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);
}
static PetscErrorCode PCSetUp_LU(PC pc)
{
PetscErrorCode ierr;
PC_LU *dir = (PC_LU*)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);}
if (dir->col) {ierr = ISDestroy(dir->col);CHKERRQ(ierr);}
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)dir)->ordering,&dir->row,&dir->col);CHKERRQ(ierr);
if (dir->row) {
ierr = PetscLogObjectParent(pc,dir->row);CHKERRQ(ierr);
ierr = PetscLogObjectParent(pc,dir->col);CHKERRQ(ierr);
}
ierr = MatLUFactor(pc->pmat,dir->row,dir->col,&((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);
if (dir->nonzerosalongdiagonal) {
ierr = MatReorderForNonzeroDiagonal(pc->pmat,dir->nonzerosalongdiagonaltol,dir->row,dir->col);CHKERRQ(ierr);
}
if (dir->row) {
ierr = PetscLogObjectParent(pc,dir->row);CHKERRQ(ierr);
ierr = PetscLogObjectParent(pc,dir->col);CHKERRQ(ierr);
}
ierr = MatGetFactor(pc->pmat,((PC_Factor*)dir)->solvertype,MAT_FACTOR_LU,&((PC_Factor*)dir)->fact);CHKERRQ(ierr);
ierr = MatLUFactorSymbolic(((PC_Factor*)dir)->fact,pc->pmat,dir->row,dir->col,&((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) {
if (dir->row && dir->col && dir->row != dir->col) {ierr = ISDestroy(dir->row);CHKERRQ(ierr);}
if (dir->col) {ierr = ISDestroy(dir->col);CHKERRQ(ierr);}
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)dir)->ordering,&dir->row,&dir->col);CHKERRQ(ierr);
if (dir->nonzerosalongdiagonal) {
ierr = MatReorderForNonzeroDiagonal(pc->pmat,dir->nonzerosalongdiagonaltol,dir->row,dir->col);CHKERRQ(ierr);
}
if (dir->row) {
ierr = PetscLogObjectParent(pc,dir->row);CHKERRQ(ierr);
ierr = PetscLogObjectParent(pc,dir->col);CHKERRQ(ierr);
}
}
ierr = MatDestroy(((PC_Factor*)dir)->fact);CHKERRQ(ierr);
ierr = MatGetFactor(pc->pmat,((PC_Factor*)dir)->solvertype,MAT_FACTOR_LU,&((PC_Factor*)dir)->fact);CHKERRQ(ierr);
ierr = MatLUFactorSymbolic(((PC_Factor*)dir)->fact,pc->pmat,dir->row,dir->col,&((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 = MatLUFactorNumeric(((PC_Factor*)dir)->fact,pc->pmat,&((PC_Factor*)dir)->info);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
PetscErrorCode PCFactorSetUpMatSolverPackage_Factor(PC pc)
{
PC_Factor *icc = (PC_Factor*)pc->data;
PetscErrorCode ierr;
PetscFunctionBegin;
if (!pc->setupcalled && !((PC_Factor*)icc)->fact) {
ierr = MatGetFactor(pc->pmat,((PC_Factor*)icc)->solvertype,((PC_Factor*)icc)->factortype,&((PC_Factor*)icc)->fact);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
int main(int argc,char **args)
{
Mat A,F;
PetscViewer fd; /* viewer */
char file[PETSC_MAX_PATH_LEN]; /* input file name */
PetscErrorCode ierr;
PetscBool flg;
Vec x,y,w;
MatFactorInfo iluinfo;
IS perm;
PetscInt m;
PetscReal norm;
PetscInitialize(&argc,&args,(char*)0,help);
/*
Determine file from which we read the matrix
*/
ierr = PetscOptionsGetString(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");
/*
Open binary file. Note that we use FILE_MODE_READ to indicate
reading from this file.
*/
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file,FILE_MODE_READ,&fd);CHKERRQ(ierr);
/*
Load the matrix; then destroy the viewer.
*/
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetType(A,MATSEQBAIJ);CHKERRQ(ierr);
ierr = MatLoad(A,fd);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecLoad(x,fd);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&fd);CHKERRQ(ierr);
ierr = VecDuplicate(x,&y);CHKERRQ(ierr);
ierr = VecDuplicate(x,&w);CHKERRQ(ierr);
ierr = MatGetFactor(A,"petsc",MAT_FACTOR_ILU,&F);CHKERRQ(ierr);
iluinfo.fill = 1.0;
ierr = MatGetSize(A,&m,0);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_WORLD,m,0,1,&perm);CHKERRQ(ierr);
ierr = MatLUFactorSymbolic(F,A,perm,perm,&iluinfo);CHKERRQ(ierr);
ierr = MatLUFactorNumeric(F,A,&iluinfo);CHKERRQ(ierr);
ierr = MatSolveTranspose(F,x,y);CHKERRQ(ierr);
F->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_N;
ierr = MatSolveTranspose(F,x,w);CHKERRQ(ierr);
/* VecView(w,0);VecView(y,0); */
ierr = VecAXPY(w,-1.0,y);CHKERRQ(ierr);
ierr = VecNorm(w,NORM_2,&norm);CHKERRQ(ierr);
if (norm) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Norm of difference is nonzero %g\n",norm);CHKERRQ(ierr);
}
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&F);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&w);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Mat C,A;
PetscInt i,j,m = 5,n = 5,Ii,J;
PetscErrorCode ierr;
PetscScalar v,five = 5.0,one = 1.0;
IS isrow,row,col;
Vec x,u,b;
PetscReal norm;
MatFactorInfo info;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-m",&m,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,m*n,m*n,5,NULL,&C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
/* create the matrix for the five point stencil, YET AGAIN*/
for (i=0; i<m; i++) {
for (j=0; j<n; j++) {
v = -1.0; Ii = j + n*i;
if (i>0) {J = Ii - n; ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
if (i<m-1) {J = Ii + n; ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
if (j>0) {J = Ii - 1; ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
if (j<n-1) {J = Ii + 1; ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);}
v = 4.0; ierr = MatSetValues(C,1,&Ii,1,&Ii,&v,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF,(m*n)/2,0,2,&isrow);CHKERRQ(ierr);
