Date: 2026-05-01T10:02:11+00:00

Actual source code: ex8.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[] = "Estimates the 2-norm condition number of a matrix A, that is, the ratio of the largest to the smallest singular values of A.\n\n"
     12:   "The matrix is a Grcar matrix.\n\n"
     13:   "The command line options are:\n"
     14:   "  -n <n>, where <n> = matrix dimension.\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;

     42:   PetscFunctionBeginUser;
     43:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     45:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL));
     46:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nEstimate the condition number of a Grcar matrix, n=%" PetscInt_FMT "\n\n",N));

     48:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     49:         Generate the matrix
     50:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     52:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
     53:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
     54:   PetscCall(MatSetFromOptions(A));

     56:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
     57:   for (i=Istart;i<Iend;i++) {
     58:     col[0]=i-1; col[1]=i; col[2]=i+1; col[3]=i+2; col[4]=i+3;
     59:     if (i==0) PetscCall(MatSetValues(A,1,&i,PetscMin(4,N-i),col+1,value+1,INSERT_VALUES));
     60:     else PetscCall(MatSetValues(A,1,&i,PetscMin(5,N-i+1),col,value,INSERT_VALUES));
     61:   }

     63:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
     64:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));

     66:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     67:              Create the singular value solver and set the solution method
     68:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     70:   /*
     71:      Create singular value context
     72:   */
     73:   PetscCall(SVDCreate(PETSC_COMM_WORLD,&svd));

     75:   /*
     76:      Set operator
     77:   */
     78:   PetscCall(SVDSetOperators(svd,A,NULL));

     80:   /*
     81:      Set solver parameters at runtime
     82:   */
     83:   PetscCall(SVDSetFromOptions(svd));
     84:   PetscCall(SVDSetDimensions(svd,1,PETSC_DETERMINE,PETSC_DETERMINE));

     86:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     87:                       Solve the singular value problem
     88:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     90:   /*
     91:      First request a singular value from one end of the spectrum
     92:   */
     93:   PetscCall(SVDSetWhichSingularTriplets(svd,SVD_LARGEST));
     94:   PetscCall(SVDSolve(svd));
     95:   /*
     96:      Get number of converged singular values
     97:   */
     98:   PetscCall(SVDGetConverged(svd,&nconv1));
     99:   /*
    100:      Get converged singular values: largest singular value is stored in sigma_1.
    101:      In this example, we are not interested in the singular vectors
    102:   */
    103:   if (nconv1 > 0) PetscCall(SVDGetSingularTriplet(svd,0,&sigma_1,NULL,NULL));
    104:   else PetscCall(PetscPrintf(PETSC_COMM_WORLD," Unable to compute large singular value!\n\n"));

    106:   /*
    107:      Request a singular value from the other end of the spectrum
    108:   */
    109:   PetscCall(SVDSetWhichSingularTriplets(svd,SVD_SMALLEST));
    110:   PetscCall(SVDSolve(svd));
    111:   /*
    112:      Get number of converged singular triplets
    113:   */
    114:   PetscCall(SVDGetConverged(svd,&nconv2));
    115:   /*
    116:      Get converged singular values: smallest singular value is stored in sigma_n.
    117:      As before, we are not interested in the singular vectors
    118:   */
    119:   if (nconv2 > 0) PetscCall(SVDGetSingularTriplet(svd,0,&sigma_n,NULL,NULL));
    120:   else PetscCall(PetscPrintf(PETSC_COMM_WORLD," Unable to compute small singular value!\n\n"));

    122:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    123:                     Display solution and clean up
    124:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    125:   if (nconv1 > 0 && nconv2 > 0) {
    126:     PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computed singular values: sigma_1=%.4f, sigma_n=%.4f\n",(double)sigma_1,(double)sigma_n));
    127:     PetscCall(PetscPrintf(PETSC_COMM_WORLD," Estimated condition number: sigma_1/sigma_n=%.4f\n\n",(double)(sigma_1/sigma_n)));
    128:   }

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

    139: /*TEST

    141:    test:
    142:       suffix: 1

    144: TEST*/