierr = MatDiagonalScale(sB,x,x);CHKERRQ(ierr);
ierr = MatMultEqual(A,sB,10,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"Error in MatDiagonalScale");
ierr = MatGetDiagonal(A,s1);CHKERRQ(ierr);
ierr = MatGetDiagonal(sB,s2);CHKERRQ(ierr);
ierr = VecAXPY(s2,neg_one,s1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm1);CHKERRQ(ierr);
if (norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatGetDiagonal(), ||s1-s2||=%G\n",norm1);CHKERRQ(ierr);
}
{
PetscScalar alpha=0.1;
ierr = MatScale(A,alpha);CHKERRQ(ierr);
ierr = MatScale(sB,alpha);CHKERRQ(ierr);
}
#endif
/* Test MatGetRowMaxAbs() */
ierr = MatGetRowMaxAbs(A,s1,NULL);CHKERRQ(ierr);
ierr = MatGetRowMaxAbs(sB,s2,NULL);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatGetRowMaxAbs() \n");CHKERRQ(ierr);
}
/* Test MatMult() */
for (i=0; i<40; i++) {
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
ierr = MatMult(A,x,s1);CHKERRQ(ierr);
ierr = MatMult(sB,x,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMult(), norm1-norm2: %G\n",norm1);CHKERRQ(ierr);
}
}
/* MatMultAdd() */
for (i=0; i<40; i++) {
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
ierr = VecSetRandom(y,rdm);CHKERRQ(ierr);
ierr = MatMultAdd(A,x,y,s1);CHKERRQ(ierr);
ierr = MatMultAdd(sB,x,y,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatMultAdd(), norm1-norm2: %G\n",norm1);CHKERRQ(ierr);
}
}
/* Test MatCholeskyFactor(), MatICCFactor() with natural ordering */
ierr = MatGetOrdering(A,MATORDERINGNATURAL,&perm,&iscol);CHKERRQ(ierr);
ierr = ISDestroy(&iscol);CHKERRQ(ierr);
norm1 = tol;
inc = bs;
/* initialize factinfo */
ierr = PetscMemzero(&factinfo,sizeof(MatFactorInfo));CHKERRQ(ierr);
for (lf=-1; lf<10; lf += inc) {
if (lf==-1) { /* Cholesky factor of sB (duplicate sA) */
factinfo.fill = 5.0;
ierr = MatGetFactor(sB,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&sC);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(sC,sB,perm,&factinfo);CHKERRQ(ierr);
} else if (!doIcc) break;
else { /* incomplete Cholesky factor */
factinfo.fill = 5.0;
factinfo.levels = lf;
ierr = MatGetFactor(sB,MATSOLVERPETSC,MAT_FACTOR_ICC,&sC);CHKERRQ(ierr);
ierr = MatICCFactorSymbolic(sC,sB,perm,&factinfo);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorNumeric(sC,sB,&factinfo);CHKERRQ(ierr);
/* MatView(sC, PETSC_VIEWER_DRAW_WORLD); */
/* test MatGetDiagonal on numeric factor */
/*
if (lf == -1) {
ierr = MatGetDiagonal(sC,s1);CHKERRQ(ierr);
printf(" in ex74.c, diag: \n");
ierr = VecView(s1,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
*/
ierr = MatMult(sB,x,b);CHKERRQ(ierr);
/* test MatForwardSolve() and MatBackwardSolve() */
if (lf == -1) {
ierr = MatForwardSolve(sC,b,s1);CHKERRQ(ierr);
ierr = MatBackwardSolve(sC,s1,s2);CHKERRQ(ierr);
ierr = VecAXPY(s2,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&norm2);CHKERRQ(ierr);
if (10*norm1 < norm2) {
ierr = PetscPrintf(PETSC_COMM_SELF,"MatForwardSolve and BackwardSolve: Norm of error=%G, bs=%d\n",norm2,bs);CHKERRQ(ierr);
}
}
/* test MatSolve() */
ierr = MatSolve(sC,b,y);CHKERRQ(ierr);
ierr = MatDestroy(&sC);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(y,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr);
/* printf("lf: %d, error: %G\n", lf,norm2); */
if (10*norm1 < norm2 && lf-inc != -1) {
ierr = PetscPrintf(PETSC_COMM_SELF,"lf=%D, %D, Norm of error=%G, %G\n",lf-inc,lf,norm1,norm2);CHKERRQ(ierr);
}
norm1 = norm2;
if (norm2 < tol && lf != -1) break;
}
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&sB);CHKERRQ(ierr);
ierr = MatDestroy(&sA);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&s1);CHKERRQ(ierr);
ierr = VecDestroy(&s2);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
Example: mpiexec -n <np> ./ex168 -f <matrix binary file> \n\n";
#include <petscmat.h>
int main(int argc,char **args)
{
Mat A,F;
Vec u,x,b;
PetscErrorCode ierr;
PetscMPIInt rank,size;
PetscInt m,n,nfact;
PetscReal norm,tol=1.e-12,Anorm;
IS perm,iperm;
MatFactorInfo info;
PetscBool flg,testMatSolve=PETSC_TRUE;
PetscViewer fd; /* viewer */
char file[PETSC_MAX_PATH_LEN]; /* input file name */
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);
/* Determine file from which we read the matrix A */
ierr = PetscOptionsGetString(NULL,NULL,"-f",file,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_WORLD,1,"Must indicate binary file with the -f option");
/* Load matrix A */
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file,FILE_MODE_READ,&fd);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatLoad(A,fd);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&b);CHKERRQ(ierr);
ierr = VecLoad(b,fd);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&fd);CHKERRQ(ierr);
ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
if (m != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ, "This example is not intended for rectangular matrices (%d, %d)", m, n);
ierr = MatNorm(A,NORM_INFINITY,&Anorm);CHKERRQ(ierr);
/* Create vectors */
ierr = VecDuplicate(b,&x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&u);CHKERRQ(ierr); /* save the true solution */
/* Test Cholesky Factorization */
ierr = MatGetOrdering(A,MATORDERINGNATURAL,&perm,&iperm);CHKERRQ(ierr);
if (!rank) printf(" Clique Cholesky:\n");
ierr = MatGetFactor(A,MATSOLVERCLIQUE,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
info.fill = 5.0;
ierr = MatCholeskyFactorSymbolic(F,A,perm,&info);CHKERRQ(ierr);
for (nfact = 0; nfact < 1; nfact++) {
if (!rank) printf(" %d-the Cholesky numfactorization \n",nfact);
ierr = MatCholeskyFactorNumeric(F,A,&info);CHKERRQ(ierr);
/* Test MatSolve() */
if (testMatSolve && nfact == 2) {
ierr = MatSolve(F,b,x);CHKERRQ(ierr);
/* Check the residual */
ierr = MatMult(A,x,u);CHKERRQ(ierr);
ierr = VecAXPY(u,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(u,NORM_INFINITY,&norm);CHKERRQ(ierr);
/* if (norm > tol) { */
if (!rank) {
ierr = PetscPrintf(PETSC_COMM_SELF,"MatSolve: rel residual %g/%g = %g, LU numfact %d\n",norm,Anorm,norm/Anorm,nfact);CHKERRQ(ierr);
}
/*} */
}
}
/* Free data structures */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&F);CHKERRQ(ierr);
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = ISDestroy(&iperm);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **args)
{
Vec x,y,b;
Mat A; /* linear system matrix */
Mat sA,sC; /* symmetric part of the matrices */
PetscInt n,mbs=16,bs=1,nz=3,prob=1,i,j,col[3],block, row,Ii,J,n1,lvl;
PetscErrorCode ierr;
PetscMPIInt size;
PetscReal norm2,tol=1.e-10,err[10];
PetscScalar neg_one = -1.0,four=4.0,value[3];
IS perm,cperm;
PetscRandom rdm;
PetscBool reorder = PETSC_FALSE,displ = PETSC_FALSE;
MatFactorInfo factinfo;
PetscBool equal;
PetscBool TestAIJ = PETSC_FALSE,TestBAIJ = PETSC_TRUE;
PetscInt TestShift=0;
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only!");
ierr = PetscOptionsGetInt(NULL,NULL,"-bs",&bs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-mbs",&mbs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-reorder",&reorder,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-testaij",&TestAIJ,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-testShift",&TestShift,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-displ",&displ,NULL);CHKERRQ(ierr);
