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;
28: PetscInt *ii;
30: PetscInitialize(&argc,&args,(char *)0,help);
31: PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
32: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
33: PetscOptionsGetInt(PETSC_NULL,"-lf",&lf,PETSC_NULL);
35: PetscViewerDrawOpen(PETSC_COMM_SELF,0,0,0,0,400,400,&viewer1);
36: PetscViewerDrawOpen(PETSC_COMM_SELF,0,0,400,0,400,400,&viewer2);
38: MatCreate(PETSC_COMM_SELF,&C);
39: MatSetSizes(C,m*n,m*n,m*n,m*n);
40: MatSetFromOptions(C);
42: /* Create matrix C in seqaij format and sC in seqsbaij. (This is five-point stencil with some extra elements) */
43: for (i=0; i<m; i++) {
44: for (j=0; j<n; j++) {
45: v = -1.0; Ii = j + n*i;
46: J = Ii - n; if (J>=0) {MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
47: J = Ii + n; if (J<m*n) {MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
48: J = Ii - 1; if (J>=0) {MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
49: J = Ii + 1; if (J<m*n) {MatSetValues(C,1,&Ii,1,&J,&v,INSERT_VALUES);}
50: v = 4.0; MatSetValues(C,1,&Ii,1,&Ii,&v,INSERT_VALUES);
51: }
52: }
53: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
54: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
56: MatConvert(C,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&sC);
58: MatIsSymmetric(C,0.0,&flg);
59: if (!flg) SETERRQ(1,"C is non-symmetric");
61: /* Create vectors for error checking */
62: MatGetVecs(C,&x,&b);
63: VecDuplicate(x,&y);
64: VecDuplicate(x,&ytmp);
65: PetscRandomCreate(PETSC_COMM_SELF,&rdm);
66: PetscRandomSetFromOptions(rdm);
67: VecSetRandom(x,rdm);
68: MatMult(C,x,b);
70: MatGetOrdering(C,MATORDERING_RCM,&row,&col);
71: /* replace row or col with natural ordering for testing */
72: PetscOptionsHasName(PETSC_NULL,"-no_rowperm",&flg);
73: if (flg){
74: ISDestroy(row);
75: PetscMalloc(m*n*sizeof(PetscInt),&ii);
76: for (i=0; i<m*n; i++) ii[i] = i;
77: ISCreateGeneral(PETSC_COMM_SELF,m*n,ii,&row);
78: PetscFree(ii);
79: ISSetIdentity(row);
80: ISSetPermutation(row);
81: }
82: PetscOptionsHasName(PETSC_NULL,"-no_colperm",&flg);
83: if (flg){
84: ISDestroy(col);
85: PetscMalloc(m*n*sizeof(PetscInt),&ii);
86: for (i=0; i<m*n; i++) ii[i] = i;
87: ISCreateGeneral(PETSC_COMM_SELF,m*n,ii,&col);
88: PetscFree(ii);
89: ISSetIdentity(col);
90: ISSetPermutation(col);
91: }
93: printf("original matrix:\n");
94: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_INFO);
95: MatView(C,PETSC_VIEWER_STDOUT_SELF);
96: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_SELF);
97: MatView(C,PETSC_VIEWER_STDOUT_SELF);
98: MatView(C,viewer1);
100: /* Compute LU or ILU factor A */
101: MatFactorInfoInitialize(&info);
102: info.fill = 1.0;
103: info.diagonal_fill = 0;
104: info.shiftnz = 0;
105: info.zeropivot = 0.0;
106: PetscOptionsHasName(PETSC_NULL,"-lu",&LU);
107: if (LU){
108: MatGetFactor(C,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&A);
109: MatLUFactorSymbolic(A,C,row,col,&info);
110: } else {
111: info.levels = lf;
112: MatGetFactor(C,MAT_SOLVER_PETSC,MAT_FACTOR_ILU,&A);
113: MatILUFactorSymbolic(A,C,row,col,&info);
114: }
115: MatLUFactorNumeric(A,C,&info);
117: printf("factored matrix:\n");
118: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_INFO);
119: MatView(A,PETSC_VIEWER_STDOUT_SELF);
120: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_SELF);
121: MatView(A,PETSC_VIEWER_STDOUT_SELF);
122: MatView(A,viewer2);
124: /* Solve A*y = b, then check the error */
125: MatSolve(A,b,y);
126: VecAXPY(y,-1.0,x);
