Actual source code: ex9.c
2: static char help[] = "Solves a problem associated to the Brusselator wave model in chemical reactions, illustrating the use of shell matrices.\n\n"
3: "The command line options are:\n\n"
4: " -n <n>, where <n> = block dimension of the 2x2 block matrix.\n"
5: " -L <L>, where <L> = bifurcation parameter.\n"
6: " -alpha <alpha>, -beta <beta>, -delta1 <delta1>, -delta2 <delta2>,\n"
7: " where <alpha> <beta> <delta1> <delta2> = model parameters.\n\n";
9: #include slepceps.h
11: /*
12: This example computes the eigenvalues with largest real part of the
13: following matrix
15: A = [ tau1*T+(beta-1)*I alpha^2*I
16: -beta*I tau2*T-alpha^2*I ],
18: where
20: T = tridiag{1,-2,1}
21: h = 1/(n+1)
22: tau1 = delta1/(h*L)^2
23: tau2 = delta2/(h*L)^2
24: */
27: /*
28: Matrix operations
29: */
30: extern int MatBrussel_Mult(Mat,Vec,Vec);
31: extern int MatBrussel_Shift(PetscScalar*,Mat);
32: extern int MatBrussel_GetDiagonal(Mat,Vec);
34: typedef struct {
35: Mat T;
36: Vec x1, x2, y1, y2;
37: PetscScalar alpha, beta, tau1, tau2, sigma;
38: } CTX_BRUSSEL;
42: int main( int argc, char **argv )
43: {
44: Mat A; /* eigenvalue problem matrix */
45: EPS eps; /* eigenproblem solver context */
46: EPSType type;
47: PetscReal error, tol, re, im;
48: PetscScalar delta1, delta2, L, h, kr, ki, value[3];
49: int N=30, n, nev, ierr, maxit, i, its, nconv,
50: col[3], Istart, Iend, FirstBlock=0, LastBlock=0;
51: CTX_BRUSSEL *ctx;
53: SlepcInitialize(&argc,&argv,(char*)0,help);
55: PetscOptionsGetInt(PETSC_NULL,"-n",&N,PETSC_NULL);
56: PetscPrintf(PETSC_COMM_WORLD,"\nBrusselator wave model, n=%d\n\n",N);
58: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
59: Generate the matrix
60: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
62: /*
63: Create shell matrix context and set default parameters
64: */
65: PetscNew(CTX_BRUSSEL,&ctx);
66: ctx->alpha = 2.0;
67: ctx->beta = 5.45;
68: delta1 = 0.008;
69: delta2 = 0.004;
70: L = 0.51302;
72: /*
73: Look the command line for user-provided parameters
74: */
75: PetscOptionsGetScalar(PETSC_NULL,"-L",&L,PETSC_NULL);
76: PetscOptionsGetScalar(PETSC_NULL,"-alpha",&ctx->alpha,PETSC_NULL);
77: PetscOptionsGetScalar(PETSC_NULL,"-beta",&ctx->beta,PETSC_NULL);
78: PetscOptionsGetScalar(PETSC_NULL,"-delta1",&delta1,PETSC_NULL);
79: PetscOptionsGetScalar(PETSC_NULL,"-delta2",&delta2,PETSC_NULL);
81: /*
82: Create matrix T
83: */
84: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,N,N,&ctx->T);
85: MatSetFromOptions(ctx->T);
86:
87: MatGetOwnershipRange(ctx->T,&Istart,&Iend);
88: if (Istart==0) FirstBlock=PETSC_TRUE;
89: if (Iend==N) LastBlock=PETSC_TRUE;
90: value[0]=1.0; value[1]=-2.0; value[2]=1.0;
91: for( i=(FirstBlock? Istart+1: Istart); i<(LastBlock? Iend-1: Iend); i++ ) {
92: col[0]=i-1; col[1]=i; col[2]=i+1;
93: MatSetValues(ctx->T,1,&i,3,col,value,INSERT_VALUES);
94: }
95: if (LastBlock) {
96: i=N-1; col[0]=N-2; col[1]=N-1;
97: MatSetValues(ctx->T,1,&i,2,col,value,INSERT_VALUES);
98: }
99: if (FirstBlock) {