n = mbs*bs;
if (TestAIJ) { /* A is in aij format */
ierr = MatCreateSeqAIJ(PETSC_COMM_WORLD,n,n,nz,NULL,&A);CHKERRQ(ierr);
TestBAIJ = PETSC_FALSE;
} else { /* A is in baij format */
ierr =MatCreateSeqBAIJ(PETSC_COMM_WORLD,bs,n,n,nz,NULL,&A);CHKERRQ(ierr);
TestAIJ = PETSC_FALSE;
}
/* Assemble matrix */
if (bs == 1) {
ierr = PetscOptionsGetInt(NULL,NULL,"-test_problem",&prob,NULL);CHKERRQ(ierr);
if (prob == 1) { /* tridiagonal matrix */
value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
for (i=1; i<n-1; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = n - 1; col[0]=0; col[1] = n - 2; col[2] = n - 1;
value[0]= 0.1; value[1]=-1; value[2]=2;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0; col[0] = 0; col[1] = 1; col[2]=n-1;
value[0] = 2.0; value[1] = -1.0; value[2]=0.1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
} else if (prob ==2) { /* matrix for the five point stencil */
n1 = (PetscInt) (PetscSqrtReal((PetscReal)n) + 0.001);
if (n1*n1 - n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"sqrt(n) must be a positive interger!");
for (i=0; i<n1; i++) {
for (j=0; j<n1; j++) {
Ii = j + n1*i;
if (i>0) {
J = Ii - n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (i<n1-1) {
J = Ii + n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j>0) {
J = Ii - 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j<n1-1) {
J = Ii + 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatSetValues(A,1,&Ii,1,&Ii,&four,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
} else { /* bs > 1 */
for (block=0; block<n/bs; block++) {
/* diagonal blocks */
value[0] = -1.0; value[1] = 4.0; value[2] = -1.0;
for (i=1+block*bs; i<bs-1+block*bs; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = bs - 1+block*bs; col[0] = bs - 2+block*bs; col[1] = bs - 1+block*bs;
value[0]=-1.0; value[1]=4.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0+block*bs; col[0] = 0+block*bs; col[1] = 1+block*bs;
value[0]=4.0; value[1] = -1.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
/* off-diagonal blocks */
value[0]=-1.0;
for (i=0; i<(n/bs-1)*bs; i++) {
col[0]=i+bs;
ierr = MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
col[0]=i; row=i+bs;
ierr = MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
}
if (TestShift) {
/* set diagonals in the 0-th block as 0 for testing shift numerical factor */
for (i=0; i<bs; i++) {
row = i; col[0] = i; value[0] = 0.0;
ierr = MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Test MatConvert */
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&sA);CHKERRQ(ierr);
ierr = MatMultEqual(A,sA,20,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"A != sA");
/* Test MatGetOwnershipRange() */
ierr = MatGetOwnershipRange(A,&Ii,&J);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(sA,&i,&j);CHKERRQ(ierr);
if (i-Ii || j-J) {
PetscPrintf(PETSC_COMM_SELF,"Error: MatGetOwnershipRange() in MatSBAIJ format\n");CHKERRQ(ierr);
}
/* Vectors */
ierr = PetscRandomCreate(PETSC_COMM_SELF,&rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,n,&x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecDuplicate(x,&y);CHKERRQ(ierr);
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
/* Test MatReordering() - not work on sbaij matrix */
if (reorder) {
ierr = MatGetOrdering(A,MATORDERINGRCM,&perm,&cperm);CHKERRQ(ierr);
} else {
ierr = MatGetOrdering(A,MATORDERINGNATURAL,&perm,&cperm);CHKERRQ(ierr);
}
ierr = ISDestroy(&cperm);CHKERRQ(ierr);
/* initialize factinfo */
ierr = MatFactorInfoInitialize(&factinfo);CHKERRQ(ierr);
if (TestShift == 1) {
factinfo.shifttype = (PetscReal)MAT_SHIFT_NONZERO;
factinfo.shiftamount = 0.1;
} else if (TestShift == 2) {
factinfo.shifttype = (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE;
}
/* Test MatCholeskyFactor(), MatICCFactor() */
/*------------------------------------------*/
/* Test aij matrix A */
if (TestAIJ) {
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"AIJ: \n");CHKERRQ(ierr);
}
i = 0;
for (lvl=-1; lvl<10; lvl++) {
if (lvl==-1) { /* Cholesky factor */
factinfo.fill = 5.0;
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&sC);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(sC,A,perm,&factinfo);CHKERRQ(ierr);
} else { /* incomplete Cholesky factor */
factinfo.fill = 5.0;
factinfo.levels = lvl;
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_ICC,&sC);CHKERRQ(ierr);
ierr = MatICCFactorSymbolic(sC,A,perm,&factinfo);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorNumeric(sC,A,&factinfo);CHKERRQ(ierr);
ierr = MatMult(A,x,b);CHKERRQ(ierr);
ierr = MatSolve(sC,b,y);CHKERRQ(ierr);
ierr = MatDestroy(&sC);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(y,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr);
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD," lvl: %D, error: %g\n", lvl,(double)norm2);CHKERRQ(ierr);
}
err[i++] = norm2;
}
}
/* Test baij matrix A */
if (TestBAIJ) {
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"BAIJ: \n");CHKERRQ(ierr);
}
i = 0;
for (lvl=-1; lvl<10; lvl++) {
if (lvl==-1) { /* Cholesky factor */
factinfo.fill = 5.0;
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&sC);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(sC,A,perm,&factinfo);CHKERRQ(ierr);
} else { /* incomplete Cholesky factor */
factinfo.fill = 5.0;
factinfo.levels = lvl;
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_ICC,&sC);CHKERRQ(ierr);
ierr = MatICCFactorSymbolic(sC,A,perm,&factinfo);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorNumeric(sC,A,&factinfo);CHKERRQ(ierr);
ierr = MatMult(A,x,b);CHKERRQ(ierr);
ierr = MatSolve(sC,b,y);CHKERRQ(ierr);
ierr = MatDestroy(&sC);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(y,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr);
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD," lvl: %D, error: %g\n", lvl,(double)norm2);CHKERRQ(ierr);
}
err[i++] = norm2;
}
}
/* Test sbaij matrix sA */
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"SBAIJ: \n");CHKERRQ(ierr);
}
i = 0;
for (lvl=-1; lvl<10; lvl++) {
if (lvl==-1) { /* Cholesky factor */
factinfo.fill = 5.0;
ierr = MatGetFactor(sA,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&sC);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(sC,sA,perm,&factinfo);CHKERRQ(ierr);
} else { /* incomplete Cholesky factor */
factinfo.fill = 5.0;
factinfo.levels = lvl;
ierr = MatGetFactor(sA,MATSOLVERPETSC,MAT_FACTOR_ICC,&sC);CHKERRQ(ierr);
ierr = MatICCFactorSymbolic(sC,sA,perm,&factinfo);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorNumeric(sC,sA,&factinfo);CHKERRQ(ierr);
if (lvl==0 && bs==1) { /* Test inplace ICC(0) for sbaij sA - does not work for new datastructure */
/*
Mat B;
ierr = MatDuplicate(sA,MAT_COPY_VALUES,&B);CHKERRQ(ierr);
ierr = MatICCFactor(B,perm,&factinfo);CHKERRQ(ierr);
ierr = MatEqual(sC,B,&equal);CHKERRQ(ierr);
if (!equal) {
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"in-place Cholesky factor != out-place Cholesky factor");
}
ierr = MatDestroy(&B);CHKERRQ(ierr);
*/
}
ierr = MatMult(sA,x,b);CHKERRQ(ierr);
ierr = MatSolve(sC,b,y);CHKERRQ(ierr);
/* Test MatSolves() */
if (bs == 1) {
Vecs xx,bb;
