Date: 2026-03-09T09:12:10+00:00

Actual source code: test12.c

      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 block orthogonalization on a rank-deficient BV.\n\n";

     13: #include <slepcbv.h>

     15: int main(int argc,char **argv)
     16: {
     17:   BV             X,Z;
     18:   Mat            M,R;
     19:   Vec            v,w,t;
     20:   PetscInt       i,j,n=20,k=8;
     21:   PetscViewer    view;
     22:   PetscBool      verbose;
     23:   PetscReal      norm;
     24:   PetscScalar    alpha;

     26:   PetscFunctionBeginUser;
     27:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     28:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     29:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL));
     30:   PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));
     31:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Test BV block orthogonalization (length %" PetscInt_FMT ", k=%" PetscInt_FMT ").\n",n,k));
     32:   PetscCheck(k>5,PETSC_COMM_WORLD,PETSC_ERR_USER_INPUT,"k must be at least 6");

     34:   /* Create template vector */
     35:   PetscCall(VecCreate(PETSC_COMM_WORLD,&t));
     36:   PetscCall(VecSetSizes(t,PETSC_DECIDE,n));
     37:   PetscCall(VecSetFromOptions(t));

     39:   /* Create BV object X */
     40:   PetscCall(BVCreate(PETSC_COMM_WORLD,&X));
     41:   PetscCall(PetscObjectSetName((PetscObject)X,"X"));
     42:   PetscCall(BVSetSizesFromVec(X,t,k));
     43:   PetscCall(BVSetFromOptions(X));

     45:   /* Set up viewer */
     46:   PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&view));
     47:   if (verbose) PetscCall(PetscViewerPushFormat(view,PETSC_VIEWER_ASCII_MATLAB));

     49:   /* Fill X entries (first half) */
     50:   for (j=0;j<k/2;j++) {
     51:     PetscCall(BVGetColumn(X,j,&v));
     52:     PetscCall(VecSet(v,0.0));
     53:     for (i=0;i<=n/2;i++) {
     54:       if (i+j<n) {
     55:         alpha = (3.0*i+j-2)/(2*(i+j+1));
     56:         PetscCall(VecSetValue(v,i+j,alpha,INSERT_VALUES));
     57:       }
     58:     }
     59:     PetscCall(VecAssemblyBegin(v));
     60:     PetscCall(VecAssemblyEnd(v));
     61:     PetscCall(BVRestoreColumn(X,j,&v));
     62:   }

     64:   /* make middle column linearly dependent wrt columns 0 and 1 */
     65:   PetscCall(BVCopyColumn(X,0,j));
     66:   PetscCall(BVGetColumn(X,j,&v));
     67:   PetscCall(BVGetColumn(X,1,&w));
     68:   PetscCall(VecAXPY(v,0.5,w));
     69:   PetscCall(BVRestoreColumn(X,1,&w));
     70:   PetscCall(BVRestoreColumn(X,j,&v));
     71:   j++;

     73:   /* Fill X entries (second half) */
     74:   for (;j<k-1;j++) {
     75:     PetscCall(BVGetColumn(X,j,&v));
     76:     PetscCall(VecSet(v,0.0));
     77:     for (i=0;i<=n/2;i++) {
     78:       if (i+j<n) {
     79:         alpha = (3.0*i+j-2)/(2*(i+j+1));
     80:         PetscCall(VecSetValue(v,i+j,alpha,INSERT_VALUES));
     81:       }
     82:     }
     83:     PetscCall(VecAssemblyBegin(v));
     84:     PetscCall(VecAssemblyEnd(v));
     85:     PetscCall(BVRestoreColumn(X,j,&v));
     86:   }

     88:   /* make middle column linearly dependent wrt columns 1 and k/2+1 */
     89:   PetscCall(BVCopyColumn(X,1,j));
     90:   PetscCall(BVGetColumn(X,j,&v));
     91:   PetscCall(BVGetColumn(X,k/2+1,&w));
     92:   PetscCall(VecAXPY(v,-1.2,w));
     93:   PetscCall(BVRestoreColumn(X,k/2+1,&w));
     94:   PetscCall(BVRestoreColumn(X,j,&v));

     96:   if (verbose) PetscCall(BVView(X,view));

     98:   /* Create a copy on Z */
     99:   PetscCall(BVDuplicate(X,&Z));
    100:   PetscCall(PetscObjectSetName((PetscObject)Z,"Z"));
    101:   PetscCall(BVCopy(X,Z));

    103:   /* Test BVOrthogonalize */
    104:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&R));
    105:   PetscCall(PetscObjectSetName((PetscObject)R,"R"));
    106:   PetscCall(BVOrthogonalize(X,R));
    107:   if (verbose) {
    108:     PetscCall(BVView(X,view));
    109:     PetscCall(MatView(R,view));
    110:   }

    112:   /* Check orthogonality */
    113:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&M));
    114:   PetscCall(MatShift(M,1.0));   /* set leading part to identity */
    115:   PetscCall(BVDot(X,X,M));
    116:   PetscCall(MatShift(M,-1.0));
    117:   PetscCall(MatNorm(M,NORM_1,&norm));
    118:   if (norm<100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality < 100*eps\n"));
    119:   else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality: %g\n",(double)norm));

    121:   /* Check residual */
    122:   PetscCall(BVMult(Z,-1.0,1.0,X,R));
    123:   PetscCall(BVNorm(Z,NORM_FROBENIUS,&norm));
    124:   if (norm<100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Residual ||X-QR|| < 100*eps\n"));
    125:   else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Residual ||X-QR||: %g\n",(double)norm));

    127:   PetscCall(MatDestroy(&R));
    128:   PetscCall(MatDestroy(&M));
    129:   PetscCall(BVDestroy(&X));
    130:   PetscCall(BVDestroy(&Z));
    131:   PetscCall(VecDestroy(&t));
    132:   PetscCall(SlepcFinalize());
    133:   return 0;
    134: }

    136: /*TEST

    138:    test:
    139:       suffix: 1
    140:       nsize: 1
    141:       args: -bv_orthog_block gs -bv_type {{vecs contiguous svec mat}shared output}
    142:       output_file: output/test12_1.out

    144: TEST*/