100: i=0; col[0]=0; col[1]=1; value[0]=-2.0; value[1]=1.0;
101: MatSetValues(ctx->T,1,&i,2,col,value,INSERT_VALUES);
102: }
104: MatAssemblyBegin(ctx->T,MAT_FINAL_ASSEMBLY);
105: MatAssemblyEnd(ctx->T,MAT_FINAL_ASSEMBLY);
106: MatGetLocalSize(ctx->T,&n,PETSC_NULL);
108: /*
109: Fill the remaining information in the shell matrix context
110: and create auxiliary vectors
111: */
112: h = 1.0 / (double)(N+1);
113: ctx->tau1 = delta1 / ((h*L)*(h*L));
114: ctx->tau2 = delta2 / ((h*L)*(h*L));
115: ctx->sigma = 0.0;
116: VecCreateMPIWithArray(PETSC_COMM_WORLD,n,PETSC_DECIDE,PETSC_NULL,&ctx->x1);
117: VecCreateMPIWithArray(PETSC_COMM_WORLD,n,PETSC_DECIDE,PETSC_NULL,&ctx->x2);
118: VecCreateMPIWithArray(PETSC_COMM_WORLD,n,PETSC_DECIDE,PETSC_NULL,&ctx->y1);
119: VecCreateMPIWithArray(PETSC_COMM_WORLD,n,PETSC_DECIDE,PETSC_NULL,&ctx->y2);
121: /*
122: Create the shell matrix
123: */
124: MatCreateShell(PETSC_COMM_WORLD,2*n,2*n,2*N,2*N,(void*)ctx,&A);
125: MatShellSetOperation(A,MATOP_MULT,(void(*)())MatBrussel_Mult);
126: MatShellSetOperation(A,MATOP_SHIFT,(void(*)())MatBrussel_Shift);
127: MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)())MatBrussel_GetDiagonal);
129: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130: Create the eigensolver and set various options
131: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
133: /*
134: Create eigensolver context
135: */
136: EPSCreate(PETSC_COMM_WORLD,&eps);
138: /*
139: Set operators. In this case, it is a standard eigenvalue problem
140: */
141: EPSSetOperators(eps,A,PETSC_NULL);
142: EPSSetProblemType(eps,EPS_NHEP);
144: /*
145: Force to use ARPACK if it is installed and ask for the rightmost eigenvalues
146: */
147: #if defined(SLEPC_HAVE_ARPACK)
148: EPSSetType(eps,EPSARPACK);
149: #else
150: EPSSetType(eps, EPSLAPACK);
151: #endif
152: EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL);
154: /*
155: Set other solver options at runtime
156: */
157: EPSSetFromOptions(eps);
159: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160: Solve the eigensystem
161: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
163: EPSSolve(eps);
164: EPSGetIterationNumber(eps, &its);
165: PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %d\n",its);
166:
167: /*
168: Optional: Get some information from the solver and display it
169: */
170: EPSGetType(eps,&type);
171: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
172: EPSGetDimensions(eps,&nev,PETSC_NULL);
173: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %d\n",nev);
174: EPSGetTolerances(eps,&tol,&maxit);
175: PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%d\n",tol,maxit);
177: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178: Display solution and clean up
179: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
181: /*
182: Get number of converged eigenpairs
183: */
184: EPSGetConverged(eps,&nconv);
185: PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate eigenpairs: %d\n\n",nconv);
187: if (nconv>0) {
188: /*
189: Display eigenvalues and relative errors