ierr = VecsCreateSeq(PETSC_COMM_SELF,n,4,&xx);CHKERRQ(ierr);
ierr = VecsDuplicate(xx,&bb);CHKERRQ(ierr);
ierr = MatSolves(sC,bb,xx);CHKERRQ(ierr);
ierr = VecsDestroy(xx);CHKERRQ(ierr);
ierr = VecsDestroy(bb);CHKERRQ(ierr);
}
ierr = MatDestroy(&sC);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(y,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr);
if (displ) {
ierr = PetscPrintf(PETSC_COMM_WORLD," lvl: %D, error: %g\n", lvl,(double)norm2);CHKERRQ(ierr);
}
err[i] -= norm2;
if (err[i] > tol) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_USER," level: %d, err: %g\n", lvl,(double)err[i]);
}
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&sA);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **args)
{
Mat C,F,Cpetsc,Csymm;
Vec u,x,b,bpla;
PetscErrorCode ierr;
PetscMPIInt rank,nproc;
PetscInt i,j,k,M = 10,m,nfact,nsolve,Istart,Iend,*im,*in,start,end;
PetscScalar *array,rval;
PetscReal norm,tol=1.e-12;
IS perm,iperm;
MatFactorInfo info;
PetscRandom rand;
PetscInitialize(&argc,&args,(char *)0,help);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &nproc);CHKERRQ(ierr);
/* Test non-symmetric operations */
/*-------------------------------*/
/* Create a Plapack dense matrix C */
ierr = PetscOptionsGetInt(PETSC_NULL,"-M",&M,PETSC_NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,M,M);CHKERRQ(ierr);
ierr = MatSetType(C,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
/* Create vectors */
ierr = MatGetOwnershipRange(C,&start,&end);CHKERRQ(ierr);
m = end - start;
/* printf("[%d] C - local size m: %d\n",rank,m); */
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,m,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecDuplicate(x,&bpla);CHKERRQ(ierr);
ierr = VecDuplicate(x,&u);CHKERRQ(ierr); /* save the true solution */
/* Create a petsc dense matrix Cpetsc */
ierr = PetscOptionsGetInt(PETSC_NULL,"-M",&M,PETSC_NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&Cpetsc);CHKERRQ(ierr);
ierr = MatSetSizes(Cpetsc,m,m,M,M);CHKERRQ(ierr);
ierr = MatSetType(Cpetsc,MATDENSE);CHKERRQ(ierr);
ierr = MatMPIDenseSetPreallocation(Cpetsc,PETSC_NULL);CHKERRQ(ierr);
ierr = MatSetFromOptions(Cpetsc);CHKERRQ(ierr);
ierr = MatSetUp(Cpetsc);CHKERRQ(ierr);
ierr = MatSetOption(Cpetsc,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr);
ierr = MatSetOption(C,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr);
/* Assembly */
/* PLAPACK doesn't support INSERT_VALUES mode, zero all entries before calling MatSetValues() */
ierr = MatZeroEntries(C);CHKERRQ(ierr);
ierr = MatZeroEntries(Cpetsc);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rand);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rand);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(C,&Istart,&Iend);CHKERRQ(ierr);
/* printf(" [%d] C m: %d, Istart/end: %d %d\n",rank,m,Istart,Iend); */
ierr = PetscMalloc((m*M+1)*sizeof(PetscScalar),&array);CHKERRQ(ierr);
ierr = PetscMalloc2(m,PetscInt,&im,M,PetscInt,&in);CHKERRQ(ierr);
k = 0;
for (j=0; j<M; j++){ /* column oriented! */
in[j] = j;
for (i=0; i<m; i++){
im[i] = i+Istart;
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[k++] = rval;
}
}
ierr = MatSetValues(Cpetsc,m,im,M,in,array,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(C,m,im,M,in,array,ADD_VALUES);CHKERRQ(ierr);
ierr = PetscFree(array);CHKERRQ(ierr);
ierr = PetscFree2(im,in);CHKERRQ(ierr);
ierr = MatAssemblyBegin(Cpetsc,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Cpetsc,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/*
if (!rank) {printf("main, Cpetsc: \n");}
ierr = MatView(Cpetsc,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
*/
ierr = MatGetOrdering(C,MATORDERINGNATURAL,&perm,&iperm);CHKERRQ(ierr);
/* Test nonsymmetric MatMult() */
ierr = VecGetArray(x,&array);CHKERRQ(ierr);
for (i=0; i<m; i++){
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[i] = rval;
}
ierr = VecRestoreArray(x,&array);CHKERRQ(ierr);
ierr = MatMult(Cpetsc,x,b);CHKERRQ(ierr);
ierr = MatMult(C,x,bpla);CHKERRQ(ierr);
ierr = VecAXPY(bpla,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(bpla,NORM_2,&norm);CHKERRQ(ierr);
if (norm > 1.e-12 && !rank){
ierr = PetscPrintf(PETSC_COMM_SELF,"Nonsymmetric MatMult_Plapack error: |b_pla - b|= %g\n",norm);CHKERRQ(ierr);
}
/* Test LU Factorization */
if (nproc == 1){
ierr = MatGetFactor(C,MATSOLVERPETSC,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
} else {
ierr = MatGetFactor(C,MATSOLVERPLAPACK,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
}
ierr = MatLUFactorSymbolic(F,C,perm,iperm,&info);CHKERRQ(ierr);
for (nfact = 0; nfact < 2; nfact++){
if (!rank) printf(" LU nfact %d\n",nfact);
if (nfact>0){ /* change matrix value for testing repeated MatLUFactorNumeric() */
if (!rank){
i = j = 0;
rval = nfact;
ierr = MatSetValues(Cpetsc,1,&i,1,&j,&rval,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(C,1,&i,1,&j,&rval,ADD_VALUES);CHKERRQ(ierr);
} else { /* PLAPACK seems requiring all processors call MatSetValues(), so we add 0.0 on processesses with rank>0! */
i = j = 0;
rval = 0.0;
ierr = MatSetValues(Cpetsc,1,&i,1,&j,&rval,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(C,1,&i,1,&j,&rval,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(Cpetsc,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Cpetsc,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
ierr = MatLUFactorNumeric(F,C,&info);CHKERRQ(ierr);
/* Test MatSolve() */
for (nsolve = 0; nsolve < 2; nsolve++){
ierr = VecGetArray(x,&array);CHKERRQ(ierr);
for (i=0; i<m; i++){
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[i] = rval;
/* array[i] = rank + 1; */
}
ierr = VecRestoreArray(x,&array);CHKERRQ(ierr);
ierr = VecCopy(x,u);CHKERRQ(ierr);
ierr = MatMult(C,x,b);CHKERRQ(ierr);
ierr = MatSolve(F,b,x);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(u,-1.0,x);CHKERRQ(ierr); /* u <- (-1.0)x + u */
ierr = VecNorm(u,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol){
if (!rank){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: Norm of error %g, LU nfact %d\n",norm,nfact);CHKERRQ(ierr);
}
}
}
}
ierr = MatDestroy(&F);CHKERRQ(ierr);
/* Test non-symmetric operations */
/*-------------------------------*/
/* Create a symmetric Plapack dense matrix Csymm */
ierr = MatCreate(PETSC_COMM_WORLD,&Csymm);CHKERRQ(ierr);
ierr = MatSetSizes(Csymm,PETSC_DECIDE,PETSC_DECIDE,M,M);CHKERRQ(ierr);
ierr = MatSetType(Csymm,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(Csymm);CHKERRQ(ierr);
ierr = MatSetUp(Csymm);CHKERRQ(ierr);
ierr = MatSetOption(Csymm,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr);
ierr = MatSetOption(Csymm,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatSetOption(Csymm,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatZeroEntries(Csymm);CHKERRQ(ierr);
ierr = MatZeroEntries(Cpetsc);CHKERRQ(ierr);
for (i=Istart; i<Iend; i++){
for (j=0; j<=i; j++){
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
ierr = MatSetValues(Cpetsc,1,&i,1,&j,&rval,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(Csymm,1,&i,1,&j,&rval,ADD_VALUES);CHKERRQ(ierr);
if (j<i){
/* Although PLAPACK only requires lower triangular entries, we must add all the entries.
