Actual source code: ex30.c

  2: static char help[] = "Tests ILU and ICC factorization with matrix ordering, 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,sC,sA;;
 18:   PetscInt       i,j,m = 5,n = 5,Ii,J,lf = 0;
 20:   PetscTruth     LU=PETSC_FALSE,flg;
 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;
 27:   PetscRandom    rdm;

 29:   PetscInitialize(&argc,&args,(char *)0,help);
 30:   PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
 31:   PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
 32:   PetscOptionsGetInt(PETSC_NULL,"-lf",&lf,PETSC_NULL);

 34:   PetscViewerDrawOpen(PETSC_COMM_SELF,0,0,0,0,400,400,&viewer1);
 35:   PetscViewerDrawOpen(PETSC_COMM_SELF,0,0,400,0,400,400,&viewer2);

 37:   MatCreate(PETSC_COMM_SELF,&C);
 38:   MatSetSizes(C,m*n,m*n,m*n,m*n);
 39:   MatSetFromOptions(C);
 40:   MatSeqBDiagSetPreallocation(C,0,1,PETSC_NULL,PETSC_NULL);
 41:   MatSeqAIJSetPreallocation(C,5,PETSC_NULL);

 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)  {MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
 48:       J = Ii + n; if (J<m*n) {MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
 49:       J = Ii - 1; if (J>=0)  {MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
 50:       J = Ii + 1; if (J<m*n) {MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
 51:       v = 4.0; MatSetValues(C,1,&Ii,1,&Ii,&v,INSERT_VALUES);
 52:     }
 53:   }
 54:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
 55:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

 57:   MatConvert(C,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&sC);

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

 62:   /* Create vectors for error checking */
 63:   MatGetVecs(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:   MatGetOrdering(C,MATORDERING_RCM,&row,&col);
 72:   /* replace row or col with natural ordering for testing */
 73:   PetscOptionsHasName(PETSC_NULL,"-no_rowperm",&flg);
 74:   if (flg){
 75:     ISDestroy(row);
 76:     PetscInt *ii;
 77:     PetscMalloc(m*n*sizeof(PetscInt),&ii);
 78:     for (i=0; i<m*n; i++) ii[i] = i;
 79:     ISCreateGeneral(PETSC_COMM_SELF,m*n,ii,&row);
 80:     PetscFree(ii);
 81:     ISSetIdentity(row);
 82:     ISSetPermutation(row);
 83:   }
 84:   PetscOptionsHasName(PETSC_NULL,"-no_colperm",&flg);
 85:   if (flg){
 86:     ISDestroy(col);
 87:     PetscInt *ii;
 88:     PetscMalloc(m*n*sizeof(PetscInt),&ii);
 89:     for (i=0; i<m*n; i++) ii[i] = i;
 90:     ISCreateGeneral(PETSC_COMM_SELF,m*n,ii,&col);
 91:     PetscFree(ii);
 92:     ISSetIdentity(col);
 93:     ISSetPermutation(col);
 94:   }

 96:   printf("original matrix:\n");
 97:   PetscViewerPushFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_INFO);
 98:   MatView(C,PETSC_VIEWER_STDOUT_SELF);
 99:   PetscViewerPopFormat(PETSC_VIEWER_STDOUT_SELF);
100:   MatView(C,PETSC_VIEWER_STDOUT_SELF);
101:   MatView(C,viewer1);

103:   /* Compute LU or ILU factor A */
104:   MatFactorInfoInitialize(&info);
105:   info.fill          = 1.0;
106:   info.diagonal_fill = 0;
107:   info.shiftnz       = 0;
108:   info.zeropivot     = 0.0;
109:   PetscOptionsHasName(PETSC_NULL,"-lu",&LU);
110:   if (LU){
111:     MatLUFactorSymbolic(C,row,col,&info,&A);
112:   } else {
113:     info.levels = lf;
114:     MatILUFactorSymbolic(C,row,col,&info,&A);
115:   }
116:   MatLUFactorNumeric(C,&info,&A);

118:   printf("factored matrix:\n");
119:   PetscViewerPushFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_INFO);
120:   MatView(A,PETSC_VIEWER_STDOUT_SELF);
121:   PetscViewerPopFormat(PETSC_VIEWER_STDOUT_SELF);
122:   MatView(A,PETSC_VIEWER_STDOUT_SELF);
123:   MatView(A,viewer2);

125:   /* Solve A*y = b, then check the error */
126:   MatSolve(A,b,y);
127:   VecAXPY(y,-1.0,x);
128:   VecNorm(y,NORM_2,&norm2);
129:   MatDestroy(A);

