Actual source code: ex9.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 a problem associated to the Brusselator wave model in chemical reactions, illustrating the use of shell matrices.\n\n"
12: "The command line options are:\n"
13: " -n <n>, where <n> = block dimension of the 2x2 block matrix.\n"
14: " -L <L>, where <L> = bifurcation parameter.\n"
15: " -alpha <alpha>, -beta <beta>, -delta1 <delta1>, -delta2 <delta2>,\n"
16: " where <alpha> <beta> <delta1> <delta2> = model parameters.\n\n";
18: #include <slepceps.h>
20: /*
21: This example computes the eigenvalues with largest real part of the
22: following matrix
24: A = [ tau1*T+(beta-1)*I alpha^2*I
25: -beta*I tau2*T-alpha^2*I ],
27: where
29: T = tridiag{1,-2,1}
30: h = 1/(n+1)
31: tau1 = delta1/(h*L)^2
32: tau2 = delta2/(h*L)^2
33: */
35: /*
36: Matrix operations
37: */
38: PetscErrorCode MatMult_Brussel(Mat,Vec,Vec);
39: PetscErrorCode MatMultTranspose_Brussel(Mat,Vec,Vec);
40: PetscErrorCode MatGetDiagonal_Brussel(Mat,Vec);
42: typedef struct {
43: Mat T;
44: Vec x1,x2,y1,y2;
45: PetscScalar alpha,beta,tau1,tau2,sigma;
46: } CTX_BRUSSEL;
48: int main(int argc,char **argv)
49: {
50: Mat A; /* eigenvalue problem matrix */
51: EPS eps; /* eigenproblem solver context */
52: EPSType type;
53: PetscScalar delta1,delta2,L,h;
54: PetscInt N=30,n,i,Istart,Iend,nev;
55: CTX_BRUSSEL *ctx;
56: PetscBool terse;
57: PetscViewer viewer;
59: PetscFunctionBeginUser;
60: PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
62: PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL));
63: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nBrusselator wave model, n=%" PetscInt_FMT "\n\n",N));
65: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
66: Generate the matrix
67: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
69: /*
70: Create shell matrix context and set default parameters
71: */
72: PetscCall(PetscNew(&ctx));
73: ctx->alpha = 2.0;
74: ctx->beta = 5.45;
75: delta1 = 0.008;
76: delta2 = 0.004;
77: L = 0.51302;
79: /*
80: Look the command line for user-provided parameters
81: */
82: PetscCall(PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL));
83: PetscCall(PetscOptionsGetScalar(NULL,NULL,"-alpha",&ctx->alpha,NULL));
84: PetscCall(PetscOptionsGetScalar(NULL,NULL,"-beta",&ctx->beta,NULL));
85: PetscCall(PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL));
86: PetscCall(PetscOptionsGetScalar(NULL,NULL,"-delta2",&delta2,NULL));
88: /*
89: Create matrix T
90: */
91: PetscCall(MatCreate(PETSC_COMM_WORLD,&ctx->T));
92: PetscCall(MatSetSizes(ctx->T,PETSC_DECIDE,PETSC_DECIDE,N,N));
93: PetscCall(MatSetFromOptions(ctx->T));
95: PetscCall(MatGetOwnershipRange(ctx->T,&Istart,&Iend));
96: for (i=Istart;i<Iend;i++) {
97: if (i>0) PetscCall(MatSetValue(ctx->T,i,i-1,1.0,INSERT_VALUES));
98: if (i<N-1) PetscCall(MatSetValue(ctx->T,i,i+1,1.0,INSERT_VALUES));
99: PetscCall(MatSetValue(ctx->T,i,i,-2.0,INSERT_VALUES));
100: }
101: PetscCall(MatAssemblyBegin(ctx->T,MAT_FINAL_ASSEMBLY));
102: PetscCall(MatAssemblyEnd(ctx->T,MAT_FINAL_ASSEMBLY));
103: PetscCall(MatGetLocalSize(ctx->T,&n,NULL));
105: /*
106: Fill the remaining information in the shell matrix context
107: and create auxiliary vectors
108: */
109: h = 1.0 / (PetscReal)(N+1);
110: ctx->tau1 = delta1 / ((h*L)*(h*L));
111: ctx->tau2 = delta2 / ((h*L)*(h*L));
112: ctx->sigma = 0.0;
113: PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x1));
114: PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x2));
115: PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y1));
116: PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y2));
118: /*
119: Create the shell matrix
120: */
