Date: 2026-03-09T09:12:04+00:00

Actual source code: test19.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 RSVD on a low-rank matrix.\n\n";

     13: #include <slepcsvd.h>

     15: int main(int argc,char **argv)
     16: {
     17:   Mat            A,Ur,Vr;
     18:   SVD            svd;
     19:   PetscInt       m=80,n=40,rank=3,Istart,Iend,i,j;
     20:   PetscScalar    *u;
     21:   PetscReal      tol=PETSC_SMALL;

     23:   PetscFunctionBeginUser;
     24:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     26:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     27:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL));
     28:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-rank",&rank,NULL));
     29:   PetscCheck(rank>0,PETSC_COMM_WORLD,PETSC_ERR_USER_INPUT,"The rank must be >=1");
     30:   PetscCheck(rank<PetscMin(m,n),PETSC_COMM_WORLD,PETSC_ERR_USER_INPUT,"The rank must be <min(m,n)");
     31:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nSVD of low-rank matrix, size %" PetscInt_FMT "x%" PetscInt_FMT ", rank %" PetscInt_FMT "\n\n",m,n,rank));

     33:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     34:                   Create a low-rank matrix A = Ur*Vr'
     35:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     37:   PetscCall(MatCreate(PETSC_COMM_WORLD,&Ur));
     38:   PetscCall(MatSetSizes(Ur,PETSC_DECIDE,PETSC_DECIDE,m,rank));
     39:   PetscCall(MatSetType(Ur,MATDENSE));
     40:   PetscCall(MatGetOwnershipRange(Ur,&Istart,&Iend));
     41:   PetscCall(MatDenseGetArray(Ur,&u));
     42:   for (i=Istart;i<Iend;i++) {
     43:     if (i<m/2) u[i-Istart] = 1.0;
     44:     if (i==0) u[i+Iend-2*Istart] = -2.0;
     45:     if (i==1) u[i+Iend-2*Istart] = -1.0;
     46:     if (i==2) u[i+Iend-2*Istart] = -1.0;
     47:     for (j=2;j<rank;j++) if (i==j) u[j+j*Iend-(j+1)*Istart] = j;
     48:   }
     49:   PetscCall(MatDenseRestoreArray(Ur,&u));
     50:   PetscCall(MatAssemblyBegin(Ur,MAT_FINAL_ASSEMBLY));
     51:   PetscCall(MatAssemblyEnd(Ur,MAT_FINAL_ASSEMBLY));
     52:   PetscCall(MatCreate(PETSC_COMM_WORLD,&Vr));
     53:   PetscCall(MatSetSizes(Vr,PETSC_DECIDE,PETSC_DECIDE,n,rank));
     54:   PetscCall(MatSetType(Vr,MATDENSE));
     55:   PetscCall(MatGetOwnershipRange(Vr,&Istart,&Iend));
     56:   PetscCall(MatDenseGetArray(Vr,&u));
     57:   for (i=Istart;i<Iend;i++) {
     58:     if (i>n/2) u[i-Istart] = 1.0;
     59:     if (i==0) u[i+Iend-2*Istart] = 1.0;
     60:     if (i==1) u[i+Iend-2*Istart] = 2.0;
     61:     if (i==2) u[i+Iend-2*Istart] = 2.0;
     62:     for (j=2;j<rank;j++) if (i==j) u[j+j*Iend-(j+1)*Istart] = j;
     63:   }
     64:   PetscCall(MatDenseRestoreArray(Vr,&u));
     65:   PetscCall(MatAssemblyBegin(Vr,MAT_FINAL_ASSEMBLY));
     66:   PetscCall(MatAssemblyEnd(Vr,MAT_FINAL_ASSEMBLY));
     67:   PetscCall(MatCreateLRC(NULL,Ur,NULL,Vr,&A));
     68:   PetscCall(MatDestroy(&Ur));
     69:   PetscCall(MatDestroy(&Vr));

     71:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     72:                      Create the SVD solver
     73:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     75:   PetscCall(SVDCreate(PETSC_COMM_WORLD,&svd));
     76:   PetscCall(SVDSetOperators(svd,A,NULL));
     77:   PetscCall(SVDSetType(svd,SVDRANDOMIZED));
     78:   PetscCall(SVDSetDimensions(svd,2,PETSC_DETERMINE,PETSC_DETERMINE));
     79:   PetscCall(SVDSetConvergenceTest(svd,SVD_CONV_MAXIT));
     80:   PetscCall(SVDSetTolerances(svd,tol,1));   /* maxit=1 to disable outer iteration */
     81:   PetscCall(SVDSetFromOptions(svd));

     83:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     84:                 Compute the singular triplets and display solution
     85:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     87:   PetscCall(SVDSolve(svd));
     88:   PetscCall(SVDErrorView(svd,SVD_ERROR_RELATIVE,NULL));
     89:   PetscCall(SVDDestroy(&svd));
     90:   PetscCall(MatDestroy(&A));
     91:   PetscCall(SlepcFinalize());
     92:   return 0;
     93: }

     95: /*TEST

     97:    test:
     98:       args: -bv_orthog_block tsqr # currently fail with other block orthogonalization methods
     99:       requires: !single

    101: TEST*/