GCC Code Coverage Report

Directory: ./
File: src/eps/tutorials/ex60.c
Date: 2026-09-30 04:15:21
Exec Total Coverage
Lines: 159 168 94.6%
Functions: 8 8 100.0%
Branches: 404 704 57.4%
Line Branch Exec Source
1 /*
2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3 SLEPc - Scalable Library for Eigenvalue Problem Computations
4 Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
5
6 This file is part of SLEPc.
7 SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9 */
10
11 static char help[] = "2-D discrete Gross-Pitaevskii model solved as a Nonlinear Eigenvalue Problem with eigenvector dependence (NEPv).\n\n"
12 "Implemented by embedding an EPS inside a nonlinear SNES loop.\n\n"
13 "The Gross-Pitaevskii (GP) equation models the ground state of a rotating Bose-Einstein Condensate (BEC).\n"
14 "The goal is to self-consistently find the macroscopic wavefunction (eigenvector) and its corresponding\n"
15 "chemical potential or ground-state energy (eigenvalue) under a magnetic trap.\n\n"
16 "The nonlinear Hamiltonian matrix is defined as H(x) = A0 + beta * Diag(rho(x)), where:\n"
17 " A0 = base linear Hamiltonian containing 2-D kinetic energy, a harmonic trap potential, and angular momentum rotation.\n"
18 " rho = condensate density vector computed from the ground-state wavefunction x as rho = |x|^2.\n\n"
19 "The command line options are:\n"
20 " -n <n>, where <n> = number of grid points per dimension.\n"
21 " -beta <beta>, where <beta> = real scaling parameter controlling the nonlinearity and strength of the atomic interactions.\n"
22 " -symm <bool>: trap potential profile (true = symmetric, false = asymmetric).\n"
23 " -verbose, to print the converged Hamiltonian diagonal and its sum.\n\n";
24
25 #include <slepceps.h>
26
27 /*
28 Context structure to store the necessary data regarding the discrete Gross-Pitaevskii (DGP) problem
29 as well as the objects needed for the nonlinear iteration loop.
30 */
31 typedef struct {
32 // DGP context
33
34 // Inputs
35 PetscInt N; // Number of points per dimension
36 PetscReal beta; // Parameter controlling the nonlinearity
37 PetscBool symm; // True: Symmetric potential, False: Asymmetric potential
38
39 // Constants
40 PetscReal L; // Length of the semi-domain [-L, L]
41 PetscReal h; // Step size
42 PetscReal omega; // Angular frequency
43
44 // Working vectors and matrices
45 Vec rho; // Vector to store the condensate density
46 Vec z; // Intermediate vector to store the result z = beta * rho
47 Mat A0; // Base linear Hamiltonian
48
49 // Nonlinear iteration context
50 EPS eps; // Solver for each H
51 Mat H; // Hamiltonian
52 Vec x; // Eigenvector
53 } DGPContext;
54
55 /*
56 Initialize the context for the 2D discrete Gross-Pitaevskii problem.
57
58 This function allocates the necessary memory and builds the base linear
59 Hamiltonian A0 as
60
61 A0 = h^2 * ( -0.5*L + V - omega*1i*L_z )
62
63 where
64 L is the discrete 2-D Laplacian,
65 L_z is the discrete 2-D angular momentum operator (without scaling), and
66 V is a diagonal matrix with the potential for each coordinate (x,y):
67 (x.^2+y.^2)/2 for the symmetric case, (x.^2+100*y.^2)/2 for the non-symmetric case.