190: */
191: PetscPrintf(PETSC_COMM_WORLD,
192: " k ||Ax-kx||/||kx||\n"
193: " --------------------- ------------------\n" );
194: for( i=0; i<nconv; i++ ) {
195: /*
196: Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
197: ki (imaginary part)
198: */
199: EPSGetEigenpair(eps,i,&kr,&ki,PETSC_NULL,PETSC_NULL);
201: /*
202: Compute the relative error associated to each eigenpair
203: */
204: EPSComputeRelativeError(eps,i,&error);
206: #if defined(PETSC_USE_COMPLEX)
207: re = PetscRealPart(kr);
208: im = PetscImaginaryPart(kr);
209: #else
210: re = kr;
211: im = ki;
212: #endif
213: if( im != 0.0 ) {
214: PetscPrintf(PETSC_COMM_WORLD," % 6f %+6f i",re,im);
215: } else {
216: PetscPrintf(PETSC_COMM_WORLD," % 6f ",re);
217: }
218: PetscPrintf(PETSC_COMM_WORLD," % 12f\n",error);
219: }
220: PetscPrintf(PETSC_COMM_WORLD,"\n" );
221: }
222:
223: /*
224: Free work space
225: */
226: EPSDestroy(eps);
227: MatDestroy(A);
228: MatDestroy(ctx->T);
229: VecDestroy(ctx->x1);
230: VecDestroy(ctx->x2);
231: VecDestroy(ctx->y1);
232: VecDestroy(ctx->y2);
233: PetscFree(ctx);
234: SlepcFinalize();
235: return 0;
236: }
240: int MatBrussel_Mult(Mat A,Vec x,Vec y)
241: {
242: int n, ierr;
243: PetscScalar alpha, *px, *py;
244: MPI_Comm comm;
245: CTX_BRUSSEL *ctx;
247: MatShellGetContext(A,(void**)&ctx);
248: PetscObjectGetComm((PetscObject)A,&comm);
249: MatGetLocalSize(ctx->T,&n,PETSC_NULL);
250: VecGetArray(x,&px);
251: VecGetArray(y,&py);
252: VecPlaceArray(ctx->x1,px);
253: VecPlaceArray(ctx->x2,px+n);
254: VecPlaceArray(ctx->y1,py);
255: VecPlaceArray(ctx->y2,py+n);
257: MatMult(ctx->T,ctx->x1,ctx->y1);
258: VecScale(&ctx->tau1,ctx->y1);
259: alpha = ctx->beta - 1.0 + ctx->sigma;
260: VecAXPY(&alpha,ctx->x1,ctx->y1);
261: alpha = ctx->alpha * ctx->alpha;
262: VecAXPY(&alpha,ctx->x2,ctx->y1);
264: MatMult(ctx->T,ctx->x2,ctx->y2);
265: VecScale(&ctx->tau2,ctx->y2);
266: alpha = -ctx->beta;
267: VecAXPY(&alpha,ctx->x1,ctx->y2);
268: alpha = -ctx->alpha * ctx->alpha + ctx->sigma;
269: VecAXPY(&alpha,ctx->x2,ctx->y2);
271: VecRestoreArray(x,&px);
272: VecRestoreArray(y,&py);
274: return 0;
275: }
279: int MatBrussel_Shift( PetscScalar* a, Mat Y )
280: {
281: CTX_BRUSSEL *ctx;
282: int ierr;
284: MatShellGetContext( Y, (void**)&ctx );
285: ctx->sigma += *a;
286: return(0);
287: }
291: int MatBrussel_GetDiagonal(Mat A,Vec diag)
292: {
293: Vec d1, d2;
294: int n, ierr;
295: PetscScalar alpha, *pd;
296: MPI_Comm comm;
297: CTX_BRUSSEL *ctx;
299: MatShellGetContext(A,(void**)&ctx);
300: PetscObjectGetComm((PetscObject)A,&comm);
301: MatGetLocalSize(ctx->T,&n,PETSC_NULL);
302: VecGetArray(diag,&pd);
303: VecCreateMPIWithArray(comm,n,PETSC_DECIDE,pd,&d1);
304: VecCreateMPIWithArray(comm,n,PETSC_DECIDE,pd+n,&d2);
306: alpha = -2.0*ctx->tau1 + ctx->beta - 1.0 + ctx->sigma;
307: VecSet(&alpha,d1);
308: alpha = -2.0*ctx->tau2 - ctx->alpha*ctx->alpha + ctx->sigma;
309: VecSet(&alpha,d2);
311: VecDestroy(d1);
312: VecDestroy(d2);
313: VecRestoreArray(diag,&pd);
315: return 0;
316: }