ierr = MatZeroRowsIS(C,isrow,five,0,0);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,m*n,&u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&x);CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = VecSet(u,one);CHKERRQ(ierr);
ierr = MatMultTranspose(C,u,b);CHKERRQ(ierr);
/* Set default ordering to be Quotient Minimum Degree; also read
orderings from the options database */
ierr = MatGetOrdering(C,MATORDERINGQMD,&row,&col);CHKERRQ(ierr);
ierr = MatFactorInfoInitialize(&info);CHKERRQ(ierr);
ierr = MatGetFactor(C,MATSOLVERPETSC,MAT_FACTOR_LU,&A);CHKERRQ(ierr);
ierr = MatLUFactorSymbolic(A,C,row,col,&info);CHKERRQ(ierr);
ierr = MatLUFactorNumeric(A,C,&info);CHKERRQ(ierr);
ierr = MatSolveTranspose(A,b,x);CHKERRQ(ierr);
ierr = ISView(row,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = VecAXPY(x,-1.0,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"Norm of error %g\n",(double)norm);CHKERRQ(ierr);
ierr = ISDestroy(&row);CHKERRQ(ierr);
ierr = ISDestroy(&col);CHKERRQ(ierr);
ierr = ISDestroy(&isrow);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&A);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;
}
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 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);
}
static PetscErrorCode PCSetUp_ILU(PC pc)
{
PetscErrorCode ierr;
PC_ILU *ilu = (PC_ILU*)pc->data;
MatInfo info;
PetscBool flg;
PetscFunctionBegin;
/* ugly hack to change default, since it is not support by some matrix types */
if (((PC_Factor*)ilu)->info.shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATSEQAIJ,&flg);CHKERRQ(ierr);
if (!flg) {
ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATMPIAIJ,&flg);CHKERRQ(ierr);
if (!flg) {
((PC_Factor*)ilu)->info.shifttype = (PetscReal)MAT_SHIFT_INBLOCKS;
PetscInfo(pc,"Changing shift type from NONZERO to INBLOCKS because block matrices do not support NONZERO");CHKERRQ(ierr);
}
}
}
if (ilu->inplace) {
CHKMEMQ;
if (!pc->setupcalled) {
/* In-place factorization only makes sense with the natural ordering,
so we only need to get the ordering once, even if nonzero structure changes */
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);CHKERRQ(ierr);
if (ilu->row) {ierr = PetscLogObjectParent(pc,ilu->row);CHKERRQ(ierr);}
if (ilu->col) {ierr = PetscLogObjectParent(pc,ilu->col);CHKERRQ(ierr);}
}
/* In place ILU only makes sense with fill factor of 1.0 because
cannot have levels of fill */
((PC_Factor*)ilu)->info.fill = 1.0;
((PC_Factor*)ilu)->info.diagonal_fill = 0.0;
ierr = MatILUFactor(pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);CHKERRQ(ierr);CHKMEMQ;
((PC_Factor*)ilu)->fact = pc->pmat;
} else {
if (!pc->setupcalled) {
/* first time in so compute reordering and symbolic factorization */
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);CHKERRQ(ierr);
if (ilu->row) {ierr = PetscLogObjectParent(pc,ilu->row);CHKERRQ(ierr);}
if (ilu->col) {ierr = PetscLogObjectParent(pc,ilu->col);CHKERRQ(ierr);}
/* Remove zeros along diagonal? */
if (ilu->nonzerosalongdiagonal) {
ierr = MatReorderForNonzeroDiagonal(pc->pmat,ilu->nonzerosalongdiagonaltol,ilu->row,ilu->col);CHKERRQ(ierr);
}
if (!((PC_Factor*)ilu)->fact){
ierr = MatGetFactor(pc->pmat,((PC_Factor*)ilu)->solvertype,MAT_FACTOR_ILU,&((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
}
ierr = MatILUFactorSymbolic(((PC_Factor*)ilu)->fact,pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)ilu)->fact,MAT_LOCAL,&info);CHKERRQ(ierr);
ilu->actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent(pc,((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
} else if (pc->flag != SAME_NONZERO_PATTERN) {
if (!ilu->reuseordering) {
/* compute a new ordering for the ILU */
ierr = ISDestroy(&ilu->row);CHKERRQ(ierr);
ierr = ISDestroy(&ilu->col);CHKERRQ(ierr);
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);CHKERRQ(ierr);
if (ilu->row) {ierr = PetscLogObjectParent(pc,ilu->row);CHKERRQ(ierr);}
if (ilu->col) {ierr = PetscLogObjectParent(pc,ilu->col);CHKERRQ(ierr);}
/* Remove zeros along diagonal? */
if (ilu->nonzerosalongdiagonal) {
ierr = MatReorderForNonzeroDiagonal(pc->pmat,ilu->nonzerosalongdiagonaltol,ilu->row,ilu->col);CHKERRQ(ierr);
}
}
ierr = MatDestroy(&((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
ierr = MatGetFactor(pc->pmat,((PC_Factor*)ilu)->solvertype,MAT_FACTOR_ILU,&((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
ierr = MatILUFactorSymbolic(((PC_Factor*)ilu)->fact,pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)ilu)->fact,MAT_LOCAL,&info);CHKERRQ(ierr);
ilu->actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent(pc,((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
}
CHKMEMQ;
ierr = MatLUFactorNumeric(((PC_Factor*)ilu)->fact,pc->pmat,&((PC_Factor*)ilu)->info);CHKERRQ(ierr);
CHKMEMQ;
}
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)
{
Mat A,RHS,C,F,X;
Vec u,x,b;
PetscErrorCode ierr;
PetscMPIInt rank,nproc;
PetscInt i,m,n,nfact,nsolve,nrhs,ipack=0;
PetscScalar *array,rval;
PetscReal norm,tol=1.e-12;
IS perm,iperm;
MatFactorInfo info;
PetscRandom rand;
PetscBool flg,testMatSolve=PETSC_TRUE,testMatMatSolve=PETSC_TRUE;
PetscViewer fd; /* viewer */
char file[PETSC_MAX_PATH_LEN]; /* input file name */
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);
