Actual source code: test22.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[] = "Test DSGSVD with compact storage.\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;
 22:   PetscScalar    *U,*V,*w,d;
 23:   PetscInt       i,n=10,l=0,k=0,ld;
 24:   PetscViewer    viewer;
 25:   PetscBool      verbose,test_dsview,extrarow;

 27:   SlepcInitialize(&argc,&argv,(char*)0,help);
 28:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 29:   PetscPrintf(PETSC_COMM_WORLD,"Solve a Dense System of type GSVD with compact storage - dimension %" PetscInt_FMT "x%" PetscInt_FMT ".\n",n,n);
 30:   PetscOptionsGetInt(NULL,NULL,"-l",&l,NULL);
 31:   PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL);
 33:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
 34:   PetscOptionsHasName(NULL,NULL,"-test_dsview",&test_dsview);
 35:   PetscOptionsHasName(NULL,NULL,"-extrarow",&extrarow);

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

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

 54:   if (test_dsview) {
 55:     /* Fill A and B with dummy values to test DSView */
 56:     DSGetArrayReal(ds,DS_MAT_T,&T);
 57:     DSGetArrayReal(ds,DS_MAT_D,&D);
 58:     for (i=0;i<n;i++) { T[i] = i+1; D[i] = -i-1; }
 59:     for (i=0;i<n-1;i++) { T[i+ld] = -1.0; T[i+2*ld] = 1.0; }
 60:     DSRestoreArrayReal(ds,DS_MAT_T,&T);
 61:     DSRestoreArrayReal(ds,DS_MAT_D,&D);
 62:     DSView(ds,viewer);
 63:   }

 65:   /* Fill A and B with upper arrow-bidiagonal matrices
 66:      verifying that [A;B] has orthonormal columns */
 67:   DSGetArrayReal(ds,DS_MAT_T,&T);
 68:   DSGetArrayReal(ds,DS_MAT_D,&D);
 69:   for (i=0;i<n;i++) T[i] = (PetscReal)(i+1)/(n+1); /* diagonal of matrix A */
 70:   for (i=0;i<k;i++) D[i] = PetscSqrtReal(1.0-T[i]*T[i]);
 71:   for (i=l;i<k;i++) {
 72:     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 */
 73:     T[i+2*ld] = -T[i+ld]*T[i]/D[i]; /* upper diagonal of matrix B */
 74:   }
 75:   aux = 1.0-T[k]*T[k];
 76:   for (i=l;i<k;i++) aux -= T[i+ld]*T[i+ld]+T[i+2*ld]*T[i+2*ld];
 77:   D[k] = PetscSqrtReal(aux);
 78:   for (i=k;i<n-1;i++) {
 79:     T[i+ld] = PetscSqrtReal((1.0-T[i+1]*T[i+1])/(1.0+T[i]*T[i]/(D[i]*D[i])))*0.5; /* upper diagonal of matrix A */
 80:     T[i+2*ld] = -T[i+ld]*T[i]/D[i]; /* upper diagonal of matrix B */
 81:     D[i+1] = PetscSqrtReal(1.0-T[i+1]*T[i+1]-T[ld+i]*T[ld+i]-T[2*ld+i]*T[2*ld+i]); /* diagonal of matrix B */
 82:   }
 83:   if (extrarow) { T[n-1+ld]=-1.0; T[n-1+2*ld]=1.0; }
 84:   /* Fill locked eigenvalues */
 85:   PetscMalloc1(n,&w);
 86:   for (i=0;i<l;i++) w[i] = T[i]/D[i];
 87:   DSRestoreArrayReal(ds,DS_MAT_T,&T);
 88:   DSRestoreArrayReal(ds,DS_MAT_D,&D);
 89:   if (l==0 && k==0) DSSetState(ds,DS_STATE_INTERMEDIATE);
 90:   else DSSetState(ds,DS_STATE_RAW);
 91:   if (verbose) {
 92:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
 93:     PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n");
 94:     DSView(ds,viewer);
 95:   }

 97:   /* Solve */
 98:   DSGetSlepcSC(ds,&sc);
 99:   sc->comparison    = SlepcCompareLargestReal;
100:   sc->comparisonctx = NULL;
101:   sc->map           = NULL;
102:   sc->mapobj        = NULL;
103:   DSSolve(ds,w,NULL);
104:   DSSort(ds,w,NULL,NULL,NULL,NULL);
105:   if (extrarow) DSUpdateExtraRow(ds);
106:   DSSynchronize(ds,w,NULL);
107:   if (verbose) {
108:     PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n");
109:     DSView(ds,viewer);
110:   }

112:   /* Print singular values */
113:   PetscPrintf(PETSC_COMM_WORLD,"Computed singular values =\n");
114:   for (i=0;i<n;i++) {
115:     sigma = PetscRealPart(w[i]);
116:     PetscViewerASCIIPrintf(viewer,"  %.5f\n",(double)sigma);
117:   }

119:   if (extrarow) {
120:     /* Check that extra row is correct */
121:     DSGetArrayReal(ds,DS_MAT_T,&T);
122:     DSGetArray(ds,DS_MAT_U,&U);
123:     DSGetArray(ds,DS_MAT_V,&V);
124:     d = 0.0;
125:     for (i=0;i<n;i++) d += T[i+ld]+U[n-1+i*ld];
126:     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));
127:     d = 0.0;
128:     for (i=0;i<n;i++) d += T[i+2*ld]-V[n-1+i*ld];
129:     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));
130:     DSRestoreArrayReal(ds,DS_MAT_T,&T);
131:     DSRestoreArray(ds,DS_MAT_U,&U);
132:     DSRestoreArray(ds,DS_MAT_V,&V);
133:   }

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

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

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

161:   PetscFree(w);
162:   DSDestroy(&ds);
163:   SlepcFinalize();
164:   return 0;
165: }

167: /*TEST

169:    testset:
170:       requires: double
171:       test:
172:          suffix: 1
173:          args: -test_dsview
174:       test:
175:          suffix: 2
176:          args: -l 1 -k 4
177:       test:
178:          suffix: 2_extrarow
179:          filter: sed -e "s/extrarow//"
180:          args: -l 1 -k 4 -extrarow
181:          output_file: output/test22_2.out

183: TEST*/