121: PetscCall(MatCreateShell(PETSC_COMM_WORLD,2*n,2*n,2*N,2*N,(void*)ctx,&A));
122: PetscCall(MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_Brussel));
123: PetscCall(MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMultTranspose_Brussel));
124: PetscCall(MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Brussel));
126: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
127: Create the eigensolver and set various options
128: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
130: /*
131: Create eigensolver context
132: */
133: PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
135: /*
136: Set operators. In this case, it is a standard eigenvalue problem
137: */
138: PetscCall(EPSSetOperators(eps,A,NULL));
139: PetscCall(EPSSetProblemType(eps,EPS_NHEP));
141: /*
142: Ask for the rightmost eigenvalues
143: */
144: PetscCall(EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL));
146: /*
147: Set other solver options at runtime
148: */
149: PetscCall(EPSSetFromOptions(eps));
151: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
152: Solve the eigensystem
153: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
155: PetscCall(EPSSolve(eps));
157: /*
158: Optional: Get some information from the solver and display it
159: */
160: PetscCall(EPSGetType(eps,&type));
161: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
162: PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
163: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));
165: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
166: Display solution and clean up
167: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
169: /* show detailed info unless -terse option is given by user */
170: PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
171: if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
172: else {
173: PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
174: PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL));
175: PetscCall(EPSConvergedReasonView(eps,viewer));
176: PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer));
177: PetscCall(PetscViewerPopFormat(viewer));
178: }
179: PetscCall(EPSDestroy(&eps));
180: PetscCall(MatDestroy(&A));
181: PetscCall(MatDestroy(&ctx->T));
182: PetscCall(VecDestroy(&ctx->x1));
183: PetscCall(VecDestroy(&ctx->x2));
184: PetscCall(VecDestroy(&ctx->y1));
185: PetscCall(VecDestroy(&ctx->y2));
186: PetscCall(PetscFree(ctx));
187: PetscCall(SlepcFinalize());
188: return 0;
189: }
191: PetscErrorCode MatMult_Brussel(Mat A,Vec x,Vec y)
192: {
193: PetscInt n;
194: const PetscScalar *px;
195: PetscScalar *py;
196: CTX_BRUSSEL *ctx;
198: PetscFunctionBeginUser;
199: PetscCall(MatShellGetContext(A,&ctx));
200: PetscCall(MatGetLocalSize(ctx->T,&n,NULL));
201: PetscCall(VecGetArrayRead(x,&px));
202: PetscCall(VecGetArray(y,&py));
203: PetscCall(VecPlaceArray(ctx->x1,px));
204: PetscCall(VecPlaceArray(ctx->x2,px+n));
205: PetscCall(VecPlaceArray(ctx->y1,py));
206: PetscCall(VecPlaceArray(ctx->y2,py+n));
208: PetscCall(MatMult(ctx->T,ctx->x1,ctx->y1));
209: PetscCall(VecScale(ctx->y1,ctx->tau1));
210: PetscCall(VecAXPY(ctx->y1,ctx->beta-1.0+ctx->sigma,ctx->x1));
211: PetscCall(VecAXPY(ctx->y1,ctx->alpha*ctx->alpha,ctx->x2));
213: PetscCall(MatMult(ctx->T,ctx->x2,ctx->y2));
214: PetscCall(VecScale(ctx->y2,ctx->tau2));
215: PetscCall(VecAXPY(ctx->y2,-ctx->beta,ctx->x1));
216: PetscCall(VecAXPY(ctx->y2,-ctx->alpha*ctx->alpha+ctx->sigma,ctx->x2));
218: PetscCall(VecRestoreArrayRead(x,&px));
219: PetscCall(VecRestoreArray(y,&py));
220: PetscCall(VecResetArray(ctx->x1));
221: PetscCall(VecResetArray(ctx->x2));
222: PetscCall(VecResetArray(ctx->y1));
223: PetscCall(VecResetArray(ctx->y2));
