Actual source code: ex3.c
slepc-3.6.3 2016-03-29
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2015, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
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 MatMult_Laplacian2D(Mat A,Vec x,Vec y);
34: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag);
38: int main(int argc,char **argv)
39: {
40: Mat A; /* operator matrix */
41: EPS eps; /* eigenproblem solver context */
42: EPSType type;
43: PetscMPIInt size;
44: PetscInt N,n=10,nev;
45: PetscBool terse;
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(NULL,"-n",&n,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(*)())MatMult_Laplacian2D);
63: MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)())MatMult_Laplacian2D);
64: MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)())MatGetDiagonal_Laplacian2D);
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,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);
92: /*
93: Optional: Get some information from the solver and display it
94: */
95: EPSGetType(eps,&type);
96: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
97: EPSGetDimensions(eps,&nev,NULL,NULL);
98: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
100: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
101: Display solution and clean up
102: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
104: /* show detailed info unless -terse option is given by user */
105: PetscOptionsHasName(NULL,"-terse",&terse);
106: if (terse) {
107: EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
108: } else {
109: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
110: EPSReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
111: EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
112: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
113: }
114: EPSDestroy(&eps);
115: MatDestroy(&A);
116: SlepcFinalize();
117: return 0;
118: }
120: /*
121: Compute the matrix vector multiplication y<---T*x where T is a nx by nx
122: tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
123: DU on the superdiagonal.
124: */
125: static void tv(int nx,const PetscScalar *x,PetscScalar *y)
126: {
127: PetscScalar dd,dl,du;
128: int j;
130: dd = 4.0;
131: dl = -1.0;
132: du = -1.0;
134: y[0] = dd*x[0] + du*x[1];
135: for (j=1;j<nx-1;j++)
136: y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
137: y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
138: }
142: /*
143: Matrix-vector product subroutine for the 2D Laplacian.
145: The matrix used is the 2 dimensional discrete Laplacian on unit square with
146: zero Dirichlet boundary condition.
148: Computes y <-- A*x, where A is the block tridiagonal matrix
150: | T -I |
151: |-I T -I |
152: A = | -I T |
153: | ... -I|
154: | -I T|
156: The subroutine TV is called to compute y<--T*x.
157: */
158: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y)
159: {
160: void *ctx;
161: int nx,lo,i,j;
162: const PetscScalar *px;
163: PetscScalar *py;
164: PetscErrorCode ierr;
167: MatShellGetContext(A,&ctx);
168: nx = *(int*)ctx;
169: VecGetArrayRead(x,&px);
170: VecGetArray(y,&py);
172: tv(nx,&px[0],&py[0]);
173: for (i=0;i<nx;i++) py[i] -= px[nx+i];
175: for (j=2;j<nx;j++) {
176: lo = (j-1)*nx;
177: tv(nx,&px[lo],&py[lo]);
178: for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i];
179: }
181: lo = (nx-1)*nx;
182: tv(nx,&px[lo],&py[lo]);
183: for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i];
185: VecRestoreArrayRead(x,&px);
186: VecRestoreArray(y,&py);
187: return(0);
188: }
192: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
193: {
197: VecSet(diag,4.0);
198: return(0);
199: }