Actual source code: test2.c

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

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

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

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

     48:   /* Fill A with an upper Hessenberg Toeplitz matrix */
     49:   PetscCall(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:   PetscCall(MatDenseRestoreArray(A,&As));

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

     62:   /* Fill B with the 1-D Laplacian matrix */
     63:   PetscCall(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:   PetscCall(MatDenseRestoreArray(B,&Bs));

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

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

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

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

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

    111:   PetscCall(MatDestroy(&A));
    112:   PetscCall(MatDestroy(&B));
    113:   PetscCall(MatDestroy(&C));
    114:   PetscCall(MatDestroy(&X));
    115:   PetscCall(LMEDestroy(&lme));
    116:   PetscCall(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*/