1 2 static char help[] = "Tests ILU and ICC factorization with and without matrix ordering on seqaij format, and illustrates drawing of matrix sparsity structure with MatView().\n\ 3 Input parameters are:\n\ 4 -lf <level> : level of fill for ILU (default is 0)\n\ 5 -lu : use full LU or Cholesky factorization\n\ 6 -m <value>,-n <value> : grid dimensions\n\ 7 Note that most users should employ the KSP interface to the\n\ 8 linear solvers instead of using the factorization routines\n\ 9 directly.\n\n"; 10 11 #include <petscmat.h> 12 13 int main(int argc,char **args) 14 { 15 Mat C,A; 16 PetscInt i,j,m = 5,n = 5,Ii,J,lf = 0; 17 PetscErrorCode ierr; 18 PetscBool LU=PETSC_FALSE,CHOLESKY,TRIANGULAR=PETSC_FALSE,MATDSPL=PETSC_FALSE,flg,matordering; 19 PetscScalar v; 20 IS row,col; 21 PetscViewer viewer1,viewer2; 22 MatFactorInfo info; 23 Vec x,y,b,ytmp; 24 PetscReal norm2,norm2_inplace, tol = 100.*PETSC_MACHINE_EPSILON; 25 PetscRandom rdm; 26 PetscMPIInt size; 27 28 ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr; 29 ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr); 30 if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!"); 31 ierr = PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);CHKERRQ(ierr); 32 ierr = PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);CHKERRQ(ierr); 33 ierr = PetscOptionsGetInt(NULL,NULL,"-lf",&lf,NULL);CHKERRQ(ierr); 34 35 ierr = PetscViewerDrawOpen(PETSC_COMM_SELF,0,0,0,0,400,400,&viewer1);CHKERRQ(ierr); 36 ierr = PetscViewerDrawOpen(PETSC_COMM_SELF,0,0,400,0,400,400,&viewer2);CHKERRQ(ierr); 37 38 ierr = MatCreate(PETSC_COMM_SELF,&C);CHKERRQ(ierr); 39 ierr = MatSetSizes(C,m*n,m*n,m*n,m*n);CHKERRQ(ierr); 40 ierr = MatSetFromOptions(C);CHKERRQ(ierr); 41 ierr = MatSetUp(C);CHKERRQ(ierr); 42 43 /* Create matrix C in seqaij format and sC in seqsbaij. (This is five-point stencil with some extra elements) */ 44 for (i=0; i<m; i++) { 45 for (j=0; j<n; j++) { 46 v = -1.0; Ii = j + n*i; 47 J = Ii - n; if (J>=0) {ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);} 48 J = Ii + n; if (J<m*n) {ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);} 49 J = Ii - 1; if (J>=0) {ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);} 50 J = Ii + 1; if (J<m*n) {ierr = MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);CHKERRQ(ierr);} 51 v = 4.0; ierr = MatSetValues(C,1,&Ii,1,&Ii,&v,INSERT_VALUES);CHKERRQ(ierr); 52 } 53 } 54 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 55 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 56 57 ierr = MatIsSymmetric(C,0.0,&flg);CHKERRQ(ierr); 58 if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"C is non-symmetric"); 59 60 /* Create vectors for error checking */ 61 ierr = MatCreateVecs(C,&x,&b);CHKERRQ(ierr); 62 ierr = VecDuplicate(x,&y);CHKERRQ(ierr); 63 ierr = VecDuplicate(x,&ytmp);CHKERRQ(ierr); 64 ierr = PetscRandomCreate(PETSC_COMM_SELF,&rdm);CHKERRQ(ierr); 65 ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr); 66 ierr = VecSetRandom(x,rdm);CHKERRQ(ierr); 