Date: 2026-01-20T11:35:17+00:00

Actual source code: test1.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 the solution of a SVD without calling SVDSetFromOptions (based on ex8.c).\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = matrix dimension.\n"
     14:   "  -type <svd_type> = svd type to test.\n\n";

     16: #include <slepcsvd.h>

     18: /*
     19:    This example computes the singular values of an nxn Grcar matrix,
     20:    which is a nonsymmetric Toeplitz matrix:

     22:               |  1  1  1  1               |
     23:               | -1  1  1  1  1            |
     24:               |    -1  1  1  1  1         |
     25:               |       .  .  .  .  .       |
     26:           A = |          .  .  .  .  .    |
     27:               |            -1  1  1  1  1 |
     28:               |               -1  1  1  1 |
     29:               |                  -1  1  1 |
     30:               |                     -1  1 |

     32:  */

     34: int main(int argc,char **argv)
     35: {
     36:   Mat            A;               /* Grcar matrix */
     37:   SVD            svd;             /* singular value solver context */
     38:   PetscInt       N=30,Istart,Iend,i,col[5],nconv1,nconv2;
     39:   PetscScalar    value[] = { -1, 1, 1, 1, 1 };
     40:   PetscReal      sigma_1,sigma_n;
     41:   char           svdtype[30] = "cross",epstype[30] = "";
     42:   PetscBool      flg;
     43:   EPS            eps;

     45:   PetscFunctionBeginUser;
     46:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     48:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL));
     49:   PetscCall(PetscOptionsGetString(NULL,NULL,"-type",svdtype,sizeof(svdtype),NULL));
     50:   PetscCall(PetscOptionsGetString(NULL,NULL,"-epstype",epstype,sizeof(epstype),&flg));
     51:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nEstimate the condition number of a Grcar matrix, n=%" PetscInt_FMT,N));
     52:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n\n"));

     54:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     55:         Generate the matrix
     56:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     58:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
     59:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
     60:   PetscCall(MatSetFromOptions(A));

     62:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
     63:   for (i=Istart;i<Iend;i++) {
     64:     col[0]=i-1; col[1]=i; col[2]=i+1; col[3]=i+2; col[4]=i+3;
     65:     if (i==0) PetscCall(MatSetValues(A,1,&i,4,col+1,value+1,INSERT_VALUES));
     66:     else PetscCall(MatSetValues(A,1,&i,PetscMin(5,N-i+1),col,value,INSERT_VALUES));
     67:   }

     69:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
     70:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));

     72:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     73:          Create the singular value solver and set the solution method
     74:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     76:   /*
     77:      Create singular value context
     78:   */
     79:   PetscCall(SVDCreate(PETSC_COMM_WORLD,&svd));

     81:   /*
     82:      Set operator
     83:   */
     84:   PetscCall(SVDSetOperators(svd,A,NULL));

     86:   /*
     87:      Set solver parameters at runtime
     88:   */
     89:   PetscCall(SVDSetType(svd,svdtype));
     90:   if (flg) {
     91:     PetscCall(PetscObjectTypeCompare((PetscObject)svd,SVDCROSS,&flg));
     92:     if (flg) {
     93:       PetscCall(SVDCrossGetEPS(svd,&eps));
     94:       PetscCall(EPSSetType(eps,epstype));
     95:     }
     96:     PetscCall(PetscObjectTypeCompare((PetscObject)svd,SVDCYCLIC,&flg));
     97:     if (flg) {
     98:       PetscCall(SVDCyclicGetEPS(svd,&eps));
     99:       PetscCall(EPSSetType(eps,epstype));
    100:     }
    101:   }
    102:   PetscCall(SVDSetDimensions(svd,1,PETSC_DETERMINE,PETSC_DETERMINE));
    103:   PetscCall(SVDSetTolerances(svd,1e-6,1000));

    105:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    106:                       Compute the singular values
    107:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    109:   /*
    110:      First request the largest singular value
    111:   */
    112:   PetscCall(SVDSetWhichSingularTriplets(svd,SVD_LARGEST));
    113:   PetscCall(SVDSolve(svd));
    114:   /*
    115:      Get number of converged singular values
    116:   */
    117:   PetscCall(SVDGetConverged(svd,&nconv1));
    118:   /*
    119:      Get converged singular values: largest singular value is stored in sigma_1.
    120:      In this example, we are not interested in the singular vectors
    121:   */
    122:   if (nconv1 > 0) PetscCall(SVDGetSingularTriplet(svd,0,&sigma_1,NULL,NULL));
    123:   else PetscCall(PetscPrintf(PETSC_COMM_WORLD," Unable to compute large singular value!\n\n"));

    125:   /*
    126:      Request the smallest singular value
    127:   */
    128:   PetscCall(SVDSetWhichSingularTriplets(svd,SVD_SMALLEST));
    129:   PetscCall(SVDSolve(svd));
    130:   /*
    131:      Get number of converged triplets
    132:   */
    133:   PetscCall(SVDGetConverged(svd,&nconv2));
    134:   /*
    135:      Get converged singular values: smallest singular value is stored in sigma_n.
    136:      As before, we are not interested in the singular vectors
    137:   */
    138:   if (nconv2 > 0) PetscCall(SVDGetSingularTriplet(svd,0,&sigma_n,NULL,NULL));
    139:   else PetscCall(PetscPrintf(PETSC_COMM_WORLD," Unable to compute small singular value!\n\n"));

    141:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    142:                     Display solution and clean up
    143:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    144:   if (nconv1 > 0 && nconv2 > 0) {
    145:     PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computed singular values: sigma_1=%.4f, sigma_n=%.4f\n",(double)sigma_1,(double)sigma_n));
    146:     PetscCall(PetscPrintf(PETSC_COMM_WORLD," Estimated condition number: sigma_1/sigma_n=%.4f\n\n",(double)(sigma_1/sigma_n)));
    147:   }

    149:   /*
    150:      Free work space
    151:   */
    152:   PetscCall(SVDDestroy(&svd));
    153:   PetscCall(MatDestroy(&A));
    154:   PetscCall(SlepcFinalize());
    155:   return 0;
    156: }

    158: /*TEST

    160:    test:
    161:       suffix: 1
    162:       args: -type {{lanczos trlanczos cross cyclic lapack}}

    164:    test:
    165:       suffix: 1_cross_gd
    166:       args: -type cross -epstype gd
    167:       output_file: output/test1_1.out
    168:       requires: !single

    170:    test:
    171:       suffix: 1_cyclic_gd
    172:       args: -type cyclic -epstype gd
    173:       output_file: output/test1_1.out
    174:       requires: !single

    176:    test:
    177:       suffix: 1_primme
    178:       args: -type primme
    179:       requires: primme
    180:       output_file: output/test1_1.out

    182: TEST*/