Actual source code: ex3.c
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2011, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7:
8: SLEPc is free software: you can redistribute it and/or modify it under the
9: terms of version 3 of the GNU Lesser General Public License as published by
10: the Free Software Foundation.
12: SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
13: WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
14: FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
15: more details.
17: You should have received a copy of the GNU Lesser General Public License
18: along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
19: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
20: */
22: static char help[] = "Solves the same eigenproblem as in example ex2, but using a shell matrix. "
23: "The problem is a standard symmetric eigenproblem corresponding to the 2-D Laplacian operator.\n\n"
24: "The command line options are:\n"
25: " -n <n>, where <n> = number of grid subdivisions in both x and y dimensions.\n\n";
27: #include <slepceps.h>
28: #include <petscblaslapack.h>
30: /*
31: User-defined routines
32: */
33: PetscErrorCode MatLaplacian2D_Mult(Mat A,Vec x,Vec y);
34: PetscErrorCode MatLaplacian2D_GetDiagonal(Mat A,Vec diag);
38: int main(int argc,char **argv)
39: {
40: Mat A; /* operator matrix */
41: EPS eps; /* eigenproblem solver context */
42: const EPSType type;
43: PetscReal tol;
44: PetscMPIInt size;
45: PetscInt N,n=10,nev,maxit,its;
48: SlepcInitialize(&argc,&argv,(char*)0,help);
49: MPI_Comm_size(PETSC_COMM_WORLD,&size);
50: if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only!");
52: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
53: N = n*n;
54: PetscPrintf(PETSC_COMM_WORLD,"\n2-D Laplacian Eigenproblem (matrix-free version), N=%D (%Dx%D grid)\n\n",N,n,n);
56: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
57: Compute the operator matrix that defines the eigensystem, Ax=kx
58: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
60: MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&A);
61: MatSetFromOptions(A);
62: MatShellSetOperation(A,MATOP_MULT,(void(*)())MatLaplacian2D_Mult);
63: MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)())MatLaplacian2D_Mult);
64: MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)())MatLaplacian2D_GetDiagonal);
66: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
67: Create the eigensolver and set various options
68: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
70: /*
71: Create eigensolver context
72: */
73: EPSCreate(PETSC_COMM_WORLD,&eps);
75: /*
76: Set operators. In this case, it is a standard eigenvalue problem
77: */
78: EPSSetOperators(eps,A,PETSC_NULL);
79: EPSSetProblemType(eps,EPS_HEP);
81: /*
82: Set solver parameters at runtime
83: */
84: EPSSetFromOptions(eps);
86: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
87: Solve the eigensystem
88: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
90: EPSSolve(eps);
91: EPSGetIterationNumber(eps,&its);
92: PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %D\n",its);
94: /*
95: Optional: Get some information from the solver and display it
96: */
97: EPSGetType(eps,&type);
98: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
99: EPSGetDimensions(eps,&nev,PETSC_NULL,PETSC_NULL);
100: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
101: EPSGetTolerances(eps,&tol,&maxit);
102: PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4G, maxit=%D\n",tol,maxit);
104: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
105: Display solution and clean up
106: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
108: EPSPrintSolution(eps,PETSC_NULL);
109: EPSDestroy(&eps);
110: MatDestroy(&A);
111: SlepcFinalize();
112: return 0;
113: }
115: /*
116: Compute the matrix vector multiplication y<---T*x where T is a nx by nx
117: tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
118: DU on the superdiagonal.
119: */
120: static void tv(int nx,const PetscScalar *x,PetscScalar *y)
121: {
122: PetscScalar dd,dl,du;
123: int j;
125: dd = 4.0;
126: dl = -1.0;
127: du = -1.0;
129: y[0] = dd*x[0] + du*x[1];
130: for (j=1;j<nx-1;j++)
131: y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
132: y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
133: }
137: /*
138: Matrix-vector product subroutine for the 2D Laplacian.
140: The matrix used is the 2 dimensional discrete Laplacian on unit square with
141: zero Dirichlet boundary condition.
142:
143: Computes y <-- A*x, where A is the block tridiagonal matrix
144:
145: | T -I |
146: |-I T -I |
147: A = | -I T |
148: | ... -I|
149: | -I T|
150:
151: The subroutine TV is called to compute y<--T*x.
152: */
153: PetscErrorCode MatLaplacian2D_Mult(Mat A,Vec x,Vec y)
154: {
155: void *ctx;
156: int nx,lo,j,one=1;
157: const PetscScalar *px;
158: PetscScalar *py,dmone=-1.0;
159: PetscErrorCode ierr;
160:
162: MatShellGetContext(A,&ctx);
163: nx = *(int*)ctx;
164: VecGetArrayRead(x,&px);
165: VecGetArray(y,&py);
167: tv(nx,&px[0],&py[0]);
168: BLASaxpy_(&nx,&dmone,&px[nx],&one,&py[0],&one);
170: for (j=2;j<nx;j++) {
171: lo = (j-1)*nx;
172: tv(nx,&px[lo],&py[lo]);
173: BLASaxpy_(&nx,&dmone,&px[lo-nx],&one,&py[lo],&one);
174: BLASaxpy_(&nx,&dmone,&px[lo+nx],&one,&py[lo],&one);
175: }
177: lo = (nx-1)*nx;
178: tv(nx,&px[lo],&py[lo]);
179: BLASaxpy_(&nx,&dmone,&px[lo-nx],&one,&py[lo],&one);
181: VecRestoreArrayRead(x,&px);
182: VecRestoreArray(y,&py);
183: return(0);
184: }
188: PetscErrorCode MatLaplacian2D_GetDiagonal(Mat A,Vec diag)
189: {
193: VecSet(diag,4.0);
194: return(0);
195: }