Actual source code: test24.c

      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[] = "Test DSGSVD with compact storage and rectangular matrix A.\n\n";

     13: #include <slepcds.h>

     15: int main(int argc,char **argv)
     16: {
     17:   DS             ds;
     18:   Mat            X;
     19:   Vec            x0;
     20:   SlepcSC        sc;
     21:   PetscReal      *T,*D,sigma,rnorm,aux,cond;
     22:   PetscScalar    *U,*V,*w,d;
     23:   PetscInt       i,n=10,m,l=0,k=0,ld;
     24:   PetscViewer    viewer;
     25:   PetscBool      verbose,extrarow;

     27:   PetscFunctionBeginUser;
     28:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     29:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     30:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Solve a Dense System of type GSVD with compact storage - dimension %" PetscInt_FMT "x%" PetscInt_FMT ".\n",n+1,n));
     31:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-l",&l,NULL));
     32:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL));
     33:   PetscCheck(l<=n && k<=n && l<=k,PETSC_COMM_WORLD,PETSC_ERR_USER_INPUT,"Wrong value of dimensions");
     34:   PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));
     35:   PetscCall(PetscOptionsHasName(NULL,NULL,"-extrarow",&extrarow));
     36:   m = n+1;

     38:   /* Create DS object */
     39:   PetscCall(DSCreate(PETSC_COMM_WORLD,&ds));
     40:   PetscCall(DSSetType(ds,DSGSVD));
     41:   PetscCall(DSSetFromOptions(ds));
     42:   ld = n+2;  /* test leading dimension larger than n */
     43:   PetscCall(DSAllocate(ds,ld));
     44:   PetscCall(DSSetDimensions(ds,m,l,k));
     45:   PetscCall(DSGSVDSetDimensions(ds,n,n));
     46:   PetscCall(DSSetCompact(ds,PETSC_TRUE));
     47:   PetscCall(DSSetExtraRow(ds,extrarow));

     49:   /* Set up viewer */
     50:   PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
     51:   PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL));
     52:   PetscCall(DSView(ds,viewer));
     53:   PetscCall(PetscViewerPopFormat(viewer));

     55:   /* Fill A and B with lower/upper arrow-bidiagonal matrices
     56:      verifying that [A;B] has orthonormal columns */
     57:   PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
     58:   PetscCall(DSGetArrayReal(ds,DS_MAT_D,&D));
     59:   for (i=0;i<n;i++) T[i] = (PetscReal)(i+1)/(n+1); /* diagonal of matrix A */
     60:   for (i=0;i<k;i++) D[i] = PetscSqrtReal(1.0-T[i]*T[i]);
     61:   for (i=l;i<k;i++) {
     62:     T[i+ld] = PetscSqrtReal((1.0-T[k]*T[k])/(1.0+T[i]*T[i]/(D[i]*D[i])))*0.5*(1.0/k); /* upper diagonal of matrix A */
     63:     T[i+2*ld] = -T[i+ld]*T[i]/D[i]; /* upper diagonal of matrix B */
     64:   }
     65:   aux = 1.0-T[k]*T[k];
     66:   for (i=l;i<k;i++) aux -= T[i+ld]*T[i+ld]+T[i+2*ld]*T[i+2*ld];
     67:   T[k+ld] = PetscSqrtReal((1.0-aux)*.1);
     68:   aux -= T[k+ld]*T[k+ld];
     69:   D[k] = PetscSqrtReal(aux);
     70:   for (i=k+1;i<n;i++) {
     71:     T[i-1+2*ld] = -T[i-1+ld]*T[i]/D[i-1]; /* upper diagonal of matrix B */
     72:     aux = 1.0-T[i]*T[i]-T[2*ld+i-1]*T[2*ld+i-1];
     73:     T[i+ld] = PetscSqrtReal(aux)*.1; /* upper diagonal of matrix A */
     74:     D[i] = PetscSqrtReal(aux-T[i+ld]*T[i+ld]);
     75:   }
     76:   if (extrarow) { T[n]=-1.0; T[n-1+2*ld]=1.0; }
     77:   /* Fill locked eigenvalues */
     78:   PetscCall(PetscMalloc1(n,&w));
     79:   for (i=0;i<l;i++) w[i] = T[i]/D[i];
     80:   PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
     81:   PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&D));
     82:   if (l==0 && k==0) PetscCall(DSSetState(ds,DS_STATE_INTERMEDIATE));
     83:   else PetscCall(DSSetState(ds,DS_STATE_RAW));
     84:   if (verbose) {
     85:     PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB));
     86:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n"));
     87:     PetscCall(DSView(ds,viewer));
     88:   }

