Actual source code: ex15.c

slepc-3.17.1 2022-04-11
Report Typos and Errors
  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;

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

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

 33:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 34:                           Build the Lauchli matrix
 35:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

 53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 54:           Create the singular value solver and set various options
 55:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 57:   /*
 58:      Create singular value solver context
 59:   */
 60:   SVDCreate(PETSC_COMM_WORLD,&svd);

 62:   /*
 63:      Set operators and problem type
 64:   */
 65:   SVDSetOperators(svd,A,NULL);
 66:   SVDSetProblemType(svd,SVD_STANDARD);

 68:   /*
 69:      Use thick-restart Lanczos as default solver
 70:   */
 71:   SVDSetType(svd,SVDTRLANCZOS);

 73:   /*
 74:      Set solver parameters at runtime
 75:   */
 76:   SVDSetFromOptions(svd);

 78:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 79:                       Solve the singular value system
 80:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 86:   /*
 87:      Optional: Get some information from the solver and display it
 88:   */
 89:   SVDGetType(svd,&type);
 90:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
 91:   SVDGetDimensions(svd,&nsv,NULL,NULL);
 92:   PetscPrintf(PETSC_COMM_WORLD," Number of requested singular values: %" PetscInt_FMT "\n",nsv);
 93:   SVDGetTolerances(svd,&tol,&maxit);
 94:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit);

 96:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 97:                     Display solution and clean up
 98:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

100:   /*
101:      Get number of converged singular triplets
102:   */
103:   SVDGetConverged(svd,&nconv);
104:   PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate singular triplets: %" PetscInt_FMT "\n\n",nconv);

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

119:       /*
120:          Compute the error associated to each singular triplet
121:       */
122:       SVDComputeError(svd,i,SVD_ERROR_RELATIVE,&error);

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

130:   /*
131:      Free work space
132:   */
133:   SVDDestroy(&svd);
134:   MatDestroy(&A);
135:   VecDestroy(&u);
136:   VecDestroy(&v);
137:   SlepcFinalize();
138:   return 0;
139: }

141: /*TEST

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

154: TEST*/