Actual source code: ex8.c

  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:       SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:       Copyright (c) 2002-2007, Universidad Politecnica de Valencia, Spain

  6:       This file is part of SLEPc. See the README file for conditions of use
  7:       and additional information.
  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:  */

 36: int main( int argc, char **argv )
 37: {
 39:   Mat                  A;                  /* Grcar matrix */
 40:   SVD            svd;             /* singular value solver context */
 41:   PetscInt             N=30, Istart, Iend, i, col[5];
 42:   int                  nconv1, nconv2;
 43:   PetscScalar          value[] = { -1, 1, 1, 1, 1 };
 44:   PetscReal            sigma_1, sigma_n;

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

 48:   PetscOptionsGetInt(PETSC_NULL,"-n",&N,PETSC_NULL);
 49:   PetscPrintf(PETSC_COMM_WORLD,"\nEstimate the condition number of a Grcar matrix, n=%d\n\n",N);

 51:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 52:         Generate the matrix 
 53:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 55:   MatCreate(PETSC_COMM_WORLD,&A);
 56:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
 57:   MatSetFromOptions(A);

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

 87:   /*
 88:      Set solver parameters at runtime
 89:   */
 90:   SVDSetFromOptions(svd);
 91:   SVDSetDimensions(svd,1,PETSC_DECIDE);

 93:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 94:                       Solve the eigensystem
 95:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 97:   /*
 98:      First request an eigenvalue from one end of the spectrum
 99:   */
100:   SVDSetWhichSingularTriplets(svd,SVD_LARGEST);
101:   SVDSolve(svd);
102:   /* 
103:      Get number of converged singular values
104:   */
105:   SVDGetConverged(svd,&nconv1);
106:   /* 
107:      Get converged singular values: largest singular value is stored in sigma_1.
108:      In this example, we are not interested in the singular vectors
109:   */
110:   if (nconv1 > 0) {
111:     SVDGetSingularTriplet(svd,0,&sigma_1,PETSC_NULL,PETSC_NULL);
112:   } else {
113:     PetscPrintf(PETSC_COMM_WORLD," Unable to compute large singular value!\n\n");
114:   }

116:   /*
117:      Request an eigenvalue from the other end of the spectrum
118:   */
119:   SVDSetWhichSingularTriplets(svd,SVD_SMALLEST);
120:   SVDSolve(svd);
121:   /* 
122:      Get number of converged eigenpairs
123:   */
124:   SVDGetConverged(svd,&nconv2);
125:   /* 
126:      Get converged singular values: smallest singular value is stored in sigma_n. 
127:      As before, we are not interested in the singular vectors
128:   */
129:   if (nconv2 > 0) {
130:     SVDGetSingularTriplet(svd,0,&sigma_n,PETSC_NULL,PETSC_NULL);
131:   } else {
132:     PetscPrintf(PETSC_COMM_WORLD," Unable to compute small singular value!\n\n");
133:   }

135:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
136:                     Display solution and clean up
137:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
138:   if (nconv1 > 0 && nconv2 > 0) {
139:     PetscPrintf(PETSC_COMM_WORLD," Computed singular values: sigma_1=%6f, sigma_n=%6f\n",sigma_1,sigma_n);
140:     PetscPrintf(PETSC_COMM_WORLD," Estimated condition number: sigma_1/sigma_n=%6f\n\n",sigma_1/sigma_n);
141:   }
142: 
143:   /* 
144:      Free work space
145:   */
146:   SVDDestroy(svd);
147:   MatDestroy(A);
148:   SlepcFinalize();
149:   return 0;
150: }