Date: 2022-11-02T11:47:13+00:00

Actual source code: test1.c
slepc-3.18.1 2022-11-02
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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[] = "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;

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

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

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

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

     63:   MatGetOwnershipRange(A,&Istart,&Iend);
     64:   for (i=Istart;i<Iend;i++) {
     65:     col[0]=i-1; col[1]=i; col[2]=i+1; col[3]=i+2; col[4]=i+3;
     66:     if (i==0) MatSetValues(A,1,&i,4,col+1,value+1,INSERT_VALUES);
     67:     else MatSetValues(A,1,&i,PetscMin(5,N-i+1),col,value,INSERT_VALUES);
     68:   }

     70:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     71:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     73:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     74:          Create the singular value solver and set the solution method
     75:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

    106:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    107:                       Compute the singular values
    108:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

    142:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    143:                     Display solution and clean up
    144:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    145:   if (nconv1 > 0 && nconv2 > 0) {
    146:     PetscPrintf(PETSC_COMM_WORLD," Computed singular values: sigma_1=%.4f, sigma_n=%.4f\n",(double)sigma_1,(double)sigma_n);
    147:     PetscPrintf(PETSC_COMM_WORLD," Estimated condition number: sigma_1/sigma_n=%.4f\n\n",(double)(sigma_1/sigma_n));
    148:   }

    150:   /*
    151:      Free work space
    152:   */
    153:   SVDDestroy(&svd);
    154:   MatDestroy(&A);
    155:   SlepcFinalize();
    156:   return 0;
    157: }

    159: /*TEST

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

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

    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*/