Date: 2023-09-05T10:18:54+00:00

Actual source code: test11.c
slepc-3.19.2 2023-09-05
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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;

     24:   PetscFunctionBeginUser;
     25:   PetscCall(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:   PetscCall(MatDenseRestoreArrayRead(A,&pA));
     35:   PetscFunctionReturn(PETSC_SUCCESS);
     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:   PetscFunctionBeginUser;
     50:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
     51:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     52:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-l",&l,NULL));
     53:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL));
     54:   PetscCall(PetscOptionsHasName(NULL,NULL,"-withb",&withb));
     55:   PetscCall(PetscOptionsHasName(NULL,NULL,"-resid",&resid));
     56:   PetscCall(PetscOptionsHasName(NULL,NULL,"-rand",&rand));
     57:   PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));
     58:   PetscCall(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":""));

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

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

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

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

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

    102:     PetscCall(MatGetOwnershipRange(B,&Istart,&Iend));
    103:     for (i=Istart;i<Iend;i++) {
    104:       if (i>0) PetscCall(MatSetValue(B,i,i-1,-1.0,INSERT_VALUES));
    105:       if (i<n-1) PetscCall(MatSetValue(B,i,i+1,-1.0,INSERT_VALUES));
    106:       PetscCall(MatSetValue(B,i,i,2.0,INSERT_VALUES));
    107:     }
    108:     PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
    109:     PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
    110:     if (verbose) PetscCall(MatView(B,view));
    111:     PetscCall(BVSetMatrix(X,B,PETSC_FALSE));
    112:   }

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

    120:   if (resid) {
    121:     /* Create matrix R to store triangular factor */
    122:     PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&R));
    123:     PetscCall(PetscObjectSetName((PetscObject)R,"R"));
    124:   }

    126:   if (l>0) {
    127:     /* First orthogonalize leading columns */
    128:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Orthogonalizing leading columns\n"));
    129:     PetscCall(BVSetActiveColumns(Y,0,l));
    130:     PetscCall(BVSetActiveColumns(X,0,l));
    131:     PetscCall(BVOrthogonalize(Y,R));
    132:     if (verbose) {
    133:       PetscCall(BVView(Y,view));
    134:       if (resid) PetscCall(MatView(R,view));
    135:     }

    137:     if (withb) {
    138:       /* Extract cached BV and check it is equal to B*X */
    139:       PetscCall(BVGetCachedBV(Y,&cached));
    140:       PetscCall(BVDuplicate(X,&Z));
    141:       PetscCall(BVSetMatrix(Z,NULL,PETSC_FALSE));
    142:       PetscCall(BVSetActiveColumns(Z,0,l));
    143:       PetscCall(BVCopy(X,Z));
    144:       PetscCall(BVMatMult(X,B,Z));
    145:       PetscCall(BVMult(Z,-1.0,1.0,cached,NULL));
    146:       PetscCall(BVNorm(Z,NORM_FROBENIUS,&norm));
    147:       if (norm<100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"  Difference ||cached-BX|| < 100*eps\n"));
    148:       else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"  Difference ||cached-BX||: %g\n",(double)norm));
    149:       PetscCall(BVDestroy(&Z));
    150:     }

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

    158:     if (resid) {
    159:       /* Check residual */
    160:       PetscCall(BVDuplicate(X,&Z));
    161:       PetscCall(BVSetMatrix(Z,NULL,PETSC_FALSE));
    162:       PetscCall(BVSetActiveColumns(Z,0,l));
    163:       PetscCall(BVCopy(X,Z));
    164:       PetscCall(BVMult(Z,-1.0,1.0,Y,R));
    165:       PetscCall(BVNorm(Z,NORM_FROBENIUS,&norm));
    166:       if (norm<100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"  Residual ||X1-Q1*R11|| < 100*eps\n"));
    167:       else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"  Residual ||X1-Q1*R11||: %g\n",(double)norm));
    168:       PetscCall(BVDestroy(&Z));
    169:     }

    171:   }

    173:   /* Now orthogonalize the rest of columns */
    174:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Orthogonalizing active columns\n"));
    175:   PetscCall(BVSetActiveColumns(Y,l,k));
    176:   PetscCall(BVSetActiveColumns(X,l,k));
    177:   PetscCall(BVOrthogonalize(Y,R));
    178:   if (verbose) {
    179:     PetscCall(BVView(Y,view));
    180:     if (resid) PetscCall(MatView(R,view));
    181:   }

    183:   if (l>0) {
    184:     /* Check orthogonality */
    185:     PetscCall(BVDot(Y,Y,M));
    186:     PetscCall(MyMatNorm(M,k,l,k,1.0,&norm));
    187:     if (norm<100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"  Level of orthogonality of Q2 < 100*eps\n"));
    188:     else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"  Level of orthogonality of Q2: %g\n",(double)norm));
    189:   }

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

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

    202:   if (resid) {
    203:     /* Check residual */
    204:     PetscCall(BVMult(X,-1.0,1.0,Y,R));
    205:     PetscCall(BVSetMatrix(X,NULL,PETSC_FALSE));
    206:     PetscCall(BVNorm(X,NORM_FROBENIUS,&norm));
    207:     if (norm<100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"  Residual ||X-Q*R|| < 100*eps\n"));
    208:     else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"  Residual ||X-Q*R||: %g\n",(double)norm));
    209:     PetscCall(MatDestroy(&R));
    210:   }

    212:   if (B) PetscCall(MatDestroy(&B));
    213:   PetscCall(MatDestroy(&M));
    214:   PetscCall(BVDestroy(&X));
    215:   PetscCall(BVDestroy(&Y));
    216:   PetscCall(VecDestroy(&t));
    217:   PetscCall(SlepcFinalize());
    218:   return 0;
    219: }

    221: /*TEST

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

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

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

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

    271:    testset:
    272:       args: -bv_orthog_block tsqr
    273:       nsize: 7
    274:       output_file: output/test11_1.out
    275:       test:
    276:          suffix: 11
    277:          args: -bv_type {{vecs contiguous svec mat}shared output}
    278:          requires: !defined(PETSCTEST_VALGRIND)
    279:       test:
    280:          suffix: 11_cuda
    281:          TODO: too many processes accessing the GPU
    282:          args: -bv_type svec -vec_type cuda
    283:          requires: cuda !defined(PETSCTEST_VALGRIND)

    285:    testset:
    286:       args: -resid -n 180 -l 0 -k 7 -bv_orthog_block tsqr
    287:       nsize: 9
    288:       output_file: output/test11_12.out
    289:       test:
    290:          suffix: 12
    291:          args: -bv_type {{vecs contiguous svec mat}shared output}
    292:          requires: !single !defined(PETSCTEST_VALGRIND)
    293:       test:
    294:          suffix: 12_cuda
    295:          TODO: too many processes accessing the GPU
    296:          args: -bv_type svec -vec_type cuda
    297:          requires: cuda !single !defined(PETSCTEST_VALGRIND)

    299: TEST*/