Actual source code: cs1.c
1: /* XH: todo add cs1f.F90 and asjust makefile */
2: /*
3: Include "petsctao.h" so that we can use TAO solvers. Note that this
4: file automatically includes libraries such as:
5: petsc.h - base PETSc routines petscvec.h - vectors
6: petscsys.h - system routines petscmat.h - matrices
7: petscis.h - index sets petscksp.h - Krylov subspace methods
8: petscviewer.h - viewers petscpc.h - preconditioners
10: */
12: #include <petsctao.h>
14: /*
15: Description: Compressive sensing test example 1.
16: 0.5*||Ax-b||^2 + lambda*||D*x||_1
17: Xiang Huang: Nov 19, 2018
19: Reference: None
20: */
22: static char help[] = "Finds the least-squares solution to the under constraint linear model Ax = b, with L1-norm regularizer. \n\
23: A is a M*N real matrix (M<N), x is sparse. \n\
24: We find the sparse solution by solving 0.5*||Ax-b||^2 + lambda*||D*x||_1, where lambda (by default 1e-4) is a user specified weight.\n\
25: D is the K*N transform matrix so that D*x is sparse. By default D is identity matrix, so that D*x = x.\n";
27: #define M 3
28: #define N 5
29: #define K 4
31: /* User-defined application context */
32: typedef struct {
33: /* Working space. linear least square: f(x) = A*x - b */
34: PetscReal A[M][N]; /* array of coefficients */
35: PetscReal b[M]; /* array of observations */
36: PetscReal xGT[M]; /* array of ground truth object, which can be used to compare the reconstruction result */
37: PetscReal D[K][N]; /* array of coefficients for 0.5*||Ax-b||^2 + lambda*||D*x||_1 */
38: PetscReal J[M][N]; /* dense jacobian matrix array. For linear least square, J = A. For nonlinear least square, it is different from A */
39: PetscInt idm[M]; /* Matrix row, column indices for jacobian and dictionary */
40: PetscInt idn[N];
41: PetscInt idk[K];
42: } AppCtx;
44: /* User provided Routines */
45: PetscErrorCode InitializeUserData(AppCtx *);
46: PetscErrorCode FormStartingPoint(Vec);
47: PetscErrorCode FormDictionaryMatrix(Mat, AppCtx *);
48: PetscErrorCode EvaluateFunction(Tao, Vec, Vec, void *);
49: PetscErrorCode EvaluateJacobian(Tao, Vec, Mat, Mat, void *);
51: /*--------------------------------------------------------------------*/
52: int main(int argc, char **argv)
53: {
54: Vec x, f; /* solution, function f(x) = A*x-b */
55: Mat J, D; /* Jacobian matrix, Transform matrix */
56: Tao tao; /* Tao solver context */
57: PetscInt i; /* iteration information */
58: PetscReal hist[100], resid[100];
59: PetscInt lits[100];
60: AppCtx user; /* user-defined work context */
62: PetscFunctionBeginUser;
63: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
65: /* Allocate solution and vector function vectors */
66: PetscCall(VecCreateSeq(PETSC_COMM_SELF, N, &x));
67: PetscCall(VecCreateSeq(PETSC_COMM_SELF, M, &f));
69: /* Allocate Jacobian and Dictionary matrix. */
70: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, M, N, NULL, &J));
71: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, K, N, NULL, &D)); /* XH: TODO: dense -> sparse/dense/shell etc, do it on fly */
73: for (i = 0; i < M; i++) user.idm[i] = i;
74: for (i = 0; i < N; i++) user.idn[i] = i;
75: for (i = 0; i < K; i++) user.idk[i] = i;