/* Determine file from which we read the matrix A */
ierr = PetscOptionsGetString(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 = 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);
/* Create dense matrix C and X; C holds true solution with identical colums */
nrhs = 2;
ierr = PetscOptionsGetInt(NULL,"-nrhs",&nrhs,NULL);CHKERRQ(ierr);
if (!rank) printf("ex125: nrhs %d\n",nrhs);
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 */
/* Test LU Factorization */
ierr = MatGetOrdering(A,MATORDERINGND,&perm,&iperm);CHKERRQ(ierr);
/*ierr = ISView(perm,PETSC_VIEWER_STDOUT_WORLD);*/
/*ierr = ISView(perm,PETSC_VIEWER_STDOUT_SELF);*/
ierr = PetscOptionsGetInt(NULL,"-mat_solver_package",&ipack,NULL);CHKERRQ(ierr);
switch (ipack) {
case 0:
#if defined(PETSC_HAVE_SUPERLU)
if (!rank) printf(" SUPERLU LU:\n");
ierr = MatGetFactor(A,MATSOLVERSUPERLU,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
break;
#endif
case 1:
#if defined(PETSC_HAVE_SUPERLU_DIST)
if (!rank) printf(" SUPERLU_DIST LU:\n");
ierr = MatGetFactor(A,MATSOLVERSUPERLU_DIST,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
break;
#endif
case 2:
#if defined(PETSC_HAVE_MUMPS)
if (!rank) printf(" MUMPS LU:\n");
ierr = MatGetFactor(A,MATSOLVERMUMPS,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
{
/* test mumps options */
PetscInt icntl_7 = 5;
ierr = MatMumpsSetIcntl(F,7,icntl_7);CHKERRQ(ierr);
}
break;
#endif
default:
if (!rank) printf(" PETSC LU:\n");
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
}
info.fill = 5.0;
ierr = MatLUFactorSymbolic(F,A,perm,iperm,&info);CHKERRQ(ierr);
for (nfact = 0; nfact < 2; nfact++) {
if (!rank) printf(" %d-the LU numfactorization \n",nfact);
ierr = MatLUFactorNumeric(F,A,&info);CHKERRQ(ierr);
/* Test MatMatSolve() */
/*
if ((ipack == 0 || ipack == 2) && testMatMatSolve) {
printf(" MatMatSolve() is not implemented for this package. Skip the testing.\n");
testMatMatSolve = PETSC_FALSE;
}
*/
if (testMatMatSolve) {
if (!nfact) {
ierr = MatMatMult(A,C,MAT_INITIAL_MATRIX,2.0,&RHS);CHKERRQ(ierr);
} else {
ierr = MatMatMult(A,C,MAT_REUSE_MATRIX,2.0,&RHS);CHKERRQ(ierr);
}
for (nsolve = 0; nsolve < 2; nsolve++) {
if (!rank) printf(" %d-the MatMatSolve \n",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) {
if (!rank) {
ierr = PetscPrintf(PETSC_COMM_SELF,"1st MatMatSolve: Norm of error %g, nsolve %d\n",norm,nsolve);CHKERRQ(ierr);
}
}
}
}
/* Test MatSolve() */
if (testMatSolve) {
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(A,x,b);CHKERRQ(ierr);
if (!rank) printf(" %d-the MatSolve \n",nsolve);
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) {
ierr = MatMult(A,x,u);CHKERRQ(ierr); /* u = A*x */
PetscReal resi;
ierr = VecAXPY(u,-1.0,b);CHKERRQ(ierr); /* u <- (-1.0)b + u */
ierr = VecNorm(u,NORM_2,&resi);CHKERRQ(ierr);
if (!rank) {
ierr = PetscPrintf(PETSC_COMM_SELF,"MatSolve: Norm of error %g, resi %g, LU numfact %d\n",norm,resi,nfact);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);
if (testMatMatSolve) {
ierr = MatDestroy(&RHS);CHKERRQ(ierr);
}
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 = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Mat A,B,Fact;
Vec xx,s1,s2,yy;
PetscErrorCode ierr;
PetscInt m=45,rows[2],cols[2],bs=1,i,row,col,*idx,M;
PetscScalar rval,vals1[4],vals2[4];
PetscRandom rdm;
IS is1,is2;
PetscReal s1norm,s2norm,rnorm,tol = 1.e-4;
PetscBool flg;
MatFactorInfo info;
PetscInitialize(&argc,&args,(char*)0,help);
/* Test MatSetValues() and MatGetValues() */
ierr = PetscOptionsGetInt(NULL,"-mat_block_size",&bs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-mat_size",&m,NULL);CHKERRQ(ierr);
M = m*bs;
ierr = MatCreateSeqBAIJ(PETSC_COMM_SELF,bs,M,M,1,NULL,&A);CHKERRQ(ierr);
ierr = MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,M,M,15,NULL,&B);CHKERRQ(ierr);
ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_SELF,&rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,M,&xx);CHKERRQ(ierr);
ierr = VecDuplicate(xx,&s1);CHKERRQ(ierr);
ierr = VecDuplicate(xx,&s2);CHKERRQ(ierr);
ierr = VecDuplicate(xx,&yy);CHKERRQ(ierr);
/* For each row add atleast 15 elements */
for (row=0; row<M; row++) {
for (i=0; i<25*bs; i++) {
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
col = (PetscInt)(PetscRealPart(rval)*M);
ierr = MatSetValues(A,1,&row,1,&col,&rval,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(B,1,&row,1,&col,&rval,INSERT_VALUES);CHKERRQ(ierr);
}
}
/* Now set blocks of values */
for (i=0; i<20*bs; i++) {
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
cols[0] = (PetscInt)(PetscRealPart(rval)*M);
vals1[0] = rval;
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
cols[1] = (PetscInt)(PetscRealPart(rval)*M);
vals1[1] = rval;
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
rows[0] = (PetscInt)(PetscRealPart(rval)*M);
vals1[2] = rval;
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
rows[1] = (PetscInt)(PetscRealPart(rval)*M);
vals1[3] = rval;
ierr = MatSetValues(A,2,rows,2,cols,vals1,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(B,2,rows,2,cols,vals1,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Test MatNorm() */
ierr = MatNorm(A,NORM_FROBENIUS,&s1norm);CHKERRQ(ierr);
ierr = MatNorm(B,NORM_FROBENIUS,&s2norm);CHKERRQ(ierr);
