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: PetscInitialize(&argc,&argv,(char *)0,help);
64: /* Allocate solution and vector function vectors */
65: VecCreateSeq(PETSC_COMM_SELF,N,&x);
66: VecCreateSeq(PETSC_COMM_SELF,M,&f);
68: /* Allocate Jacobian and Dictionary matrix. */
69: MatCreateSeqDense(PETSC_COMM_SELF,M,N,NULL,&J);
70: MatCreateSeqDense(PETSC_COMM_SELF,K,N,NULL,&D); /* XH: TODO: dense -> sparse/dense/shell etc, do it on fly */
72: for (i=0;i<M;i++) user.idm[i] = i;
73: for (i=0;i<N;i++) user.idn[i] = i;
74: for (i=0;i<K;i++) user.idk[i] = i;
76: /* Create TAO solver and set desired solution method */
77: TaoCreate(PETSC_COMM_SELF,&tao);
78: TaoSetType(tao,TAOBRGN);
80: /* User set application context: A, D matrice, and b vector. */
81: InitializeUserData(&user);
83: /* Set initial guess */
84: FormStartingPoint(x);
86: /* Fill the content of matrix D from user application Context */
87: FormDictionaryMatrix(D,&user);
89: /* Bind x to tao->solution. */
90: TaoSetSolution(tao,x);
91: /* Bind D to tao->data->D */
92: TaoBRGNSetDictionaryMatrix(tao,D);
94: /* Set the function and Jacobian routines. */
95: TaoSetResidualRoutine(tao,f,EvaluateFunction,(void*)&user);
96: TaoSetJacobianResidualRoutine(tao,J,J,EvaluateJacobian,(void*)&user);
98: /* Check for any TAO command line arguments */
99: TaoSetFromOptions(tao);
101: TaoSetConvergenceHistory(tao,hist,resid,0,lits,100,PETSC_TRUE);
103: /* Perform the Solve */
104: TaoSolve(tao);
106: /* XH: Debug: View the result, function and Jacobian. */
107: PetscPrintf(PETSC_COMM_SELF, "-------- result x, residual f=A*x-b, and Jacobian=A. -------- \n");
108: VecView(x,PETSC_VIEWER_STDOUT_SELF);
109: VecView(f,PETSC_VIEWER_STDOUT_SELF);
110: MatView(J,PETSC_VIEWER_STDOUT_SELF);
111: MatView(D,PETSC_VIEWER_STDOUT_SELF);
113: /* Free TAO data structures */
114: TaoDestroy(&tao);
116: /* Free PETSc data structures */
117: VecDestroy(&x);
118: VecDestroy(&f);
119: MatDestroy(&J);
120: MatDestroy(&D);
122: PetscFinalize();
123: return 0;
124: }
126: /*--------------------------------------------------------------------*/
127: PetscErrorCode EvaluateFunction(Tao tao, Vec X, Vec F, void *ptr)
128: {
129: AppCtx *user = (AppCtx *)ptr;
130: PetscInt m,n;
131: const PetscReal *x;
132: PetscReal *b=user->b,*f;
134: VecGetArrayRead(X,&x);
135: VecGetArray(F,&f);
137: /* 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 */
138: for (m=0;m<M;m++) {
139: f[m] = -b[m];
140: for (n=0;n<N;n++) {
141: f[m] += user->A[m][n]*x[n];
142: }
143: }
144: VecRestoreArrayRead(X,&x);
145: VecRestoreArray(F,&f);
146: PetscLogFlops(2.0*M*N);
147: return 0;
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: VecGetArrayRead(X,&x); /* not used for linear least square, but keep for future nonlinear least square) */
159: /* 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?
