Actual source code: ex30.c

petsc-3.7.3 2016-08-01
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  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";

 11: #include <petscmat.h>

 15: int main(int argc,char **args)
 16: {
 17:   Mat            C,A;
 18:   PetscInt       i,j,m = 5,n = 5,Ii,J,lf = 0;
 20:   PetscBool      LU=PETSC_FALSE,CHOLESKY,TRIANGULAR=PETSC_FALSE,MATDSPL=PETSC_FALSE,flg,matordering;
 21:   PetscScalar    v;
 22:   IS             row,col;
 23:   PetscViewer    viewer1,viewer2;
 24:   MatFactorInfo  info;
 25:   Vec            x,y,b,ytmp;
 26:   PetscReal      norm2,norm2_inplace, tol = 100.*PETSC_MACHINE_EPSILON;
 27:   PetscRandom    rdm;
 28:   PetscMPIInt    size;

 30:   PetscInitialize(&argc,&args,(char*)0,help);
 31:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 32:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This is a uniprocessor example only!");
 33:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 34:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 35:   PetscOptionsGetInt(NULL,NULL,"-lf",&lf,NULL);

 37:   PetscViewerDrawOpen(PETSC_COMM_SELF,0,0,0,0,400,400,&viewer1);
 38:   PetscViewerDrawOpen(PETSC_COMM_SELF,0,0,400,0,400,400,&viewer2);

 40:   MatCreate(PETSC_COMM_SELF,&C);
 41:   MatSetSizes(C,m*n,m*n,m*n,m*n);
 42:   MatSetFromOptions(C);
 43:   MatSetUp(C);

 45:   /* Create matrix C in seqaij format and sC in seqsbaij. (This is five-point stencil with some extra elements) */
 46:   for (i=0; i<m; i++) {
 47:     for (j=0; j<n; j++) {
 48:       v = -1.0;  Ii = j + n*i;
 49:       J = Ii - n; if (J>=0)  {MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
 50:       J = Ii + n; if (J<m*n) {MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
 51:       J = Ii - 1; if (J>=0)  {MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
 52:       J = Ii + 1; if (J<m*n) {MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
 53:       v = 4.0; MatSetValues(C,1,&Ii,1,&Ii,&v,INSERT_VALUES);
 54:     }
 55:   }
 56:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
 57:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

 59:   MatIsSymmetric(C,0.0,&flg);
 60:   if (!flg) SETERRQ(PETSC_COMM_SELF,1,"C is non-symmetric");

 62:   /* Create vectors for error checking */
 63:   MatCreateVecs(C,&x,&b);
 64:   VecDuplicate(x,&y);
 65:   VecDuplicate(x,&ytmp);
 66:   PetscRandomCreate(PETSC_COMM_SELF,&rdm);
 67:   PetscRandomSetFromOptions(rdm);
 68:   VecSetRandom(x,rdm);
 69:   MatMult(C,x,b);

 71:   PetscOptionsHasName(NULL,NULL,"-mat_ordering",&matordering);
 72:   if (matordering) {
 73:     MatGetOrdering(C,MATORDERINGRCM,&row,&col);
 74:   } else {
 75:     MatGetOrdering(C,MATORDERINGNATURAL,&row,&col);
 76:   }

 78:   PetscOptionsHasName(NULL,NULL,"-display_matrices",&MATDSPL);
 79:   if (MATDSPL) {
 80:     printf("original matrix:\n");
 81:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_INFO);
 82:     MatView(C,PETSC_VIEWER_STDOUT_SELF);
 83:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_SELF);
 84:     MatView(C,PETSC_VIEWER_STDOUT_SELF);
 85:     MatView(C,viewer1);
 86:   }

 88:   /* Compute LU or ILU factor A */
 89:   MatFactorInfoInitialize(&info);

 91:   info.fill          = 1.0;
 92:   info.diagonal_fill = 0;
 93:   info.zeropivot     = 0.0;

 95:   PetscOptionsHasName(NULL,NULL,"-lu",&LU);
 96:   if (LU) {
 97:     printf("Test LU...\n");
 98:     MatGetFactor(C,MATSOLVERPETSC,MAT_FACTOR_LU,&A);
 99:     MatLUFactorSymbolic(A,C,row,col,&info);
100:   } else {
101:     printf("Test ILU...\n");
102:     info.levels = lf;

