Actual source code: ex3.c
slepc-3.21.0 2024-03-30
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 the same eigenproblem as in example ex2, but using a shell matrix. "
12: "The problem is a standard symmetric eigenproblem corresponding to the 2-D Laplacian operator.\n\n"
13: "The command line options are:\n"
14: " -n <n>, where <n> = number of grid subdivisions in both x and y dimensions.\n\n";
16: #include <slepceps.h>
18: /*
19: User-defined routines
20: */
21: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y);
22: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag);
24: int main(int argc,char **argv)
25: {
26: Mat A; /* operator matrix */
27: EPS eps; /* eigenproblem solver context */
28: EPSType type;
29: PetscMPIInt size;
30: PetscInt N,n=10,nev;
31: PetscBool terse;
33: PetscFunctionBeginUser;
34: PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
35: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size));
36: PetscCheck(size==1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only");
38: PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
39: N = n*n;
40: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n2-D Laplacian Eigenproblem (matrix-free version), N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,n));
42: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
43: Create the operator matrix that defines the eigensystem, Ax=kx
44: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
46: PetscCall(MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&A));
47: PetscCall(MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_Laplacian2D));
48: PetscCall(MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMult_Laplacian2D));
49: PetscCall(MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Laplacian2D));
51: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
52: Create the eigensolver and set various options
53: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
55: /*
56: Create eigensolver context
57: */
58: PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
60: /*
61: Set operators. In this case, it is a standard eigenvalue problem
62: */
63: PetscCall(EPSSetOperators(eps,A,NULL));
64: PetscCall(EPSSetProblemType(eps,EPS_HEP));
66: /*
67: Set solver parameters at runtime
68: */
69: PetscCall(EPSSetFromOptions(eps));
71: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
72: Solve the eigensystem
73: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
75: PetscCall(EPSSolve(eps));
77: /*
78: Optional: Get some information from the solver and display it
79: */
80: PetscCall(EPSGetType(eps,&type));
81: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
82: PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
83: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));
85: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
86: Display solution and clean up
87: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
89: /* show detailed info unless -terse option is given by user */
90: PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
91: if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
92: else {
93: PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
94: PetscCall(EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD));
95: PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
96: PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
97: }
98: PetscCall(EPSDestroy(&eps));
99: PetscCall(MatDestroy(&A));
100: PetscCall(SlepcFinalize());
101: return 0;
102: }
104: /*
105: Compute the matrix vector multiplication y<---T*x where T is a nx by nx
106: tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
107: DU on the superdiagonal.
108: */
109: static void tv(int nx,const PetscScalar *x,PetscScalar *y)
110: {
111: PetscScalar dd,dl,du;
112: int j;
114: dd = 4.0;
115: dl = -1.0;
116: du = -1.0;
118: y[0] = dd*x[0] + du*x[1];
119: for (j=1;j<nx-1;j++)
120: y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
121: y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
122: }
124: /*
125: Matrix-vector product subroutine for the 2D Laplacian.
127: The matrix used is the 2 dimensional discrete Laplacian on unit square with
128: zero Dirichlet boundary condition.
130: Computes y <-- A*x, where A is the block tridiagonal matrix
132: | T -I |
133: |-I T -I |
134: A = | -I T |
135: | ... -I|
136: | -I T|
138: The subroutine TV is called to compute y<--T*x.
139: */
140: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y)
141: {
142: void *ctx;
143: int nx,lo,i,j;
144: const PetscScalar *px;
145: PetscScalar *py;
147: PetscFunctionBeginUser;
148: PetscCall(MatShellGetContext(A,&ctx));
149: nx = *(int*)ctx;
150: PetscCall(VecGetArrayRead(x,&px));
151: PetscCall(VecGetArray(y,&py));
153: tv(nx,&px[0],&py[0]);
154: for (i=0;i<nx;i++) py[i] -= px[nx+i];
156: for (j=2;j<nx;j++) {
157: lo = (j-1)*nx;
158: tv(nx,&px[lo],&py[lo]);
159: for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i];
160: }
162: lo = (nx-1)*nx;
163: tv(nx,&px[lo],&py[lo]);
164: for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i];
166: PetscCall(VecRestoreArrayRead(x,&px));
167: PetscCall(VecRestoreArray(y,&py));
168: PetscFunctionReturn(PETSC_SUCCESS);
169: }
171: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
172: {
173: PetscFunctionBeginUser;
174: PetscCall(VecSet(diag,4.0));
175: PetscFunctionReturn(PETSC_SUCCESS);
176: }
178: /*TEST
180: test:
181: suffix: 1
182: args: -n 72 -eps_nev 4 -eps_ncv 20 -terse
183: requires: !single
185: TEST*/