Actual source code: ex145.c

petsc-3.14.6 2021-03-30
Report Typos and Errors

  2: static char help[] = "Tests LU, Cholesky factorization and MatMatSolve() for an Elemental dense matrix.\n\n";

  4: #include <petscmat.h>

  6: int main(int argc,char **argv)
  7: {
  8:   Mat            A,F,B,X,C,Aher,G;
  9:   Vec            b,x,c,d,e;
 11:   PetscInt       m = 5,n,p,i,j,nrows,ncols;
 12:   PetscScalar    *v,*barray,rval;
 13:   PetscReal      norm,tol=1.e-11;
 14:   PetscMPIInt    size,rank;
 15:   PetscRandom    rand;
 16:   const PetscInt *rows,*cols;
 17:   IS             isrows,iscols;
 18:   PetscBool      mats_view=PETSC_FALSE;
 19:   MatFactorInfo  finfo;

 21:   PetscInitialize(&argc,&argv,(char*) 0,help);if (ierr) return ierr;
 22:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 23:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

 25:   PetscRandomCreate(PETSC_COMM_WORLD,&rand);
 26:   PetscRandomSetFromOptions(rand);

 28:   /* Get local dimensions of matrices */
 29:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 30:   n    = m;
 31:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 32:   p    = m/2;
 33:   PetscOptionsGetInt(NULL,NULL,"-p",&p,NULL);
 34:   PetscOptionsHasName(NULL,NULL,"-mats_view",&mats_view);

 36:   /* Create matrix A */
 37:   PetscPrintf(PETSC_COMM_WORLD," Create Elemental matrix A\n");
 38:   MatCreate(PETSC_COMM_WORLD,&A);
 39:   MatSetSizes(A,m,n,PETSC_DECIDE,PETSC_DECIDE);
 40:   MatSetType(A,MATELEMENTAL);
 41:   MatSetFromOptions(A);
 42:   MatSetUp(A);
 43:   /* Set local matrix entries */
 44:   MatGetOwnershipIS(A,&isrows,&iscols);
 45:   ISGetLocalSize(isrows,&nrows);
 46:   ISGetIndices(isrows,&rows);
 47:   ISGetLocalSize(iscols,&ncols);
 48:   ISGetIndices(iscols,&cols);
 49:   PetscMalloc1(nrows*ncols,&v);
 50:   for (i=0; i<nrows; i++) {
 51:     for (j=0; j<ncols; j++) {
 52:       PetscRandomGetValue(rand,&rval);
 53:       v[i*ncols+j] = rval;
 54:     }
 55:   }
 56:   MatSetValues(A,nrows,rows,ncols,cols,v,INSERT_VALUES);
 57:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 58:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 59:   ISRestoreIndices(isrows,&rows);
 60:   ISRestoreIndices(iscols,&cols);
 61:   ISDestroy(&isrows);
 62:   ISDestroy(&iscols);
 63:   PetscFree(v);
 64:   if (mats_view) {
 65:     PetscPrintf(PETSC_COMM_WORLD, "A: nrows %d, m %d; ncols %d, n %d\n",nrows,m,ncols,n);
 66:     MatView(A,PETSC_VIEWER_STDOUT_WORLD);
 67:   }

 69:   /* Create rhs matrix B */
 70:   PetscPrintf(PETSC_COMM_WORLD," Create rhs matrix B\n");
 71:   MatCreate(PETSC_COMM_WORLD,&B);
 72:   MatSetSizes(B,m,p,PETSC_DECIDE,PETSC_DECIDE);
 73:   MatSetType(B,MATELEMENTAL);
 74:   MatSetFromOptions(B);
 75:   MatSetUp(B);
 76:   MatGetOwnershipIS(B,&isrows,&iscols);
 77:   ISGetLocalSize(isrows,&nrows);
 78:   ISGetIndices(isrows,&rows);
 79:   ISGetLocalSize(iscols,&ncols);
 80:   ISGetIndices(iscols,&cols);
 81:   PetscMalloc1(nrows*ncols,&v);
 82:   for (i=0; i<nrows; i++) {
 83:     for (j=0; j<ncols; j++) {
 84:       PetscRandomGetValue(rand,&rval);
 85:       v[i*ncols+j] = rval;
 86:     }
 87:   }
 88:   MatSetValues(B,nrows,rows,ncols,cols,v,INSERT_VALUES);
 89:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 90:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
 91:   ISRestoreIndices(isrows,&rows);
 92:   ISRestoreIndices(iscols,&cols);
 93:   ISDestroy(&isrows);
 94:   ISDestroy(&iscols);
 95:   PetscFree(v);
 96:   if (mats_view) {
 97:     PetscPrintf(PETSC_COMM_WORLD, "B: nrows %d, m %d; ncols %d, p %d\n",nrows,m,ncols,p);
 98:     MatView(B,PETSC_VIEWER_STDOUT_WORLD);
 99:   }

