Actual source code: test2.c

slepc-3.20.1 2023-11-27
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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:   PetscFunctionBeginUser;
 25:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,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*/