Date: 2022-10-01T06:40:50+00:00

Actual source code: test2.c
slepc-3.18.0 2022-10-01
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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;

     25:   SlepcInitialize(&argc,&argv,(char*)0,help);
     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=%" PetscInt_FMT ".\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) PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);

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

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

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

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

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

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

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

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

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

    111:   MatDestroy(&A);
    112:   MatDestroy(&B);
    113:   MatDestroy(&C);
    114:   MatDestroy(&X);
    115:   LMEDestroy(&lme);
    116:   SlepcFinalize();
    117:   return 0;
    118: }

    120: /*TEST

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

    127: TEST*/