Date: 2026-01-20T11:35:19+00:00

Actual source code: ex15.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[] = "Singular value decomposition of the Lauchli matrix.\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = matrix dimension.\n"
     14:   "  -mu <mu>, where <mu> = subdiagonal value.\n\n";

     16: #include <slepcsvd.h>

     18: int main(int argc,char **argv)
     19: {
     20:   Mat            A;               /* operator matrix */
     21:   Vec            u,v;             /* left and right singular vectors */
     22:   SVD            svd;             /* singular value problem solver context */
     23:   SVDType        type;
     24:   PetscReal      error,tol,sigma,mu=PETSC_SQRT_MACHINE_EPSILON;
     25:   PetscInt       n=100,i,j,Istart,Iend,nsv,maxit,its,nconv;

     27:   PetscFunctionBeginUser;
     28:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     30:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     31:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-mu",&mu,NULL));
     32:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nLauchli singular value decomposition, (%" PetscInt_FMT " x %" PetscInt_FMT ") mu=%g\n\n",n+1,n,(double)mu));

     34:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     35:                           Build the Lauchli matrix
     36:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     38:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
     39:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n+1,n));
     40:   PetscCall(MatSetFromOptions(A));

     42:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
     43:   for (i=Istart;i<Iend;i++) {
     44:     if (i == 0) {
     45:       for (j=0;j<n;j++) PetscCall(MatSetValue(A,0,j,1.0,INSERT_VALUES));
     46:     } else PetscCall(MatSetValue(A,i,i-1,mu,INSERT_VALUES));
     47:   }

     49:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
     50:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
     51:   PetscCall(MatCreateVecs(A,&v,&u));

     53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     54:           Create the singular value solver and set various options
     55:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     57:   /*
     58:      Create singular value solver context
     59:   */
     60:   PetscCall(SVDCreate(PETSC_COMM_WORLD,&svd));

     62:   /*
     63:      Set operators and problem type
     64:   */
     65:   PetscCall(SVDSetOperators(svd,A,NULL));
     66:   PetscCall(SVDSetProblemType(svd,SVD_STANDARD));

     68:   /*
     69:      Use thick-restart Lanczos as default solver
     70:   */
     71:   PetscCall(SVDSetType(svd,SVDTRLANCZOS));

     73:   /*
     74:      Set solver parameters at runtime
     75:   */
     76:   PetscCall(SVDSetFromOptions(svd));

     78:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     79:                       Solve the singular value system
     80:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     82:   PetscCall(SVDSolve(svd));
     83:   PetscCall(SVDGetIterationNumber(svd,&its));
     84:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",its));

     86:   /*
     87:      Optional: Get some information from the solver and display it
     88:   */
     89:   PetscCall(SVDGetType(svd,&type));
     90:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
     91:   PetscCall(SVDGetDimensions(svd,&nsv,NULL,NULL));
     92:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested singular values: %" PetscInt_FMT "\n",nsv));
     93:   PetscCall(SVDGetTolerances(svd,&tol,&maxit));
     94:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit));

     96:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     97:                     Display solution and clean up
     98:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    100:   /*
    101:      Get number of converged singular triplets
    102:   */
    103:   PetscCall(SVDGetConverged(svd,&nconv));
    104:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate singular triplets: %" PetscInt_FMT "\n\n",nconv));

    106:   if (nconv>0) {
    107:     /*
    108:        Display singular values and relative errors
    109:     */
    110:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,
    111:          "          sigma           relative error\n"
    112:          "  --------------------- ------------------\n"));
    113:     for (i=0;i<nconv;i++) {
    114:       /*
    115:          Get converged singular triplets: i-th singular value is stored in sigma
    116:       */
    117:       PetscCall(SVDGetSingularTriplet(svd,i,&sigma,u,v));

    119:       /*
    120:          Compute the error associated to each singular triplet
    121:       */
    122:       PetscCall(SVDComputeError(svd,i,SVD_ERROR_RELATIVE,&error));

    124:       PetscCall(PetscPrintf(PETSC_COMM_WORLD,"       % 6f      ",(double)sigma));
    125:       PetscCall(PetscPrintf(PETSC_COMM_WORLD," % 12g\n",(double)error));
    126:     }
    127:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
    128:   }

    130:   /*
    131:      Free work space
    132:   */
    133:   PetscCall(SVDDestroy(&svd));
    134:   PetscCall(MatDestroy(&A));
    135:   PetscCall(VecDestroy(&u));
    136:   PetscCall(VecDestroy(&v));
    137:   PetscCall(SlepcFinalize());
    138:   return 0;
    139: }

    141: /*TEST

    143:    testset:
    144:       filter: sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
    145:       requires: double
    146:       test:
    147:          suffix: 1
    148:       test:
    149:          suffix: 1_scalapack
    150:          nsize: {{1 2}}
    151:          args: -svd_type scalapack
    152:          requires: scalapack

    154: TEST*/