Actual source code: test2.c

slepc-3.13.2 2020-05-12
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2020, 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 dense LME functions.\n\n";

 13:  #include <slepclme.h>

 15: int main(int argc,char **argv)
 16: {
 18:   LME            lme;
 19:   Mat            A,B,C,X;
 20:   PetscInt       i,j,n=10,k=2;
 21:   PetscScalar    *As,*Bs,*Cs,*Xs;
 22:   PetscViewer    viewer;
 23:   PetscBool      verbose;

 25:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 26:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 27:   PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL);
 28:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
 29:   PetscPrintf(PETSC_COMM_WORLD,"Dense matrix equations, n=%D.\n",n);

 31:   /* Create LME object */
 32:   LMECreate(PETSC_COMM_WORLD,&lme);

 34:   /* Set up viewer */
 35:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
 36:   if (verbose) {
 37:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
 38:   }

 40:   /* Create matrices */
 41:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
 42:   PetscObjectSetName((PetscObject)A,"A");
 43:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&B);
 44:   PetscObjectSetName((PetscObject)B,"B");
 45:   MatCreateSeqDense(PETSC_COMM_SELF,n,k,NULL,&C);
 46:   PetscObjectSetName((PetscObject)C,"C");
 47:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&X);
 48:   PetscObjectSetName((PetscObject)X,"X");

 50:   /* Fill A with an upper Hessenberg Toeplitz matrix */
 51:   MatDenseGetArray(A,&As);
 52:   for (i=0;i<n;i++) As[i+i*n]=3.0-(PetscReal)n/2;
 53:   for (i=0;i<n-1;i++) As[i+1+i*n]=0.5;
 54:   for (j=1;j<3;j++) {
 55:     for (i=0;i<n-j;i++) As[i+(i+j)*n]=1.0;
 56:   }
 57:   MatDenseRestoreArray(A,&As);

 59:   if (verbose) {
 60:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
 61:     MatView(A,viewer);
 62:   }

 64:   /* Fill B with the 1-D Laplacian matrix */
 65:   MatDenseGetArray(B,&Bs);
 66:   for (i=0;i<n;i++) Bs[i+i*n]=2.0;
 67:   for (i=0;i<n-1;i++) { Bs[i+1+i*n]=-1; Bs[i+(i+1)*n]=-1; }
 68:   MatDenseRestoreArray(B,&Bs);

 70:   if (verbose) {
 71:     PetscPrintf(PETSC_COMM_WORLD,"Matrix B - - - - - - - -\n");
 72:     MatView(B,viewer);
 73:   }

 75:   /* Solve Lyapunov equation A*X+X*A'= -B */
 76:   PetscPrintf(PETSC_COMM_WORLD,"Solving Lyapunov equation for B\n");
 77:   MatDenseGetArray(A,&As);
 78:   MatDenseGetArray(B,&Bs);
 79:   MatDenseGetArray(X,&Xs);
 80:   LMEDenseLyapunov(lme,n,As,n,Bs,n,Xs,n);
 81:   MatDenseRestoreArray(A,&As);
 82:   MatDenseRestoreArray(B,&Bs);
 83:   MatDenseRestoreArray(X,&Xs);
 84:   if (verbose) {
 85:     PetscPrintf(PETSC_COMM_WORLD,"Solution X - - - - - - - -\n");
 86:     MatView(X,viewer);
 87:   }

 89:   /* Fill C with a full-rank nx2 matrix */
 90:   MatDenseGetArray(C,&Cs);
 91:   for (i=0;i<k;i++) Cs[i+i*n] = (i%2)? -1.0: 1.0;
 92:   MatDenseRestoreArray(C,&Cs);

 94:   if (verbose) {
 95:     PetscPrintf(PETSC_COMM_WORLD,"Matrix C - - - - - - - -\n");
 96:     MatView(C,viewer);
 97:   }

 99:   /* Solve Lyapunov equation A*X+X*A'= -C*C' */
100:   PetscPrintf(PETSC_COMM_WORLD,"Solving Lyapunov equation for C (Cholesky)\n");
101:   MatDenseGetArray(A,&As);
102:   MatDenseGetArray(C,&Cs);
103:   MatDenseGetArray(X,&Xs);
104:   LMEDenseHessLyapunovChol(lme,n,As,n,2,Cs,n,Xs,n,NULL);
105:   MatDenseRestoreArray(A,&As);
106:   MatDenseRestoreArray(C,&Cs);
107:   MatDenseRestoreArray(X,&Xs);
108:   if (verbose) {
109:     PetscPrintf(PETSC_COMM_WORLD,"Solution X - - - - - - - -\n");
110:     MatView(X,viewer);
111:   }

113:   MatDestroy(&A);
114:   MatDestroy(&B);
115:   MatDestroy(&C);
116:   MatDestroy(&X);
117:   LMEDestroy(&lme);
118:   SlepcFinalize();
119:   return ierr;
120: }

122: /*TEST

124:    test:
125:       args: -info :lme
126:       requires: double
127:       filter: sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/1e-\\1/g"

129: TEST*/