101:   /* Create rhs vector b and solution x (same size as b) */
102:   VecCreate(PETSC_COMM_WORLD,&b);
103:   VecSetSizes(b,m,PETSC_DECIDE);
104:   VecSetFromOptions(b);
105:   VecGetArray(b,&barray);
106:   for (j=0; j<m; j++) {
107:     PetscRandomGetValue(rand,&rval);
108:     barray[j] = rval;
109:   }
110:   VecRestoreArray(b,&barray);
111:   VecAssemblyBegin(b);
112:   VecAssemblyEnd(b);
113:   if (mats_view) {
114:     PetscSynchronizedPrintf(PETSC_COMM_WORLD, "[%d] b: m %d\n",rank,m);
115:     PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
116:     VecView(b,PETSC_VIEWER_STDOUT_WORLD);
117:   }
118:   VecDuplicate(b,&x);

120:   /* Create matrix X - same size as B */
121:   PetscPrintf(PETSC_COMM_WORLD," Create solution matrix X\n");
122:   MatCreate(PETSC_COMM_WORLD,&X);
123:   MatSetSizes(X,m,p,PETSC_DECIDE,PETSC_DECIDE);
124:   MatSetType(X,MATELEMENTAL);
125:   MatSetFromOptions(X);
126:   MatSetUp(X);
127:   MatAssemblyBegin(X,MAT_FINAL_ASSEMBLY);
128:   MatAssemblyEnd(X,MAT_FINAL_ASSEMBLY);

130:   /* Cholesky factorization */
131:   /*------------------------*/
132:   PetscPrintf(PETSC_COMM_WORLD," Create Elemental matrix Aher\n");
133:   MatHermitianTranspose(A,MAT_INITIAL_MATRIX,&Aher);
134:   MatAXPY(Aher,1.0,A,SAME_NONZERO_PATTERN); /* Aher = A + A^T */
135:   if (!rank) { /* add 100.0 to diagonals of Aher to make it spd */

137:     /* TODO: Replace this with a call to El::ShiftDiagonal( A, 100.),
138:              or at least pre-allocate the right amount of space */
139:     PetscInt M,N;
140:     MatGetSize(Aher,&M,&N);
141:     for (i=0; i<M; i++) {
142:       rval = 100.0;
143:       MatSetValues(Aher,1,&i,1,&i,&rval,ADD_VALUES);
144:     }
145:   }
146:   MatAssemblyBegin(Aher,MAT_FINAL_ASSEMBLY);
147:   MatAssemblyEnd(Aher,MAT_FINAL_ASSEMBLY);
148:   if (mats_view) {
149:     PetscPrintf(PETSC_COMM_WORLD, "Aher:\n");
150:     MatView(Aher,PETSC_VIEWER_STDOUT_WORLD);
151:   }

153:   /* Cholesky factorization */
154:   /*------------------------*/
155:   PetscPrintf(PETSC_COMM_WORLD," Test Cholesky Solver \n");
156:   /* In-place Cholesky */
157:   /* Create matrix factor G, then copy Aher to G */
158:   MatCreate(PETSC_COMM_WORLD,&G);
159:   MatSetSizes(G,m,n,PETSC_DECIDE,PETSC_DECIDE);
160:   MatSetType(G,MATELEMENTAL);
161:   MatSetFromOptions(G);
162:   MatSetUp(G);
163:   MatAssemblyBegin(G,MAT_FINAL_ASSEMBLY);
164:   MatAssemblyEnd(G,MAT_FINAL_ASSEMBLY);
165:   MatCopy(Aher,G,SAME_NONZERO_PATTERN);

167:   /* Only G = U^T * U is implemented for now */
168:   MatCholeskyFactor(G,0,0);
169:   if (mats_view) {
170:     PetscPrintf(PETSC_COMM_WORLD, "Cholesky Factor G:\n");
171:     MatView(G,PETSC_VIEWER_STDOUT_WORLD);
172:   }

174:   /* Solve U^T * U x = b and U^T * U X = B */
175:   MatSolve(G,b,x);
176:   MatMatSolve(G,B,X);
177:   MatDestroy(&G);

179:   /* Out-place Cholesky */
180:   MatGetFactor(Aher,MATSOLVERELEMENTAL,MAT_FACTOR_CHOLESKY,&G);
181:   MatCholeskyFactorSymbolic(G,Aher,0,&finfo);
182:   MatCholeskyFactorNumeric(G,Aher,&finfo);
183:   if (mats_view) {
184:     MatView(G,PETSC_VIEWER_STDOUT_WORLD);
185:   }
186:   MatSolve(G,b,x);
187:   MatMatSolve(G,B,X);
188:   MatDestroy(&G);

