Date: 2022-03-31T15:29:39+00:00

Actual source code: ex32.c
slepc-3.17.0 2022-03-31
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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[] = "Solves a Lypunov equation with the shifted 2-D Laplacian.\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
     14:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

     16: #include <slepclme.h>

     18: int main(int argc,char **argv)
     19: {
     20:   Mat                A;           /* problem matrix */
     21:   Mat                C,C1;        /* right-hand side */
     22:   Mat                X,X1;        /* solution */
     23:   LME                lme;
     24:   PetscReal          tol,errest,error;
     25:   PetscScalar        *u,sigma=0.0;
     26:   PetscInt           N,n=10,m,Istart,Iend,II,maxit,its,ncv,i,j,rank=0;
     27:   PetscBool          flag;
     28:   LMEConvergedReason reason;

     30:   SlepcInitialize(&argc,&argv,(char*)0,help);

     32:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     33:   PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
     34:   if (!flag) m=n;
     35:   N = n*m;
     36:   PetscOptionsGetScalar(NULL,NULL,"-sigma",&sigma,NULL);
     37:   PetscOptionsGetInt(NULL,NULL,"-rank",&rank,NULL);
     38:   PetscPrintf(PETSC_COMM_WORLD,"\nLyapunov equation, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m);

     40:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     41:                        Create the 2-D Laplacian, A
     42:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     44:   MatCreate(PETSC_COMM_WORLD,&A);
     45:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     46:   MatSetFromOptions(A);
     47:   MatSetUp(A);
     48:   MatGetOwnershipRange(A,&Istart,&Iend);
     49:   for (II=Istart;II<Iend;II++) {
     50:     i = II/n; j = II-i*n;
     51:     if (i>0) MatSetValue(A,II,II-n,1.0,INSERT_VALUES);
     52:     if (i<m-1) MatSetValue(A,II,II+n,1.0,INSERT_VALUES);
     53:     if (j>0) MatSetValue(A,II,II-1,1.0,INSERT_VALUES);
     54:     if (j<n-1) MatSetValue(A,II,II+1,1.0,INSERT_VALUES);
     55:     MatSetValue(A,II,II,-4.0-sigma,INSERT_VALUES);
     56:   }
     57:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     58:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     60:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     61:        Create a low-rank Mat to store the right-hand side C = C1*C1'
     62:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     64:   MatCreate(PETSC_COMM_WORLD,&C1);
     65:   MatSetSizes(C1,PETSC_DECIDE,PETSC_DECIDE,N,2);
     66:   MatSetType(C1,MATDENSE);
     67:   MatSetUp(C1);
     68:   MatGetOwnershipRange(C1,&Istart,&Iend);
     69:   MatDenseGetArray(C1,&u);
     70:   for (i=Istart;i<Iend;i++) {
     71:     if (i<N/2) u[i-Istart] = 1.0;
     72:     if (i==0) u[i+Iend-2*Istart] = -2.0;
     73:     if (i==1) u[i+Iend-2*Istart] = -1.0;
     74:     if (i==2) u[i+Iend-2*Istart] = -1.0;
     75:   }
     76:   MatDenseRestoreArray(C1,&u);
     77:   MatAssemblyBegin(C1,MAT_FINAL_ASSEMBLY);
     78:   MatAssemblyEnd(C1,MAT_FINAL_ASSEMBLY);
     79:   MatCreateLRC(NULL,C1,NULL,NULL,&C);
     80:   MatDestroy(&C1);

     82:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     83:                 Create the solver and set various options
     84:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     85:   /*
     86:      Create the matrix equation solver context
     87:   */
     88:   LMECreate(PETSC_COMM_WORLD,&lme);

     90:   /*
     91:      Set the type of equation
     92:   */
     93:   LMESetProblemType(lme,LME_LYAPUNOV);

     95:   /*
     96:      Set the matrix coefficients, the right-hand side, and the solution.
     97:      In this case, it is a Lyapunov equation A*X+X*A'=-C where both
     98:      C and X are symmetric and low-rank, C=C1*C1', X=X1*X1'
     99:   */
    100:   LMESetCoefficients(lme,A,NULL,NULL,NULL);
    101:   LMESetRHS(lme,C);

    103:   if (rank) {  /* Create X only if the user has specified a nonzero value of rank */
    104:     PetscPrintf(PETSC_COMM_WORLD," Computing a solution with prescribed rank=%" PetscInt_FMT "\n",rank);
    105:     MatCreate(PETSC_COMM_WORLD,&X1);
    106:     MatSetSizes(X1,PETSC_DECIDE,PETSC_DECIDE,N,rank);
    107:     MatSetType(X1,MATDENSE);
    108:     MatSetUp(X1);
    109:     MatAssemblyBegin(X1,MAT_FINAL_ASSEMBLY);
    110:     MatAssemblyEnd(X1,MAT_FINAL_ASSEMBLY);
    111:     MatCreateLRC(NULL,X1,NULL,NULL,&X);
    112:     MatDestroy(&X1);
    113:     LMESetSolution(lme,X);
    114:     MatDestroy(&X);
    115:   }

    117:   /*
    118:      (Optional) Set other solver options
    119:   */
    120:   LMESetTolerances(lme,1e-07,PETSC_DEFAULT);

    122:   /*
    123:      Set solver parameters at runtime
    124:   */
    125:   LMESetFromOptions(lme);

    127:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    128:                    Solve the matrix equation, A*X+X*A'=-C
    129:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    131:   LMESolve(lme);
    132:   LMEGetConvergedReason(lme,&reason);

    135:   if (!rank) {  /* X1 was created by the solver, so extract it and see how many columns it has */
    136:     LMEGetSolution(lme,&X);
    137:     MatLRCGetMats(X,NULL,&X1,NULL,NULL);
    138:     MatGetSize(X1,NULL,&rank);
    139:     PetscPrintf(PETSC_COMM_WORLD," The solver has computed a solution with rank=%" PetscInt_FMT "\n",rank);
    140:   }

    142:   /*
    143:      Optional: Get some information from the solver and display it
    144:   */
    145:   LMEGetIterationNumber(lme,&its);
    146:   PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",its);
    147:   LMEGetDimensions(lme,&ncv);
    148:   PetscPrintf(PETSC_COMM_WORLD," Subspace dimension: %" PetscInt_FMT "\n",ncv);
    149:   LMEGetTolerances(lme,&tol,&maxit);
    150:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit);

    152:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    153:                         Compute residual error
    154:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    156:   LMEGetErrorEstimate(lme,&errest);
    157:   PetscPrintf(PETSC_COMM_WORLD," Error estimate reported by the solver: %.4g\n",(double)errest);
    158:   if (n<=150) {
    159:     LMEComputeError(lme,&error);
    160:     PetscPrintf(PETSC_COMM_WORLD," Computed residual norm: %.4g\n\n",(double)error);
    161:   } else PetscPrintf(PETSC_COMM_WORLD," Matrix too large to compute residual norm\n\n");

    163:   /*
    164:      Free work space
    165:   */
    166:   LMEDestroy(&lme);
    167:   MatDestroy(&A);
    168:   MatDestroy(&C);
    169:   SlepcFinalize();
    170:   return 0;
    171: }

    173: /*TEST

    175:    test:
    176:       suffix: 1
    177:       requires: !single

    179:    test:
    180:       suffix: 2
    181:       args: -rank 40
    182:       requires: !single

    184: TEST*/