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

 30:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
 31:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-mu",&mu,NULL));
 32:   PetscCall(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:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
 39:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n+1,n));
 40:   PetscCall(MatSetFromOptions(A));

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

 49:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
 50:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
 51:   PetscCall(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:   PetscCall(SVDCreate(PETSC_COMM_WORLD,&svd));

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

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

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

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

 82:   PetscCall(SVDSolve(svd));
 83:   PetscCall(SVDGetIterationNumber(svd,&its));
 84:   PetscCall(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:   PetscCall(SVDGetType(svd,&type));
 90:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
 91:   PetscCall(SVDGetDimensions(svd,&nsv,NULL,NULL));
 92:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested singular values: %" PetscInt_FMT "\n",nsv));
 93:   PetscCall(SVDGetTolerances(svd,&tol,&maxit));
 94:   PetscCall(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:   PetscCall(SVDGetConverged(svd,&nconv));
104:   PetscCall(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:       PetscCall(SVDGetSingularTriplet(svd,i,&sigma,u,v));

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

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

130:   /*
131:      Free work space
132:   */
133:   PetscCall(SVDDestroy(&svd));
134:   PetscCall(MatDestroy(&A));
135:   PetscCall(VecDestroy(&u));
136:   PetscCall(VecDestroy(&v));
137:   PetscCall(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*/