190:   /* Check norm(Aher*x - b) */
191:   VecCreate(PETSC_COMM_WORLD,&c);
192:   VecSetSizes(c,m,PETSC_DECIDE);
193:   VecSetFromOptions(c);
194:   MatMult(Aher,x,c);
195:   VecAXPY(c,-1.0,b);
196:   VecNorm(c,NORM_1,&norm);
197:   if (norm > tol) {
198:     PetscPrintf(PETSC_COMM_WORLD,"Warning: |Aher*x - b| for Cholesky %g\n",(double)norm);
199:   }

201:   /* Check norm(Aher*X - B) */
202:   MatMatMult(Aher,X,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&C);
203:   MatAXPY(C,-1.0,B,SAME_NONZERO_PATTERN);
204:   MatNorm(C,NORM_1,&norm);
205:   if (norm > tol) {
206:     PetscPrintf(PETSC_COMM_WORLD,"Warning: |Aher*X - B| for Cholesky %g\n",(double)norm);
207:   }

209:   /* LU factorization */
210:   /*------------------*/
211:   PetscPrintf(PETSC_COMM_WORLD," Test LU Solver \n");
212:   /* In-place LU */
213:   /* Create matrix factor F, then copy A to F */
214:   MatCreate(PETSC_COMM_WORLD,&F);
215:   MatSetSizes(F,m,n,PETSC_DECIDE,PETSC_DECIDE);
216:   MatSetType(F,MATELEMENTAL);
217:   MatSetFromOptions(F);
218:   MatSetUp(F);
219:   MatAssemblyBegin(F,MAT_FINAL_ASSEMBLY);
220:   MatAssemblyEnd(F,MAT_FINAL_ASSEMBLY);
221:   MatCopy(A,F,SAME_NONZERO_PATTERN);
222:   /* Create vector d to test MatSolveAdd() */
223:   VecDuplicate(x,&d);
224:   VecCopy(x,d);

226:   /* PF=LU or F=LU factorization - perms is ignored by Elemental;
227:      set finfo.dtcol !0 or 0 to enable/disable partial pivoting */
228:   finfo.dtcol = 0.1;
229:   MatLUFactor(F,0,0,&finfo);

231:   /* Solve LUX = PB or LUX = B */
232:   MatSolveAdd(F,b,d,x);
233:   MatMatSolve(F,B,X);
234:   MatDestroy(&F);

236:   /* Check norm(A*X - B) */
237:   VecCreate(PETSC_COMM_WORLD,&e);
238:   VecSetSizes(e,m,PETSC_DECIDE);
239:   VecSetFromOptions(e);
240:   MatMult(A,x,c);
241:   MatMult(A,d,e);
242:   VecAXPY(c,-1.0,e);
243:   VecAXPY(c,-1.0,b);
244:   VecNorm(c,NORM_1,&norm);
245:   if (norm > tol) {
246:     PetscPrintf(PETSC_COMM_WORLD,"Warning: |A*x - b| for LU %g\n",(double)norm);
247:   }
248:   /* Reuse product C; replace Aher with A */
249:   MatProductReplaceMats(A,NULL,NULL,C);
250:   MatMatMult(A,X,MAT_REUSE_MATRIX,PETSC_DEFAULT,&C);
251:   MatAXPY(C,-1.0,B,SAME_NONZERO_PATTERN);
252:   MatNorm(C,NORM_1,&norm);
253:   if (norm > tol) {
254:     PetscPrintf(PETSC_COMM_WORLD,"Warning: |A*X - B| for LU %g\n",(double)norm);
255:   }

257:   /* Out-place LU */
258:   MatGetFactor(A,MATSOLVERELEMENTAL,MAT_FACTOR_LU,&F);
259:   MatLUFactorSymbolic(F,A,0,0,&finfo);
260:   MatLUFactorNumeric(F,A,&finfo);
261:   if (mats_view) {
262:     MatView(F,PETSC_VIEWER_STDOUT_WORLD);
263:   }
264:   MatSolve(F,b,x);
265:   MatMatSolve(F,B,X);
266:   MatDestroy(&F);

268:   /* Free space */
269:   MatDestroy(&A);
270:   MatDestroy(&Aher);
271:   MatDestroy(&B);
272:   MatDestroy(&C);
273:   MatDestroy(&X);
274:   VecDestroy(&b);
275:   VecDestroy(&c);
276:   VecDestroy(&d);
277:   VecDestroy(&e);
278:   VecDestroy(&x);
279:   PetscRandomDestroy(&rand);
280:   PetscFinalize();
281:   return ierr;
282: }

284: /*TEST

286:    build:
287:       requires: elemental

289:    test:
290:       nsize: 2
291:       output_file: output/ex145.out

293:    test:
294:       suffix: 2
295:       nsize: 6
296:       output_file: output/ex145.out

298: TEST*/