Actual source code: ex3.c
slepc-3.17.1 2022-04-11
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: SlepcInitialize(&argc,&argv,(char*)0,help);
34: MPI_Comm_size(PETSC_COMM_WORLD,&size);
37: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
38: N = n*n;
39: 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);
41: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
42: Create the operator matrix that defines the eigensystem, Ax=kx
43: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
45: MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&A);
46: MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_Laplacian2D);
47: MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMult_Laplacian2D);
48: MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Laplacian2D);
50: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
51: Create the eigensolver and set various options
52: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
54: /*
55: Create eigensolver context
56: */
57: EPSCreate(PETSC_COMM_WORLD,&eps);
59: /*
60: Set operators. In this case, it is a standard eigenvalue problem
61: */
62: EPSSetOperators(eps,A,NULL);
63: EPSSetProblemType(eps,EPS_HEP);
65: /*
66: Set solver parameters at runtime
67: */
68: EPSSetFromOptions(eps);
70: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
71: Solve the eigensystem
72: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
74: EPSSolve(eps);
76: /*
77: Optional: Get some information from the solver and display it
78: */
79: EPSGetType(eps,&type);
80: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
81: EPSGetDimensions(eps,&nev,NULL,NULL);
82: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);
84: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
85: Display solution and clean up
86: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
88: /* show detailed info unless -terse option is given by user */
89: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
90: if (terse) EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
91: else {
92: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
93: EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
94: EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
95: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
96: }
97: EPSDestroy(&eps);
98: MatDestroy(&A);
99: SlepcFinalize();
100: return 0;
101: }
103: /*
104: Compute the matrix vector multiplication y<---T*x where T is a nx by nx
105: tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
106: DU on the superdiagonal.
107: */
108: static void tv(int nx,const PetscScalar *x,PetscScalar *y)
109: {
110: PetscScalar dd,dl,du;
111: int j;
113: dd = 4.0;
114: dl = -1.0;
115: du = -1.0;
117: y[0] = dd*x[0] + du*x[1];
118: for (j=1;j<nx-1;j++)
119: y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
120: y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
121: }
123: /*
124: Matrix-vector product subroutine for the 2D Laplacian.
126: The matrix used is the 2 dimensional discrete Laplacian on unit square with
127: zero Dirichlet boundary condition.
129: Computes y <-- A*x, where A is the block tridiagonal matrix
131: | T -I |
132: |-I T -I |
133: A = | -I T |
134: | ... -I|
135: | -I T|
137: The subroutine TV is called to compute y<--T*x.
138: */
139: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y)
140: {
141: void *ctx;
142: int nx,lo,i,j;
143: const PetscScalar *px;
144: PetscScalar *py;
147: MatShellGetContext(A,&ctx);
148: nx = *(int*)ctx;
149: VecGetArrayRead(x,&px);
150: VecGetArray(y,&py);
152: tv(nx,&px[0],&py[0]);
153: for (i=0;i<nx;i++) py[i] -= px[nx+i];
155: for (j=2;j<nx;j++) {
156: lo = (j-1)*nx;
157: tv(nx,&px[lo],&py[lo]);
158: for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i];
159: }
161: lo = (nx-1)*nx;
162: tv(nx,&px[lo],&py[lo]);
163: for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i];
165: VecRestoreArrayRead(x,&px);
166: VecRestoreArray(y,&py);
167: PetscFunctionReturn(0);
168: }
170: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
171: {
173: VecSet(diag,4.0);
174: PetscFunctionReturn(0);
175: }
177: /*TEST
179: test:
180: suffix: 1
181: args: -n 72 -eps_nev 4 -eps_ncv 20 -terse
182: requires: !single
184: TEST*/