Date: 2023-01-26T12:18:09+00:00

Actual source code: test24.c
slepc-3.18.2 2023-01-26
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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[] = "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;

     28:   SlepcInitialize(&argc,&argv,(char*)0,help);
     29:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     30:   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:   PetscOptionsGetInt(NULL,NULL,"-l",&l,NULL);
     32:   PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL);
     34:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
     35:   PetscOptionsHasName(NULL,NULL,"-extrarow",&extrarow);
     36:   m = n+1;

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

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

     55:   /* Fill A and B with lower/upper arrow-bidiagonal matrices
     56:      verifying that [A;B] has orthonormal columns */
     57:   DSGetArrayReal(ds,DS_MAT_T,&T);
     58:   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:   PetscMalloc1(n,&w);
     79:   for (i=0;i<l;i++) w[i] = T[i]/D[i];
     80:   DSRestoreArrayReal(ds,DS_MAT_T,&T);
     81:   DSRestoreArrayReal(ds,DS_MAT_D,&D);
     82:   if (l==0 && k==0) DSSetState(ds,DS_STATE_INTERMEDIATE);
     83:   else DSSetState(ds,DS_STATE_RAW);
     84:   if (verbose) {
     85:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
     86:     PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n");
     87:     DSView(ds,viewer);
     88:   }

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

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

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

    116:   if (extrarow) {
    117:     /* Check that extra row is correct */
    118:     DSGetArrayReal(ds,DS_MAT_T,&T);
    119:     DSGetArray(ds,DS_MAT_U,&U);
    120:     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) 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) PetscPrintf(PETSC_COMM_WORLD,"Warning: there is a mismatch in B's extra row of %g\n",(double)PetscAbsScalar(d));
    127:     DSRestoreArrayReal(ds,DS_MAT_T,&T);
    128:     DSRestoreArray(ds,DS_MAT_U,&U);
    129:     DSRestoreArray(ds,DS_MAT_V,&V);
    130:   }

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

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

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

    158:   PetscFree(w);
    159:   DSDestroy(&ds);
    160:   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*/