68
69 Arguments:
70 N - Grid size per dimension
71 beta - Parameter controlling the repulsive interaction of the condensate
72 symm - Defines the shape of the magnetic trap (True = symmetric, False = asymmetric)
73 ctx_out - Pointer to the memory address where the created context will be stored
74 */
75 20 PetscErrorCode DGPCreateContext(MPI_Comm comm,PetscInt N,PetscReal beta,PetscBool symm,DGPContext **ctx_out)
76 {
77 20 DGPContext *ctx;
78
79 20 PetscInt Istart,Iend,i,II,j;
80 20 PetscReal h2;
81 20 PetscReal x,y,V;
82 20 PetscScalar alpha;
83
84
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 20 PetscFunctionBeginUser;
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 20 PetscCall(PetscNew(&ctx));
86
87 // Inputs
88 20 ctx->N=N;
89 20 ctx->beta=beta;
90 20 ctx->symm=symm;
91
92 // Constants
93 20 ctx->L=1.0;
94 20 ctx->h=2.0*ctx->L/(ctx->N+1.0);
95 20 ctx->omega=0.85;
96 20 h2=ctx->h*ctx->h;
97 // Scaling factor for h^2 * (-omega * 1i * L_z) with L_z = (x or y)/(2h)
98 20 alpha = -h2*ctx->omega/(2.0*ctx->h)*PETSC_i;
99
100 // 1. Create A0
101
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 20 PetscCall(MatCreate(comm,&ctx->A0));
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 20 PetscCall(MatSetSizes(ctx->A0,PETSC_DECIDE,PETSC_DECIDE,N*N,N*N));
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 20 PetscCall(MatSetFromOptions(ctx->A0));
104
105 // 2. Fill A0
106
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 20 PetscCall(MatGetOwnershipRange(ctx->A0,&Istart,&Iend));
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 200 for (II=Istart;II<Iend;II++) {
109 180 i=II/ctx->N; j=II%ctx->N;
110
111 // Potential for mesh point with coordinates (x,y)
112 180 x=-ctx->L+(j+1)*ctx->h;
113 180 y=-ctx->L+(i+1)*ctx->h;
114
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 180 if (ctx->symm) V=0.5*(x*x+y*y);
115 ✗ else V=0.5*(x*x+100.0*y*y);
116
117 // Diagonal: h^2*(-0.5*L + V - omega*1i*L_z) with L_diag = -4/h^2 and L_z_diag = 0
118
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 180 PetscCall(MatSetValue(ctx->A0,II,II,0.5*4.0+h2*V,INSERT_VALUES));
119
120 // Off-diagonal: h^2*(-0.5*L + V - omega*1i*L_z) with L_offdiag = 1/h^2, V_offdiag = 0, and L_z_offdiag = +/- (x or y)/(2h)
121
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 180 if (i>0) PetscCall(MatSetValue(ctx->A0,II,II-ctx->N,-0.5+alpha*x,INSERT_VALUES));
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 180 if (i<ctx->N-1) PetscCall(MatSetValue(ctx->A0,II,II+ctx->N,-0.5-alpha*x,INSERT_VALUES));
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 180 if (j>0) PetscCall(MatSetValue(ctx->A0,II,II-1,-0.5-alpha*y,INSERT_VALUES));
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 180 if (j<ctx->N-1) PetscCall(MatSetValue(ctx->A0,II,II+1,-0.5+alpha*y,INSERT_VALUES));
125 }
126
127
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 20 PetscCall(MatAssemblyBegin(ctx->A0,MAT_FINAL_ASSEMBLY));
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 20 PetscCall(MatAssemblyEnd(ctx->A0,MAT_FINAL_ASSEMBLY));
129
130 // 3. Create vectors to store the condensate density
131
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 20 PetscCall(MatCreateVecs(ctx->A0,&ctx->rho,&ctx->z));
132
133 20 *ctx_out=ctx;
134
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 20 PetscFunctionReturn(PETSC_SUCCESS);
135 }
136
137 /*
138 Configure the SLEPc objects necessary for the nonlinear iteration.
139
140 This function prepares the Hamiltonian matrix by cloning the structure of A0,
141 initializes the vector to store the condensate state, and configures the eigenvalue
142 solver (EPS) by defining the problem type and adjusting its tolerance.
