Actual source code: test11.c

slepc-3.16.3 2022-04-11
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2021, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.
  7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
  8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  9: */

 11: static char help[] = "Test BV block orthogonalization.\n\n";

 13: #include <slepcbv.h>

 15: /*
 16:    Compute the Frobenius norm ||A(l:k,l:k)-diag||_F
 17:  */
 18: PetscErrorCode MyMatNorm(Mat A,PetscInt lda,PetscInt l,PetscInt k,PetscScalar diag,PetscReal *norm)
 19: {
 20:   PetscErrorCode    ierr;
 21:   PetscInt          i,j;
 22:   const PetscScalar *pA;
 23:   PetscReal         s,val;

 26:   MatDenseGetArrayRead(A,&pA);
 27:   s = 0.0;
 28:   for (i=l;i<k;i++) {
 29:     for (j=l;j<k;j++) {
 30:       val = (i==j)? PetscAbsScalar(pA[i+j*lda]-diag): PetscAbsScalar(pA[i+j*lda]);
 31:       s += val*val;
 32:     }
 33:   }
 34:   *norm = PetscSqrtReal(s);
 35:   MatDenseRestoreArrayRead(A,&pA);
 36:   return(0);
 37: }

 39: int main(int argc,char **argv)
 40: {
 42:   BV             X,Y,Z,cached;
 43:   Mat            B=NULL,M,R=NULL;
 44:   Vec            v,t;
 45:   PetscInt       i,j,n=20,l=2,k=8,Istart,Iend;
 46:   PetscViewer    view;
 47:   PetscBool      withb,resid,rand,verbose;
 48:   PetscReal      norm;
 49:   PetscScalar    alpha;

 51:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 52:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 53:   PetscOptionsGetInt(NULL,NULL,"-l",&l,NULL);
 54:   PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL);
 55:   PetscOptionsHasName(NULL,NULL,"-withb",&withb);
 56:   PetscOptionsHasName(NULL,NULL,"-resid",&resid);
 57:   PetscOptionsHasName(NULL,NULL,"-rand",&rand);
 58:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
 59:   PetscPrintf(PETSC_COMM_WORLD,"Test BV block orthogonalization (length %D, l=%D, k=%D)%s.\n",n,l,k,withb?" with non-standard inner product":"");

 61:   /* Create template vector */
 62:   VecCreate(PETSC_COMM_WORLD,&t);
 63:   VecSetSizes(t,PETSC_DECIDE,n);
 64:   VecSetFromOptions(t);

 66:   /* Create BV object X */
 67:   BVCreate(PETSC_COMM_WORLD,&X);
 68:   PetscObjectSetName((PetscObject)X,"X");
 69:   BVSetSizesFromVec(X,t,k);
 70:   BVSetFromOptions(X);

 72:   /* Set up viewer */
 73:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&view);
 74:   if (verbose) {
 75:     PetscViewerPushFormat(view,PETSC_VIEWER_ASCII_MATLAB);
 76:   }

 78:   /* Fill X entries */
 79:   if (rand) {
 80:     BVSetRandom(X);
 81:   } else {
 82:     for (j=0;j<k;j++) {
 83:       BVGetColumn(X,j,&v);
 84:       VecSet(v,0.0);
 85:       for (i=0;i<=n/2;i++) {
 86:         if (i+j<n) {
 87:           alpha = (3.0*i+j-2)/(2*(i+j+1));
 88:           VecSetValue(v,i+j,alpha,INSERT_VALUES);
 89:         }
 90:       }
 91:       VecAssemblyBegin(v);
 92:       VecAssemblyEnd(v);
 93:       BVRestoreColumn(X,j,&v);
 94:     }
 95:   }
 96:   if (verbose) {
 97:     BVView(X,view);
 98:   }

100:   if (withb) {
101:     /* Create inner product matrix */
102:     MatCreate(PETSC_COMM_WORLD,&B);
103:     MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
104:     MatSetFromOptions(B);
105:     MatSetUp(B);
106:     PetscObjectSetName((PetscObject)B,"B");

108:     MatGetOwnershipRange(B,&Istart,&Iend);
109:     for (i=Istart;i<Iend;i++) {
110:       if (i>0) { MatSetValue(B,i,i-1,-1.0,INSERT_VALUES); }
111:       if (i<n-1) { MatSetValue(B,i,i+1,-1.0,INSERT_VALUES); }
112:       MatSetValue(B,i,i,2.0,INSERT_VALUES);
113:     }
114:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
115:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
116:     if (verbose) {
117:       MatView(B,view);
118:     }
119:     BVSetMatrix(X,B,PETSC_FALSE);
120:   }