104:     MatGetFactor(C,MATSOLVERPETSC,MAT_FACTOR_ILU,&A);
105:     MatILUFactorSymbolic(A,C,row,col,&info);
106:   }
107:   MatLUFactorNumeric(A,C,&info);

109:   /* Solve A*y = b, then check the error */
110:   MatSolve(A,b,y);
111:   VecAXPY(y,-1.0,x);
112:   VecNorm(y,NORM_2,&norm2);
113:   MatDestroy(&A);

115:   /* Test in-place ILU(0) and compare it with the out-place ILU(0) */
116:   if (!LU && lf==0) {
117:     MatDuplicate(C,MAT_COPY_VALUES,&A);
118:     MatILUFactor(A,row,col,&info);
119:     /*
120:     printf("In-place factored matrix:\n");
121:     MatView(C,PETSC_VIEWER_STDOUT_SELF);
122:     */
123:     MatSolve(A,b,y);
124:     VecAXPY(y,-1.0,x);
125:     VecNorm(y,NORM_2,&norm2_inplace);
126:     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);
127:     MatDestroy(&A);
128:   }

130:   /* Test Cholesky and ICC on seqaij matrix with matrix reordering on aij matrix C */
131:   CHOLESKY = LU;
132:   if (CHOLESKY) {
133:     printf("Test Cholesky...\n");
134:     lf   = -1;
135:     MatGetFactor(C,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&A);
136:     MatCholeskyFactorSymbolic(A,C,row,&info);
137:   } else {
138:     printf("Test ICC...\n");
139:     info.levels        = lf;
140:     info.fill          = 1.0;
141:     info.diagonal_fill = 0;
142:     info.zeropivot     = 0.0;

144:     MatGetFactor(C,MATSOLVERPETSC,MAT_FACTOR_ICC,&A);
145:     MatICCFactorSymbolic(A,C,row,&info);
146:   }
147:   MatCholeskyFactorNumeric(A,C,&info);

149:   /* test MatForwardSolve() and MatBackwardSolve() with matrix reordering on aij matrix C */
150:   if (lf == -1) {
151:     PetscOptionsHasName(NULL,NULL,"-triangular_solve",&TRIANGULAR);
152:     if (TRIANGULAR) {
153:       printf("Test MatForwardSolve...\n");
154:       MatForwardSolve(A,b,ytmp);
155:       printf("Test MatBackwardSolve...\n");
156:       MatBackwardSolve(A,ytmp,y);
157:       VecAXPY(y,-1.0,x);
158:       VecNorm(y,NORM_2,&norm2);
159:       if (norm2 > tol) {
160:         PetscPrintf(PETSC_COMM_SELF,"MatForwardSolve and BackwardSolve: Norm of error=%g\n",(double)norm2);
161:       }
162:     }
163:   }

165:   MatSolve(A,b,y);
166:   MatDestroy(&A);
167:   VecAXPY(y,-1.0,x);
168:   VecNorm(y,NORM_2,&norm2);
169:   if (lf == -1 && norm2 > tol) {
170:     PetscPrintf(PETSC_COMM_SELF, " reordered SEQAIJ:   Cholesky/ICC levels %d, residual %g\n",lf,norm2);
171:   }

173:   /* Test in-place ICC(0) and compare it with the out-place ICC(0) */
174:   if (!CHOLESKY && lf==0 && !matordering) {
175:     MatConvert(C,MATSBAIJ,MAT_INITIAL_MATRIX,&A);
176:     MatICCFactor(A,row,&info);
177:     /*
178:     printf("In-place factored matrix:\n");
179:     MatView(A,PETSC_VIEWER_STDOUT_SELF);
180:     */
181:     MatSolve(A,b,y);
182:     VecAXPY(y,-1.0,x);
183:     VecNorm(y,NORM_2,&norm2_inplace);
184:     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);
185:     MatDestroy(&A);
186:   }

188:   /* Free data structures */
189:   ISDestroy(&row);
190:   ISDestroy(&col);
191:   MatDestroy(&C);
192:   PetscViewerDestroy(&viewer1);
193:   PetscViewerDestroy(&viewer2);
194:   PetscRandomDestroy(&rdm);
195:   VecDestroy(&x);
196:   VecDestroy(&y);
197:   VecDestroy(&ytmp);
198:   VecDestroy(&b);
199:   PetscFinalize();
200:   return 0;
201: }