160: For nonlinear least square, we require x to compute J, keep codes here for future nonlinear least square*/
161: for (m=0; m<M; ++m) {
162: for (n=0; n<N; ++n) {
163: user->J[m][n] = user->A[m][n];
164: }
165: }
167: MatSetValues(J,M,user->idm,N,user->idn,(PetscReal *)user->J,INSERT_VALUES);
168: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
169: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
171: VecRestoreArrayRead(X,&x);/* not used for linear least square, but keep for future nonlinear least square) */
172: PetscLogFlops(0); /* 0 for linear least square, >0 for nonlinear least square */
173: return 0;
174: }
176: /* ------------------------------------------------------------ */
177: /* Currently fixed matrix, in future may be dynamic for D(x)? */
178: PetscErrorCode FormDictionaryMatrix(Mat D,AppCtx *user)
179: {
180: MatSetValues(D,K,user->idk,N,user->idn,(PetscReal *)user->D,INSERT_VALUES);
181: MatAssemblyBegin(D,MAT_FINAL_ASSEMBLY);
182: MatAssemblyEnd(D,MAT_FINAL_ASSEMBLY);
184: PetscLogFlops(0); /* 0 for fixed dictionary matrix, >0 for varying dictionary matrix */
185: return 0;
186: }
188: /* ------------------------------------------------------------ */
189: PetscErrorCode FormStartingPoint(Vec X)
190: {
191: VecSet(X,0.0);
192: return 0;
193: }
195: /* ---------------------------------------------------------------------- */
196: PetscErrorCode InitializeUserData(AppCtx *user)
197: {
198: PetscReal *b=user->b; /* **A=user->A, but we don't kown the dimension of A in this way, how to fix? */
199: PetscInt m,n,k; /* loop index for M,N,K dimension. */
201: /* b = A*x while x = [0;0;1;0;0] here*/
202: m = 0;
203: b[m++] = 0.28;
204: b[m++] = 0.55;
205: b[m++] = 0.96;
207: /* matlab generated random matrix, uniformly distributed in [0,1] with 2 digits accuracy. rng(0); A = rand(M, N); A = round(A*100)/100;
208: A = [0.81 0.91 0.28 0.96 0.96
209: 0.91 0.63 0.55 0.16 0.49
210: 0.13 0.10 0.96 0.97 0.80]
211: */
212: m=0; n=0; user->A[m][n++] = 0.81; user->A[m][n++] = 0.91; user->A[m][n++] = 0.28; user->A[m][n++] = 0.96; user->A[m][n++] = 0.96;
213: ++m; n=0; user->A[m][n++] = 0.91; user->A[m][n++] = 0.63; user->A[m][n++] = 0.55; user->A[m][n++] = 0.16; user->A[m][n++] = 0.49;
214: ++m; n=0; user->A[m][n++] = 0.13; user->A[m][n++] = 0.10; user->A[m][n++] = 0.96; user->A[m][n++] = 0.97; user->A[m][n++] = 0.80;
216: /* initialize to 0 */
217: for (k=0; k<K; k++) {
218: for (n=0; n<N; n++) {
219: user->D[k][n] = 0.0;
220: }
221: }
222: /* Choice I: set D to identity matrix of size N*N for testing */
223: /* for (k=0; k<K; k++) user->D[k][k] = 1.0; */
224: /* Choice II: set D to Backward difference matrix of size (N-1)*N, with zero extended boundary assumption */
225: for (k=0;k<K;k++) {
226: user->D[k][k] = -1.0;
227: user->D[k][k+1] = 1.0;
228: }
230: return 0;
231: }
233: /*TEST
235: build:
236: requires: !complex !single !quad !defined(PETSC_USE_64BIT_INDICES)
238: test:
239: localrunfiles: cs1Data_A_b_xGT
240: args: -tao_smonitor -tao_max_it 100 -tao_type pounders -tao_gatol 1.e-6
242: test:
243: suffix: 2
244: localrunfiles: cs1Data_A_b_xGT
245: 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
247: test:
248: suffix: 3
249: localrunfiles: cs1Data_A_b_xGT
250: 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
252: test:
253: suffix: 4
254: localrunfiles: cs1Data_A_b_xGT
255: 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
257: test:
258: suffix: 5
259: localrunfiles: cs1Data_A_b_xGT
260: 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
262: TEST*/