143
144 Arguments:
145 ctx - Pointer to the previously initialized DGP context
146 tol - Desired tolerance for the internal eigenvalue solver
147 */
148 20 PetscErrorCode DGPSetUpIterationWorkspace(DGPContext *ctx,PetscReal tol)
149 {
150 20 MPI_Comm comm;
151
152
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 20 PetscFunctionBeginUser;
153 20 comm = PetscObjectComm((PetscObject)ctx->A0);
154 /* Prepare the H matrix */
155
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 20 PetscCall(MatDuplicate(ctx->A0,MAT_DO_NOT_COPY_VALUES,&ctx->H));
156
157 /* Configure the eigenvector x */
158
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 20 PetscCall(MatCreateVecs(ctx->A0,&ctx->x,NULL));
159
160 /* Configure SLEPc EPS */
161
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 20 PetscCall(EPSCreate(comm,&ctx->eps));
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 20 PetscCall(EPSSetProblemType(ctx->eps,EPS_HEP));
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 20 PetscCall(EPSSetWhichEigenpairs(ctx->eps,EPS_SMALLEST_REAL));
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 20 PetscCall(EPSSetDimensions(ctx->eps,1,PETSC_DECIDE,PETSC_DECIDE));
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 20 PetscCall(EPSSetTolerances(ctx->eps,tol,PETSC_DECIDE));
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 20 PetscCall(EPSSetFromOptions(ctx->eps));
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 4 PetscFunctionReturn(PETSC_SUCCESS);
168 }
169
170 /*
171 Generate the initial guess X0 by solving the base linear Hamiltonian.
172
173 This function solves the eigenvalue problem (A0 * x = E * x) and fills
174 the vector x with the lowest energy eigenvector obtained. This
175 initial guess improves the convergence of the nonlinear iteration loop.
176
177 Arguments:
178 ctx - Pointer to the previously initialized DGP context
179 */
180 20 PetscErrorCode DGPGenerateInitialGuess(DGPContext *ctx)
181 {
182 20 PetscInt nconv;
183 20 MPI_Comm comm;
184
185
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 20 PetscFunctionBeginUser;
186 20 comm = PetscObjectComm((PetscObject)ctx->A0);
187 /* 1. Configure and solve the base linear problem A0 */
188
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 20 PetscCall(EPSSetOperators(ctx->eps,ctx->A0,NULL));
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 20 PetscCall(EPSSolve(ctx->eps));
190
191 /* Safety check: guarantee that SLEPc found the solution */
192
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 20 PetscCall(EPSGetConverged(ctx->eps,&nconv));
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 20 PetscCheck(nconv>=1,comm,PETSC_ERR_NOT_CONVERGED,"SLEPc could not find the initial linear ground state.");
194
195 /* 2. Extract the eigenvector and store it in x */
196
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 20 PetscCall(EPSGetEigenvector(ctx->eps,0,ctx->x,NULL));
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 4 PetscFunctionReturn(PETSC_SUCCESS);
198 }
199
200 /*
201 Compute the eigenvector-dependent term from the ground-state eigenvector.
202
203 In the context of the Gross-Pitaevskii model, this function computes the condensate
204 density rho(x) as the squared magnitude of the components of the eigenvector X0.
205 The formula used is: rho(x) = |x|.^2.
206
207 Arguments:
208 ctx - Pointer to the initialized DGP context
209 rho_out - Pre-created vector where the computed term will be stored
210 */
211 410 PetscErrorCode DGPComputeEigvecDependentTerm(DGPContext *ctx,Vec rho_out)
212 {
213 410 PetscInt i,n_loc;
214 410 const PetscScalar *x_local;
215 410 PetscScalar *rho_local;
216
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 410 PetscFunctionBeginUser;
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 410 PetscCall(VecSet(rho_out,0.0));
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 410 PetscCall(VecGetLocalSize(rho_out,&n_loc));
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 410 PetscCall(VecGetArray(rho_out,&rho_local));
221
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 410 PetscCall(VecGetArrayRead(ctx->x,&x_local));
223
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 4100 for (i=0;i<n_loc;i++) {
225 /* Compute the squared magnitude: rho = Real^2 + Imag^2 */
226 3690 rho_local[i]=PetscRealPart(x_local[i])*PetscRealPart(x_local[i])+PetscImaginaryPart(x_local[i])*PetscImaginaryPart(x_local[i]);
227 }
228
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 410 PetscCall(VecRestoreArrayRead(ctx->x,&x_local));
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 410 PetscCall(VecRestoreArray(rho_out,&rho_local));
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 82 PetscFunctionReturn(PETSC_SUCCESS);
232 }
233
234 /*
235 Build the Hamiltonian from an input eigenvector-dependent term.
236
237 This function assembles the updated Hamiltonian matrix stored in the context
238 using the formula: H = A0 + beta * Diag(rho_in).
