Date: 2021-09-20T09:43:45+00:00

Actual source code: test11.c
slepc-3.15.2 2021-09-20
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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*/