Actual source code: ex1.c

  2: static char help[] = "Tests LU, Cholesky factorization and MatMatSolve() for a sequential dense matrix. \n\
  3:                       For MATSEQDENSE matrix, the factorization is just a thin wrapper to LAPACK \n\n";

  5: #include <petscmat.h>

  9: int main(int argc,char **argv)
 10: {
 11:   Mat            mat,F,RHS,SOLU;
 12:   MatInfo        info;
 14:   PetscInt       m = 10,n = 10,i,j,rstart,rend,nrhs=2;
 15:   PetscScalar    value = 1.0;
 16:   Vec            x,y,b,ytmp;
 17:   PetscReal      norm;
 18:   PetscMPIInt    size;
 19:   PetscScalar    *rhs_array,*solu_array;
 20:   PetscRandom    rand;
 21:   PetscScalar    *array,rval;

 23:   PetscInitialize(&argc,&argv,(char*) 0,help);
 24:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 25:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This is a uniprocessor example only!");

 27:   /* create single vectors */
 28:   VecCreate(PETSC_COMM_WORLD,&y);
 29:   VecSetSizes(y,PETSC_DECIDE,m);
 30:   VecSetFromOptions(y);
 31:   VecDuplicate(y,&x);
 32:   VecDuplicate(y,&ytmp);
 33:   VecSet(x,value);
 34:   VecCreate(PETSC_COMM_WORLD,&b);
 35:   VecSetSizes(b,PETSC_DECIDE,n);
 36:   VecSetFromOptions(b);

 38:   /* create multiple vectors RHS and SOLU */
 39:   MatCreate(PETSC_COMM_WORLD,&RHS);
 40:   MatSetSizes(RHS,PETSC_DECIDE,PETSC_DECIDE,n,nrhs);
 41:   MatSetType(RHS,MATDENSE);
 42:   MatSetFromOptions(RHS);
 43: 
 44:   PetscRandomCreate(PETSC_COMM_WORLD,&rand);
 45:   PetscRandomSetFromOptions(rand);
 46:   MatGetArray(RHS,&array);
 47:   for (j=0; j<nrhs; j++){
 48:     for (i=0; i<n; i++){
 49:       PetscRandomGetValue(rand,&rval);
 50:       array[n*j+i] = rval;
 51:     }
 52:   }
 53:   MatRestoreArray(RHS,&array);
 54: 
 55:   MatDuplicate(RHS,MAT_DO_NOT_COPY_VALUES,&SOLU);

 57:   /* create matrix */
 58:   MatCreateSeqDense(PETSC_COMM_WORLD,m,n,PETSC_NULL,&mat);
 59:   MatGetOwnershipRange(mat,&rstart,&rend);
 60:   for (i=rstart; i<rend; i++) {
 61:     value = (PetscReal)i+1;
 62:     MatSetValues(mat,1,&i,1,&i,&value,INSERT_VALUES);
 63:   }
 64:   MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);
 65:   MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);

 67:   MatGetInfo(mat,MAT_LOCAL,&info);
 68:   PetscPrintf(PETSC_COMM_WORLD,"matrix nonzeros = %D, allocated nonzeros = %D\n",
 69:     (PetscInt)info.nz_used,(PetscInt)info.nz_allocated);

 71:   /* Cholesky factorization - perm and factinfo are ignored by LAPACK */
 72:   /* in-place Cholesky */
 73:   MatMult(mat,x,b);
 74:   MatConvert(mat,MATSAME,MAT_INITIAL_MATRIX,&F);
 75:   MatCholeskyFactor(F,0,0);
 76:   MatSolve(F,b,y);
 77:   MatDestroy(&F);
 78:   value = -1.0; VecAXPY(y,value,x);
 79:   VecNorm(y,NORM_2,&norm);
 80:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error for Cholesky %A\n",norm);
 81:   /* out-place Cholesky */
 82:   MatGetFactor(mat,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&F);
 83:   MatCholeskyFactorSymbolic(F,mat,0,0);
 84:   MatCholeskyFactorNumeric(F,mat,0);
 85:   MatSolve(F,b,y);
 86:   value = -1.0; VecAXPY(y,value,x);
 87:   VecNorm(y,NORM_2,&norm);
 88:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error for Cholesky %A\n",norm);
 89:   MatDestroy(&F);

 91:   /* LU factorization - perms and factinfo are ignored by LAPACK */
 92:   i = m-1; value = 1.0;
 93:   MatSetValues(mat,1,&i,1,&i,&value,INSERT_VALUES);
 94:   MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);
 95:   MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);
 96:   MatMult(mat,x,b);
 97:   MatConvert(mat,MATSAME,MAT_INITIAL_MATRIX,&F);

 99:   /* in-place LU */
100:   MatLUFactor(F,0,0,0);
101:   MatSolve(F,b,y);
102:   value = -1.0; VecAXPY(y,value,x);
103:   VecNorm(y,NORM_2,&norm);
104:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error for LU %A\n",norm);

106:   MatMatSolve(F,RHS,SOLU);
107:   for (j=0; j<nrhs; j++){
108:     MatGetArray(SOLU,&solu_array);
109:     MatGetArray(RHS,&rhs_array);
110:     VecPlaceArray(y,solu_array);
111:     VecPlaceArray(b,rhs_array);

113:     MatMult(mat,y,ytmp);
114:     VecAXPY(ytmp,-1.0,b); /* ytmp = mat*SOLU[:,j] - RHS[:,j] */
115:     VecNorm(ytmp,NORM_2,&norm);
116:     if (norm > 1.e-12){
117:       PetscPrintf(PETSC_COMM_WORLD,"Error: Norm of residual for LU %A\n",norm);
118:     }
119: 
120:     VecResetArray(b);
121:     VecResetArray(y);
122:     MatRestoreArray(RHS,&rhs_array);
123:     MatRestoreArray(SOLU,&solu_array);
124:   }

126:   MatDestroy(&F);
127:   /* out-place LU */
128:   MatGetFactor(mat,MATSOLVERPETSC,MAT_FACTOR_LU,&F);
129:   MatLUFactorSymbolic(F,mat,0,0,0);
130:   MatLUFactorNumeric(F,mat,0);
131:   MatSolve(F,b,y);
132:   value = -1.0; VecAXPY(y,value,x);
133:   VecNorm(y,NORM_2,&norm);
134:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error for LU %A\n",norm);

136:   /* free space */
137:   MatDestroy(&F);
138:   MatDestroy(&mat);
139:   MatDestroy(&RHS);
140:   MatDestroy(&SOLU);
141:   PetscRandomDestroy(&rand);
142:   VecDestroy(&x);
143:   VecDestroy(&b);
144:   VecDestroy(&y);
145:   VecDestroy(&ytmp);
146:   PetscFinalize();
147:   return 0;
148: }
149: