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: typedef enum {
32: TEST_L1DICT,
33: TEST_LM,
34: TEST_NONE
35: } TestType;
37: /* User-defined application context */
38: typedef struct {
39: /* Working space. linear least square: f(x) = A*x - b */
40: PetscReal A[M][N]; /* array of coefficients */
41: PetscReal b[M]; /* array of observations */
42: PetscReal xGT[M]; /* array of ground truth object, which can be used to compare the reconstruction result */
43: PetscReal D[K][N]; /* array of coefficients for 0.5*||Ax-b||^2 + lambda*||D*x||_1 */
44: PetscReal J[M][N]; /* dense jacobian matrix array. For linear least square, J = A. For nonlinear least square, it is different from A */
45: PetscInt idm[M]; /* Matrix row, column indices for jacobian and dictionary */
46: PetscInt idn[N];
47: PetscInt idk[K];
48: TestType tType;
49: PetscBool view_sol;
50: } AppCtx;
52: /* User provided Routines */
53: PetscErrorCode InitializeUserData(AppCtx *);
54: PetscErrorCode FormStartingPoint(Vec);
55: PetscErrorCode FormDictionaryMatrix(Mat, AppCtx *);
56: PetscErrorCode EvaluateFunction(Tao, Vec, Vec, void *);
57: PetscErrorCode EvaluateJacobian(Tao, Vec, Mat, Mat, void *);
59: static PetscErrorCode SetTaoOptionsFromUserOptions(Tao tao, AppCtx *ctx)
60: {
61: PetscBool isbrgn;
63: PetscFunctionBeginUser;
64: PetscCall(PetscObjectTypeCompare((PetscObject)tao, TAOBRGN, &isbrgn));
65: if (isbrgn) {
66: switch (ctx->tType) {
67: case TEST_LM:
68: PetscCall(TaoBRGNSetRegularizationType(tao, TAOBRGN_REGULARIZATION_LM));
69: break;
70: case TEST_L1DICT:
71: PetscCall(TaoBRGNSetRegularizationType(tao, TAOBRGN_REGULARIZATION_L1DICT));
72: PetscCall(TaoBRGNSetRegularizerWeight(tao, 0.0001));
73: PetscCall(TaoBRGNSetL1SmoothEpsilon(tao, 1.e-6));
74: break;
75: case TEST_NONE:
76: default:
77: break;
78: }
79: }
80: PetscFunctionReturn(PETSC_SUCCESS);
81: }
83: static PetscErrorCode TestOutType(Tao tao, AppCtx *ctx)
84: {
85: PetscBool isbrgn;
87: PetscFunctionBeginUser;
88: PetscCall(PetscObjectTypeCompare((PetscObject)tao, TAOBRGN, &isbrgn));
89: if (isbrgn) {
90: TaoBRGNRegularizationType type;
92: PetscCall(TaoBRGNGetRegularizationType(tao, &type));
93: switch (ctx->tType) {
94: case TEST_LM:
95: PetscCheck(type == TAOBRGN_REGULARIZATION_LM, PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_NOTSAMETYPE, "BRGN Regularization type is not LM!");
96: break;
97: case TEST_L1DICT:
98: PetscCheck(type == TAOBRGN_REGULARIZATION_L1DICT, PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_NOTSAMETYPE, "BRGN Regularization type is not L1DICT!");
99: break;
100: case TEST_NONE:
101: default:
102: break;
103: }
104: }
105: PetscFunctionReturn(PETSC_SUCCESS);
106: }
108: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *ctx)
109: {
110: const char *testTypes[3] = {"l1dict", "lm", "none"};
111: PetscInt run;
113: PetscFunctionBeginUser;
114: ctx->tType = TEST_NONE;
115: ctx->view_sol = PETSC_TRUE;
116: PetscOptionsBegin(comm, "", "Least squares coverage", "");
117: PetscCall(PetscOptionsBool("-view_sol", "Penalize deviation from both goals", "cs1.c", ctx->view_sol, &ctx->view_sol, NULL));
118: run = ctx->tType;
119: PetscCall(PetscOptionsEList("-test_type", "The coverage test type", "cs1.c", testTypes, 3, testTypes[ctx->tType], &run, NULL));
120: ctx->tType = (TestType)run;
121: PetscOptionsEnd();
122: PetscFunctionReturn(PETSC_SUCCESS);
123: }
125: /*--------------------------------------------------------------------*/
126: int main(int argc, char **argv)
127: {
128: Vec x, f; /* solution, function f(x) = A*x-b */
129: Mat J, D; /* Jacobian matrix, Transform matrix */
130: Tao tao; /* Tao solver context */
131: PetscInt i; /* iteration information */
132: PetscReal hist[100], resid[100];
133: PetscInt lits[100];
134: AppCtx user; /* user-defined work context */
136: PetscFunctionBeginUser;