67 ierr = MatMult(C,x,b);CHKERRQ(ierr); 68 69 ierr = PetscOptionsHasName(NULL,NULL,"-mat_ordering",&matordering);CHKERRQ(ierr); 70 if (matordering) { 71 ierr = MatGetOrdering(C,MATORDERINGRCM,&row,&col);CHKERRQ(ierr); 72 } else { 73 ierr = MatGetOrdering(C,MATORDERINGNATURAL,&row,&col);CHKERRQ(ierr); 74 } 75 76 ierr = PetscOptionsHasName(NULL,NULL,"-display_matrices",&MATDSPL);CHKERRQ(ierr); 77 if (MATDSPL) { 78 printf("original matrix:\n"); 79 ierr = PetscViewerPushFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_INFO);CHKERRQ(ierr); 80 ierr = MatView(C,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr); 81 ierr = PetscViewerPopFormat(PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr); 82 ierr = MatView(C,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr); 83 ierr = MatView(C,viewer1);CHKERRQ(ierr); 84 } 85 86 /* Compute LU or ILU factor A */ 87 ierr = MatFactorInfoInitialize(&info);CHKERRQ(ierr); 88 89 info.fill = 1.0; 90 info.diagonal_fill = 0; 91 info.zeropivot = 0.0; 92 93 ierr = PetscOptionsHasName(NULL,NULL,"-lu",&LU);CHKERRQ(ierr); 94 if (LU) { 95 printf("Test LU...\n"); 96 ierr = MatGetFactor(C,MATSOLVERPETSC,MAT_FACTOR_LU,&A);CHKERRQ(ierr); 97 ierr = MatLUFactorSymbolic(A,C,row,col,&info);CHKERRQ(ierr); 98 } else { 99 printf("Test ILU...\n"); 100 info.levels = lf; 101 102 ierr = MatGetFactor(C,MATSOLVERPETSC,MAT_FACTOR_ILU,&A);CHKERRQ(ierr); 103 ierr = MatILUFactorSymbolic(A,C,row,col,&info);CHKERRQ(ierr); 104 } 105 ierr = MatLUFactorNumeric(A,C,&info);CHKERRQ(ierr); 106 107 /* Solve A*y = b, then check the error */ 108 ierr = MatSolve(A,b,y);CHKERRQ(ierr); 109 ierr = VecAXPY(y,-1.0,x);CHKERRQ(ierr); 110 ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr); 111 ierr = MatDestroy(&A);CHKERRQ(ierr); 112 113 /* Test in-place ILU(0) and compare it with the out-place ILU(0) */ 114 if (!LU && lf==0) { 115 ierr = MatDuplicate(C,MAT_COPY_VALUES,&A);CHKERRQ(ierr); 116 ierr = MatILUFactor(A,row,col,&info);CHKERRQ(ierr); 117 /* 118 printf("In-place factored matrix:\n"); 119 ierr = MatView(C,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr); 120 */ 121 ierr = MatSolve(A,b,y);CHKERRQ(ierr); 122 ierr = VecAXPY(y,-1.0,x);CHKERRQ(ierr); 123 ierr = VecNorm(y,NORM_2,&norm2_inplace);CHKERRQ(ierr); 124 if (PetscAbs(norm2 - norm2_inplace) > tol) SETERRQ2(PETSC_COMM_SELF,1,"ILU(0) %g and in-place ILU(0) %g give different residuals",(double)norm2,(double)norm2_inplace); 125 ierr = MatDestroy(&A);CHKERRQ(ierr); 126 } 127 128 /* Test Cholesky and ICC on seqaij matrix with matrix reordering on aij matrix C */ 129 CHOLESKY = LU; 130 if (CHOLESKY) { 131 printf("Test Cholesky...\n"); 132 lf = -1; 133 ierr = MatGetFactor(C,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&A);CHKERRQ(ierr); 134 ierr = MatCholeskyFactorSymbolic(A,C,row,&info);CHKERRQ(ierr); 135 } else { 136 printf("Test ICC...