rnorm = PetscAbsReal(s2norm-s1norm)/s2norm;
if (rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_FROBENIUS()- NormA=%16.14e NormB=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_INFINITY,&s1norm);CHKERRQ(ierr);
ierr = MatNorm(B,NORM_INFINITY,&s2norm);CHKERRQ(ierr);
rnorm = PetscAbsReal(s2norm-s1norm)/s2norm;
if (rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_INFINITY()- NormA=%16.14e NormB=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_1,&s1norm);CHKERRQ(ierr);
ierr = MatNorm(B,NORM_1,&s2norm);CHKERRQ(ierr);
rnorm = PetscAbsReal(s2norm-s1norm)/s2norm;
if (rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_NORM_1()- NormA=%16.14e NormB=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
/* MatShift() */
rval = 10*s1norm;
ierr = MatShift(A,rval);CHKERRQ(ierr);
ierr = MatShift(B,rval);CHKERRQ(ierr);
/* Test MatTranspose() */
ierr = MatTranspose(A,MAT_REUSE_MATRIX,&A);CHKERRQ(ierr);
ierr = MatTranspose(B,MAT_REUSE_MATRIX,&B);CHKERRQ(ierr);
/* Now do MatGetValues() */
for (i=0; i<30; i++) {
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
cols[0] = (PetscInt)(PetscRealPart(rval)*M);
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
cols[1] = (PetscInt)(PetscRealPart(rval)*M);
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
rows[0] = (PetscInt)(PetscRealPart(rval)*M);
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
rows[1] = (PetscInt)(PetscRealPart(rval)*M);
ierr = MatGetValues(A,2,rows,2,cols,vals1);CHKERRQ(ierr);
ierr = MatGetValues(B,2,rows,2,cols,vals2);CHKERRQ(ierr);
ierr = PetscMemcmp(vals1,vals2,4*sizeof(PetscScalar),&flg);CHKERRQ(ierr);
if (!flg) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetValues bs = %D\n",bs);CHKERRQ(ierr);
}
}
/* Test MatMult(), MatMultAdd() */
for (i=0; i<40; i++) {
ierr = VecSetRandom(xx,rdm);CHKERRQ(ierr);
ierr = VecSet(s2,0.0);CHKERRQ(ierr);
ierr = MatMult(A,xx,s1);CHKERRQ(ierr);
ierr = MatMultAdd(A,xx,s2,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"MatMult not equal to MatMultAdd Norm1=%e Norm2=%e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
}
/* Test MatMult() */
ierr = MatMultEqual(A,B,10,&flg);CHKERRQ(ierr);
if (!flg) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMult()\n");CHKERRQ(ierr);
}
/* Test MatMultAdd() */
ierr = MatMultAddEqual(A,B,10,&flg);CHKERRQ(ierr);
if (!flg) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMultAdd()\n");CHKERRQ(ierr);
}
/* Test MatMultTranspose() */
ierr = MatMultTransposeEqual(A,B,10,&flg);CHKERRQ(ierr);
if (!flg) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMultTranspose()\n");CHKERRQ(ierr);
}
/* Test MatMultTransposeAdd() */
ierr = MatMultTransposeAddEqual(A,B,10,&flg);CHKERRQ(ierr);
if (!flg) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMultTransposeAdd()\n");CHKERRQ(ierr);
}
/* Do LUFactor() on both the matrices */
ierr = PetscMalloc1(M,&idx);CHKERRQ(ierr);
for (i=0; i<M; i++) idx[i] = i;
ierr = ISCreateGeneral(PETSC_COMM_SELF,M,idx,PETSC_COPY_VALUES,&is1);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,M,idx,PETSC_COPY_VALUES,&is2);CHKERRQ(ierr);
ierr = PetscFree(idx);CHKERRQ(ierr);
ierr = ISSetPermutation(is1);CHKERRQ(ierr);
ierr = ISSetPermutation(is2);CHKERRQ(ierr);
ierr = MatFactorInfoInitialize(&info);CHKERRQ(ierr);
info.fill = 2.0;
info.dtcol = 0.0;
info.zeropivot = 1.e-14;
info.pivotinblocks = 1.0;
if (bs < 4) {
ierr = MatGetFactor(A,"petsc",MAT_FACTOR_LU,&Fact);CHKERRQ(ierr);
ierr = MatLUFactorSymbolic(Fact,A,is1,is2,&info);CHKERRQ(ierr);
ierr = MatLUFactorNumeric(Fact,A,&info);CHKERRQ(ierr);
ierr = VecSetRandom(yy,rdm);CHKERRQ(ierr);
ierr = MatForwardSolve(Fact,yy,xx);CHKERRQ(ierr);
ierr = MatBackwardSolve(Fact,xx,s1);CHKERRQ(ierr);
ierr = MatDestroy(&Fact);CHKERRQ(ierr);
ierr = VecScale(s1,-1.0);CHKERRQ(ierr);
ierr = MatMultAdd(A,s1,yy,yy);CHKERRQ(ierr);
ierr = VecNorm(yy,NORM_2,&rnorm);CHKERRQ(ierr);
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatForwardSolve/MatBackwardSolve - Norm1=%16.14e bs = %D\n",rnorm,bs);CHKERRQ(ierr);
}
}
ierr = MatLUFactor(B,is1,is2,&info);CHKERRQ(ierr);
ierr = MatLUFactor(A,is1,is2,&info);CHKERRQ(ierr);
/* Test MatSolveAdd() */
for (i=0; i<10; i++) {
ierr = VecSetRandom(xx,rdm);CHKERRQ(ierr);
ierr = VecSetRandom(yy,rdm);CHKERRQ(ierr);
ierr = MatSolveAdd(B,xx,yy,s2);CHKERRQ(ierr);
ierr = MatSolveAdd(A,xx,yy,s1);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatSolveAdd - Norm1=%16.14e Norm2=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
}
/* Test MatSolveAdd() when x = A'b +x */
for (i=0; i<10; i++) {
ierr = VecSetRandom(xx,rdm);CHKERRQ(ierr);
ierr = VecSetRandom(s1,rdm);CHKERRQ(ierr);
ierr = VecCopy(s2,s1);CHKERRQ(ierr);
ierr = MatSolveAdd(B,xx,s2,s2);CHKERRQ(ierr);
ierr = MatSolveAdd(A,xx,s1,s1);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatSolveAdd(same) - Norm1=%16.14e Norm2=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
}
/* Test MatSolve() */
for (i=0; i<10; i++) {
ierr = VecSetRandom(xx,rdm);CHKERRQ(ierr);
ierr = MatSolve(B,xx,s2);CHKERRQ(ierr);
ierr = MatSolve(A,xx,s1);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatSolve - Norm1=%16.14e Norm2=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
}
/* Test MatSolveTranspose() */
if (bs < 8) {
for (i=0; i<10; i++) {
ierr = VecSetRandom(xx,rdm);CHKERRQ(ierr);