77: /* Create TAO solver and set desired solution method */
78: PetscCall(TaoCreate(PETSC_COMM_SELF, &tao));
79: PetscCall(TaoSetType(tao, TAOBRGN));
81: /* User set application context: A, D matrice, and b vector. */
82: PetscCall(InitializeUserData(&user));
84: /* Set initial guess */
85: PetscCall(FormStartingPoint(x));
87: /* Fill the content of matrix D from user application Context */
88: PetscCall(FormDictionaryMatrix(D, &user));
90: /* Bind x to tao->solution. */
91: PetscCall(TaoSetSolution(tao, x));
92: /* Bind D to tao->data->D */
93: PetscCall(TaoBRGNSetDictionaryMatrix(tao, D));
95: /* Set the function and Jacobian routines. */
96: PetscCall(TaoSetResidualRoutine(tao, f, EvaluateFunction, (void *)&user));
97: PetscCall(TaoSetJacobianResidualRoutine(tao, J, J, EvaluateJacobian, (void *)&user));
99: /* Check for any TAO command line arguments */
100: PetscCall(TaoSetFromOptions(tao));
102: PetscCall(TaoSetConvergenceHistory(tao, hist, resid, 0, lits, 100, PETSC_TRUE));
104: /* Perform the Solve */
105: PetscCall(TaoSolve(tao));
107: /* XH: Debug: View the result, function and Jacobian. */
108: PetscCall(PetscPrintf(PETSC_COMM_SELF, "-------- result x, residual f=A*x-b, and Jacobian=A. -------- \n"));
109: PetscCall(VecView(x, PETSC_VIEWER_STDOUT_SELF));
110: PetscCall(VecView(f, PETSC_VIEWER_STDOUT_SELF));
111: PetscCall(MatView(J, PETSC_VIEWER_STDOUT_SELF));
112: PetscCall(MatView(D, PETSC_VIEWER_STDOUT_SELF));
114: /* Free TAO data structures */
115: PetscCall(TaoDestroy(&tao));
117: /* Free PETSc data structures */
118: PetscCall(VecDestroy(&x));
119: PetscCall(VecDestroy(&f));
120: PetscCall(MatDestroy(&J));
121: PetscCall(MatDestroy(&D));
123: PetscCall(PetscFinalize());
124: return 0;
125: }
127: /*--------------------------------------------------------------------*/
128: PetscErrorCode EvaluateFunction(Tao tao, Vec X, Vec F, void *ptr)
129: {
130: AppCtx *user = (AppCtx *)ptr;
131: PetscInt m, n;
132: const PetscReal *x;
133: PetscReal *b = user->b, *f;
135: PetscFunctionBegin;
136: PetscCall(VecGetArrayRead(X, &x));
137: PetscCall(VecGetArray(F, &f));
139: /* Even for linear least square, we do not direct use matrix operation f = A*x - b now, just for future modification and compatibility for nonlinear least square */
140: for (m = 0; m < M; m++) {
141: f[m] = -b[m];
142: for (n = 0; n < N; n++) f[m] += user->A[m][n] * x[n];
143: }
144: PetscCall(VecRestoreArrayRead(X, &x));
145: PetscCall(VecRestoreArray(F, &f));
146: PetscCall(PetscLogFlops(2.0 * M * N));
147: PetscFunctionReturn(PETSC_SUCCESS);
148: }
150: /*------------------------------------------------------------*/
151: /* J[m][n] = df[m]/dx[n] */
152: PetscErrorCode EvaluateJacobian(Tao tao, Vec X, Mat J, Mat Jpre, void *ptr)
153: {
154: AppCtx *user = (AppCtx *)ptr;
155: PetscInt m, n;
156: const PetscReal *x;
158: PetscFunctionBegin;
159: PetscCall(VecGetArrayRead(X, &x)); /* not used for linear least square, but keep for future nonlinear least square) */
160: /* XH: TODO: For linear least square, we can just set J=A fixed once, instead of keep update it! Maybe just create a function getFixedJacobian?
