Date: 2023-01-26T12:19:10+00:00

Actual source code: ex8.c
slepc-3.18.2 2023-01-26
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      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. "
     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;

     43:   SlepcInitialize(&argc,&argv,(char*)0,help);

     45:   PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL);
     46:   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:   MatCreate(PETSC_COMM_WORLD,&A);
     53:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     54:   MatSetFromOptions(A);
     55:   MatSetUp(A);

     57:   MatGetOwnershipRange(A,&Istart,&Iend);
     58:   for (i=Istart;i<Iend;i++) {
     59:     col[0]=i-1; col[1]=i; col[2]=i+1; col[3]=i+2; col[4]=i+3;
     60:     if (i==0) MatSetValues(A,1,&i,PetscMin(4,N-i),col+1,value+1,INSERT_VALUES);
     61:     else MatSetValues(A,1,&i,PetscMin(5,N-i+1),col,value,INSERT_VALUES);
     62:   }

     64:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     65:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     67:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     68:              Create the singular value solver and set the solution method
     69:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

     87:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     88:                       Solve the singular value problem
     89:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

    123:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    124:                     Display solution and clean up
    125:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    126:   if (nconv1 > 0 && nconv2 > 0) {
    127:     PetscPrintf(PETSC_COMM_WORLD," Computed singular values: sigma_1=%.4f, sigma_n=%.4f\n",(double)sigma_1,(double)sigma_n);
    128:     PetscPrintf(PETSC_COMM_WORLD," Estimated condition number: sigma_1/sigma_n=%.4f\n\n",(double)(sigma_1/sigma_n));
    129:   }

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

    140: /*TEST

    142:    test:
    143:       suffix: 1

    145: TEST*/