ierr = MatSolveTranspose(B,xx,s2);CHKERRQ(ierr);
ierr = MatSolveTranspose(A,xx,s1);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatSolveTranspose - Norm1=%16.14e Norm2=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
}
}
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = VecDestroy(&xx);CHKERRQ(ierr);
ierr = VecDestroy(&s1);CHKERRQ(ierr);
ierr = VecDestroy(&s2);CHKERRQ(ierr);
ierr = VecDestroy(&yy);CHKERRQ(ierr);
ierr = ISDestroy(&is1);CHKERRQ(ierr);
ierr = ISDestroy(&is2);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 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;
}
Example: mpiexec -n <np> ./ex130 -f <matrix binary file> -mat_solver_package 1 -mat_superlu_equil \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,ipack=0;
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 LU Factorization */
ierr = MatGetOrdering(A,MATORDERINGNATURAL,&perm,&iperm);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-mat_solver_package",&ipack,NULL);CHKERRQ(ierr);
switch (ipack) {
case 1:
#if defined(PETSC_HAVE_SUPERLU)
if (!rank) printf(" SUPERLU LU:\n");
ierr = MatGetFactor(A,MATSOLVERSUPERLU,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
break;
#endif
case 2:
#if defined(PETSC_HAVE_MUMPS)
if (!rank) printf(" MUMPS LU:\n");
ierr = MatGetFactor(A,MATSOLVERMUMPS,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
{
/* test mumps options */
PetscInt icntl_7 = 5;
ierr = MatMumpsSetIcntl(F,7,icntl_7);CHKERRQ(ierr);
}
break;
#endif
default:
if (!rank) printf(" PETSC LU:\n");
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
}
info.fill = 5.0;
ierr = MatLUFactorSymbolic(F,A,perm,iperm,&info);CHKERRQ(ierr);
for (nfact = 0; nfact < 1; nfact++) {
if (!rank) printf(" %d-the LU numfactorization \n",nfact);
ierr = MatLUFactorNumeric(F,A,&info);CHKERRQ(ierr);
/* Test MatSolve() */
if (testMatSolve) {
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)
{
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;
}
static PetscErrorCode PCSetUp_ILU(PC pc)
{
PetscErrorCode ierr;
PC_ILU *ilu = (PC_ILU*)pc->data;
MatInfo info;
PetscBool flg;
const MatSolverPackage stype;
MatFactorError err;
PetscFunctionBegin;
pc->failedreason = PC_NOERROR;
/* ugly hack to change default, since it is not support by some matrix types */
if (((PC_Factor*)ilu)->info.shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATSEQAIJ,&flg);CHKERRQ(ierr);
if (!flg) {
ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATMPIAIJ,&flg);CHKERRQ(ierr);
if (!flg) {
((PC_Factor*)ilu)->info.shifttype = (PetscReal)MAT_SHIFT_INBLOCKS;
PetscInfo(pc,"Changing shift type from NONZERO to INBLOCKS because block matrices do not support NONZERO\n");CHKERRQ(ierr);
}
}
}
ierr = MatSetErrorIfFailure(pc->pmat,pc->erroriffailure);CHKERRQ(ierr);
if (ilu->hdr.inplace) {
if (!pc->setupcalled) {
/* In-place factorization only makes sense with the natural ordering,
so we only need to get the ordering once, even if nonzero structure changes */
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);CHKERRQ(ierr);
if (ilu->row) {ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->row);CHKERRQ(ierr);}
if (ilu->col) {ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->col);CHKERRQ(ierr);}
}
/* In place ILU only makes sense with fill factor of 1.0 because
cannot have levels of fill */
((PC_Factor*)ilu)->info.fill = 1.0;
((PC_Factor*)ilu)->info.diagonal_fill = 0.0;
ierr = MatILUFactor(pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);CHKERRQ(ierr);CHKERRQ(ierr);
ierr = MatFactorGetError(pc->pmat,&err);CHKERRQ(ierr);
if (err) { /* Factor() fails */
pc->failedreason = (PCFailedReason)err;
PetscFunctionReturn(0);
}
((PC_Factor*)ilu)->fact = pc->pmat;
/* must update the pc record of the matrix state or the PC will attempt to run PCSetUp() yet again */
ierr = PetscObjectStateGet((PetscObject)pc->pmat,&pc->matstate);CHKERRQ(ierr);
} else {
if (!pc->setupcalled) {
/* first time in so compute reordering and symbolic factorization */
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);CHKERRQ(ierr);
if (ilu->row) {ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->row);CHKERRQ(ierr);}
if (ilu->col) {ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->col);CHKERRQ(ierr);}
/* Remove zeros along diagonal? */
if (ilu->nonzerosalongdiagonal) {
ierr = MatReorderForNonzeroDiagonal(pc->pmat,ilu->nonzerosalongdiagonaltol,ilu->row,ilu->col);CHKERRQ(ierr);
}
if (!((PC_Factor*)ilu)->fact) {
ierr = MatGetFactor(pc->pmat,((PC_Factor*)ilu)->solvertype,MAT_FACTOR_ILU,&((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
}
ierr = MatILUFactorSymbolic(((PC_Factor*)ilu)->fact,pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)ilu)->fact,MAT_LOCAL,&info);CHKERRQ(ierr);
ilu->hdr.actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
} else if (pc->flag != SAME_NONZERO_PATTERN) {
if (!ilu->hdr.reuseordering) {
/* compute a new ordering for the ILU */
ierr = ISDestroy(&ilu->row);CHKERRQ(ierr);
ierr = ISDestroy(&ilu->col);CHKERRQ(ierr);
ierr = MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);CHKERRQ(ierr);
if (ilu->row) {ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->row);CHKERRQ(ierr);}
if (ilu->col) {ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->col);CHKERRQ(ierr);}
