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, (char *)0, 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;
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:   }
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*/
```