MatSetValues_Plapack() will ignore the upper triangular entries AFTER an index map! */
ierr = MatSetValues(Cpetsc,1,&j,1,&i,&rval,ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(Csymm,1,&j,1,&i,&rval,ADD_VALUES);CHKERRQ(ierr);
}
}
}
ierr = MatAssemblyBegin(Cpetsc,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Cpetsc,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(Csymm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Csymm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Test symmetric MatMult() */
ierr = VecGetArray(x,&array);CHKERRQ(ierr);
for (i=0; i<m; i++){
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[i] = rval;
}
ierr = VecRestoreArray(x,&array);CHKERRQ(ierr);
ierr = MatMult(Cpetsc,x,b);CHKERRQ(ierr);
ierr = MatMult(Csymm,x,bpla);CHKERRQ(ierr);
ierr = VecAXPY(bpla,-1.0,b);CHKERRQ(ierr);
ierr = VecNorm(bpla,NORM_2,&norm);CHKERRQ(ierr);
if (norm > 1.e-12 && !rank){
ierr = PetscPrintf(PETSC_COMM_SELF,"Symmetric MatMult_Plapack error: |b_pla - b|= %g\n",norm);CHKERRQ(ierr);
}
/* Test Cholesky Factorization */
ierr = MatShift(Csymm,M);CHKERRQ(ierr); /* make Csymm positive definite */
if (nproc == 1){
ierr = MatGetFactor(Csymm,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
} else {
ierr = MatGetFactor(Csymm,MATSOLVERPLAPACK,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorSymbolic(F,Csymm,perm,&info);CHKERRQ(ierr);
for (nfact = 0; nfact < 2; nfact++){
if (!rank) printf(" Cholesky nfact %d\n",nfact);
ierr = MatCholeskyFactorNumeric(F,Csymm,&info);CHKERRQ(ierr);
/* Test MatSolve() */
for (nsolve = 0; nsolve < 2; nsolve++){
ierr = VecGetArray(x,&array);CHKERRQ(ierr);
for (i=0; i<m; i++){
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[i] = rval;
}
ierr = VecRestoreArray(x,&array);CHKERRQ(ierr);
ierr = VecCopy(x,u);CHKERRQ(ierr);
ierr = MatMult(Csymm,x,b);CHKERRQ(ierr);
ierr = MatSolve(F,b,x);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(u,-1.0,x);CHKERRQ(ierr); /* u <- (-1.0)x + u */
ierr = VecNorm(u,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol){
if (!rank){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: Norm of error %g, Cholesky nfact %d\n",norm,nfact);CHKERRQ(ierr);
}
}
}
}
ierr = MatDestroy(&F);CHKERRQ(ierr);
/* Free data structures */
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = ISDestroy(&iperm);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = VecDestroy(&bpla);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = MatDestroy(&Cpetsc);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&Csymm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
PetscErrorCode MatSOR_BlockMat_Symmetric(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
{
Mat_BlockMat *a = (Mat_BlockMat*)A->data;
PetscScalar *x;
const Mat *v;
const PetscScalar *b;
PetscErrorCode ierr;
PetscInt n = A->cmap->n,i,mbs = n/A->rmap->bs,j,bs = A->rmap->bs;
const PetscInt *idx;
IS row,col;
MatFactorInfo info;
Vec left = a->left,right = a->right, middle = a->middle;
Mat *diag;
PetscFunctionBegin;
its = its*lits;
if (its <= 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Relaxation requires global its %D and local its %D both positive",its,lits);
if (flag & SOR_EISENSTAT) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for Eisenstat");
if (omega != 1.0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for omega not equal to 1.0");
if (fshift) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for fshift");
if ((flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) && !(flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP)) {
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Cannot do backward sweep without forward sweep");
}
if (!a->diags) {
ierr = PetscMalloc1(mbs,&a->diags);CHKERRQ(ierr);
ierr = MatFactorInfoInitialize(&info);CHKERRQ(ierr);
for (i=0; i<mbs; i++) {
ierr = MatGetOrdering(a->a[a->diag[i]], MATORDERINGND,&row,&col);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(a->diags[i],a->a[a->diag[i]],row,&info);CHKERRQ(ierr);
ierr = MatCholeskyFactorNumeric(a->diags[i],a->a[a->diag[i]],&info);CHKERRQ(ierr);
ierr = ISDestroy(&row);CHKERRQ(ierr);
ierr = ISDestroy(&col);CHKERRQ(ierr);
}
ierr = VecDuplicate(bb,&a->workb);CHKERRQ(ierr);
}
diag = a->diags;
ierr = VecSet(xx,0.0);CHKERRQ(ierr);
ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
/* copy right hand side because it must be modified during iteration */
ierr = VecCopy(bb,a->workb);CHKERRQ(ierr);
ierr = VecGetArrayRead(a->workb,&b);CHKERRQ(ierr);
/* need to add code for when initial guess is zero, see MatSOR_SeqAIJ */
while (its--) {
if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
for (i=0; i<mbs; i++) {
n = a->i[i+1] - a->i[i] - 1;
idx = a->j + a->i[i] + 1;
v = a->a + a->i[i] + 1;
ierr = VecSet(left,0.0);CHKERRQ(ierr);
for (j=0; j<n; j++) {
ierr = VecPlaceArray(right,x + idx[j]*bs);CHKERRQ(ierr);
ierr = MatMultAdd(v[j],right,left,left);CHKERRQ(ierr);
ierr = VecResetArray(right);CHKERRQ(ierr);
}
ierr = VecPlaceArray(right,b + i*bs);CHKERRQ(ierr);
ierr = VecAYPX(left,-1.0,right);CHKERRQ(ierr);
ierr = VecResetArray(right);CHKERRQ(ierr);
ierr = VecPlaceArray(right,x + i*bs);CHKERRQ(ierr);
ierr = MatSolve(diag[i],left,right);CHKERRQ(ierr);
/* now adjust right hand side, see MatSOR_SeqSBAIJ */
for (j=0; j<n; j++) {
ierr = MatMultTranspose(v[j],right,left);CHKERRQ(ierr);
ierr = VecPlaceArray(middle,b + idx[j]*bs);CHKERRQ(ierr);
ierr = VecAXPY(middle,-1.0,left);CHKERRQ(ierr);
ierr = VecResetArray(middle);CHKERRQ(ierr);
}
ierr = VecResetArray(right);CHKERRQ(ierr);
}
}
if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
for (i=mbs-1; i>=0; i--) {
n = a->i[i+1] - a->i[i] - 1;
idx = a->j + a->i[i] + 1;
v = a->a + a->i[i] + 1;
ierr = VecSet(left,0.0);CHKERRQ(ierr);
for (j=0; j<n; j++) {
ierr = VecPlaceArray(right,x + idx[j]*bs);CHKERRQ(ierr);
ierr = MatMultAdd(v[j],right,left,left);CHKERRQ(ierr);
ierr = VecResetArray(right);CHKERRQ(ierr);
}
ierr = VecPlaceArray(right,b + i*bs);CHKERRQ(ierr);
ierr = VecAYPX(left,-1.0,right);CHKERRQ(ierr);
ierr = VecResetArray(right);CHKERRQ(ierr);
ierr = VecPlaceArray(right,x + i*bs);CHKERRQ(ierr);
ierr = MatSolve(diag[i],left,right);CHKERRQ(ierr);
ierr = VecResetArray(right);CHKERRQ(ierr);
}
}
}
ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(a->workb,&b);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode PCSetUp_Cholesky(PC pc)
{
PetscErrorCode ierr;
PetscBool flg;
PC_Cholesky *dir = (PC_Cholesky*)pc->data;
const MatSolverPackage stype;
MatFactorError err;
PetscFunctionBegin;
pc->failedreason = PC_NOERROR;
if (dir->hdr.reusefill && pc->setupcalled) ((PC_Factor*)dir)->info.fill = dir->hdr.actualfill;
ierr = MatSetErrorIfFailure(pc->pmat,pc->erroriffailure);
CHKERRQ(ierr);
if (dir->hdr.inplace) {
if (dir->row && dir->col && (dir->row != dir->col)) {
ierr = ISDestroy(&dir->row);
CHKERRQ(ierr);
}
ierr = ISDestroy(&dir->col);
CHKERRQ(ierr);
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)dir)->ordering,&dir->row,&dir->col);
CHKERRQ(ierr);
if (dir->col && (dir->row != dir->col)) { /* only use row ordering for SBAIJ */
ierr = ISDestroy(&dir->col);
CHKERRQ(ierr);
}
if (dir->row) {
ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)dir->row);
CHKERRQ(ierr);
}
