Actual source code: ex76.c

  1: /*$Id: ex76.c,v 1.18 2001/08/07 21:30:08 bsmith Exp $*/

  3: static char help[] = "Tests matrix permutation for factorization and solve on matrix with MatSBAIJ format. Modified from ex74.cn";

 5:  #include petscmat.h

  7: #undef __FUNCT__
  9: int main(int argc,char **args)
 10: {
 11:   Vec         x,y,b;
 12:   Mat         A;           /* linear system matrix */
 13:   Mat         sA,sC;       /* symmetric part of the matrices */
 14:   int         n,mbs=16,bs=1,nz=3,prob=1;
 15:   int         ierr,i,j,col[3],size,block, row,I,J,n1,*ip_ptr;
 16:   int         lf;          /* level of fill for icc */
 17:   PetscReal   norm1,norm2,tol=1.e-10,fill;
 18:   PetscScalar neg_one = -1.0,four=4.0,value[3];
 19:   IS          perm;
 20:   PetscRandom rand;
 21:   PetscTruth  reorder=PETSC_TRUE;

 23:   PetscInitialize(&argc,&args,(char *)0,help);
 24:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 25:   if (size != 1) SETERRQ(1,"This is a uniprocessor example only!");
 26:   PetscOptionsGetInt(PETSC_NULL,"-bs",&bs,PETSC_NULL);
 27:   PetscOptionsGetInt(PETSC_NULL,"-mbs",&mbs,PETSC_NULL);

 29:   n = mbs*bs;
 30:   ierr=MatCreateSeqBAIJ(PETSC_COMM_WORLD,bs,n,n,nz,PETSC_NULL, &A);
 31:   ierr=MatCreateSeqSBAIJ(PETSC_COMM_WORLD,bs,n,n,nz,PETSC_NULL, &sA);

 33:   /* Test MatGetOwnershipRange() */
 34:   MatGetOwnershipRange(A,&I,&J);
 35:   MatGetOwnershipRange(sA,&i,&j);
 36:   if (i-I || j-J){
 37:     PetscPrintf(PETSC_COMM_SELF,"Error: MatGetOwnershipRange() in MatSBAIJ formatn");
 38:   }

 40:   /* Assemble matrix */
 41:   if (bs == 1){
 42:     PetscOptionsGetInt(PETSC_NULL,"-test_problem",&prob,PETSC_NULL);
 43:     if (prob == 1){ /* tridiagonal matrix */
 44:       value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
 45:       for (i=1; i<n-1; i++) {
 46:         col[0] = i-1; col[1] = i; col[2] = i+1;
 47:         MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
 48:         MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);
 49:       }
 50:       i = n - 1; col[0]=0; col[1] = n - 2; col[2] = n - 1;
 51:       value[0]= 0.1; value[1]=-1; value[2]=2;
 52:       MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
 53:       MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);

 55:       i = 0; col[0] = 0; col[1] = 1; col[2]=n-1;
 56:       value[0] = 2.0; value[1] = -1.0; value[2]=0.1;
 57:       MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
 58:       MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);
 59:     }
 60:     else if (prob ==2){ /* matrix for the five point stencil */
 61:       n1 = (int) (sqrt((PetscReal)n) + 0.001);
 62:       if (n1*n1 - n) SETERRQ(PETSC_ERR_ARG_WRONG,"sqrt(n) must be a positive interger!");
 63:       for (i=0; i<n1; i++) {
 64:         for (j=0; j<n1; j++) {
 65:           I = j + n1*i;
 66:           if (i>0)   {
 67:             J = I - n1;
 68:             MatSetValues(A,1,&I,1,&J,&neg_one,INSERT_VALUES);
 69:             MatSetValues(sA,1,&I,1,&J,&neg_one,INSERT_VALUES);
 70:           }
 71:           if (i<n1-1) {
 72:             J = I + n1;
 73:             MatSetValues(A,1,&I,1,&J,&neg_one,INSERT_VALUES);
 74:             MatSetValues(sA,1,&I,1,&J,&neg_one,INSERT_VALUES);
 75:           }
 76:           if (j>0)   {
 77:             J = I - 1;
 78:             MatSetValues(A,1,&I,1,&J,&neg_one,INSERT_VALUES);
 79:             MatSetValues(sA,1,&I,1,&J,&neg_one,INSERT_VALUES);
 80:           }
 81:           if (j<n1-1) {
 82:             J = I + 1;
 83:             MatSetValues(A,1,&I,1,&J,&neg_one,INSERT_VALUES);
 84:             MatSetValues(sA,1,&I,1,&J,&neg_one,INSERT_VALUES);
 85:           }
 86:           MatSetValues(A,1,&I,1,&I,&four,INSERT_VALUES);
 87:           MatSetValues(sA,1,&I,1,&I,&four,INSERT_VALUES);
 88:         }
 89:       }
 90:     }
 91:   }
 92:   else { /* bs > 1 */
 93:     for (block=0; block<n/bs; block++){
 94:       /* diagonal blocks */
 95:       value[0] = -1.0; value[1] = 4.0; value[2] = -1.0;
 96:       for (i=1+block*bs; i<bs-1+block*bs; i++) {
 97:         col[0] = i-1; col[1] = i; col[2] = i+1;
 98:         MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
 99:         MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);
100:       }
101:       i = bs - 1+block*bs; col[0] = bs - 2+block*bs; col[1] = bs - 1+block*bs;
102:       value[0]=-1.0; value[1]=4.0;
103:       MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
104:       MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);