131:   /* Test in-place ILU(0) and compare it with the out-place ILU(0) */
132:   if (!LU && lf==0){
133:     MatDuplicate(C,MAT_COPY_VALUES,&A);
134:     MatILUFactor(A,row,col,&info);
135:     /*
136:     printf("In-place factored matrix:\n");
137:     MatView(C,PETSC_VIEWER_STDOUT_SELF);
138:     */
139:     MatSolve(A,b,y);
140:     VecAXPY(y,-1.0,x);
141:     VecNorm(y,NORM_2,&norm2_inplace);
142:     if (PetscAbs(norm2 - norm2_inplace) > 1.e-16) SETERRQ2(1,"ILU(0) %G and in-place ILU(0) %G give different residuals",norm2,norm2_inplace);
143:     MatDestroy(A);
144:   }

146:   /* Test Cholesky and ICC on seqaij matrix with matrix reordering */
147:   if (LU){
148:     lf = -1;
149:     MatCholeskyFactorSymbolic(C,row,&info,&A);
150:   } else {
151:     info.levels        = lf;
152:     info.fill          = 1.0;
153:     info.diagonal_fill = 0;
154:     info.shiftnz       = 0;
155:     info.zeropivot     = 0.0;
156:     MatICCFactorSymbolic(C,row,&info,&A);
157:   }
158:   MatCholeskyFactorNumeric(C,&info,&A);

160:   /* test MatForwardSolve() and MatBackwardSolve() with matrix reordering */
161:   if (lf == -1){
162:     MatForwardSolve(A,b,ytmp);
163:     MatBackwardSolve(A,ytmp,y);
164:     VecAXPY(y,-1.0,x);
165:     VecNorm(y,NORM_2,&norm2);
166:     if (norm2 > 1.e-14){
167:       PetscPrintf(PETSC_COMM_SELF,"MatForwardSolve and BackwardSolve: Norm of error=%G\n",norm2);
168:     }
169:   }

171:   MatSolve(A,b,y);
172:   MatDestroy(A);
173:   VecAXPY(y,-1.0,x);
174:   VecNorm(y,NORM_2,&norm2);
175:   if (lf == -1 && norm2 > 1.e-14){
176:     PetscPrintf(PETSC_COMM_SELF, " reordered SEQAIJ:   Cholesky/ICC levels %d, residual %g\n",lf,norm2);
177:   }
178: 
179:   /* Test Cholesky and ICC on seqaij matrix without matrix reordering */
180:   ISDestroy(row);
181:   ISDestroy(col);
182:   MatGetOrdering(C,MATORDERING_NATURAL,&row,&col);
183:   if (LU){
184:     lf = -1;
185:     MatCholeskyFactorSymbolic(C,row,&info,&A);
186:   } else {
187:     info.levels        = lf;
188:     info.fill          = 1.0;
189:     info.diagonal_fill = 0;
190:     info.shiftnz       = 0;
191:     info.zeropivot     = 0.0;
192:     MatICCFactorSymbolic(C,row,&info,&A);
193:   }
194:   MatCholeskyFactorNumeric(C,&info,&A);

196:   /* test MatForwardSolve() and MatBackwardSolve() */
197:   if (lf == -1){
198:     MatForwardSolve(A,b,ytmp);
199:     MatBackwardSolve(A,ytmp,y);
200:     VecAXPY(y,-1.0,x);
201:     VecNorm(y,NORM_2,&norm2);
202:     if (norm2 > 1.e-14){
203:       PetscPrintf(PETSC_COMM_SELF,"MatForwardSolve and BackwardSolve: Norm of error=%G\n",norm2);
204:     }
205:   }

207:   /* Test MatSolve() */
208:   MatSolve(A,b,y);
209:   VecAXPY(y,-1.0,x);
210:   VecNorm(y,NORM_2,&norm2);
211:   if (lf == -1 && norm2 > 1.e-14){
212:     printf(" SEQAIJ:   Cholesky/ICC levels %d, residual %g\n",lf,norm2);
213:   }

215:   /* Test Cholesky and ICC on seqsbaij matrix without matrix reordering */
216:   if (LU){
217:     MatCholeskyFactorSymbolic(sC,row,&info,&sA);
218:   } else {
219:     MatICCFactorSymbolic(sC,row,&info,&sA);
220:   }
221:   MatCholeskyFactorNumeric(sC,&info,&sA);
222:   MatEqual(A,sA,&flg);
223:   if (!flg) SETERRQ(1,"CholeskyFactors for aij and sbaij matrices are different");
224:   MatDestroy(sC);
225:   MatDestroy(sA);
226:   MatDestroy(A);

228:   /* Free data structures */
229:   MatDestroy(C);
230:   ISDestroy(row);
231:   ISDestroy(col);
232:   PetscViewerDestroy(viewer1);
233:   PetscViewerDestroy(viewer2);
234:   PetscRandomDestroy(rdm);
235:   VecDestroy(x);
236:   VecDestroy(y);
237:   VecDestroy(ytmp);
238:   VecDestroy(b);
239:   PetscFinalize();
240:   return 0;
241: }