ierr = MatCholeskyFactor(pc->pmat,dir->row,&((PC_Factor*)dir)->info);
CHKERRQ(ierr);
ierr = MatFactorGetError(pc->pmat,&err);
CHKERRQ(ierr);
if (err) { /* Factor() fails */
pc->failedreason = (PCFailedReason)err;
PetscFunctionReturn(0);
}
((PC_Factor*)dir)->fact = pc->pmat;
} else {
MatInfo info;
if (!pc->setupcalled) {
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)dir)->ordering,&dir->row,&dir->col);
CHKERRQ(ierr);
/* check if dir->row == dir->col */
ierr = ISEqual(dir->row,dir->col,&flg);
CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"row and column permutations must equal");
ierr = ISDestroy(&dir->col);
CHKERRQ(ierr); /* only pass one ordering into CholeskyFactor */
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(((PetscObject)pc)->options,((PetscObject)pc)->prefix,"-pc_factor_nonzeros_along_diagonal",&flg,NULL);
CHKERRQ(ierr);
if (flg) {
PetscReal tol = 1.e-10;
ierr = PetscOptionsGetReal(((PetscObject)pc)->options,((PetscObject)pc)->prefix,"-pc_factor_nonzeros_along_diagonal",&tol,NULL);
CHKERRQ(ierr);
ierr = MatReorderForNonzeroDiagonal(pc->pmat,tol,dir->row,dir->row);
CHKERRQ(ierr);
}
if (dir->row) {
ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)dir->row);
CHKERRQ(ierr);
}
if (!((PC_Factor*)dir)->fact) {
ierr = MatGetFactor(pc->pmat,((PC_Factor*)dir)->solvertype,MAT_FACTOR_CHOLESKY,&((PC_Factor*)dir)->fact);
CHKERRQ(ierr);
}
ierr = MatCholeskyFactorSymbolic(((PC_Factor*)dir)->fact,pc->pmat,dir->row,&((PC_Factor*)dir)->info);
CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)dir)->fact,MAT_LOCAL,&info);
CHKERRQ(ierr);
dir->hdr.actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)((PC_Factor*)dir)->fact);
CHKERRQ(ierr);
} else if (pc->flag != SAME_NONZERO_PATTERN) {
if (!dir->hdr.reuseordering) {
ierr = ISDestroy(&dir->row);
CHKERRQ(ierr);
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)dir)->ordering,&dir->row,&dir->col);
CHKERRQ(ierr);
ierr = ISDestroy(&dir->col);
CHKERRQ(ierr); /* only use dir->row ordering in CholeskyFactor */
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(((PetscObject)pc)->options,((PetscObject)pc)->prefix,"-pc_factor_nonzeros_along_diagonal",&flg,NULL);
CHKERRQ(ierr);
if (flg) {
PetscReal tol = 1.e-10;
ierr = PetscOptionsGetReal(((PetscObject)pc)->options,((PetscObject)pc)->prefix,"-pc_factor_nonzeros_along_diagonal",&tol,NULL);
CHKERRQ(ierr);
ierr = MatReorderForNonzeroDiagonal(pc->pmat,tol,dir->row,dir->row);
CHKERRQ(ierr);
}
if (dir->row) {
ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)dir->row);
CHKERRQ(ierr);
}
}
ierr = MatDestroy(&((PC_Factor*)dir)->fact);
CHKERRQ(ierr);
ierr = MatGetFactor(pc->pmat,((PC_Factor*)dir)->solvertype,MAT_FACTOR_CHOLESKY,&((PC_Factor*)dir)->fact);
CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(((PC_Factor*)dir)->fact,pc->pmat,dir->row,&((PC_Factor*)dir)->info);
CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)dir)->fact,MAT_LOCAL,&info);
CHKERRQ(ierr);
dir->hdr.actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)((PC_Factor*)dir)->fact);
CHKERRQ(ierr);
} else {
ierr = MatFactorGetError(((PC_Factor*)dir)->fact,&err);
CHKERRQ(ierr);
if (err == MAT_FACTOR_NUMERIC_ZEROPIVOT) {
ierr = MatFactorClearError(((PC_Factor*)dir)->fact);
CHKERRQ(ierr);
pc->failedreason = PC_NOERROR;
}
}
ierr = MatFactorGetError(((PC_Factor*)dir)->fact,&err);
CHKERRQ(ierr);
if (err) { /* FactorSymbolic() fails */
pc->failedreason = (PCFailedReason)err;
PetscFunctionReturn(0);
}
ierr = MatCholeskyFactorNumeric(((PC_Factor*)dir)->fact,pc->pmat,&((PC_Factor*)dir)->info);
CHKERRQ(ierr);
ierr = MatFactorGetError(((PC_Factor*)dir)->fact,&err);
CHKERRQ(ierr);
if (err) { /* FactorNumeric() fails */
pc->failedreason = (PCFailedReason)err;
}
}
ierr = PCFactorGetMatSolverPackage(pc,&stype);
CHKERRQ(ierr);
if (!stype) {
const MatSolverPackage solverpackage;
ierr = MatFactorGetSolverPackage(((PC_Factor*)dir)->fact,&solverpackage);
CHKERRQ(ierr);
ierr = PCFactorSetMatSolverPackage(pc,solverpackage);
CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
int main(int argc,char **args)
{
Mat C,C1,F;
Vec u,x,b;
PetscErrorCode ierr;
PetscMPIInt rank,nproc;
PetscInt i,M = 10,m,n,nfact,nsolve;
PetscScalar *array,rval;
PetscReal norm,tol=1.e-12;
IS perm,iperm;
MatFactorInfo info;
PetscRandom rand;
PetscTruth flg;
PetscInitialize(&argc,&args,(char *)0,help);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &nproc);CHKERRQ(ierr);
/* Create matrix and vectors */
ierr = PetscOptionsGetInt(PETSC_NULL,"-M",&M,PETSC_NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,M,M);CHKERRQ(ierr);
ierr = MatSetType(C,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatGetLocalSize(C,&m,&n);CHKERRQ(ierr);
if (m != n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Matrix local size m %d must equal n %d",m,n);
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,n,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecDuplicate(x,&u);CHKERRQ(ierr); /* save the true solution */
/* Assembly */
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rand);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rand);CHKERRQ(ierr);
ierr = MatGetArray(C,&array);CHKERRQ(ierr);
for (i=0; i<m*M; i++){
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[i] = rval;
}
ierr = MatRestoreArray(C,&array);CHKERRQ(ierr);
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/*if (!rank) {printf("main, C: \n");}
ierr = MatView(C,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); */
/* Test MatDuplicate() */
ierr = MatDuplicate(C,MAT_COPY_VALUES,&C1);CHKERRQ(ierr);
ierr = MatEqual(C,C1,&flg);CHKERRQ(ierr);
if (!flg){
SETERRQ(PETSC_ERR_ARG_WRONG,"Duplicate C1 != C");
}
/* Test LU Factorization */
ierr = MatGetOrdering(C1,MATORDERING_NATURAL,&perm,&iperm);CHKERRQ(ierr);
if (nproc == 1){
ierr = MatGetFactor(C1,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
} else {
ierr = MatGetFactor(C1,MAT_SOLVER_PLAPACK,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
}
ierr = MatLUFactorSymbolic(F,C1,perm,iperm,&info);CHKERRQ(ierr);
for (nfact = 0; nfact < 2; nfact++){
if (!rank) printf(" LU nfact %d\n",nfact);
ierr = MatLUFactorNumeric(F,C1,&info);CHKERRQ(ierr);
/* Test MatSolve() */
for (nsolve = 0; nsolve < 5; nsolve++){
ierr = VecGetArray(x,&array);CHKERRQ(ierr);
for (i=0; i<m; i++){
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[i] = rval;
}
ierr = VecRestoreArray(x,&array);CHKERRQ(ierr);
ierr = VecCopy(x,u);CHKERRQ(ierr);
ierr = MatMult(C,x,b);CHKERRQ(ierr);
ierr = MatSolve(F,b,x);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(u,-1.0,x);CHKERRQ(ierr); /* u <- (-1.0)x + u */
ierr = VecNorm(u,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol){
if (!rank){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: Norm of error %g, LU nfact %d\n",norm,nfact);CHKERRQ(ierr);
}
}
}
}
ierr = MatDestroy(C1);CHKERRQ(ierr);
ierr = MatDestroy(F);CHKERRQ(ierr);
/* Test Cholesky Factorization */
ierr = MatTranspose(C,MAT_INITIAL_MATRIX,&C1);CHKERRQ(ierr); /* C1 = C^T */
ierr = MatAXPY(C,1.0,C1,SAME_NONZERO_PATTERN);CHKERRQ(ierr); /* make C symmetric: C <- C + C^T */
ierr = MatShift(C,M);CHKERRQ(ierr); /* make C positive definite */
ierr = MatDestroy(C1);CHKERRQ(ierr);
