Actual source code: test11.c

slepc-3.17.0 2022-03-31
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-, 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:   PetscInt          i,j;
 21:   const PetscScalar *pA;
 22:   PetscReal         s,val;

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

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

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

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

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

 70:   /* Set up viewer */
 71:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&view);
 72:   if (verbose) PetscViewerPushFormat(view,PETSC_VIEWER_ASCII_MATLAB);

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

 93:   if (withb) {
 94:     /* Create inner product matrix */
 95:     MatCreate(PETSC_COMM_WORLD,&B);
 96:     MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
 97:     MatSetFromOptions(B);
 98:     MatSetUp(B);
 99:     PetscObjectSetName((PetscObject)B,"B");

101:     MatGetOwnershipRange(B,&Istart,&Iend);
102:     for (i=Istart;i<Iend;i++) {
103:       if (i>0) MatSetValue(B,i,i-1,-1.0,INSERT_VALUES);
104:       if (i<n-1) MatSetValue(B,i,i+1,-1.0,INSERT_VALUES);
105:       MatSetValue(B,i,i,2.0,INSERT_VALUES);
106:     }
107:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
108:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
109:     if (verbose) MatView(B,view);
110:     BVSetMatrix(X,B,PETSC_FALSE);
111:   }

113:   /* Create copy on Y */
114:   BVDuplicate(X,&Y);
115:   PetscObjectSetName((PetscObject)Y,"Y");
116:   BVCopy(X,Y);
117:   MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&M);

119:   if (resid) {
120:     /* Create matrix R to store triangular factor */
121:     MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&R);
122:     PetscObjectSetName((PetscObject)R,"R");
123:   }

125:   if (l>0) {
126:     /* First orthogonalize leading columns */
127:     PetscPrintf(PETSC_COMM_WORLD,"Orthogonalizing leading columns\n");
128:     BVSetActiveColumns(Y,0,l);
129:     BVSetActiveColumns(X,0,l);
130:     BVOrthogonalize(Y,R);
131:     if (verbose) {
132:       BVView(Y,view);
133:       if (resid) MatView(R,view);
134:     }

136:     if (withb) {
137:       /* Extract cached BV and check it is equal to B*X */
138:       BVGetCachedBV(Y,&cached);
139:       BVDuplicate(X,&Z);
140:       BVSetMatrix(Z,NULL,PETSC_FALSE);
141:       BVSetActiveColumns(Z,0,l);
142:       BVCopy(X,Z);
143:       BVMatMult(X,B,Z);
144:       BVMult(Z,-1.0,1.0,cached,NULL);
145:       BVNorm(Z,NORM_FROBENIUS,&norm);
146:       if (norm<100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"  Difference ||cached-BX|| < 100*eps\n");
147:       else PetscPrintf(PETSC_COMM_WORLD,"  Difference ||cached-BX||: %g\n",(double)norm);
148:       BVDestroy(&Z);
149:     }

151:     /* Check orthogonality */
152:     BVDot(Y,Y,M);
153:     MyMatNorm(M,k,0,l,1.0,&norm);
154:     if (norm<100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"  Level of orthogonality of Q1 < 100*eps\n");
155:     else PetscPrintf(PETSC_COMM_WORLD,"  Level of orthogonality of Q1: %g\n",(double)norm);

157:     if (resid) {
158:       /* Check residual */
159:       BVDuplicate(X,&Z);
160:       BVSetMatrix(Z,NULL,PETSC_FALSE);
161:       BVSetActiveColumns(Z,0,l);
162:       BVCopy(X,Z);
163:       BVMult(Z,-1.0,1.0,Y,R);
164:       BVNorm(Z,NORM_FROBENIUS,&norm);
165:       if (norm<100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"  Residual ||X1-Q1*R11|| < 100*eps\n");
166:       else PetscPrintf(PETSC_COMM_WORLD,"  Residual ||X1-Q1*R11||: %g\n",(double)norm);
167:       BVDestroy(&Z);
168:     }

170:   }

172:   /* Now orthogonalize the rest of columns */
173:   PetscPrintf(PETSC_COMM_WORLD,"Orthogonalizing active columns\n");
174:   BVSetActiveColumns(Y,l,k);
175:   BVSetActiveColumns(X,l,k);
176:   BVOrthogonalize(Y,R);
177:   if (verbose) {
178:     BVView(Y,view);
179:     if (resid) MatView(R,view);
180:   }

