Date: 2021-02-01T14:42:09+00:00

Actual source code: test11.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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[] = "Tests a user-defined convergence test (based on ex8.c).\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = matrix dimension.\n\n";

     15: #include <slepcsvd.h>

     17: /*
     18:    This example computes the singular values of an nxn Grcar matrix,
     19:    which is a nonsymmetric Toeplitz matrix:

     21:               |  1  1  1  1               |
     22:               | -1  1  1  1  1            |
     23:               |    -1  1  1  1  1         |
     24:               |       .  .  .  .  .       |
     25:           A = |          .  .  .  .  .    |
     26:               |            -1  1  1  1  1 |
     27:               |               -1  1  1  1 |
     28:               |                  -1  1  1 |
     29:               |                     -1  1 |

     31:  */

     33: /*
     34:   MyConvergedRel - Convergence test relative to the norm of A (given in ctx).
     35: */
     36: PetscErrorCode MyConvergedRel(SVD svd,PetscReal sigma,PetscReal res,PetscReal *errest,void *ctx)
     37: {
     38:   PetscReal norm = *(PetscReal*)ctx;

     41:   *errest = res/norm;
     42:   return(0);
     43: }

     45: int main(int argc,char **argv)
     46: {
     47:   Mat            A;               /* Grcar matrix */
     48:   SVD            svd;             /* singular value solver context */
     49:   PetscInt       N=30,Istart,Iend,i,col[5],nconv1,nconv2;
     50:   PetscScalar    value[] = { -1, 1, 1, 1, 1 };
     51:   PetscReal      sigma_1,sigma_n;

     54:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

     56:   PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL);
     57:   PetscPrintf(PETSC_COMM_WORLD,"\nEstimate the condition number of a Grcar matrix, n=%D\n\n",N);

     59:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     60:         Generate the matrix
     61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     63:   MatCreate(PETSC_COMM_WORLD,&A);
     64:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     65:   MatSetFromOptions(A);
     66:   MatSetUp(A);
     67:   MatGetOwnershipRange(A,&Istart,&Iend);
     68:   for (i=Istart;i<Iend;i++) {
     69:     col[0]=i-1; col[1]=i; col[2]=i+1; col[3]=i+2; col[4]=i+3;
     70:     if (i==0) {
     71:       MatSetValues(A,1,&i,PetscMin(4,N-i),col+1,value+1,INSERT_VALUES);
     72:     } else {
     73:       MatSetValues(A,1,&i,PetscMin(5,N-i+1),col,value,INSERT_VALUES);
     74:     }
     75:   }
     76:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     77:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     79:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     80:              Create the SVD solver and set the solution method
     81:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     83:   SVDCreate(PETSC_COMM_WORLD,&svd);
     84:   SVDSetOperator(svd,A);
     85:   SVDSetType(svd,SVDTRLANCZOS);
     86:   SVDSetFromOptions(svd);

     88:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     89:                       Solve the singular value problem
     90:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     92:   SVDSetWhichSingularTriplets(svd,SVD_LARGEST);
     93:   SVDSolve(svd);
     94:   SVDGetConverged(svd,&nconv1);
     95:   if (nconv1 > 0) {
     96:     SVDGetSingularTriplet(svd,0,&sigma_1,NULL,NULL);
     97:   } else {
     98:     PetscPrintf(PETSC_COMM_WORLD," Unable to compute large singular value!\n\n");
     99:   }

    101:   /* compute smallest singular value relative to the matrix norm */
    102:   SVDSetConvergenceTestFunction(svd,MyConvergedRel,&sigma_1,NULL);
    103:   SVDSetWhichSingularTriplets(svd,SVD_SMALLEST);
    104:   SVDSolve(svd);
    105:   SVDGetConverged(svd,&nconv2);
    106:   if (nconv2 > 0) {
    107:     SVDGetSingularTriplet(svd,0,&sigma_n,NULL,NULL);
    108:   } else {
    109:     PetscPrintf(PETSC_COMM_WORLD," Unable to compute small singular value!\n\n");
    110:   }

    112:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    113:                     Display solution and clean up
    114:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    115:   if (nconv1 > 0 && nconv2 > 0) {
    116:     PetscPrintf(PETSC_COMM_WORLD," Computed singular values: sigma_1=%.4f, sigma_n=%.4f\n",(double)sigma_1,(double)sigma_n);
    117:     PetscPrintf(PETSC_COMM_WORLD," Estimated condition number: sigma_1/sigma_n=%.4f\n\n",(double)(sigma_1/sigma_n));
    118:   }

    120:   SVDDestroy(&svd);
    121:   MatDestroy(&A);
    122:   SlepcFinalize();
    123:   return ierr;
    124: }

    126: /*TEST

    128:    test:
    129:       suffix: 1

    131: TEST*/