ierr = MatSetOption(C,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatSetOption(C,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);CHKERRQ(ierr);
if (nproc == 1){
ierr = MatGetFactor(C,MAT_SOLVER_PETSC,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
} else {
ierr = MatGetFactor(C,MAT_SOLVER_PLAPACK,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorSymbolic(F,C,perm,&info);CHKERRQ(ierr);
for (nfact = 0; nfact < 2; nfact++){
if (!rank) printf(" Cholesky nfact %d\n",nfact);
ierr = MatCholeskyFactorNumeric(F,C,&info);CHKERRQ(ierr);
/* Test MatSolve() */
for (nsolve = 0; nsolve < 5; nsolve++){
ierr = VecGetArray(x,&array);CHKERRQ(ierr);
for (i=0; i<m; i++){
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[i] = rval;
}
ierr = VecRestoreArray(x,&array);CHKERRQ(ierr);
ierr = VecCopy(x,u);CHKERRQ(ierr);
ierr = MatMult(C,x,b);CHKERRQ(ierr);
ierr = MatSolve(F,b,x);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(u,-1.0,x);CHKERRQ(ierr); /* u <- (-1.0)x + u */
ierr = VecNorm(u,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol){
if (!rank){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: Norm of error %g, Cholesky nfact %d\n",norm,nfact);CHKERRQ(ierr);
}
}
}
}
ierr = MatDestroy(F);CHKERRQ(ierr);
/* Free data structures */
ierr = PetscRandomDestroy(rand);CHKERRQ(ierr);
ierr = ISDestroy(perm);CHKERRQ(ierr);
ierr = ISDestroy(iperm);CHKERRQ(ierr);
ierr = VecDestroy(x);CHKERRQ(ierr);
ierr = VecDestroy(b);CHKERRQ(ierr);
ierr = VecDestroy(u);CHKERRQ(ierr);
ierr = MatDestroy(C);CHKERRQ(ierr);
ierr = PetscFinalize();CHKERRQ(ierr);
return 0;
}
int main(int argc,char **args)
{
Mat A,RHS,C,F,X,S;
Vec u,x,b;
Vec xschur,bschur,uschur;
IS is_schur;
PetscErrorCode ierr;
PetscMPIInt size;
PetscInt isolver=0,size_schur,m,n,nfact,nsolve,nrhs;
PetscReal norm,tol=PETSC_SQRT_MACHINE_EPSILON;
PetscRandom rand;
PetscBool data_provided,herm,symm,use_lu;
PetscReal sratio = 5.1/12.;
PetscViewer fd; /* viewer */
char solver[256];
char file[PETSC_MAX_PATH_LEN]; /* input file name */
PetscInitialize(&argc,&args,(char*)0,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);
if (size > 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor test");
/* Determine which type of solver we want to test for */
herm = PETSC_FALSE;
symm = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,NULL,"-symmetric_solve",&symm,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-hermitian_solve",&herm,NULL);CHKERRQ(ierr);
if (herm) symm = PETSC_TRUE;
/* Determine file from which we read the matrix A */
ierr = PetscOptionsGetString(NULL,NULL,"-f",file,PETSC_MAX_PATH_LEN,&data_provided);CHKERRQ(ierr);
if (!data_provided) { /* get matrices from PETSc distribution */
sprintf(file,PETSC_DIR);
ierr = PetscStrcat(file,"/share/petsc/datafiles/matrices/");CHKERRQ(ierr);
if (symm) {
#if defined (PETSC_USE_COMPLEX)
ierr = PetscStrcat(file,"hpd-complex-");CHKERRQ(ierr);
#else
ierr = PetscStrcat(file,"spd-real-");CHKERRQ(ierr);
#endif
} else {
#if defined (PETSC_USE_COMPLEX)
ierr = PetscStrcat(file,"nh-complex-");CHKERRQ(ierr);
#else
ierr = PetscStrcat(file,"ns-real-");CHKERRQ(ierr);
#endif
}
#if defined(PETSC_USE_64BIT_INDICES)
ierr = PetscStrcat(file,"int64-");CHKERRQ(ierr);
#else
ierr = PetscStrcat(file,"int32-");CHKERRQ(ierr);
#endif
#if defined (PETSC_USE_REAL_SINGLE)
ierr = PetscStrcat(file,"float32");CHKERRQ(ierr);
#else
ierr = PetscStrcat(file,"float64");CHKERRQ(ierr);
#endif
}
/* Load matrix A */
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file,FILE_MODE_READ,&fd);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatLoad(A,fd);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&fd);CHKERRQ(ierr);
ierr = MatGetSize(A,&m,&n);CHKERRQ(ierr);
if (m != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ, "This example is not intended for rectangular matrices (%d, %d)", m, n);
/* Create dense matrix C and X; C holds true solution with identical colums */
nrhs = 2;
ierr = PetscOptionsGetInt(NULL,NULL,"-nrhs",&nrhs,NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,m,PETSC_DECIDE,PETSC_DECIDE,nrhs);CHKERRQ(ierr);
ierr = MatSetType(C,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rand);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rand);CHKERRQ(ierr);
ierr = MatSetRandom(C,rand);CHKERRQ(ierr);
ierr = MatDuplicate(C,MAT_DO_NOT_COPY_VALUES,&X);CHKERRQ(ierr);
/* Create vectors */
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,n,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecDuplicate(x,&u);CHKERRQ(ierr); /* save the true solution */
ierr = PetscOptionsGetInt(NULL,NULL,"-solver",&isolver,NULL);CHKERRQ(ierr);
switch (isolver) {
#if defined(PETSC_HAVE_MUMPS)
case 0:
ierr = PetscStrcpy(solver,MATSOLVERMUMPS);CHKERRQ(ierr);
break;
#endif
#if defined(PETSC_HAVE_MKL_PARDISO)
case 1:
ierr = PetscStrcpy(solver,MATSOLVERMKL_PARDISO);CHKERRQ(ierr);
break;
#endif
default:
ierr = PetscStrcpy(solver,MATSOLVERPETSC);CHKERRQ(ierr);
break;
}
#if defined (PETSC_USE_COMPLEX)
if (isolver == 0 && symm && !data_provided) { /* MUMPS (5.0.0) does not have support for hermitian matrices, so make them symmetric */
PetscScalar im = PetscSqrtScalar((PetscScalar)-1.);
PetscScalar val = -1.0;
val = val + im;
ierr = MatSetValue(A,1,0,val,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
#endif
ierr = PetscOptionsGetReal(NULL,NULL,"-schur_ratio",&sratio,NULL);CHKERRQ(ierr);
if (sratio < 0. || sratio > 1.) {
SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ, "Invalid ratio for schur degrees of freedom %f", sratio);
}
size_schur = (PetscInt)(sratio*m);
ierr = PetscPrintf(PETSC_COMM_SELF,"Solving with %s: nrhs %d, sym %d, herm %d, size schur %d, size mat %d\n",solver,nrhs,symm,herm,size_schur,m);CHKERRQ(ierr);
/* Test LU/Cholesky Factorization */
use_lu = PETSC_FALSE;
if (!symm) use_lu = PETSC_TRUE;
#if defined (PETSC_USE_COMPLEX)
if (isolver == 1) use_lu = PETSC_TRUE;
#endif
if (herm && !use_lu) { /* test also conversion routines inside the solver packages */
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatConvert(A,MATSEQSBAIJ,MAT_INPLACE_MATRIX,&A);CHKERRQ(ierr);
}
if (use_lu) {
ierr = MatGetFactor(A,solver,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
} else {
if (herm) {
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatSetOption(A,MAT_SPD,PETSC_TRUE);CHKERRQ(ierr);
} else {
ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatSetOption(A,MAT_SPD,PETSC_FALSE);CHKERRQ(ierr);
}
ierr = MatGetFactor(A,solver,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
}
ierr = ISCreateStride(PETSC_COMM_SELF,size_schur,m-size_schur,1,&is_schur);CHKERRQ(ierr);
ierr = MatFactorSetSchurIS(F,is_schur);CHKERRQ(ierr);
ierr = ISDestroy(&is_schur);CHKERRQ(ierr);
if (use_lu) {
ierr = MatLUFactorSymbolic(F,A,NULL,NULL,NULL);CHKERRQ(ierr);
} else {
ierr = MatCholeskyFactorSymbolic(F,A,NULL,NULL);CHKERRQ(ierr);
}
for (nfact = 0; nfact < 3; nfact++) {
Mat AD;
if (!nfact) {
ierr = VecSetRandom(x,rand);CHKERRQ(ierr);
if (symm && herm) {
ierr = VecAbs(x);CHKERRQ(ierr);
}
ierr = MatDiagonalSet(A,x,ADD_VALUES);CHKERRQ(ierr);
}
if (use_lu) {
ierr = MatLUFactorNumeric(F,A,NULL);CHKERRQ(ierr);
} else {
ierr = MatCholeskyFactorNumeric(F,A,NULL);CHKERRQ(ierr);
}
ierr = MatFactorCreateSchurComplement(F,&S);CHKERRQ(ierr);