239
240 Arguments:
241 ctx - Pointer to the initialized DGP context (ctx->H is updated)
242 rho_in - Vector with the proposed input eigenvector-dependent term
243 */
244 390 PetscErrorCode DGPBuildHamiltonian(DGPContext *ctx,Vec rho_in)
245 {
246
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 390 PetscFunctionBeginUser;
247 // 1. Build H = A0 + beta * Diag(rho_in)
248
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 390 PetscCall(MatCopy(ctx->A0,ctx->H,SAME_NONZERO_PATTERN));
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 390 PetscCall(VecCopy(rho_in,ctx->z));
250
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 390 PetscCall(VecScale(ctx->z,ctx->beta));
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 390 PetscCall(MatDiagonalSet(ctx->H,ctx->z,ADD_VALUES));
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 78 PetscFunctionReturn(PETSC_SUCCESS);
254 }
255
256 /*
257 Evaluation function (Callback) for the SNES nonlinear solver in DGP.
258
259 In each SNES iteration, this function receives a proposed eigenvector-dependent
260 term (rho_in), builds the Hamiltonian, solves the eigenvalue equation, computes the
261 resulting term, and returns the residual F = rho_out - rho_in.
262
263 Arguments:
264 snes - The nonlinear solver context
265 rho_in - Input state (eigenvector-dependent term) proposed by SNES
266 F - Vector where the computed residual will be stored
267 ctx_void - Pointer to the user's DGP context (DGPContext)
268 */
269 390 PetscErrorCode DGPNonlinearIteration(SNES snes,Vec rho_in,Vec F,void *ctx_void)
270 {
271 390 DGPContext *ctx=(DGPContext*)ctx_void;
272 390 PetscInt nconv;
273 390 MPI_Comm comm;
274
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 390 PetscFunctionBeginUser;
276 390 comm = PetscObjectComm((PetscObject)ctx->A0);
277 /* 1. Build the physics (Hamiltonian) with the guess proposed by SNES */
278
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 390 PetscCall(DGPBuildHamiltonian(ctx,rho_in));
279
280 /* 2. Solve the eigenvalue problem with the current H, using the previous state as initial guess */
281
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 390 PetscCall(EPSSetOperators(ctx->eps,ctx->H,NULL));
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 390 PetscCall(EPSSetInitialSpace(ctx->eps,1,&ctx->x));
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 390 PetscCall(EPSSolve(ctx->eps));
284
285 // Safety check: verify that SLEPc found the ground state
286
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 390 PetscCall(EPSGetConverged(ctx->eps,&nconv));
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 390 PetscCheck(nconv>=1,comm,PETSC_ERR_NOT_CONVERGED,"SLEPc did not find the ground state in this SNES iteration");
288
289 /* 3. Extract the new eigenvector and store it directly in ctx->x */
290
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 390 PetscCall(EPSGetEigenvector(ctx->eps,0,ctx->x,NULL));
291
292 /* 4. Compute the new eigenvector-dependent term (rho_out) generated by this eigenvector */
293 // Store the result in ctx->rho
294
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 390 PetscCall(DGPComputeEigvecDependentTerm(ctx,ctx->rho));
295
296 /* 5. Calculate the nonlinear residual: F = rho_in - rho_out */
297
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 390 PetscCall(VecWAXPY(F,-1.0,ctx->rho,rho_in));
298
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 78 PetscFunctionReturn(PETSC_SUCCESS);
299 }
300
301 /*
302 Free the memory associated with the DGP context.
303
304 This function destroys all internal PETSc objects created during
305 initialization and frees the memory of the main structure.