     90:   /* Condition number */
     91:   PetscCall(DSCond(ds,&cond));
     92:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Condition number = %.3f\n",(double)cond));

     94:   /* Solve */
     95:   PetscCall(DSGetSlepcSC(ds,&sc));
     96:   sc->comparison    = SlepcCompareLargestReal;
     97:   sc->comparisonctx = NULL;
     98:   sc->map           = NULL;
     99:   sc->mapobj        = NULL;
    100:   PetscCall(DSSolve(ds,w,NULL));
    101:   PetscCall(DSSort(ds,w,NULL,NULL,NULL,NULL));
    102:   if (extrarow) PetscCall(DSUpdateExtraRow(ds));
    103:   PetscCall(DSSynchronize(ds,w,NULL));
    104:   if (verbose) {
    105:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n"));
    106:     PetscCall(DSView(ds,viewer));
    107:   }

    109:   /* Print singular values */
    110:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Computed singular values =\n"));
    111:   for (i=0;i<n;i++) {
    112:     sigma = PetscRealPart(w[i]);
    113:     PetscCall(PetscViewerASCIIPrintf(viewer,"  %.5f\n",(double)sigma));
    114:   }

    116:   if (extrarow) {
    117:     /* Check that extra row is correct */
    118:     PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
    119:     PetscCall(DSGetArray(ds,DS_MAT_U,&U));
    120:     PetscCall(DSGetArray(ds,DS_MAT_V,&V));
    121:     d = 0.0;
    122:     for (i=0;i<n;i++) d += T[i+ld]+U[n+i*ld];
    123:     if (PetscAbsScalar(d)>10*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: there is a mismatch in A's extra row of %g\n",(double)PetscAbsScalar(d)));
    124:     d = 0.0;
    125:     for (i=0;i<n;i++) d += T[i+2*ld]-V[n-1+i*ld];
    126:     if (PetscAbsScalar(d)>10*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: there is a mismatch in B's extra row of %g\n",(double)PetscAbsScalar(d)));
    127:     PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
    128:     PetscCall(DSRestoreArray(ds,DS_MAT_U,&U));
    129:     PetscCall(DSRestoreArray(ds,DS_MAT_V,&V));
    130:   }

    132:   /* Singular vectors */
    133:   PetscCall(DSVectors(ds,DS_MAT_X,NULL,NULL));  /* all singular vectors */
    134:   PetscCall(DSGetMat(ds,DS_MAT_X,&X));
    135:   PetscCall(MatCreateVecs(X,NULL,&x0));
    136:   PetscCall(MatGetColumnVector(X,x0,0));
    137:   PetscCall(VecNorm(x0,NORM_2,&rnorm));
    138:   PetscCall(DSRestoreMat(ds,DS_MAT_X,&X));
    139:   PetscCall(VecDestroy(&x0));
    140:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Norm of 1st X vector = %.3f\n",(double)rnorm));

    142:   PetscCall(DSGetMat(ds,DS_MAT_U,&X));
    143:   PetscCall(MatCreateVecs(X,NULL,&x0));
    144:   PetscCall(MatGetColumnVector(X,x0,0));
    145:   PetscCall(VecNorm(x0,NORM_2,&rnorm));
    146:   PetscCall(DSRestoreMat(ds,DS_MAT_U,&X));
    147:   PetscCall(VecDestroy(&x0));
    148:   if (PetscAbs(rnorm-1.0)>10*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: the 1st U vector has norm %g\n",(double)rnorm));

    150:   PetscCall(DSGetMat(ds,DS_MAT_V,&X));
    151:   PetscCall(MatCreateVecs(X,NULL,&x0));
    152:   PetscCall(MatGetColumnVector(X,x0,0));
    153:   PetscCall(VecNorm(x0,NORM_2,&rnorm));
    154:   PetscCall(DSRestoreMat(ds,DS_MAT_V,&X));
    155:   PetscCall(VecDestroy(&x0));
    156:   if (PetscAbs(rnorm-1.0)>10*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: the 1st V vector has norm %g\n",(double)rnorm));

    158:   PetscCall(PetscFree(w));
    159:   PetscCall(DSDestroy(&ds));
    160:   PetscCall(SlepcFinalize());
    161:   return 0;
    162: }

    164: /*TEST

    166:    testset:
    167:       requires: double
    168:       output_file: output/test24_1.out
    169:       test:
    170:          suffix: 1
    171:          args: -l 1 -k 4
    172:       test:
    173:          suffix: 1_extrarow
    174:          filter: sed -e "s/extrarow//"
    175:          args: -l 1 -k 4 -extrarow

    177: TEST*/