/* Remove zeros along diagonal? */
if (ilu->nonzerosalongdiagonal) {
ierr = MatReorderForNonzeroDiagonal(pc->pmat,ilu->nonzerosalongdiagonaltol,ilu->row,ilu->col);CHKERRQ(ierr);
}
}
ierr = MatDestroy(&((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
ierr = MatGetFactor(pc->pmat,((PC_Factor*)ilu)->solvertype,MAT_FACTOR_ILU,&((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
ierr = MatILUFactorSymbolic(((PC_Factor*)ilu)->fact,pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);CHKERRQ(ierr);
ierr = MatGetInfo(((PC_Factor*)ilu)->fact,MAT_LOCAL,&info);CHKERRQ(ierr);
ilu->hdr.actualfill = info.fill_ratio_needed;
ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)((PC_Factor*)ilu)->fact);CHKERRQ(ierr);
}
ierr = MatFactorGetError(((PC_Factor*)ilu)->fact,&err);CHKERRQ(ierr);
if (err) { /* FactorSymbolic() fails */
pc->failedreason = (PCFailedReason)err;
PetscFunctionReturn(0);
}
ierr = MatLUFactorNumeric(((PC_Factor*)ilu)->fact,pc->pmat,&((PC_Factor*)ilu)->info);CHKERRQ(ierr);
ierr = MatFactorGetError(((PC_Factor*)ilu)->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*)ilu)->fact,&solverpackage);CHKERRQ(ierr);
ierr = PCFactorSetMatSolverPackage(pc,solverpackage);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
/*
DMDAGetFaceInterpolation - Gets the interpolation for a face based coarse space
*/
PetscErrorCode DMDAGetFaceInterpolation(DM da,PC_Exotic *exotic,Mat Aglobal,MatReuse reuse,Mat *P)
{
PetscErrorCode ierr;
PetscInt dim,i,j,k,m,n,p,dof,Nint,Nface,Nwire,Nsurf,*Iint,*Isurf,cint = 0,csurf = 0,istart,jstart,kstart,*II,N,c = 0;
PetscInt mwidth,nwidth,pwidth,cnt,mp,np,pp,Ntotal,gl[6],*globals,Ng,*IIint,*IIsurf,Nt;
Mat Xint, Xsurf,Xint_tmp;
IS isint,issurf,is,row,col;
ISLocalToGlobalMapping ltg;
MPI_Comm comm;
Mat A,Aii,Ais,Asi,*Aholder,iAii;
MatFactorInfo info;
PetscScalar *xsurf,*xint;
#if defined(PETSC_USE_DEBUG_foo)
PetscScalar tmp;
#endif
PetscTable ht;
PetscFunctionBegin;
ierr = DMDAGetInfo(da,&dim,0,0,0,&mp,&np,&pp,&dof,0,0,0,0,0);
CHKERRQ(ierr);
if (dof != 1) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_SUP,"Only for single field problems");
if (dim != 3) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_SUP,"Only coded for 3d problems");
ierr = DMDAGetCorners(da,0,0,0,&m,&n,&p);
CHKERRQ(ierr);
ierr = DMDAGetGhostCorners(da,&istart,&jstart,&kstart,&mwidth,&nwidth,&pwidth);
CHKERRQ(ierr);
istart = istart ? -1 : 0;
jstart = jstart ? -1 : 0;
kstart = kstart ? -1 : 0;
/*
the columns of P are the interpolation of each coarse grid point (one for each vertex and edge)
to all the local degrees of freedom (this includes the vertices, edges and faces).
Xint are the subset of the interpolation into the interior
Xface are the interpolation onto faces but not into the interior
Xsurf are the interpolation onto the vertices and edges (the surfbasket)
Xint
Symbolically one could write P = (Xface) after interchanging the rows to match the natural ordering on the domain
Xsurf
*/
N = (m - istart)*(n - jstart)*(p - kstart);
Nint = (m-2-istart)*(n-2-jstart)*(p-2-kstart);
Nface = 2*((m-2-istart)*(n-2-jstart) + (m-2-istart)*(p-2-kstart) + (n-2-jstart)*(p-2-kstart));
Nwire = 4*((m-2-istart) + (n-2-jstart) + (p-2-kstart)) + 8;
Nsurf = Nface + Nwire;
ierr = MatCreateSeqDense(MPI_COMM_SELF,Nint,6,NULL,&Xint);
CHKERRQ(ierr);
ierr = MatCreateSeqDense(MPI_COMM_SELF,Nsurf,6,NULL,&Xsurf);
CHKERRQ(ierr);
ierr = MatDenseGetArray(Xsurf,&xsurf);
CHKERRQ(ierr);
/*
Require that all 12 edges and 6 faces have at least one grid point. Otherwise some of the columns of
Xsurf will be all zero (thus making the coarse matrix singular).
*/
if (m-istart < 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Number of grid points per process in X direction must be at least 3");
if (n-jstart < 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Number of grid points per process in Y direction must be at least 3");
if (p-kstart < 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Number of grid points per process in Z direction must be at least 3");
cnt = 0;
for (j=1; j<n-1-jstart; j++) {
for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 0*Nsurf] = 1;
}
for (k=1; k<p-1-kstart; k++) {
for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 1*Nsurf] = 1;
for (j=1; j<n-1-jstart; j++) {
xsurf[cnt++ + 2*Nsurf] = 1;
/* these are the interior nodes */
xsurf[cnt++ + 3*Nsurf] = 1;
}
for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 4*Nsurf] = 1;
}
for (j=1; j<n-1-jstart; j++) {
for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 5*Nsurf] = 1;
}
#if defined(PETSC_USE_DEBUG_foo)
for (i=0; i<Nsurf; i++) {
tmp = 0.0;
for (j=0; j<6; j++) tmp += xsurf[i+j*Nsurf];
if (PetscAbsScalar(tmp-1.0) > 1.e-10) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Wrong Xsurf interpolation at i %D value %g",i,(double)PetscAbsScalar(tmp));
}
#endif
ierr = MatDenseRestoreArray(Xsurf,&xsurf);
CHKERRQ(ierr);
/* ierr = MatView(Xsurf,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);*/
/*
I are the indices for all the needed vertices (in global numbering)
Iint are the indices for the interior values, I surf for the surface values
(This is just for the part of the global matrix obtained with MatGetSubMatrix(), it
is NOT the local DMDA ordering.)