224: PetscFunctionReturn(PETSC_SUCCESS);
225: }
227: PetscErrorCode MatMultTranspose_Brussel(Mat A,Vec x,Vec y)
228: {
229: PetscInt n;
230: const PetscScalar *px;
231: PetscScalar *py;
232: CTX_BRUSSEL *ctx;
234: PetscFunctionBeginUser;
235: PetscCall(MatShellGetContext(A,&ctx));
236: PetscCall(MatGetLocalSize(ctx->T,&n,NULL));
237: PetscCall(VecGetArrayRead(x,&px));
238: PetscCall(VecGetArray(y,&py));
239: PetscCall(VecPlaceArray(ctx->x1,px));
240: PetscCall(VecPlaceArray(ctx->x2,px+n));
241: PetscCall(VecPlaceArray(ctx->y1,py));
242: PetscCall(VecPlaceArray(ctx->y2,py+n));
244: PetscCall(MatMultTranspose(ctx->T,ctx->x1,ctx->y1));
245: PetscCall(VecScale(ctx->y1,ctx->tau1));
246: PetscCall(VecAXPY(ctx->y1,ctx->beta-1.0+ctx->sigma,ctx->x1));
247: PetscCall(VecAXPY(ctx->y1,-ctx->beta,ctx->x2));
249: PetscCall(MatMultTranspose(ctx->T,ctx->x2,ctx->y2));
250: PetscCall(VecScale(ctx->y2,ctx->tau2));
251: PetscCall(VecAXPY(ctx->y2,ctx->alpha*ctx->alpha,ctx->x1));
252: PetscCall(VecAXPY(ctx->y2,-ctx->alpha*ctx->alpha+ctx->sigma,ctx->x2));
254: PetscCall(VecRestoreArrayRead(x,&px));
255: PetscCall(VecRestoreArray(y,&py));
256: PetscCall(VecResetArray(ctx->x1));
257: PetscCall(VecResetArray(ctx->x2));
258: PetscCall(VecResetArray(ctx->y1));
259: PetscCall(VecResetArray(ctx->y2));
260: PetscFunctionReturn(PETSC_SUCCESS);
261: }
263: PetscErrorCode MatGetDiagonal_Brussel(Mat A,Vec diag)
264: {
265: Vec d1,d2;
266: PetscInt n;
267: PetscScalar *pd;
268: MPI_Comm comm;
269: CTX_BRUSSEL *ctx;
271: PetscFunctionBeginUser;
272: PetscCall(MatShellGetContext(A,&ctx));
273: PetscCall(PetscObjectGetComm((PetscObject)A,&comm));
274: PetscCall(MatGetLocalSize(ctx->T,&n,NULL));
275: PetscCall(VecGetArray(diag,&pd));
276: PetscCall(VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd,&d1));
277: PetscCall(VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd+n,&d2));
279: PetscCall(VecSet(d1,-2.0*ctx->tau1 + ctx->beta - 1.0 + ctx->sigma));
280: PetscCall(VecSet(d2,-2.0*ctx->tau2 - ctx->alpha*ctx->alpha + ctx->sigma));
282: PetscCall(VecDestroy(&d1));
283: PetscCall(VecDestroy(&d2));
284: PetscCall(VecRestoreArray(diag,&pd));
285: PetscFunctionReturn(PETSC_SUCCESS);
286: }
288: /*TEST
290: test:
291: suffix: 1
292: args: -n 50 -eps_nev 4 -eps_two_sided {{0 1}} -eps_type {{krylovschur lapack}} -terse
293: requires: !single
294: filter: grep -v method
296: test:
297: suffix: 2
298: args: -eps_nev 8 -eps_max_it 300 -eps_target -28 -rg_type interval -rg_interval_endpoints -40,-20,-.1,.1 -terse
299: requires: !single
301: test:
302: suffix: 3
303: args: -n 50 -eps_nev 4 -eps_balance twoside -terse
304: requires: double
305: filter: grep -v method
306: output_file: output/ex9_1.out
308: test:
309: suffix: 4
310: args: -eps_smallest_imaginary -eps_ncv 24 -terse
311: requires: !complex !single
313: test:
314: suffix: 4_complex
315: args: -eps_smallest_imaginary -eps_ncv 24 -terse
316: requires: complex !single
318: test:
319: suffix: 5
320: args: -eps_nev 4 -eps_target_real -eps_target -3 -terse
321: requires: !single
323: test:
324: suffix: 6
325: args: -eps_nev 2 -eps_target_imaginary -eps_target 3i -terse
326: requires: complex !single
328: test:
329: suffix: 7
330: args: -n 40 -eps_nev 1 -eps_type arnoldi -eps_smallest_real -eps_refined -eps_ncv 42 -eps_max_it 300 -terse
331: requires: double
333: test:
334: suffix: 8
335: args: -eps_nev 2 -eps_target -30 -eps_type jd -st_matmode shell -eps_jd_fix 0.0001 -eps_jd_const_correction_tol 0 -terse
336: requires: !single
337: filter: sed -e "s/[+-]0\.0*i//g"
338: timeoutfactor: 2
340: test:
341: suffix: 9
342: args: -eps_largest_imaginary -eps_ncv 24 -terse
343: requires: !single
345: TEST*/