Actual source code: ex8.c

slepc-3.11.2 2019-07-30
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2019, 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);if (ierr) return ierr;

 45:   PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL);
 46:   PetscPrintf(PETSC_COMM_WORLD,"\nEstimate the condition number of a Grcar matrix, n=%D\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) {
 61:       MatSetValues(A,1,&i,PetscMin(4,N-i),col+1,value+1,INSERT_VALUES);
 62:     } else {
 63:       MatSetValues(A,1,&i,PetscMin(5,N-i+1),col,value,INSERT_VALUES);
 64:     }
 65:   }

 67:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 68:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 70:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 71:              Create the singular value solver and set the solution method
 72:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 74:   /*
 75:      Create singular value context
 76:   */
 77:   SVDCreate(PETSC_COMM_WORLD,&svd);

 79:   /*
 80:      Set operator
 81:   */
 82:   SVDSetOperator(svd,A);

 84:   /*
 85:      Set solver parameters at runtime
 86:   */
 87:   SVDSetFromOptions(svd);
 88:   SVDSetDimensions(svd,1,PETSC_DEFAULT,PETSC_DEFAULT);

 90:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 91:                       Solve the singular value problem
 92:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 94:   /*
 95:      First request a singular value from one end of the spectrum
 96:   */
 97:   SVDSetWhichSingularTriplets(svd,SVD_LARGEST);
 98:   SVDSolve(svd);
 99:   /*
100:      Get number of converged singular values
101:   */
102:   SVDGetConverged(svd,&nconv1);
103:   /*
104:      Get converged singular values: largest singular value is stored in sigma_1.
105:      In this example, we are not interested in the singular vectors
106:   */
107:   if (nconv1 > 0) {
108:     SVDGetSingularTriplet(svd,0,&sigma_1,NULL,NULL);
109:   } else {
110:     PetscPrintf(PETSC_COMM_WORLD," Unable to compute large singular value!\n\n");
111:   }

113:   /*
114:      Request a singular value from the other end of the spectrum
115:   */
116:   SVDSetWhichSingularTriplets(svd,SVD_SMALLEST);
117:   SVDSolve(svd);
118:   /*
119:      Get number of converged singular triplets
120:   */
121:   SVDGetConverged(svd,&nconv2);
122:   /*
123:      Get converged singular values: smallest singular value is stored in sigma_n.
124:      As before, we are not interested in the singular vectors
125:   */
126:   if (nconv2 > 0) {
127:     SVDGetSingularTriplet(svd,0,&sigma_n,NULL,NULL);
128:   } else {
129:     PetscPrintf(PETSC_COMM_WORLD," Unable to compute small singular value!\n\n");
130:   }

132:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
133:                     Display solution and clean up
134:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
135:   if (nconv1 > 0 && nconv2 > 0) {
136:     PetscPrintf(PETSC_COMM_WORLD," Computed singular values: sigma_1=%.4f, sigma_n=%.4f\n",(double)sigma_1,(double)sigma_n);
137:     PetscPrintf(PETSC_COMM_WORLD," Estimated condition number: sigma_1/sigma_n=%.4f\n\n",(double)(sigma_1/sigma_n));
138:   }

140:   /*
141:      Free work space
142:   */
143:   SVDDestroy(&svd);
144:   MatDestroy(&A);
145:   SlepcFinalize();
146:   return ierr;
147: }

149: /*TEST

151:    test:
152:       suffix: 1

154: TEST*/