Date: 2022-03-31T15:29:23+00:00

Actual source code: ex45.c
slepc-3.17.0 2022-03-31
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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[] = "Computes a partial generalized singular value decomposition (GSVD).\n"
     12:   "The command line options are:\n"
     13:   "  -m <m>, where <m> = number of rows of A.\n"
     14:   "  -n <n>, where <n> = number of columns of A.\n"
     15:   "  -p <p>, where <p> = number of rows of B.\n\n";

     17: #include <slepcsvd.h>

     19: int main(int argc,char **argv)
     20: {
     21:   Mat            A,B;             /* operator matrices */
     22:   Vec            u,v,x;           /* singular vectors */
     23:   SVD            svd;             /* singular value problem solver context */
     24:   SVDType        type;
     25:   Vec            uv,aux[2],*U,*V;
     26:   PetscReal      error,tol,sigma,lev1=0.0,lev2=0.0;
     27:   PetscInt       m=100,n,p=14,i,j,d,Istart,Iend,nsv,maxit,its,nconv;
     28:   PetscBool      flg,skiporth=PETSC_FALSE;

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

     32:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     33:   PetscOptionsGetInt(NULL,NULL,"-n",&n,&flg);
     34:   if (!flg) n = m;
     35:   PetscOptionsGetInt(NULL,NULL,"-p",&p,&flg);
     36:   PetscPrintf(PETSC_COMM_WORLD,"\nGeneralized singular value decomposition, (%" PetscInt_FMT "+%" PetscInt_FMT ")x%" PetscInt_FMT "\n\n",m,p,n);
     37:   PetscOptionsGetBool(NULL,NULL,"-skiporth",&skiporth,NULL);

     39:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     40:                           Build the matrices
     41:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     43:   MatCreate(PETSC_COMM_WORLD,&A);
     44:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m,n);
     45:   MatSetFromOptions(A);
     46:   MatSetUp(A);

     48:   MatGetOwnershipRange(A,&Istart,&Iend);
     49:   for (i=Istart;i<Iend;i++) {
     50:     if (i>0 && i-1<n) MatSetValue(A,i,i-1,-1.0,INSERT_VALUES);
     51:     if (i+1<n) MatSetValue(A,i,i+1,-1.0,INSERT_VALUES);
     52:     if (i<n) MatSetValue(A,i,i,2.0,INSERT_VALUES);
     53:     if (i>n) MatSetValue(A,i,n-1,1.0,INSERT_VALUES);
     54:   }
     55:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     56:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     58:   MatCreate(PETSC_COMM_WORLD,&B);
     59:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,p,n);
     60:   MatSetFromOptions(B);
     61:   MatSetUp(B);

     63:   MatGetOwnershipRange(B,&Istart,&Iend);
     64:   d = PetscMax(0,n-p);
     65:   for (i=Istart;i<Iend;i++) {
     66:     for (j=0;j<=PetscMin(i,n-1);j++) MatSetValue(B,i,j+d,1.0,INSERT_VALUES);
     67:   }
     68:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
     69:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);

     71:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     72:           Create the singular value solver and set various options
     73:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     80:   /*
     81:      Set operators and problem type
     82:   */
     83:   SVDSetOperators(svd,A,B);
     84:   SVDSetProblemType(svd,SVD_GENERALIZED);

     86:   /*
     87:      Set solver parameters at runtime
     88:   */
     89:   SVDSetFromOptions(svd);

     91:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     92:                       Solve the singular value system
     93:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     95:   SVDSolve(svd);
     96:   SVDGetIterationNumber(svd,&its);
     97:   PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",its);

     99:   /*
    100:      Optional: Get some information from the solver and display it
    101:   */
    102:   SVDGetType(svd,&type);
    103:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
    104:   SVDGetDimensions(svd,&nsv,NULL,NULL);
    105:   PetscPrintf(PETSC_COMM_WORLD," Number of requested singular values: %" PetscInt_FMT "\n",nsv);
    106:   SVDGetTolerances(svd,&tol,&maxit);
    107:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit);

    109:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    110:                     Display solution and clean up
    111:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    113:   /*
    114:      Get number of converged singular triplets
    115:   */
    116:   SVDGetConverged(svd,&nconv);
    117:   PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate singular triplets: %" PetscInt_FMT "\n\n",nconv);

    119:   if (nconv>0) {
    120:     /*
    121:        Create vectors. The interface returns u and v as stacked on top of each other
    122:        [u;v] so need to create a special vector (VecNest) to extract them
    123:     */
    124:     MatCreateVecs(A,&x,&u);
    125:     MatCreateVecs(B,NULL,&v);
    126:     aux[0] = u;
    127:     aux[1] = v;
    128:     VecCreateNest(PETSC_COMM_WORLD,2,NULL,aux,&uv);

    130:     VecDuplicateVecs(u,nconv,&U);
    131:     VecDuplicateVecs(v,nconv,&V);