122:   /* Create copy on Y */
123:   BVDuplicate(X,&Y);
124:   PetscObjectSetName((PetscObject)Y,"Y");
125:   BVCopy(X,Y);
126:   MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&M);

128:   if (resid) {
129:     /* Create matrix R to store triangular factor */
130:     MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&R);
131:     PetscObjectSetName((PetscObject)R,"R");
132:   }

134:   if (l>0) {
135:     /* First orthogonalize leading columns */
136:     PetscPrintf(PETSC_COMM_WORLD,"Orthogonalizing leading columns\n");
137:     BVSetActiveColumns(Y,0,l);
138:     BVSetActiveColumns(X,0,l);
139:     BVOrthogonalize(Y,R);
140:     if (verbose) {
141:       BVView(Y,view);
142:       if (resid) { MatView(R,view); }
143:     }

145:     if (withb) {
146:       /* Extract cached BV and check it is equal to B*X */
147:       BVGetCachedBV(Y,&cached);
148:       BVDuplicate(X,&Z);
149:       BVSetMatrix(Z,NULL,PETSC_FALSE);
150:       BVSetActiveColumns(Z,0,l);
151:       BVCopy(X,Z);
152:       BVMatMult(X,B,Z);
153:       BVMult(Z,-1.0,1.0,cached,NULL);
154:       BVNorm(Z,NORM_FROBENIUS,&norm);
155:       if (norm<100*PETSC_MACHINE_EPSILON) {
156:         PetscPrintf(PETSC_COMM_WORLD,"  Difference ||cached-BX|| < 100*eps\n");
157:       } else {
158:         PetscPrintf(PETSC_COMM_WORLD,"  Difference ||cached-BX||: %g\n",(double)norm);
159:       }
160:       BVDestroy(&Z);
161:     }

163:     /* Check orthogonality */
164:     BVDot(Y,Y,M);
165:     MyMatNorm(M,k,0,l,1.0,&norm);
166:     if (norm<100*PETSC_MACHINE_EPSILON) {
167:       PetscPrintf(PETSC_COMM_WORLD,"  Level of orthogonality of Q1 < 100*eps\n");
168:     } else {
169:       PetscPrintf(PETSC_COMM_WORLD,"  Level of orthogonality of Q1: %g\n",(double)norm);
170:     }

172:     if (resid) {
173:       /* Check residual */
174:       BVDuplicate(X,&Z);
175:       BVSetMatrix(Z,NULL,PETSC_FALSE);
176:       BVSetActiveColumns(Z,0,l);
177:       BVCopy(X,Z);
178:       BVMult(Z,-1.0,1.0,Y,R);
179:       BVNorm(Z,NORM_FROBENIUS,&norm);
180:       if (norm<100*PETSC_MACHINE_EPSILON) {
181:         PetscPrintf(PETSC_COMM_WORLD,"  Residual ||X1-Q1*R11|| < 100*eps\n");
182:       } else {
183:         PetscPrintf(PETSC_COMM_WORLD,"  Residual ||X1-Q1*R11||: %g\n",(double)norm);
184:       }
185:       BVDestroy(&Z);
186:     }

188:   }

190:   /* Now orthogonalize the rest of columns */
191:   PetscPrintf(PETSC_COMM_WORLD,"Orthogonalizing active columns\n");
192:   BVSetActiveColumns(Y,l,k);
193:   BVSetActiveColumns(X,l,k);
194:   BVOrthogonalize(Y,R);
195:   if (verbose) {
196:     BVView(Y,view);
197:     if (resid) { MatView(R,view); }
198:   }

200:   if (l>0) {
201:     /* Check orthogonality */
202:     BVDot(Y,Y,M);
203:     MyMatNorm(M,k,l,k,1.0,&norm);
204:     if (norm<100*PETSC_MACHINE_EPSILON) {
205:       PetscPrintf(PETSC_COMM_WORLD,"  Level of orthogonality of Q2 < 100*eps\n");
206:     } else {
207:       PetscPrintf(PETSC_COMM_WORLD,"  Level of orthogonality of Q2: %g\n",(double)norm);
208:     }
209:   }