ierr = MatCreateVecs(S,&xschur,&bschur);CHKERRQ(ierr);
ierr = VecDuplicate(xschur,&uschur);CHKERRQ(ierr);
if (nfact == 1) {
ierr = MatFactorInvertSchurComplement(F);CHKERRQ(ierr);
}
for (nsolve = 0; nsolve < 2; nsolve++) {
ierr = VecSetRandom(x,rand);CHKERRQ(ierr);
ierr = VecCopy(x,u);CHKERRQ(ierr);
if (nsolve) {
ierr = MatMult(A,x,b);CHKERRQ(ierr);
ierr = MatSolve(F,b,x);CHKERRQ(ierr);
} else {
ierr = MatMultTranspose(A,x,b);CHKERRQ(ierr);
ierr = MatSolveTranspose(F,b,x);CHKERRQ(ierr);
}
/* Check the error */
ierr = VecAXPY(u,-1.0,x);CHKERRQ(ierr); /* u <- (-1.0)x + u */
ierr = VecNorm(u,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol) {
PetscReal resi;
if (nsolve) {
ierr = MatMult(A,x,u);CHKERRQ(ierr); /* u = A*x */
} else {
ierr = MatMultTranspose(A,x,u);CHKERRQ(ierr); /* u = A*x */
}
ierr = VecAXPY(u,-1.0,b);CHKERRQ(ierr); /* u <- (-1.0)b + u */
ierr = VecNorm(u,NORM_2,&resi);CHKERRQ(ierr);
if (nsolve) {
ierr = PetscPrintf(PETSC_COMM_SELF,"(f %d, s %d) MatSolve error: Norm of error %g, residual %f\n",nfact,nsolve,norm,resi);CHKERRQ(ierr);
} else {
ierr = PetscPrintf(PETSC_COMM_SELF,"(f %d, s %d) MatSolveTranspose error: Norm of error %g, residual %f\n",nfact,nsolve,norm,resi);CHKERRQ(ierr);
}
}
ierr = VecSetRandom(xschur,rand);CHKERRQ(ierr);
ierr = VecCopy(xschur,uschur);CHKERRQ(ierr);
if (nsolve) {
ierr = MatMult(S,xschur,bschur);CHKERRQ(ierr);
ierr = MatFactorSolveSchurComplement(F,bschur,xschur);CHKERRQ(ierr);
} else {
ierr = MatMultTranspose(S,xschur,bschur);CHKERRQ(ierr);
ierr = MatFactorSolveSchurComplementTranspose(F,bschur,xschur);CHKERRQ(ierr);
}
/* Check the error */
ierr = VecAXPY(uschur,-1.0,xschur);CHKERRQ(ierr); /* u <- (-1.0)x + u */
ierr = VecNorm(uschur,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol) {
PetscReal resi;
if (nsolve) {
ierr = MatMult(S,xschur,uschur);CHKERRQ(ierr); /* u = A*x */
} else {
ierr = MatMultTranspose(S,xschur,uschur);CHKERRQ(ierr); /* u = A*x */
}
ierr = VecAXPY(uschur,-1.0,bschur);CHKERRQ(ierr); /* u <- (-1.0)b + u */
ierr = VecNorm(uschur,NORM_2,&resi);CHKERRQ(ierr);
if (nsolve) {
ierr = PetscPrintf(PETSC_COMM_SELF,"(f %d, s %d) MatFactorSolveSchurComplement error: Norm of error %g, residual %f\n",nfact,nsolve,norm,resi);CHKERRQ(ierr);
} else {
ierr = PetscPrintf(PETSC_COMM_SELF,"(f %d, s %d) MatFactorSolveSchurComplementTranspose error: Norm of error %g, residual %f\n",nfact,nsolve,norm,resi);CHKERRQ(ierr);
}
}
}
ierr = MatConvert(A,MATSEQAIJ,MAT_INITIAL_MATRIX,&AD);
if (!nfact) {
ierr = MatMatMult(AD,C,MAT_INITIAL_MATRIX,2.0,&RHS);CHKERRQ(ierr);
} else {
ierr = MatMatMult(AD,C,MAT_REUSE_MATRIX,2.0,&RHS);CHKERRQ(ierr);
}
ierr = MatDestroy(&AD);CHKERRQ(ierr);
for (nsolve = 0; nsolve < 2; nsolve++) {
ierr = MatMatSolve(F,RHS,X);CHKERRQ(ierr);
/* Check the error */
ierr = MatAXPY(X,-1.0,C,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatNorm(X,NORM_FROBENIUS,&norm);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"(f %D, s %D) MatMatSolve: Norm of error %g\n",nfact,nsolve,norm);CHKERRQ(ierr);
}
}
ierr = MatDestroy(&S);CHKERRQ(ierr);
ierr = VecDestroy(&xschur);CHKERRQ(ierr);
ierr = VecDestroy(&bschur);CHKERRQ(ierr);
ierr = VecDestroy(&uschur);CHKERRQ(ierr);
}
/* Free data structures */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&F);CHKERRQ(ierr);
ierr = MatDestroy(&X);CHKERRQ(ierr);
ierr = MatDestroy(&RHS);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = VecDestroy(&u);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;
}
static PetscErrorCode PCSetUp_Cholesky(PC pc)
{
PetscErrorCode ierr;
PetscBool flg;
PC_Cholesky *dir = (PC_Cholesky*)pc->data;
PetscFunctionBegin;
if (dir->reusefill && pc->setupcalled) ((PC_Factor*)dir)->info.fill = dir->actualfill;
if (dir->inplace) {
if (dir->row && dir->col && (dir->row != dir->col)) {
ierr = ISDestroy(&dir->row);CHKERRQ(ierr);
}
ierr = ISDestroy(&dir->col);CHKERRQ(ierr);
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)dir)->ordering,&dir->row,&dir->col);CHKERRQ(ierr);
if (dir->col && (dir->row != dir->col)) { /* only use row ordering for SBAIJ */
ierr = ISDestroy(&dir->col);CHKERRQ(ierr);
}
if (dir->row) {ierr = PetscLogObjectParent(pc,dir->row);CHKERRQ(ierr);}
ierr = MatCholeskyFactor(pc->pmat,dir->row,&((PC_Factor*)dir)->info);CHKERRQ(ierr);
((PC_Factor*)dir)->fact = pc->pmat;
} else {
MatInfo info;
if (!pc->setupcalled) {
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)dir)->ordering,&dir->row,&dir->col);CHKERRQ(ierr);
/* check if dir->row == dir->col */
ierr = ISEqual(dir->row,dir->col,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"row and column permutations must equal");
ierr = ISDestroy(&dir->col);CHKERRQ(ierr); /* only pass one ordering into CholeskyFactor */
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(((PetscObject)pc)->prefix,"-pc_factor_nonzeros_along_diagonal",&flg,PETSC_NULL);CHKERRQ(ierr);
if (flg) {
PetscReal tol = 1.e-10;
ierr = PetscOptionsGetReal(((PetscObject)pc)->prefix,"-pc_factor_nonzeros_along_diagonal",&tol,PETSC_NULL);CHKERRQ(ierr);
ierr = MatReorderForNonzeroDiagonal(pc->pmat,tol,dir->row,dir->row);CHKERRQ(ierr);
}
if (dir->row) {ierr = PetscLogObjectParent(pc,dir->row);CHKERRQ(ierr);}
if (!((PC_Factor*)dir)->fact){
ierr = MatGetFactor(pc->pmat,((PC_Factor*)dir)->solvertype,MAT_FACTOR_CHOLESKY,&((PC_Factor*)dir)->fact);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorSymbolic(((PC_Factor*)dir)->fact,pc->pmat,dir->row,&((PC_Factor*)dir)->info);CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)dir)->fact,MAT_LOCAL,&info);CHKERRQ(ierr);
dir->actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent(pc,((PC_Factor*)dir)->fact);CHKERRQ(ierr);
} else if (pc->flag != SAME_NONZERO_PATTERN) {
if (!dir->reuseordering) {
ierr = ISDestroy(&dir->row);CHKERRQ(ierr);
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)dir)->ordering,&dir->row,&dir->col);CHKERRQ(ierr);
ierr = ISDestroy(&dir->col);CHKERRQ(ierr); /* only use dir->row ordering in CholeskyFactor */
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(((PetscObject)pc)->prefix,"-pc_factor_nonzeros_along_diagonal",&flg,PETSC_NULL);CHKERRQ(ierr);
if (flg) {
PetscReal tol = 1.e-10;
ierr = PetscOptionsGetReal(((PetscObject)pc)->prefix,"-pc_factor_nonzeros_along_diagonal",&tol,PETSC_NULL);CHKERRQ(ierr);
ierr = MatReorderForNonzeroDiagonal(pc->pmat,tol,dir->row,dir->row);CHKERRQ(ierr);
}
if (dir->row) {ierr = PetscLogObjectParent(pc,dir->row);CHKERRQ(ierr);}
}
ierr = MatDestroy(&((PC_Factor*)dir)->fact);CHKERRQ(ierr);
ierr = MatGetFactor(pc->pmat,((PC_Factor*)dir)->solvertype,MAT_FACTOR_CHOLESKY,&((PC_Factor*)dir)->fact);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(((PC_Factor*)dir)->fact,pc->pmat,dir->row,&((PC_Factor*)dir)->info);CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)dir)->fact,MAT_LOCAL,&info);CHKERRQ(ierr);
dir->actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent(pc,((PC_Factor*)dir)->fact);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorNumeric(((PC_Factor*)dir)->fact,pc->pmat,&((PC_Factor*)dir)->info);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
For MATSEQDENSE matrix, the factorization is just a thin wrapper to LAPACK \n\n";
#include <petscmat.h>
#undef __FUNCT__
#define __FUNCT__ "main"