\n"); 137 info.levels = lf; 138 info.fill = 1.0; 139 info.diagonal_fill = 0; 140 info.zeropivot = 0.0; 141 142 ierr = MatGetFactor(C,MATSOLVERPETSC,MAT_FACTOR_ICC,&A);CHKERRQ(ierr); 143 ierr = MatICCFactorSymbolic(A,C,row,&info);CHKERRQ(ierr); 144 } 145 ierr = MatCholeskyFactorNumeric(A,C,&info);CHKERRQ(ierr); 146 147 /* test MatForwardSolve() and MatBackwardSolve() with matrix reordering on aij matrix C */ 148 if (lf == -1) { 149 ierr = PetscOptionsHasName(NULL,NULL,"-triangular_solve",&TRIANGULAR);CHKERRQ(ierr); 150 if (TRIANGULAR) { 151 printf("Test MatForwardSolve...\n"); 152 ierr = MatForwardSolve(A,b,ytmp);CHKERRQ(ierr); 153 printf("Test MatBackwardSolve...\n"); 154 ierr = MatBackwardSolve(A,ytmp,y);CHKERRQ(ierr); 155 ierr = VecAXPY(y,-1.0,x);CHKERRQ(ierr); 156 ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr); 157 if (norm2 > tol) { 158 ierr = PetscPrintf(PETSC_COMM_SELF,"MatForwardSolve and BackwardSolve: Norm of error=%g\n",(double)norm2);CHKERRQ(ierr); 159 } 160 } 161 } 162 163 ierr = MatSolve(A,b,y);CHKERRQ(ierr); 164 ierr = MatDestroy(&A);CHKERRQ(ierr); 165 ierr = VecAXPY(y,-1.0,x);CHKERRQ(ierr); 166 ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr); 167 if (lf == -1 && norm2 > tol) { 168 PetscPrintf(PETSC_COMM_SELF, " reordered SEQAIJ: Cholesky/ICC levels %d, residual %g\n",lf,norm2);CHKERRQ(ierr); 169 } 170 171 /* Test in-place ICC(0) and compare it with the out-place ICC(0) */ 172 if (!CHOLESKY && lf==0 && !matordering) { 173 ierr = MatConvert(C,MATSBAIJ,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr); 174 ierr = MatICCFactor(A,row,&info);CHKERRQ(ierr); 175 /* 176 printf("In-place factored matrix:\n"); 177 ierr = MatView(A,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr); 178 */ 179 ierr = MatSolve(A,b,y);CHKERRQ(ierr); 180 ierr = VecAXPY(y,-1.0,x);CHKERRQ(ierr); 181 ierr = VecNorm(y,NORM_2,&norm2_inplace);CHKERRQ(ierr); 182 if (PetscAbs(norm2 - norm2_inplace) > tol) SETERRQ2(PETSC_COMM_SELF,1,"ICC(0) %g and in-place ICC(0) %g give different residuals",(double)norm2,(double)norm2_inplace); 183 ierr = MatDestroy(&A);CHKERRQ(ierr); 184 } 185 186 /* Free data structures */ 187 ierr = ISDestroy(&row);CHKERRQ(ierr); 188 ierr = ISDestroy(&col);CHKERRQ(ierr); 189 ierr = MatDestroy(&C);CHKERRQ(ierr); 190 ierr = PetscViewerDestroy(&viewer1);CHKERRQ(ierr); 191 ierr = PetscViewerDestroy(&viewer2);CHKERRQ(ierr); 192 ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr); 193 ierr = VecDestroy(&x);CHKERRQ(ierr); 194 ierr = VecDestroy(&y);CHKERRQ(ierr); 195 ierr = VecDestroy(&ytmp);CHKERRQ(ierr); 196 ierr = VecDestroy(&b);CHKERRQ(ierr); 197 ierr = PetscFinalize(); 198 return ierr; 199 } 200 201 202 /*TEST 203 204 test: 205 args: -mat_ordering -display_matrices -nox 206 filter: grep -v "MPI processes" 207 208 test: 209 suffix: 2 210 args: -mat_ordering -display_matrices -nox -lu 211 212 test: 213 suffix: 3 214 args: -mat_ordering -lu -triangular_solve 215 216 test: 217 suffix: 4 218 219 test: 220 suffix: 5 221 args: -lu 222 223 test: 224 suffix: 6 225 args: -lu -triangular_solve 226 output_file: output/ex30_3.out 227 228 TEST*/ 229