    133:     /*
    134:        Display singular values and errors relative to the norms
    135:     */
    136:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,
    137:          "          sigma           ||r||/||[A;B]||\n"
    138:          "  --------------------- ------------------\n"));
    139:     for (i=0;i<nconv;i++) {
    140:       /*
    141:          Get converged singular triplets: i-th singular value is stored in sigma
    142:       */
    143:       SVDGetSingularTriplet(svd,i,&sigma,uv,x);

    145:       /* at this point, u and v can be used normally as individual vectors */
    146:       VecCopy(u,U[i]);
    147:       VecCopy(v,V[i]);

    149:       /*
    150:          Compute the error associated to each singular triplet
    151:       */
    152:       SVDComputeError(svd,i,SVD_ERROR_NORM,&error);

    154:       PetscPrintf(PETSC_COMM_WORLD,"       % 6f      ",(double)sigma);
    155:       PetscPrintf(PETSC_COMM_WORLD,"   % 12g\n",(double)error);
    156:     }
    157:     PetscPrintf(PETSC_COMM_WORLD,"\n");

    159:     if (!skiporth) {
    160:       VecCheckOrthonormality(U,nconv,NULL,nconv,NULL,NULL,&lev1);
    161:       VecCheckOrthonormality(V,nconv,NULL,nconv,NULL,NULL,&lev2);
    162:     }
    163:     if (lev1+lev2<20*tol) PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality below the tolerance\n");
    164:     else PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality: %g (U) %g (V)\n",(double)lev1,(double)lev2);
    165:     VecDestroyVecs(nconv,&U);
    166:     VecDestroyVecs(nconv,&V);
    167:     VecDestroy(&x);
    168:     VecDestroy(&u);
    169:     VecDestroy(&v);
    170:     VecDestroy(&uv);
    171:   }

    173:   /*
    174:      Free work space
    175:   */
    176:   SVDDestroy(&svd);
    177:   MatDestroy(&A);
    178:   MatDestroy(&B);
    179:   SlepcFinalize();
    180:   return 0;
    181: }

    183: /*TEST

    185:    testset:
    186:       filter: grep -v "Solution method" | grep -v "Number of iterations" | sed -e "s/, maxit=1[0]*$//" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
    187:       requires: double
    188:       test:
    189:          args: -svd_type lapack -m 20 -n 10 -p 6
    190:          suffix: 1
    191:       test:
    192:          args: -svd_type lapack -m 15 -n 20 -p 10 -svd_smallest
    193:          suffix: 2
    194:       test:
    195:          args: -svd_type lapack -m 15 -n 20 -p 21
    196:          suffix: 3
    197:       test:
    198:          args: -svd_type lapack -m 20 -n 15 -p 21
    199:          suffix: 4

    201:    testset:
    202:       args: -m 25 -n 20 -p 21 -svd_smallest -svd_nsv 4
    203:       filter: grep -v "Solution method" | grep -v "Number of iterations" | sed -e "s/, maxit=1[0]*$//" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
    204:       requires: double
    205:       output_file: output/ex45_5.out
    206:       test:
    207:          args: -svd_type trlanczos -svd_ncv 8 -svd_trlanczos_gbidiag {{upper lower}}
    208:          suffix: 5
    209:       test:
    210:          args: -svd_type cross -svd_ncv 10 -svd_cross_explicitmatrix {{0 1}}
    211:          suffix: 5_cross
    212:       test:
    213:          args: -svd_type cyclic -svd_ncv 12 -svd_cyclic_explicitmatrix {{0 1}}
    214:          suffix: 5_cyclic
    215:          requires: !complex

    217:    testset:
    218:       args: -m 15 -n 20 -p 21 -svd_nsv 4 -svd_ncv 9
    219:       filter: grep -v "Solution method" | grep -v "Number of iterations" | sed -e "s/7.884967/7.884968/" | sed -e "s/, maxit=1[0]*$//" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
    220:       requires: double
    221:       output_file: output/ex45_6.out
    222:       test:
    223:          args: -svd_type trlanczos -svd_trlanczos_gbidiag {{single upper lower}} -svd_trlanczos_locking {{0 1}}
    224:          suffix: 6
    225:       test:
    226:          args: -svd_type cross -svd_cross_explicitmatrix {{0 1}}
    227:          suffix: 6_cross
    228:       test:
    229:          args: -svd_type cyclic -svd_cyclic_explicitmatrix {{0 1}}
    230:          suffix: 6_cyclic

    232:    testset:
    233:       args: -m 20 -n 15 -p 21 -svd_nsv 4 -svd_ncv 9
    234:       filter: grep -v "Solution method" | grep -v "Number of iterations" | sed -e "s/, maxit=1[0]*$//" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
    235:       requires: double
    236:       output_file: output/ex45_7.out
    237:       test:
    238:          args: -svd_type trlanczos -svd_trlanczos_gbidiag {{single upper lower}} -svd_trlanczos_restart 0.4
    239:          suffix: 7
    240:       test:
    241:          args: -svd_type cross -svd_cross_explicitmatrix {{0 1}}
    242:          suffix: 7_cross
    243:       test:
    244:          args: -svd_type cyclic -svd_cyclic_explicitmatrix {{0 1}}
    245:          suffix: 7_cyclic

    247: TEST*/