306
307 Arguments:
308 ctx - Pointer to the DGP context (set to NULL upon completion)
309 */
310 20 PetscErrorCode DGPDestroyContext(DGPContext **ctx)
311 {
312
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 20 PetscFunctionBeginUser;
313
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 20 if (!*ctx) PetscFunctionReturn(PETSC_SUCCESS);
314
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 20 PetscCall(MatDestroy(&(*ctx)->A0));
316
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 20 PetscCall(VecDestroy(&(*ctx)->rho));
317
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 20 PetscCall(VecDestroy(&(*ctx)->z));
318
319
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 20 PetscCall(MatDestroy(&(*ctx)->H));
320
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 20 PetscCall(VecDestroy(&(*ctx)->x));
321
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 20 PetscCall(EPSDestroy(&(*ctx)->eps));
322
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 20 PetscCall(PetscFree(*ctx));
324
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 4 PetscFunctionReturn(PETSC_SUCCESS);
325 }
326
327 20 int main(int argc,char **argv)
328 {
329 20 DGPContext *ctx;
330 20 Vec H_diag,rho_guess;
331 20 PetscScalar diagonal_sum,kr;
332 20 PetscInt n=3,maxit=100,its;
333 20 PetscInt nconv;
334 20 PetscReal beta=2.0,rtol=SLEPC_DEFAULT_TOL,stol=1e-12;
335 20 SNES snes;
336 20 Vec F; // Vector to store the residual (F = rho_out - rho_in)
337 20 PetscBool symm=PETSC_TRUE,verbose=PETSC_FALSE;
338 20 SNESConvergedReason reason;
339 20 SNESLineSearch linesearch;
340
341
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 20 PetscFunctionBeginUser;
342
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 20 PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
343
344 20 PetscCheck(PetscDefined(USE_COMPLEX),PETSC_COMM_WORLD,PETSC_ERR_SUP,"This example requires complex scalars");
345
346
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 20 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"--- DGP SNES NEPv ---\n"));
347
348 /* 1. Read DGP-specific command line options */
349
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 20 PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
350
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 20 PetscCall(PetscOptionsGetReal(NULL,NULL,"-beta",&beta,NULL));
351
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 20 PetscCall(PetscOptionsGetBool(NULL,NULL,"-symm",&symm,NULL));
352
353 /* 2. Initialization of the DGP context and base linear Hamiltonian A0 */
354
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 20 PetscCall(DGPCreateContext(PETSC_COMM_WORLD,n,beta,symm,&ctx));
355
356 /* 3. Configure objects for the nonlinear iteration (H matrix, EPS, Vec x) */
357
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 20 PetscCall(DGPSetUpIterationWorkspace(ctx,rtol*0.1));
358
359 /* 4. Generate the initial guess by solving the linear problem A0 */
360
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 20 PetscCall(DGPGenerateInitialGuess(ctx));
361
362 /* 5. Prepare the initial density (rho_guess) from the linear ground state */
363
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 20 PetscCall(VecDuplicate(ctx->rho,&rho_guess));
364
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 20 PetscCall(DGPComputeEigvecDependentTerm(ctx,rho_guess));
365
366 /* 6. Prepare the residual vector F by cloning rho */
367
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 20 PetscCall(VecDuplicate(ctx->rho,&F));
368
369 /* 7. Configure the nonlinear solver engine (SNES) with the DGP callback */
370
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 20 PetscCall(SNESCreate(PETSC_COMM_WORLD,&snes));
371
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 20 PetscCall(SNESSetFunction(snes,F,DGPNonlinearIteration,ctx));
372
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 20 PetscCall(SNESSetTolerances(snes,PETSC_DETERMINE,rtol,stol,maxit,PETSC_DETERMINE));
373
374 // Default -> NRICHARDSON with step lambda = 1.0 to simulate basic SCF
375
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 20 PetscCall(SNESSetType(snes,SNESNRICHARDSON));
376
