Date: 2022-03-31T15:28:58+00:00

Actual source code: test11.c
slepc-3.17.0 2022-03-31
Report Typos and Errors

      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*/