137: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
138: PetscCall(ProcessOptions(PETSC_COMM_WORLD, &user));
139: /* Allocate solution and vector function vectors */
140: PetscCall(VecCreateSeq(PETSC_COMM_SELF, N, &x));
141: PetscCall(VecCreateSeq(PETSC_COMM_SELF, M, &f));
143: /* Allocate Jacobian and Dictionary matrix. */
144: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, M, N, NULL, &J));
145: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, K, N, NULL, &D)); /* XH: TODO: dense -> sparse/dense/shell etc, do it on fly */
147: for (i = 0; i < M; i++) user.idm[i] = i;
148: for (i = 0; i < N; i++) user.idn[i] = i;
149: for (i = 0; i < K; i++) user.idk[i] = i;
151: /* Create TAO solver and set desired solution method */
152: PetscCall(TaoCreate(PETSC_COMM_SELF, &tao));
153: PetscCall(TaoSetType(tao, TAOBRGN));
155: /* User set application context: A, D matrice, and b vector. */
156: PetscCall(InitializeUserData(&user));
158: /* Set initial guess */
159: PetscCall(FormStartingPoint(x));
161: /* Fill the content of matrix D from user application Context */
162: PetscCall(FormDictionaryMatrix(D, &user));
164: /* If needed, set options via function for testing purpose */
165: PetscCall(SetTaoOptionsFromUserOptions(tao, &user));
166: /* Bind x to tao->solution. */
167: PetscCall(TaoSetSolution(tao, x));
168: /* Bind D to tao->data->D */
169: PetscCall(TaoBRGNSetDictionaryMatrix(tao, D));
171: /* Set the function and Jacobian routines. */
172: PetscCall(TaoSetResidualRoutine(tao, f, EvaluateFunction, (void *)&user));
173: PetscCall(TaoSetJacobianResidualRoutine(tao, J, J, EvaluateJacobian, (void *)&user));
175: /* Check for any TAO command line arguments */
176: PetscCall(TaoSetFromOptions(tao));
178: PetscCall(TaoSetConvergenceHistory(tao, hist, resid, 0, lits, 100, PETSC_TRUE));
180: /* Perform the Solve */
181: PetscCall(TaoSolve(tao));
183: /* XH: Debug: View the result, function and Jacobian. */
184: if (user.view_sol) {
185: PetscCall(PetscPrintf(PETSC_COMM_SELF, "-------- result x, residual f=A*x-b, and Jacobian=A. -------- \n"));
186: PetscCall(VecView(x, PETSC_VIEWER_STDOUT_SELF));
187: PetscCall(VecView(f, PETSC_VIEWER_STDOUT_SELF));
188: PetscCall(MatView(J, PETSC_VIEWER_STDOUT_SELF));
189: PetscCall(MatView(D, PETSC_VIEWER_STDOUT_SELF));
190: }
191: PetscCall(TestOutType(tao, &user));
193: /* Free TAO data structures */
194: PetscCall(TaoDestroy(&tao));
196: /* Free PETSc data structures */
197: PetscCall(VecDestroy(&x));
198: PetscCall(VecDestroy(&f));
199: PetscCall(MatDestroy(&J));
200: PetscCall(MatDestroy(&D));
202: PetscCall(PetscFinalize());
203: return 0;
204: }
206: /*--------------------------------------------------------------------*/
207: PetscErrorCode EvaluateFunction(Tao tao, Vec X, Vec F, void *ptr)
208: {
209: AppCtx *user = (AppCtx *)ptr;
210: PetscInt m, n;
211: const PetscReal *x;
212: PetscReal *b = user->b, *f;
214: PetscFunctionBegin;
215: PetscCall(VecGetArrayRead(X, &x));
216: PetscCall(VecGetArray(F, &f));
218: /* 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 */
219: for (m = 0; m < M; m++) {
220: f[m] = -b[m];
221: for (n = 0; n < N; n++) f[m] += user->A[m][n] * x[n];
222: }
223: PetscCall(VecRestoreArrayRead(X, &x));
224: PetscCall(VecRestoreArray(F, &f));
225: PetscCall(PetscLogFlops(2.0 * M * N));
226: PetscFunctionReturn(PETSC_SUCCESS);
227: }
229: /*------------------------------------------------------------*/
230: /* J[m][n] = df[m]/dx[n] */
231: PetscErrorCode EvaluateJacobian(Tao tao, Vec X, Mat J, Mat Jpre, void *ptr)
232: {
233: AppCtx *user = (AppCtx *)ptr;
234: PetscInt m, n;
235: const PetscReal *x;
237: PetscFunctionBegin;
238: PetscCall(VecGetArrayRead(X, &x)); /* not used for linear least square, but keep for future nonlinear least square) */
239: /* 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?