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 20 PetscCall(SNESGetLineSearch(snes,&linesearch));
377
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 20 PetscCall(SNESLineSearchSetType(linesearch,SNESLINESEARCHNONE));
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 20 PetscCall(SNESLineSearchSetDamping(linesearch,1.0));
379
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 20 PetscCall(SNESSetFromOptions(snes));
381
382
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 20 PetscCall(SNESGetTolerances(snes,NULL,&rtol,NULL,&maxit,NULL));
383
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 20 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Current parameters: n=%" PetscInt_FMT ", beta=%g, symm=%s, rtol=%g, maxit=%" PetscInt_FMT "\n",n,(double)beta,symm ? "True" : "False",(double)rtol,maxit));
384
385 /* 8. Nonlinear iteration loop */
386
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 20 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nStarting nonlinear iterations...\n"));
387
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 20 PetscCall(SNESSolve(snes,NULL,rho_guess));
388
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 20 PetscCall(SNESGetConvergedReason(snes,&reason));
390
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 20 PetscCall(SNESGetIterationNumber(snes,&its));
391
392 /* 9. Analysis of results */
393
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 20 if (reason>0) {
394
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 20 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"--> CONVERGENCE REACHED in %" PetscInt_FMT " iterations (Reason: %s).\n",its,SNESConvergedReasons[reason]));
395
396 /* Extract the eigenvalue of the converged ground state */
397
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 20 PetscCall(EPSGetConverged(ctx->eps,&nconv));
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 20 if (nconv>0) {
399
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 20 PetscCall(EPSGetEigenvalue(ctx->eps,0,&kr,NULL));
400
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 20 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nEigenvalue found = %10.6f\n",(double)PetscRealPart(kr)));
401 }
402
403
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 20 PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));
404
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 20 if (verbose) {
405 ✗ PetscCall(MatCreateVecs(ctx->H,NULL,&H_diag));
406 ✗ PetscCall(MatGetDiagonal(ctx->H,H_diag));
407 ✗ PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Diagonal of the final Hamiltonian:\n"));
408 ✗ PetscCall(VecView(H_diag,PETSC_VIEWER_STDOUT_WORLD));
409
410 ✗ PetscCall(VecSum(H_diag,&diagonal_sum));
411 ✗ PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Sum of the diagonal (Approx total energy): %g\n",(double)PetscRealPart(diagonal_sum)));
412 ✗ PetscCall(VecDestroy(&H_diag));
413 }
414
415 } else {
416 ✗ PetscCall(PetscPrintf(PETSC_COMM_WORLD,"--> ERROR: SNES did not converge (Reason: %s)\n",SNESConvergedReasons[reason]));
417 }
418
419 /* 10. Clean up memory */
420
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 20 PetscCall(VecDestroy(&F));
421
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 20 PetscCall(VecDestroy(&rho_guess));
422
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 20 PetscCall(SNESDestroy(&snes));
423
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 20 PetscCall(DGPDestroyContext(&ctx));
424
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 20 PetscCall(SlepcFinalize());
426 return 0;
427 }
428
429 /*TEST
430
431 build:
432 requires: complex
433
434 testset:
435 filter: sed -e "s/rtol=1e-05/rtol=1e-08/" -e "s/rtol=1e-16/rtol=1e-08/" -e "s/[0-9]\{1,\} iterations/23 iterations/" -e "s/CONVERGED_SNORM_RELATIVE/CONVERGED_FNORM_RELATIVE/"
436 output_file: output/ex60_1.out
437 test:
438 suffix: 1
439 test:
440 suffix: 2
441 args: -snes_type anderson -snes_anderson_m 7
442 test:
443 suffix: 3
444 args: -snes_type ngmres -npc_snes_type nrichardson -snes_npc_side right
445 test:
446 suffix: 4
447 args: -snes_type composite -snes_composite_type additiveoptimal -snes_composite_sneses anderson,nrichardson -sub_0_snes_anderson_m 7 -sub_0_snes_anderson_beta 0.4
448
449 TEST*/
450