161: For nonlinear least square, we require x to compute J, keep codes here for future nonlinear least square*/
162: for (m = 0; m < M; ++m) {
163: for (n = 0; n < N; ++n) user->J[m][n] = user->A[m][n];
164: }
166: PetscCall(MatSetValues(J, M, user->idm, N, user->idn, (PetscReal *)user->J, INSERT_VALUES));
167: PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
168: PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
170: PetscCall(VecRestoreArrayRead(X, &x)); /* not used for linear least square, but keep for future nonlinear least square) */
171: PetscCall(PetscLogFlops(0)); /* 0 for linear least square, >0 for nonlinear least square */
172: PetscFunctionReturn(PETSC_SUCCESS);
173: }
175: /* ------------------------------------------------------------ */
176: /* Currently fixed matrix, in future may be dynamic for D(x)? */
177: PetscErrorCode FormDictionaryMatrix(Mat D, AppCtx *user)
178: {
179: PetscFunctionBegin;
180: PetscCall(MatSetValues(D, K, user->idk, N, user->idn, (PetscReal *)user->D, INSERT_VALUES));
181: PetscCall(MatAssemblyBegin(D, MAT_FINAL_ASSEMBLY));
182: PetscCall(MatAssemblyEnd(D, MAT_FINAL_ASSEMBLY));
184: PetscCall(PetscLogFlops(0)); /* 0 for fixed dictionary matrix, >0 for varying dictionary matrix */
185: PetscFunctionReturn(PETSC_SUCCESS);
186: }
188: /* ------------------------------------------------------------ */
189: PetscErrorCode FormStartingPoint(Vec X)
190: {
191: PetscFunctionBegin;
192: PetscCall(VecSet(X, 0.0));
193: PetscFunctionReturn(PETSC_SUCCESS);
194: }
196: /* ---------------------------------------------------------------------- */
197: PetscErrorCode InitializeUserData(AppCtx *user)
198: {
199: PetscReal *b = user->b; /* **A=user->A, but we don't know the dimension of A in this way, how to fix? */
200: PetscInt m, n, k; /* loop index for M,N,K dimension. */
202: PetscFunctionBegin;
203: /* b = A*x while x = [0;0;1;0;0] here*/
204: m = 0;
205: b[m++] = 0.28;
206: b[m++] = 0.55;
207: b[m++] = 0.96;
209: /* MATLAB generated random matrix, uniformly distributed in [0,1] with 2 digits accuracy. rng(0); A = rand(M, N); A = round(A*100)/100;
210: A = [0.81 0.91 0.28 0.96 0.96
211: 0.91 0.63 0.55 0.16 0.49
212: 0.13 0.10 0.96 0.97 0.80]
213: */
214: m = 0;
215: n = 0;
216: user->A[m][n++] = 0.81;
217: user->A[m][n++] = 0.91;
218: user->A[m][n++] = 0.28;
219: user->A[m][n++] = 0.96;
220: user->A[m][n++] = 0.96;
221: ++m;
222: n = 0;
223: user->A[m][n++] = 0.91;
224: user->A[m][n++] = 0.63;
225: user->A[m][n++] = 0.55;
226: user->A[m][n++] = 0.16;
227: user->A[m][n++] = 0.49;
228: ++m;
229: n = 0;
230: user->A[m][n++] = 0.13;
231: user->A[m][n++] = 0.10;
232: user->A[m][n++] = 0.96;
233: user->A[m][n++] = 0.97;
234: user->A[m][n++] = 0.80;
236: /* initialize to 0 */
237: for (k = 0; k < K; k++) {
238: for (n = 0; n < N; n++) user->D[k][n] = 0.0;
239: }
240: /* Choice I: set D to identity matrix of size N*N for testing */
241: /* for (k=0; k<K; k++) user->D[k][k] = 1.0; */
242: /* Choice II: set D to Backward difference matrix of size (N-1)*N, with zero extended boundary assumption */
243: for (k = 0; k < K; k++) {
244: user->D[k][k] = -1.0;
245: user->D[k][k + 1] = 1.0;
246: }
247: PetscFunctionReturn(PETSC_SUCCESS);
248: }
250: /*TEST
252: build:
253: requires: !complex !single !quad !defined(PETSC_USE_64BIT_INDICES)
255: test:
256: localrunfiles: cs1Data_A_b_xGT
257: args: -tao_monitor_short -tao_max_it 100 -tao_type pounders -tao_gatol 1.e-6
259: test:
260: suffix: 2
261: localrunfiles: cs1Data_A_b_xGT
262: args: -tao_monitor -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type l2prox -tao_brgn_regularizer_weight 1e-8 -tao_gatol 1.e-6 -tao_brgn_subsolver_tao_bnk_ksp_converged_reason
264: test:
265: suffix: 3
266: localrunfiles: cs1Data_A_b_xGT
267: args: -tao_monitor -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type l1dict -tao_brgn_regularizer_weight 1e-8 -tao_brgn_l1_smooth_epsilon 1e-6 -tao_gatol 1.e-6
269: test:
270: suffix: 4
271: localrunfiles: cs1Data_A_b_xGT
272: args: -tao_monitor -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type l2pure -tao_brgn_regularizer_weight 1e-8 -tao_gatol 1.e-6
274: test:
275: suffix: 5
276: localrunfiles: cs1Data_A_b_xGT
277: args: -tao_monitor -tao_max_it 100 -tao_type brgn -tao_brgn_regularization_type lm -tao_gatol 1.e-6 -tao_brgn_subsolver_tao_type bnls
279: TEST*/