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,(char*)0,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_DEFAULT,PETSC_DEFAULT));
 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*/