IIint and IIsurf are the same as the Iint, Isurf except they are in the global numbering
*/
#define Endpoint(a,start,b) (a == 0 || a == (b-1-start))
ierr = PetscMalloc3(N,&II,Nint,&Iint,Nsurf,&Isurf);
CHKERRQ(ierr);
ierr = PetscMalloc2(Nint,&IIint,Nsurf,&IIsurf);
CHKERRQ(ierr);
for (k=0; k<p-kstart; k++) {
for (j=0; j<n-jstart; j++) {
for (i=0; i<m-istart; i++) {
II[c++] = i + j*mwidth + k*mwidth*nwidth;
if (!Endpoint(i,istart,m) && !Endpoint(j,jstart,n) && !Endpoint(k,kstart,p)) {
IIint[cint] = i + j*mwidth + k*mwidth*nwidth;
Iint[cint++] = i + j*(m-istart) + k*(m-istart)*(n-jstart);
} else {
IIsurf[csurf] = i + j*mwidth + k*mwidth*nwidth;
Isurf[csurf++] = i + j*(m-istart) + k*(m-istart)*(n-jstart);
}
}
}
}
if (c != N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"c != N");
if (cint != Nint) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"cint != Nint");
if (csurf != Nsurf) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csurf != Nsurf");
ierr = DMGetLocalToGlobalMapping(da,<g);
CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingApply(ltg,N,II,II);
CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingApply(ltg,Nint,IIint,IIint);
CHKERRQ(ierr);
ierr = ISLocalToGlobalMappingApply(ltg,Nsurf,IIsurf,IIsurf);
CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)da,&comm);
CHKERRQ(ierr);
ierr = ISCreateGeneral(comm,N,II,PETSC_COPY_VALUES,&is);
CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,Nint,Iint,PETSC_COPY_VALUES,&isint);
CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,Nsurf,Isurf,PETSC_COPY_VALUES,&issurf);
CHKERRQ(ierr);
ierr = PetscFree3(II,Iint,Isurf);
CHKERRQ(ierr);
ierr = ISSort(is);
CHKERRQ(ierr);
ierr = MatGetSubMatrices(Aglobal,1,&is,&is,MAT_INITIAL_MATRIX,&Aholder);
CHKERRQ(ierr);
A = *Aholder;
ierr = PetscFree(Aholder);
CHKERRQ(ierr);
ierr = MatGetSubMatrix(A,isint,isint,MAT_INITIAL_MATRIX,&Aii);
CHKERRQ(ierr);
ierr = MatGetSubMatrix(A,isint,issurf,MAT_INITIAL_MATRIX,&Ais);
CHKERRQ(ierr);
ierr = MatGetSubMatrix(A,issurf,isint,MAT_INITIAL_MATRIX,&Asi);
CHKERRQ(ierr);
/*
Solve for the interpolation onto the interior Xint
*/
ierr = MatMatMult(Ais,Xsurf,MAT_INITIAL_MATRIX,PETSC_DETERMINE,&Xint_tmp);
CHKERRQ(ierr);
ierr = MatScale(Xint_tmp,-1.0);
CHKERRQ(ierr);
if (exotic->directSolve) {
ierr = MatGetFactor(Aii,MATSOLVERPETSC,MAT_FACTOR_LU,&iAii);
CHKERRQ(ierr);
ierr = MatFactorInfoInitialize(&info);
CHKERRQ(ierr);
ierr = MatGetOrdering(Aii,MATORDERINGND,&row,&col);
CHKERRQ(ierr);
ierr = MatLUFactorSymbolic(iAii,Aii,row,col,&info);
CHKERRQ(ierr);
ierr = ISDestroy(&row);
CHKERRQ(ierr);
ierr = ISDestroy(&col);
CHKERRQ(ierr);
ierr = MatLUFactorNumeric(iAii,Aii,&info);
CHKERRQ(ierr);
ierr = MatMatSolve(iAii,Xint_tmp,Xint);
CHKERRQ(ierr);
ierr = MatDestroy(&iAii);
CHKERRQ(ierr);
} else {
Vec b,x;
PetscScalar *xint_tmp;
ierr = MatDenseGetArray(Xint,&xint);
CHKERRQ(ierr);
ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,Nint,0,&x);
CHKERRQ(ierr);
ierr = MatDenseGetArray(Xint_tmp,&xint_tmp);
CHKERRQ(ierr);
ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,Nint,0,&b);
CHKERRQ(ierr);
ierr = KSPSetOperators(exotic->ksp,Aii,Aii);
CHKERRQ(ierr);
for (i=0; i<6; i++) {
ierr = VecPlaceArray(x,xint+i*Nint);
CHKERRQ(ierr);
ierr = VecPlaceArray(b,xint_tmp+i*Nint);
CHKERRQ(ierr);
ierr = KSPSolve(exotic->ksp,b,x);
CHKERRQ(ierr);
ierr = VecResetArray(x);
CHKERRQ(ierr);
ierr = VecResetArray(b);
CHKERRQ(ierr);
}
ierr = MatDenseRestoreArray(Xint,&xint);
CHKERRQ(ierr);
ierr = MatDenseRestoreArray(Xint_tmp,&xint_tmp);
CHKERRQ(ierr);
ierr = VecDestroy(&x);
CHKERRQ(ierr);
ierr = VecDestroy(&b);
CHKERRQ(ierr);
}
ierr = MatDestroy(&Xint_tmp);
CHKERRQ(ierr);
#if defined(PETSC_USE_DEBUG_foo)
ierr = MatDenseGetArray(Xint,&xint);
CHKERRQ(ierr);
for (i=0; i<Nint; i++) {
tmp = 0.0;
for (j=0; j<6; j++) tmp += xint[i+j*Nint];
if (PetscAbsScalar(tmp-1.0) > 1.e-10) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Wrong Xint interpolation at i %D value %g",i,(double)PetscAbsScalar(tmp));
}
ierr = MatDenseRestoreArray(Xint,&xint);
CHKERRQ(ierr);
/* ierr =MatView(Xint,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); */
#endif
/* total faces */
Ntotal = mp*np*(pp+1) + mp*pp*(np+1) + np*pp*(mp+1);
/*
For each vertex, edge, face on process (in the same orderings as used above) determine its local number including ghost points
*/
cnt = 0;
{
gl[cnt++] = mwidth+1;
}
{
{
gl[cnt++] = mwidth*nwidth+1;
}
{
gl[cnt++] = mwidth*nwidth + mwidth; /* these are the interior nodes */ gl[cnt++] = mwidth*nwidth + mwidth+m-istart-1;
}
{
gl[cnt++] = mwidth*nwidth+mwidth*(n-jstart-1)+1;
}
}
{
gl[cnt++] = mwidth*nwidth*(p-kstart-1) + mwidth+1;
}
/* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */
/* convert that to global numbering and get them on all processes */
ierr = ISLocalToGlobalMappingApply(ltg,6,gl,gl);
CHKERRQ(ierr);
/* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */
ierr = PetscMalloc1(6*mp*np*pp,&globals);