240: For nonlinear least square, we require x to compute J, keep codes here for future nonlinear least square*/
241: for (m = 0; m < M; ++m) {
242: for (n = 0; n < N; ++n) user->J[m][n] = user->A[m][n];
243: }
245: PetscCall(MatSetValues(J, M, user->idm, N, user->idn, (PetscReal *)user->J, INSERT_VALUES));
246: PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
247: PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
249: PetscCall(VecRestoreArrayRead(X, &x)); /* not used for linear least square, but keep for future nonlinear least square) */
250: PetscCall(PetscLogFlops(0)); /* 0 for linear least square, >0 for nonlinear least square */
251: PetscFunctionReturn(PETSC_SUCCESS);
252: }
254: /* ------------------------------------------------------------ */
255: /* Currently fixed matrix, in future may be dynamic for D(x)? */
256: PetscErrorCode FormDictionaryMatrix(Mat D, AppCtx *user)
257: {
258: PetscFunctionBegin;
259: PetscCall(MatSetValues(D, K, user->idk, N, user->idn, (PetscReal *)user->D, INSERT_VALUES));
260: PetscCall(MatAssemblyBegin(D, MAT_FINAL_ASSEMBLY));
261: PetscCall(MatAssemblyEnd(D, MAT_FINAL_ASSEMBLY));
263: PetscCall(PetscLogFlops(0)); /* 0 for fixed dictionary matrix, >0 for varying dictionary matrix */
264: PetscFunctionReturn(PETSC_SUCCESS);
265: }
267: /* ------------------------------------------------------------ */
268: PetscErrorCode FormStartingPoint(Vec X)
269: {
270: PetscFunctionBegin;
271: PetscCall(VecSet(X, 0.0));
272: PetscFunctionReturn(PETSC_SUCCESS);
273: }
275: /* ---------------------------------------------------------------------- */
276: PetscErrorCode InitializeUserData(AppCtx *user)
277: {
278: PetscReal *b = user->b; /* **A=user->A, but we don't know the dimension of A in this way, how to fix? */
279: PetscInt m, n, k; /* loop index for M,N,K dimension. */
281: PetscFunctionBegin;
282: /* b = A*x while x = [0;0;1;0;0] here*/
283: m = 0;
284: b[m++] = 0.28;
285: b[m++] = 0.55;
286: b[m++] = 0.96;
288: /* MATLAB generated random matrix, uniformly distributed in [0,1] with 2 digits accuracy. rng(0); A = rand(M, N); A = round(A*100)/100;
289: A = [0.81 0.91 0.28 0.96 0.96
290: 0.91 0.63 0.55 0.16 0.49
291: 0.13 0.10 0.96 0.97 0.80]
292: */
293: m = 0;
294: n = 0;
295: user->A[m][n++] = 0.81;
296: user->A[m][n++] = 0.91;
297: user->A[m][n++] = 0.28;
298: user->A[m][n++] = 0.96;
299: user->A[m][n++] = 0.96;
300: ++m;
301: n = 0;
302: user->A[m][n++] = 0.91;
303: user->A[m][n++] = 0.63;
304: user->A[m][n++] = 0.55;
305: user->A[m][n++] = 0.16;
306: user->A[m][n++] = 0.49;
307: ++m;
308: n = 0;
309: user->A[m][n++] = 0.13;
310: user->A[m][n++] = 0.10;
311: user->A[m][n++] = 0.96;
312: user->A[m][n++] = 0.97;
313: user->A[m][n++] = 0.80;
315: /* initialize to 0 */
316: for (k = 0; k < K; k++) {
317: for (n = 0; n < N; n++) user->D[k][n] = 0.0;
318: }
319: /* Choice I: set D to identity matrix of size N*N for testing */
320: /* for (k=0; k<K; k++) user->D[k][k] = 1.0; */
321: /* Choice II: set D to Backward difference matrix of size (N-1)*N, with zero extended boundary assumption */
322: for (k = 0; k < K; k++) {
323: user->D[k][k] = -1.0;
324: user->D[k][k + 1] = 1.0;
325: }
326: PetscFunctionReturn(PETSC_SUCCESS);
327: }
329: /*TEST
331: build:
332: requires: !complex !single !quad !defined(PETSC_USE_64BIT_INDICES) !__float128
334: test:
335: localrunfiles: cs1Data_A_b_xGT
336: args: -tao_monitor_short -tao_max_it 100 -tao_type pounders -tao_gatol 1.e-6
338: test:
339: suffix: 2
340: localrunfiles: cs1Data_A_b_xGT
341: 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
343: test:
344: suffix: 3
345: localrunfiles: cs1Data_A_b_xGT
346: 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
348: test:
349: suffix: 4
350: localrunfiles: cs1Data_A_b_xGT
351: 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
353: test:
354: suffix: 5
355: localrunfiles: cs1Data_A_b_xGT
356: 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
358: test:
359: suffix: view_lm
360: localrunfiles: cs1Data_A_b_xGT
361: args: -tao_type brgn -test_type lm -tao_gatol 1.e-6 -view_sol 0 -tao_view
363: test:
364: suffix: view_l1dict
365: localrunfiles: cs1Data_A_b_xGT
366: args: -tao_type brgn -test_type l1dict -tao_gatol 1.e-6 -view_sol 0 -tao_view
368: TEST*/