211:   /* Check the complete decomposition */
212:   PetscPrintf(PETSC_COMM_WORLD,"Overall decomposition\n");
213:   BVSetActiveColumns(Y,0,k);
214:   BVSetActiveColumns(X,0,k);

216:   /* Check orthogonality */
217:   BVDot(Y,Y,M);
218:   MyMatNorm(M,k,0,k,1.0,&norm);
219:   if (norm<100*PETSC_MACHINE_EPSILON) {
220:     PetscPrintf(PETSC_COMM_WORLD,"  Level of orthogonality of Q < 100*eps\n");
221:   } else {
222:     PetscPrintf(PETSC_COMM_WORLD,"  Level of orthogonality of Q: %g\n",(double)norm);
223:   }

225:   if (resid) {
226:     /* Check residual */
227:     BVMult(X,-1.0,1.0,Y,R);
228:     BVSetMatrix(X,NULL,PETSC_FALSE);
229:     BVNorm(X,NORM_FROBENIUS,&norm);
230:     if (norm<100*PETSC_MACHINE_EPSILON) {
231:       PetscPrintf(PETSC_COMM_WORLD,"  Residual ||X-Q*R|| < 100*eps\n");
232:     } else {
233:       PetscPrintf(PETSC_COMM_WORLD,"  Residual ||X-Q*R||: %g\n",(double)norm);
234:     }
235:     MatDestroy(&R);
236:   }

238:   if (B) { MatDestroy(&B); }
239:   MatDestroy(&M);
240:   BVDestroy(&X);
241:   BVDestroy(&Y);
242:   VecDestroy(&t);
243:   SlepcFinalize();
244:   return ierr;
245: }

247: /*TEST

249:    testset:
250:       args: -bv_orthog_block {{gs chol tsqr tsqrchol svqb}}
251:       nsize: 2
252:       output_file: output/test11_1.out
253:       test:
254:          suffix: 1
255:          args: -bv_type {{vecs contiguous svec mat}shared output}
256:       test:
257:          suffix: 1_cuda
258:          args: -bv_type svec -vec_type cuda
259:          requires: cuda

261:    testset:
262:       args: -withb -bv_orthog_block {{gs chol svqb}}
263:       nsize: 2
264:       output_file: output/test11_4.out
265:       test:
266:          suffix: 4
267:          args: -bv_type {{vecs contiguous svec mat}shared output}
268:       test:
269:          suffix: 4_cuda
270:          args: -bv_type svec -vec_type cuda -mat_type aijcusparse
271:          requires: cuda

273:    testset:
274:       args: -resid -bv_orthog_block {{gs chol tsqr tsqrchol svqb}}
275:       nsize: 2
276:       output_file: output/test11_6.out
277:       test:
278:          suffix: 6
279:          args: -bv_type {{vecs contiguous svec mat}shared output}
280:       test:
281:          suffix: 6_cuda
282:          args: -bv_type svec -vec_type cuda
283:          requires: cuda

285:    testset:
286:       args: -resid -withb -bv_orthog_block {{gs chol svqb}}
287:       nsize: 2
288:       output_file: output/test11_9.out
289:       test:
290:          suffix: 9
291:          args: -bv_type {{vecs contiguous svec mat}shared output}
292:       test:
293:          suffix: 9_cuda
294:          args: -bv_type svec -vec_type cuda -mat_type aijcusparse
295:          requires: cuda

297:    testset:
298:       args: -bv_orthog_block tsqr
299:       nsize: 7
300:       output_file: output/test11_1.out
301:       test:
302:          suffix: 11
303:          args: -bv_type {{vecs contiguous svec mat}shared output}
304:          requires: !valgrind
305:       test:
306:          suffix: 11_cuda
307:          args: -bv_type svec -vec_type cuda
308:          requires: cuda !valgrind

310:    testset:
311:       args: -resid -n 180 -l 0 -k 7 -bv_orthog_block tsqr
312:       nsize: 9
313:       output_file: output/test11_12.out
314:       test:
315:          suffix: 12
316:          args: -bv_type {{vecs contiguous svec mat}shared output}
317:          requires: !single !valgrind
318:       test:
319:          suffix: 12_cuda
320:          args: -bv_type svec -vec_type cuda
321:          requires: !single !valgrind cuda

323: TEST*/