CHKERRQ(ierr);
ierr = MPI_Allgather(gl,6,MPIU_INT,globals,6,MPIU_INT,PetscObjectComm((PetscObject)da));
CHKERRQ(ierr);
/* Number the coarse grid points from 0 to Ntotal */
ierr = MatGetSize(Aglobal,&Nt,NULL);
CHKERRQ(ierr);
ierr = PetscTableCreate(Ntotal/3,Nt+1,&ht);
CHKERRQ(ierr);
for (i=0; i<6*mp*np*pp; i++) {
ierr = PetscTableAddCount(ht,globals[i]+1);
CHKERRQ(ierr);
}
ierr = PetscTableGetCount(ht,&cnt);
CHKERRQ(ierr);
if (cnt != Ntotal) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Hash table size %D not equal to total number coarse grid points %D",cnt,Ntotal);
ierr = PetscFree(globals);
CHKERRQ(ierr);
for (i=0; i<6; i++) {
ierr = PetscTableFind(ht,gl[i]+1,&gl[i]);
CHKERRQ(ierr);
gl[i]--;
}
ierr = PetscTableDestroy(&ht);
CHKERRQ(ierr);
/* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */
/* construct global interpolation matrix */
ierr = MatGetLocalSize(Aglobal,&Ng,NULL);
CHKERRQ(ierr);
if (reuse == MAT_INITIAL_MATRIX) {
ierr = MatCreateAIJ(PetscObjectComm((PetscObject)da),Ng,PETSC_DECIDE,PETSC_DECIDE,Ntotal,Nint+Nsurf,NULL,Nint,NULL,P);
CHKERRQ(ierr);
} else {
ierr = MatZeroEntries(*P);
CHKERRQ(ierr);
}
ierr = MatSetOption(*P,MAT_ROW_ORIENTED,PETSC_FALSE);
CHKERRQ(ierr);
ierr = MatDenseGetArray(Xint,&xint);
CHKERRQ(ierr);
ierr = MatSetValues(*P,Nint,IIint,6,gl,xint,INSERT_VALUES);
CHKERRQ(ierr);
ierr = MatDenseRestoreArray(Xint,&xint);
CHKERRQ(ierr);
ierr = MatDenseGetArray(Xsurf,&xsurf);
CHKERRQ(ierr);
ierr = MatSetValues(*P,Nsurf,IIsurf,6,gl,xsurf,INSERT_VALUES);
CHKERRQ(ierr);
ierr = MatDenseRestoreArray(Xsurf,&xsurf);
CHKERRQ(ierr);
ierr = MatAssemblyBegin(*P,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAssemblyEnd(*P,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = PetscFree2(IIint,IIsurf);
CHKERRQ(ierr);
#if defined(PETSC_USE_DEBUG_foo)
{
Vec x,y;
PetscScalar *yy;
ierr = VecCreateMPI(PetscObjectComm((PetscObject)da),Ng,PETSC_DETERMINE,&y);
CHKERRQ(ierr);
ierr = VecCreateMPI(PetscObjectComm((PetscObject)da),PETSC_DETERMINE,Ntotal,&x);
CHKERRQ(ierr);
ierr = VecSet(x,1.0);
CHKERRQ(ierr);
ierr = MatMult(*P,x,y);
CHKERRQ(ierr);
ierr = VecGetArray(y,&yy);
CHKERRQ(ierr);
for (i=0; i<Ng; i++) {
if (PetscAbsScalar(yy[i]-1.0) > 1.e-10) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Wrong p interpolation at i %D value %g",i,(double)PetscAbsScalar(yy[i]));
}
ierr = VecRestoreArray(y,&yy);
CHKERRQ(ierr);
ierr = VecDestroy(x);
CHKERRQ(ierr);
ierr = VecDestroy(y);
CHKERRQ(ierr);
}
#endif
ierr = MatDestroy(&Aii);
CHKERRQ(ierr);
ierr = MatDestroy(&Ais);
CHKERRQ(ierr);
ierr = MatDestroy(&Asi);
CHKERRQ(ierr);
ierr = MatDestroy(&A);
CHKERRQ(ierr);
ierr = ISDestroy(&is);
CHKERRQ(ierr);
ierr = ISDestroy(&isint);
CHKERRQ(ierr);
ierr = ISDestroy(&issurf);
CHKERRQ(ierr);
ierr = MatDestroy(&Xint);
CHKERRQ(ierr);
ierr = MatDestroy(&Xsurf);
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;
}
int main(int argc,char **args)
{
Mat A,LU;
Vec x,y;
PetscInt nnz[4]={2,1,1,1},col[4],i;
PetscErrorCode ierr;
PetscScalar values[4];
IS rowperm,colperm;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = MatCreateSeqAIJ(PETSC_COMM_WORLD,4,4,2,nnz,&A);CHKERRQ(ierr);
/* build test matrix */
values[0]=1.0;values[1]=-1.0;
col[0] =0;col[1]=2; i=0;
ierr = MatSetValues(A,1,&i,2,col,values,INSERT_VALUES);CHKERRQ(ierr);
values[0]=1.0;
col[0] =1;i=1;
ierr = MatSetValues(A,1,&i,1,col,values,INSERT_VALUES);CHKERRQ(ierr);
values[0]=-1.0;
col[0] =3;i=2;
ierr = MatSetValues(A,1,&i,1,col,values,INSERT_VALUES);CHKERRQ(ierr);
values[0]=1.0;
col[0] =2;i=3;
ierr = MatSetValues(A,1,&i,1,col,values,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatView(A,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = MatGetOrdering(A,MATORDERINGNATURAL,&rowperm,&colperm);CHKERRQ(ierr);
ierr = MatReorderForNonzeroDiagonal(A,1.e-12,rowperm,colperm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"column and row perms\n");CHKERRQ(ierr);
ierr = ISView(rowperm,0);CHKERRQ(ierr);
ierr = ISView(colperm,0);CHKERRQ(ierr);
ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&LU);CHKERRQ(ierr);
ierr = MatLUFactorSymbolic(LU,A,rowperm,colperm,NULL);CHKERRQ(ierr);
ierr = MatLUFactorNumeric(LU,A,NULL);CHKERRQ(ierr);
ierr = MatView(LU,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,PETSC_DECIDE,4);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&y);CHKERRQ(ierr);
values[0]=0;values[1]=1.0;values[2]=-1.0;values[3]=1.0;
for (i=0; i<4; i++) col[i]=i;
ierr = VecSetValues(x,4,col,values,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecAssemblyBegin(x);CHKERRQ(ierr);
ierr = VecAssemblyEnd(x);CHKERRQ(ierr);
ierr = VecView(x,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = MatSolve(LU,x,y);CHKERRQ(ierr);
ierr = VecView(y,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = ISDestroy(&rowperm);CHKERRQ(ierr);
ierr = ISDestroy(&colperm);CHKERRQ(ierr);
ierr = MatDestroy(&LU);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
