Date: 2013-09-02T10:06:48+00:00

Actual source code: test1.c

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2013, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.

      8:    SLEPc is free software: you can redistribute it and/or modify it under  the
      9:    terms of version 3 of the GNU Lesser General Public License as published by
     10:    the Free Software Foundation.

     12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     15:    more details.

     17:    You  should have received a copy of the GNU Lesser General  Public  License
     18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     20: */

     22: static char help[] = "Test the solution of a SVD without calling SVDSetFromOptions (based on ex8.c).\n\n"
     23:   "The command line options are:\n"
     24:   "  -n <n>, where <n> = matrix dimension.\n"
     25:   "  -type <svd_type> = svd type to test.\n\n";

     27: #include <slepcsvd.h>

     29: /*
     30:    This example computes the singular values of an nxn Grcar matrix,
     31:    which is a nonsymmetric Toeplitz matrix:

     33:               |  1  1  1  1               |
     34:               | -1  1  1  1  1            |
     35:               |    -1  1  1  1  1         |
     36:               |       .  .  .  .  .       |
     37:           A = |          .  .  .  .  .    |
     38:               |            -1  1  1  1  1 |
     39:               |               -1  1  1  1 |
     40:               |                  -1  1  1 |
     41:               |                     -1  1 |

     43:  */

     47: int main(int argc,char **argv)
     48: {
     49:   Mat            A;               /* Grcar matrix */
     50:   SVD            svd;             /* singular value solver context */
     51:   PetscInt       N=30,Istart,Iend,i,col[5],nconv1,nconv2;
     52:   PetscScalar    value[] = { -1, 1, 1, 1, 1 };
     53:   PetscReal      sigma_1,sigma_n;
     54:   char           svdtype[30] = "cross",epstype[30] = "";
     55:   PetscBool      flg;
     56:   EPS            eps;

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

     61:   PetscOptionsGetInt(NULL,"-n",&N,NULL);
     62:   PetscOptionsGetString(NULL,"-type",svdtype,30,NULL);
     63:   PetscOptionsGetString(NULL,"-epstype",epstype,30,&flg);
     64:   PetscPrintf(PETSC_COMM_WORLD,"\nEstimate the condition number of a Grcar matrix, n=%D",N);
     65:   PetscPrintf(PETSC_COMM_WORLD,"\nSVD type: %s",svdtype);
     66:   if (flg) {
     67:     PetscPrintf(PETSC_COMM_WORLD,"\nEPS type: %s",epstype);
     68:   }
     69:   PetscPrintf(PETSC_COMM_WORLD,"\n\n");

     71:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     72:         Generate the matrix
     73:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     75:   MatCreate(PETSC_COMM_WORLD,&A);
     76:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     77:   MatSetFromOptions(A);
     78:   MatSetUp(A);

     80:   MatGetOwnershipRange(A,&Istart,&Iend);
     81:   for (i=Istart;i<Iend;i++) {
     82:     col[0]=i-1; col[1]=i; col[2]=i+1; col[3]=i+2; col[4]=i+3;
     83:     if (i==0) {
     84:       MatSetValues(A,1,&i,4,col+1,value+1,INSERT_VALUES);
     85:     } else {
     86:       MatSetValues(A,1,&i,PetscMin(5,N-i+1),col,value,INSERT_VALUES);
     87:     }
     88:   }

     90:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     91:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     93:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     94:              Create the singular value solver and set the solution method
     95:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     97:   /*
     98:      Create singular value context
     99:   */
    100:   SVDCreate(PETSC_COMM_WORLD,&svd);

    102:   /*
    103:      Set operator
    104:   */
    105:   SVDSetOperator(svd,A);

    107:   /*
    108:      Set solver parameters at runtime
    109:   */
    110:   SVDSetType(svd,svdtype);
    111:   if (flg) {
    112:     PetscObjectTypeCompare((PetscObject)svd,SVDCROSS,&flg);
    113:     if (flg) {
    114:       SVDCrossGetEPS(svd,&eps);
    115:       EPSSetType(eps,epstype);
    116:     }
    117:     PetscObjectTypeCompare((PetscObject)svd,SVDCYCLIC,&flg);
    118:     if (flg) {
    119:       SVDCyclicGetEPS(svd,&eps);
    120:       EPSSetType(eps,epstype);
    121:     }
    122:   }
    123:   SVDSetDimensions(svd,1,0,0);
    124:   SVDSetTolerances(svd,1e-6,1000);

    126:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    127:                       Solve the eigensystem
    128:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    130:   /*
    131:      First request an eigenvalue from one end of the spectrum
    132:   */
    133:   SVDSetWhichSingularTriplets(svd,SVD_LARGEST);
    134:   SVDSolve(svd);
    135:   /*
    136:      Get number of converged singular values
    137:   */
    138:   SVDGetConverged(svd,&nconv1);
    139:   /*
    140:      Get converged singular values: largest singular value is stored in sigma_1.
    141:      In this example, we are not interested in the singular vectors
    142:   */
    143:   if (nconv1 > 0) {
    144:     SVDGetSingularTriplet(svd,0,&sigma_1,NULL,NULL);
    145:   } else {
    146:     PetscPrintf(PETSC_COMM_WORLD," Unable to compute large singular value!\n\n");
    147:   }

    149:   /*
    150:      Request an eigenvalue from the other end of the spectrum
    151:   */
    152:   SVDSetWhichSingularTriplets(svd,SVD_SMALLEST);
    153:   SVDSolve(svd);
    154:   /*
    155:      Get number of converged eigenpairs
    156:   */
    157:   SVDGetConverged(svd,&nconv2);
    158:   /*
    159:      Get converged singular values: smallest singular value is stored in sigma_n.
    160:      As before, we are not interested in the singular vectors
    161:   */
    162:   if (nconv2 > 0) {
    163:     SVDGetSingularTriplet(svd,0,&sigma_n,NULL,NULL);
    164:   } else {
    165:     PetscPrintf(PETSC_COMM_WORLD," Unable to compute small singular value!\n\n");
    166:   }

    168:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    169:                     Display solution and clean up
    170:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    171:   if (nconv1 > 0 && nconv2 > 0) {
    172:     PetscPrintf(PETSC_COMM_WORLD," Computed singular values: sigma_1=%6F, sigma_n=%6F\n",sigma_1,sigma_n);
    173:     PetscPrintf(PETSC_COMM_WORLD," Estimated condition number: sigma_1/sigma_n=%6F\n\n",sigma_1/sigma_n);
    174:   }

    176:   /*
    177:      Free work space
    178:   */
    179:   SVDDestroy(&svd);
    180:   MatDestroy(&A);
    181:   SlepcFinalize();
    182:   return 0;
    183: }