Actual source code: ex15.c

slepc-3.18.0 2022-10-01
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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[] = "Singular value decomposition of the Lauchli matrix.\n"
 12:   "The command line options are:\n"
 13:   "  -n <n>, where <n> = matrix dimension.\n"
 14:   "  -mu <mu>, where <mu> = subdiagonal value.\n\n";

 16: #include <slepcsvd.h>

 18: int main(int argc,char **argv)
 19: {
 20:   Mat            A;               /* operator matrix */
 21:   Vec            u,v;             /* left and right singular vectors */
 22:   SVD            svd;             /* singular value problem solver context */
 23:   SVDType        type;
 24:   PetscReal      error,tol,sigma,mu=PETSC_SQRT_MACHINE_EPSILON;
 25:   PetscInt       n=100,i,j,Istart,Iend,nsv,maxit,its,nconv;

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

 30:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 31:   PetscOptionsGetReal(NULL,NULL,"-mu",&mu,NULL);
 32:   PetscPrintf(PETSC_COMM_WORLD,"\nLauchli singular value decomposition, (%" PetscInt_FMT " x %" PetscInt_FMT ") mu=%g\n\n",n+1,n,(double)mu);

 34:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 35:                           Build the Lauchli matrix
 36:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 38:   MatCreate(PETSC_COMM_WORLD,&A);
 39:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n+1,n);
 40:   MatSetFromOptions(A);
 41:   MatSetUp(A);

 43:   MatGetOwnershipRange(A,&Istart,&Iend);
 44:   for (i=Istart;i<Iend;i++) {
 45:     if (i == 0) {
 46:       for (j=0;j<n;j++) MatSetValue(A,0,j,1.0,INSERT_VALUES);
 47:     } else MatSetValue(A,i,i-1,mu,INSERT_VALUES);
 48:   }

 50:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 51:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 52:   MatCreateVecs(A,&v,&u);

 54:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 55:           Create the singular value solver and set various options
 56:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 58:   /*
 59:      Create singular value solver context
 60:   */
 61:   SVDCreate(PETSC_COMM_WORLD,&svd);

 63:   /*
 64:      Set operators and problem type
 65:   */
 66:   SVDSetOperators(svd,A,NULL);
 67:   SVDSetProblemType(svd,SVD_STANDARD);

 69:   /*
 70:      Use thick-restart Lanczos as default solver
 71:   */
 72:   SVDSetType(svd,SVDTRLANCZOS);

 74:   /*
 75:      Set solver parameters at runtime
 76:   */
 77:   SVDSetFromOptions(svd);

 79:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 80:                       Solve the singular value system
 81:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 83:   SVDSolve(svd);
 84:   SVDGetIterationNumber(svd,&its);
 85:   PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",its);

 87:   /*
 88:      Optional: Get some information from the solver and display it
 89:   */
 90:   SVDGetType(svd,&type);
 91:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
 92:   SVDGetDimensions(svd,&nsv,NULL,NULL);
 93:   PetscPrintf(PETSC_COMM_WORLD," Number of requested singular values: %" PetscInt_FMT "\n",nsv);
 94:   SVDGetTolerances(svd,&tol,&maxit);
 95:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit);

 97:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 98:                     Display solution and clean up
 99:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

101:   /*
102:      Get number of converged singular triplets
103:   */
104:   SVDGetConverged(svd,&nconv);
105:   PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate singular triplets: %" PetscInt_FMT "\n\n",nconv);

107:   if (nconv>0) {
108:     /*
109:        Display singular values and relative errors
110:     */
111:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,
112:          "          sigma           relative error\n"
113:          "  --------------------- ------------------\n"));
114:     for (i=0;i<nconv;i++) {
115:       /*
116:          Get converged singular triplets: i-th singular value is stored in sigma
117:       */
118:       SVDGetSingularTriplet(svd,i,&sigma,u,v);

120:       /*
121:          Compute the error associated to each singular triplet
122:       */
123:       SVDComputeError(svd,i,SVD_ERROR_RELATIVE,&error);

125:       PetscPrintf(PETSC_COMM_WORLD,"       % 6f      ",(double)sigma);
126:       PetscPrintf(PETSC_COMM_WORLD," % 12g\n",(double)error);
127:     }
128:     PetscPrintf(PETSC_COMM_WORLD,"\n");
129:   }

131:   /*
132:      Free work space
133:   */
134:   SVDDestroy(&svd);
135:   MatDestroy(&A);
136:   VecDestroy(&u);
137:   VecDestroy(&v);
138:   SlepcFinalize();
139:   return 0;
140: }

142: /*TEST

144:    testset:
145:       filter: sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
146:       requires: double
147:       test:
148:          suffix: 1
149:       test:
150:          suffix: 1_scalapack
151:          nsize: {{1 2}}
152:          args: -svd_type scalapack
153:          requires: scalapack

155: TEST*/