182:   if (l>0) {
183:     /* Check orthogonality */
184:     BVDot(Y,Y,M);
185:     MyMatNorm(M,k,l,k,1.0,&norm);
186:     if (norm<100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"  Level of orthogonality of Q2 < 100*eps\n");
187:     else PetscPrintf(PETSC_COMM_WORLD,"  Level of orthogonality of Q2: %g\n",(double)norm);
188:   }

190:   /* Check the complete decomposition */
191:   PetscPrintf(PETSC_COMM_WORLD,"Overall decomposition\n");
192:   BVSetActiveColumns(Y,0,k);
193:   BVSetActiveColumns(X,0,k);

195:   /* Check orthogonality */
196:   BVDot(Y,Y,M);
197:   MyMatNorm(M,k,0,k,1.0,&norm);
198:   if (norm<100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"  Level of orthogonality of Q < 100*eps\n");
199:   else PetscPrintf(PETSC_COMM_WORLD,"  Level of orthogonality of Q: %g\n",(double)norm);

201:   if (resid) {
202:     /* Check residual */
203:     BVMult(X,-1.0,1.0,Y,R);
204:     BVSetMatrix(X,NULL,PETSC_FALSE);
205:     BVNorm(X,NORM_FROBENIUS,&norm);
206:     if (norm<100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"  Residual ||X-Q*R|| < 100*eps\n");
207:     else PetscPrintf(PETSC_COMM_WORLD,"  Residual ||X-Q*R||: %g\n",(double)norm);
208:     MatDestroy(&R);
209:   }

211:   if (B) MatDestroy(&B);
212:   MatDestroy(&M);
213:   BVDestroy(&X);
214:   BVDestroy(&Y);
215:   VecDestroy(&t);
216:   SlepcFinalize();
217:   return 0;
218: }

220: /*TEST

222:    testset:
223:       args: -bv_orthog_block {{gs chol tsqr tsqrchol svqb}}
224:       nsize: 2
225:       output_file: output/test11_1.out
226:       test:
227:          suffix: 1
228:          args: -bv_type {{vecs contiguous svec mat}shared output}
229:       test:
230:          suffix: 1_cuda
231:          args: -bv_type svec -vec_type cuda
232:          requires: cuda

234:    testset:
235:       args: -withb -bv_orthog_block {{gs chol svqb}}
236:       nsize: 2
237:       output_file: output/test11_4.out
238:       test:
239:          suffix: 4
240:          args: -bv_type {{vecs contiguous svec mat}shared output}
241:       test:
242:          suffix: 4_cuda
243:          args: -bv_type svec -vec_type cuda -mat_type aijcusparse
244:          requires: cuda

246:    testset:
247:       args: -resid -bv_orthog_block {{gs chol tsqr tsqrchol svqb}}
248:       nsize: 2
249:       output_file: output/test11_6.out
250:       test:
251:          suffix: 6
252:          args: -bv_type {{vecs contiguous svec mat}shared output}
253:       test:
254:          suffix: 6_cuda
255:          args: -bv_type svec -vec_type cuda
256:          requires: cuda

258:    testset:
259:       args: -resid -withb -bv_orthog_block {{gs chol svqb}}
260:       nsize: 2
261:       output_file: output/test11_9.out
262:       test:
263:          suffix: 9
264:          args: -bv_type {{vecs contiguous svec mat}shared output}
265:       test:
266:          suffix: 9_cuda
267:          args: -bv_type svec -vec_type cuda -mat_type aijcusparse
268:          requires: cuda

270:    testset:
271:       args: -bv_orthog_block tsqr
272:       nsize: 7
273:       output_file: output/test11_1.out
274:       test:
275:          suffix: 11
276:          args: -bv_type {{vecs contiguous svec mat}shared output}
277:          requires: !valgrind
278:       test:
279:          suffix: 11_cuda
280:          args: -bv_type svec -vec_type cuda
281:          requires: cuda !valgrind

283:    testset:
284:       args: -resid -n 180 -l 0 -k 7 -bv_orthog_block tsqr
285:       nsize: 9
286:       output_file: output/test11_12.out
287:       test:
288:          suffix: 12
289:          args: -bv_type {{vecs contiguous svec mat}shared output}
290:          requires: !single !valgrind
291:       test:
292:          suffix: 12_cuda
293:          args: -bv_type svec -vec_type cuda
294:          requires: !single !valgrind cuda

296: TEST*/