127: VecNorm(y,NORM_2,&norm2);
128: MatDestroy(A);
130: /* Test in-place ILU(0) and compare it with the out-place ILU(0) */
131: if (!LU && lf==0){
132: MatDuplicate(C,MAT_COPY_VALUES,&A);
133: MatILUFactor(A,row,col,&info);
134: /*
135: printf("In-place factored matrix:\n");
136: MatView(C,PETSC_VIEWER_STDOUT_SELF);
137: */
138: MatSolve(A,b,y);
139: VecAXPY(y,-1.0,x);
140: VecNorm(y,NORM_2,&norm2_inplace);
141: 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);
142: MatDestroy(A);
143: }
145: /* Test Cholesky and ICC on seqaij matrix with matrix reordering */
146: if (LU){
147: lf = -1;
148: MatGetFactor(C,MAT_SOLVER_PETSC,MAT_FACTOR_CHOLESKY,&A);
149: MatCholeskyFactorSymbolic(A,C,row,&info);
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: MatGetFactor(C,MAT_SOLVER_PETSC,MAT_FACTOR_ICC,&A);
157: MatICCFactorSymbolic(A,C,row,&info);
158: }
159: MatCholeskyFactorNumeric(A,C,&info);
161: /* test MatForwardSolve() and MatBackwardSolve() with matrix reordering */
162: if (lf == -1){
163: MatForwardSolve(A,b,ytmp);
164: MatBackwardSolve(A,ytmp,y);
165: VecAXPY(y,-1.0,x);
166: VecNorm(y,NORM_2,&norm2);
167: if (norm2 > 1.e-14){
168: PetscPrintf(PETSC_COMM_SELF,"MatForwardSolve and BackwardSolve: Norm of error=%G\n",norm2);
169: }
170: }
172: MatSolve(A,b,y);
173: MatDestroy(A);
174: VecAXPY(y,-1.0,x);
175: VecNorm(y,NORM_2,&norm2);
176: if (lf == -1 && norm2 > 1.e-14){
177: PetscPrintf(PETSC_COMM_SELF, " reordered SEQAIJ: Cholesky/ICC levels %d, residual %g\n",lf,norm2);
178: }
179:
180: /* Test Cholesky and ICC on seqaij matrix without matrix reordering */
181: ISDestroy(row);
182: ISDestroy(col);
183: MatGetOrdering(C,MATORDERING_NATURAL,&row,&col);
184: if (LU){
185: lf = -1;
186: MatGetFactor(C,MAT_SOLVER_PETSC,MAT_FACTOR_CHOLESKY,&A);
187: MatCholeskyFactorSymbolic(A,C,row,&info);
188: } else {
189: info.levels = lf;
190: info.fill = 1.0;
191: info.diagonal_fill = 0;
192: info.shiftnz = 0;
193: info.zeropivot = 0.0;
194: MatGetFactor(C,MAT_SOLVER_PETSC,MAT_FACTOR_ICC,&A);
195: MatICCFactorSymbolic(A,C,row,&info);
196: }
197: MatCholeskyFactorNumeric(A,C,&info);
199: /* test MatForwardSolve() and MatBackwardSolve() */
200: if (lf == -1){
201: MatForwardSolve(A,b,ytmp);
202: MatBackwardSolve(A,ytmp,y);
203: VecAXPY(y,-1.0,x);
204: VecNorm(y,NORM_2,&norm2);
205: if (norm2 > 1.e-14){
206: PetscPrintf(PETSC_COMM_SELF,"MatForwardSolve and BackwardSolve: Norm of error=%G\n",norm2);
207: }
208: }
210: /* Test MatSolve() */
211: MatSolve(A,b,y);
212: VecAXPY(y,-1.0,x);
213: VecNorm(y,NORM_2,&norm2);
214: if (lf == -1 && norm2 > 1.e-14){
215: printf(" SEQAIJ: Cholesky/ICC levels %d, residual %g\n",lf,norm2);
216: }
218: /* Test Cholesky and ICC on seqsbaij matrix without matrix reordering */
219: if (LU){
220: MatGetFactor(sC,MAT_SOLVER_PETSC,MAT_FACTOR_CHOLESKY,&sA);
221: MatCholeskyFactorSymbolic(sA,sC,row,&info);
222: } else {
223: MatGetFactor(sC,MAT_SOLVER_PETSC,MAT_FACTOR_ICC,&sA);
224: MatICCFactorSymbolic(sA,sC,row,&info);
225: }
226: MatCholeskyFactorNumeric(sA,sC,&info);
227: MatEqual(A,sA,&flg);
228: if (!flg) SETERRQ(1,"CholeskyFactors for aij and sbaij matrices are different");
229: MatDestroy(sC);
230: MatDestroy(sA);
231: MatDestroy(A);
233: /* Free data structures */
234: MatDestroy(C);
235: ISDestroy(row);
236: ISDestroy(col);
237: PetscViewerDestroy(viewer1);
238: PetscViewerDestroy(viewer2);
239: PetscRandomDestroy(rdm);
240: VecDestroy(x);
241: VecDestroy(y);
242: VecDestroy(ytmp);
243: VecDestroy(b);
244: PetscFinalize();
245: return 0;
246: }