106:       i = 0+block*bs; col[0] = 0+block*bs; col[1] = 1+block*bs;
107:       value[0]=4.0; value[1] = -1.0;
108:       MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
109:       MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);
110:     }
111:     /* off-diagonal blocks */
112:     value[0]=-1.0;
113:     for (i=0; i<(n/bs-1)*bs; i++){
114:       col[0]=i+bs;
115:       MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);
116:       MatSetValues(sA,1,&i,1,col,value,INSERT_VALUES);
117:       col[0]=i; row=i+bs;
118:       MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);
119:       MatSetValues(sA,1,&row,1,col,value,INSERT_VALUES);
120:     }
121:     if (bs == 2){
122:       /* insert a value to off-diag blocks */
123:       row = 2; col[0] = 5; value[0] = 0.01;
124:       MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);
125:       MatSetValues(sA,1,&row,1,col,value,INSERT_VALUES);
126:       row = 0; col[0] = 3; value[0] = 0.01;
127:       MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);
128:       MatSetValues(sA,1,&row,1,col,value,INSERT_VALUES);
129:     }
130:   }
131:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
132:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
133:   /* PetscPrintf(PETSC_COMM_SELF,"n The Matrix: n");
134:   MatView(A, PETSC_VIEWER_DRAW_WORLD);
135:   MatView(A, PETSC_VIEWER_STDOUT_WORLD); */

137:   MatAssemblyBegin(sA,MAT_FINAL_ASSEMBLY);
138:   MatAssemblyEnd(sA,MAT_FINAL_ASSEMBLY);
139:   /* PetscPrintf(PETSC_COMM_SELF,"n Symmetric Part of Matrix: n"); */
140:   /* MatView(sA, PETSC_VIEWER_DRAW_WORLD); */
141:   /* MatView(sA, PETSC_VIEWER_STDOUT_WORLD); */

143:   /* Vectors */
144:   PetscRandomCreate(PETSC_COMM_SELF,RANDOM_DEFAULT,&rand);
145:   VecCreateSeq(PETSC_COMM_SELF,n,&x);
146:   VecDuplicate(x,&b);
147:   VecDuplicate(x,&y);
148:   VecSetRandom(rand,x);

150:   /* Test MatReordering() */
151:   PetscMalloc(mbs*sizeof(int),&ip_ptr);
152:   for (i=0; i<mbs; i++) ip_ptr[i] = i;
153:   if(reorder){
154:     i = ip_ptr[1]; ip_ptr[1] = ip_ptr[mbs-2]; ip_ptr[mbs-2] = i;
155:     /* i = ip_ptr[0]; ip_ptr[0] = ip_ptr[mbs-1]; ip_ptr[mbs-1] = i; */
156:     /* i = ip_ptr[2]; ip_ptr[2] = ip_ptr[mbs-3]; ip_ptr[mbs-3] = i; */
157:   }
158:   ISCreateGeneral(PETSC_COMM_SELF,mbs,ip_ptr,&perm);
159:   ISSetPermutation(perm);
160: 
161:   /* Test MatCholeskyFactor(), MatICCFactor() */
162:   norm1 = tol;
163:   for (lf=-1; lf<10*bs; lf += bs){
164:     if (lf==-1) {  /* Cholesky factor */
165:       fill = 5.0;
166:       MatCholeskyFactorSymbolic(sA,perm,fill,&sC);
167:     } else {       /* incomplete Cholesky factor */
168:       fill          = 5.0;
169:       MatICCFactorSymbolic(sA,perm,fill,lf,&sC);
170:     }
171:     MatCholeskyFactorNumeric(sA,&sC);
172:     /* MatView(sC, PETSC_VIEWER_DRAW_WORLD);  */ /* view factored matrix */
173:     /* MatView(sC, PETSC_VIEWER_STDOUT_WORLD); */
174: 
175:     MatMult(sA,x,b);
176:     MatSolve(sC,b,y);
177:     if (bs == 1) {
178:       Vecs xx,bb;
179:       VecsCreateSeq(PETSC_COMM_SELF,n,4,&xx);
180:       VecsDuplicate(xx,&bb);
181:       MatSolves(sC,bb,xx);
182:       VecsDestroy(xx);
183:       VecsDestroy(bb);
184:     }
185:     MatDestroy(sC);

187:     /* Check the error */
188:     VecAXPY(&neg_one,x,y);
189:     VecNorm(y,NORM_2,&norm2);
190:     /* printf("lf: %d, error: %gn", lf,norm2); */
191:     if (10*norm1 < norm2 && lf-bs != -1){
192:       PetscPrintf(PETSC_COMM_SELF,"lf=%d, %d, Norm of error=%g, %gn",lf-bs,lf,norm1,norm2);
193:     }
194:     norm1 = norm2;
195:     if (norm2 < tol && lf != -1) break;
196:   }

198:   ISDestroy(perm);
199:   PetscFree(ip_ptr);
200:   MatDestroy(A);
201:   MatDestroy(sA);
202:   VecDestroy(x);
203:   VecDestroy(y);
204:   VecDestroy(b);
205:   PetscRandomDestroy(rand);

207:   PetscFinalize();
208:   return 0;
209: }