int main(int argc,char **argv)
{
Mat mat,F,RHS,SOLU;
MatInfo info;
PetscErrorCode ierr;
PetscInt m = 10,n = 10,i,j,rstart,rend,nrhs=2;
PetscScalar value = 1.0;
Vec x,y,b,ytmp;
PetscReal norm,tol=1.e-15;
PetscMPIInt size;
PetscScalar *rhs_array,*solu_array;
PetscRandom rand;
PetscScalar *array,rval;
PetscInitialize(&argc,&argv,(char*) 0,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This is a uniprocessor example only!");
/* create single vectors */
ierr = VecCreate(PETSC_COMM_WORLD,&y);CHKERRQ(ierr);
ierr = VecSetSizes(y,PETSC_DECIDE,m);CHKERRQ(ierr);
ierr = VecSetFromOptions(y);CHKERRQ(ierr);
ierr = VecDuplicate(y,&x);CHKERRQ(ierr);
ierr = VecDuplicate(y,&ytmp);CHKERRQ(ierr);
ierr = VecSet(x,value);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&b);CHKERRQ(ierr);
ierr = VecSetSizes(b,PETSC_DECIDE,n);CHKERRQ(ierr);
ierr = VecSetFromOptions(b);CHKERRQ(ierr);
/* create multiple vectors RHS and SOLU */
ierr = MatCreate(PETSC_COMM_WORLD,&RHS);CHKERRQ(ierr);
ierr = MatSetSizes(RHS,PETSC_DECIDE,PETSC_DECIDE,n,nrhs);CHKERRQ(ierr);
ierr = MatSetType(RHS,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(RHS);CHKERRQ(ierr);
ierr = MatSeqDenseSetPreallocation(RHS,NULL);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rand);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rand);CHKERRQ(ierr);
ierr = MatDenseGetArray(RHS,&array);CHKERRQ(ierr);
for (j=0; j<nrhs; j++) {
for (i=0; i<n; i++) {
ierr = PetscRandomGetValue(rand,&rval);CHKERRQ(ierr);
array[n*j+i] = rval;
}
}
ierr = MatDenseRestoreArray(RHS,&array);CHKERRQ(ierr);
ierr = MatDuplicate(RHS,MAT_DO_NOT_COPY_VALUES,&SOLU);CHKERRQ(ierr);
/* create matrix */
ierr = MatCreateSeqDense(PETSC_COMM_WORLD,m,n,NULL,&mat);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(mat,&rstart,&rend);CHKERRQ(ierr);
for (i=rstart; i<rend; i++) {
value = (PetscReal)i+1;
ierr = MatSetValues(mat,1,&i,1,&i,&value,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"matrix nonzeros = %D, allocated nonzeros = %D\n",
(PetscInt)info.nz_used,(PetscInt)info.nz_allocated);CHKERRQ(ierr);
/* Cholesky factorization - perm and factinfo are ignored by LAPACK */
/* in-place Cholesky */
ierr = MatMult(mat,x,b);CHKERRQ(ierr);
ierr = MatDuplicate(mat,MAT_COPY_VALUES,&F);CHKERRQ(ierr);
ierr = MatCholeskyFactor(F,0,0);CHKERRQ(ierr);
ierr = MatSolve(F,b,y);CHKERRQ(ierr);
ierr = MatDestroy(&F);CHKERRQ(ierr);
value = -1.0; ierr = VecAXPY(y,value,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Warning: Norm of error for Cholesky %G\n",norm);CHKERRQ(ierr);
}
/* out-place Cholesky */
ierr = MatGetFactor(mat,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(F,mat,0,0);CHKERRQ(ierr);
ierr = MatCholeskyFactorNumeric(F,mat,0);CHKERRQ(ierr);
ierr = MatSolve(F,b,y);CHKERRQ(ierr);
value = -1.0; ierr = VecAXPY(y,value,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Warning: Norm of error for Cholesky %G\n",norm);CHKERRQ(ierr);
}
ierr = MatDestroy(&F);CHKERRQ(ierr);
/* LU factorization - perms and factinfo are ignored by LAPACK */
i = m-1; value = 1.0;
ierr = MatSetValues(mat,1,&i,1,&i,&value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatMult(mat,x,b);CHKERRQ(ierr);
ierr = MatDuplicate(mat,MAT_COPY_VALUES,&F);CHKERRQ(ierr);
/* in-place LU */
ierr = MatLUFactor(F,0,0,0);CHKERRQ(ierr);
ierr = MatSolve(F,b,y);CHKERRQ(ierr);
value = -1.0; ierr = VecAXPY(y,value,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Warning: Norm of error for LU %G\n",norm);CHKERRQ(ierr);
}
ierr = MatMatSolve(F,RHS,SOLU);CHKERRQ(ierr);
ierr = MatDenseGetArray(SOLU,&solu_array);CHKERRQ(ierr);
ierr = MatDenseGetArray(RHS,&rhs_array);CHKERRQ(ierr);
for (j=0; j<nrhs; j++) {
ierr = VecPlaceArray(y,solu_array+j*m);CHKERRQ(ierr);
ierr = VecPlaceArray(b,rhs_array+j*m);CHKERRQ(ierr);
ierr = MatMult(mat,y,ytmp);CHKERRQ(ierr);
ierr = VecAXPY(ytmp,-1.0,b);CHKERRQ(ierr); /* ytmp = mat*SOLU[:,j] - RHS[:,j] */
ierr = VecNorm(ytmp,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Error: Norm of residual for LU %G\n",norm);CHKERRQ(ierr);
}
ierr = VecResetArray(b);CHKERRQ(ierr);
ierr = VecResetArray(y);CHKERRQ(ierr);
}
ierr = MatDenseRestoreArray(RHS,&rhs_array);CHKERRQ(ierr);
ierr = MatDenseRestoreArray(SOLU,&solu_array);CHKERRQ(ierr);
ierr = MatDestroy(&F);CHKERRQ(ierr);
/* out-place LU */
ierr = MatGetFactor(mat,MATSOLVERPETSC,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
ierr = MatLUFactorSymbolic(F,mat,0,0,0);CHKERRQ(ierr);
ierr = MatLUFactorNumeric(F,mat,0);CHKERRQ(ierr);
ierr = MatSolve(F,b,y);CHKERRQ(ierr);
value = -1.0; ierr = VecAXPY(y,value,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Warning: Norm of error for LU %G\n",norm);CHKERRQ(ierr);
}
/* free space */
ierr = MatDestroy(&F);CHKERRQ(ierr);
ierr = MatDestroy(&mat);CHKERRQ(ierr);
ierr = MatDestroy(&RHS);CHKERRQ(ierr);
ierr = MatDestroy(&SOLU);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rand);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&ytmp);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
PetscErrorCode ierr;
Mat mat,fact,B;
PetscInt ind1[2],ind2[2];
PetscScalar temp[4];
PetscInt nnz[3];
IS perm,colp;
MatFactorInfo info;
PetscMPIInt size;
ierr = PetscInitialize(&argc,&args,0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This is a uniprocessor example only!");
nnz[0]=2;nnz[1]=1;nnz[2]=1;
ierr = MatCreateSeqSBAIJ(PETSC_COMM_SELF,2,6,6,0,nnz,&mat);CHKERRQ(ierr);
ind1[0]=0;ind1[1]=1;
temp[0]=3;temp[1]=2;temp[2]=0;temp[3]=3;
ierr = MatSetValues(mat,2,ind1,2,ind1,temp,INSERT_VALUES);CHKERRQ(ierr);
ind2[0]=4;ind2[1]=5;
temp[0]=1;temp[1]=1;temp[2]=2;temp[3]=1;
ierr = MatSetValues(mat,2,ind1,2,ind2,temp,INSERT_VALUES);CHKERRQ(ierr);
ind1[0]=2;ind1[1]=3;
temp[0]=4;temp[1]=1;temp[2]=1;temp[3]=5;
ierr = MatSetValues(mat,2,ind1,2,ind1,temp,INSERT_VALUES);CHKERRQ(ierr);
ind1[0]=4;ind1[1]=5;
temp[0]=5;temp[1]=1;temp[2]=1;temp[3]=6;
ierr = MatSetValues(mat,2,ind1,2,ind1,temp,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatDuplicate(mat,MAT_SHARE_NONZERO_PATTERN,&B);CHKERRQ(ierr);
ind1[0]=0;ind1[1]=1;
temp[0]=3;temp[1]=2;temp[2]=0;temp[3]=3;
ierr = MatSetValues(mat,2,ind1,2,ind1,temp,INSERT_VALUES);CHKERRQ(ierr);
ind2[0]=4;ind2[1]=5;
temp[0]=1;temp[1]=1;temp[2]=2;temp[3]=1;
ierr = MatSetValues(mat,2,ind1,2,ind2,temp,INSERT_VALUES);CHKERRQ(ierr);
ind1[0]=2;ind1[1]=3;
temp[0]=4;temp[1]=1;temp[2]=1;temp[3]=5;
ierr = MatSetValues(mat,2,ind1,2,ind1,temp,INSERT_VALUES);CHKERRQ(ierr);
ind1[0]=4;ind1[1]=5;
temp[0]=5;temp[1]=1;temp[2]=1;temp[3]=6;
ierr = MatSetValues(mat,2,ind1,2,ind1,temp,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"mat: \n");CHKERRQ(ierr);
ierr = MatView(mat,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
/* begin cholesky factorization */
ierr = MatGetOrdering(mat,MATORDERINGNATURAL,&perm,&colp);CHKERRQ(ierr);
ierr = ISDestroy(&colp);CHKERRQ(ierr);
info.fill=1.0;
ierr = MatGetFactor(mat,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&fact);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(fact,mat,perm,&info);CHKERRQ(ierr);
ierr = MatCholeskyFactorNumeric(fact,mat,&info);CHKERRQ(ierr);
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = MatDestroy(&mat);CHKERRQ(ierr);
ierr = MatDestroy(&fact);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
