Date: 2022-08-09T09:06:00+00:00

Actual source code: test2.c
slepc-3.17.2 2022-08-09
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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 dense LME functions.\n\n";

     13: #include <slepclme.h>

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

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

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

     33:   /* Set up viewer */
     34:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
     35:   if (verbose) PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);

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

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

     56:   if (verbose) {
     57:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
     58:     MatView(A,viewer);
     59:   }

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

     67:   if (verbose) {
     68:     PetscPrintf(PETSC_COMM_WORLD,"Matrix B - - - - - - - -\n");
     69:     MatView(B,viewer);
     70:   }

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

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

     91:   if (verbose) {
     92:     PetscPrintf(PETSC_COMM_WORLD,"Matrix C - - - - - - - -\n");
     93:     MatView(C,viewer);
     94:   }

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

    110:   MatDestroy(&A);
    111:   MatDestroy(&B);
    112:   MatDestroy(&C);
    113:   MatDestroy(&X);
    114:   LMEDestroy(&lme);
    115:   SlepcFinalize();
    116:   return 0;
    117: }

    119: /*TEST

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

    126: TEST*/