Actual source code: cs1.c

petsc-master 2020-01-15
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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    - sysem 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";
26: /*T
27:    Concepts: TAO^Solving a system of nonlinear equations, nonlinear least squares
28:    Routines: TaoCreate();
29:    Routines: TaoSetType();
30:    Routines: TaoSetSeparableObjectiveRoutine();
31:    Routines: TaoSetJacobianRoutine();
32:    Routines: TaoSetInitialVector();
33:    Routines: TaoSetFromOptions();
34:    Routines: TaoSetConvergenceHistory(); TaoGetConvergenceHistory();
35:    Routines: TaoSolve();
36:    Routines: TaoView(); TaoDestroy();
37:    Processors: 1
38: T*/

40: #define M 3
41: #define N 5
42: #define K 4

44: /* User-defined application context */
45: typedef struct {
46:   /* Working space. linear least square:  f(x) = A*x - b */
47:   PetscReal A[M][N];    /* array of coefficients */
48:   PetscReal b[M];       /* array of observations */
49:   PetscReal xGT[M];     /* array of ground truth object, which can be used to compare the reconstruction result */
50:   PetscReal D[K][N];    /* array of coefficients for 0.5*||Ax-b||^2 + lambda*||D*x||_1 */
51:   PetscReal J[M][N];    /* dense jacobian matrix array. For linear least square, J = A. For nonlinear least square, it is different from A */
52:   PetscInt  idm[M];     /* Matrix row, column indices for jacobian and dictionary */
53:   PetscInt  idn[N];
54:   PetscInt  idk[K];
55: } AppCtx;

57: /* User provided Routines */
58: PetscErrorCode InitializeUserData(AppCtx *);
59: PetscErrorCode FormStartingPoint(Vec);
60: PetscErrorCode FormDictionaryMatrix(Mat,AppCtx *);
61: PetscErrorCode EvaluateFunction(Tao,Vec,Vec,void *);
62: PetscErrorCode EvaluateJacobian(Tao,Vec,Mat,Mat,void *);

64: /*--------------------------------------------------------------------*/
65: int main(int argc,char **argv)
66: {
68:   Vec            x,f;               /* solution, function f(x) = A*x-b */
69:   Mat            J,D;               /* Jacobian matrix, Transform matrix */
70:   Tao            tao;                /* Tao solver context */
71:   PetscInt       i;                  /* iteration information */
72:   PetscReal      hist[100],resid[100];
73:   PetscInt       lits[100];
74:   AppCtx         user;               /* user-defined work context */

76:   PetscInitialize(&argc,&argv,(char *)0,help);if (ierr) return ierr;

78:   /* Allocate solution and vector function vectors */
79:   VecCreateSeq(PETSC_COMM_SELF,N,&x);
80:   VecCreateSeq(PETSC_COMM_SELF,M,&f);

82:   /* Allocate Jacobian and Dictionary matrix. */
83:   MatCreateSeqDense(PETSC_COMM_SELF,M,N,NULL,&J);
84:   MatCreateSeqDense(PETSC_COMM_SELF,K,N,NULL,&D); /* XH: TODO: dense -> sparse/dense/shell etc, do it on fly  */

86:   for (i=0;i<M;i++) user.idm[i] = i;
87:   for (i=0;i<N;i++) user.idn[i] = i;
88:   for (i=0;i<K;i++) user.idk[i] = i;

90:   /* Create TAO solver and set desired solution method */
91:   TaoCreate(PETSC_COMM_SELF,&tao);
92:   TaoSetType(tao,TAOBRGN);

94:   /* User set application context: A, D matrice, and b vector. */
95:   InitializeUserData(&user);

97:   /* Set initial guess */
98:   FormStartingPoint(x);

100:   /* Fill the content of matrix D from user application Context */
101:   FormDictionaryMatrix(D,&user);

103:   /* Bind x to tao->solution. */
104:   TaoSetInitialVector(tao,x);
105:   /* Bind D to tao->data->D */
106:   TaoBRGNSetDictionaryMatrix(tao,D);

108:   /* Set the function and Jacobian routines. */
109:   TaoSetResidualRoutine(tao,f,EvaluateFunction,(void*)&user);
110:   TaoSetJacobianResidualRoutine(tao,J,J,EvaluateJacobian,(void*)&user);

112:   /* Check for any TAO command line arguments */
113:   TaoSetFromOptions(tao);

115:   TaoSetConvergenceHistory(tao,hist,resid,0,lits,100,PETSC_TRUE);

117:   /* Perform the Solve */
118:   TaoSolve(tao);

120:   /* XH: Debug: View the result, function and Jacobian.  */
121:   PetscPrintf(PETSC_COMM_SELF, "-------- result x, residual f=A*x-b, and Jacobian=A. -------- \n");
122:   VecView(x,PETSC_VIEWER_STDOUT_SELF);
123:   VecView(f,PETSC_VIEWER_STDOUT_SELF);
124:   MatView(J,PETSC_VIEWER_STDOUT_SELF);
125:   MatView(D,PETSC_VIEWER_STDOUT_SELF);

127:   /* Free TAO data structures */
128:   TaoDestroy(&tao);

130:    /* Free PETSc data structures */
131:   VecDestroy(&x);
132:   VecDestroy(&f);
133:   MatDestroy(&J);
134:   MatDestroy(&D);

136:   PetscFinalize();
137:   return ierr;
138: }

140: /*--------------------------------------------------------------------*/
141: PetscErrorCode EvaluateFunction(Tao tao, Vec X, Vec F, void *ptr)
142: {
143:   AppCtx         *user = (AppCtx *)ptr;
144:   PetscInt       m,n;
145:   const PetscReal *x;
146:   PetscReal      *b=user->b,*f;

151:   VecGetArray(F,&f);

153:   /* Even for linear least square, we do not direct use matrix operation f = A*x - b now, just for future modification and compatability for nonlinear least square */
154:   for (m=0;m<M;m++) {
155:     f[m] = -b[m];
156:     for (n=0;n<N;n++) {
157:       f[m] += user->A[m][n]*x[n];
158:     }
159:   }
161:   VecRestoreArray(F,&f);
162:   PetscLogFlops(M*N*2);
163:   return(0);
164: }

166: /*------------------------------------------------------------*/
167: /* J[m][n] = df[m]/dx[n] */
168: PetscErrorCode EvaluateJacobian(Tao tao, Vec X, Mat J, Mat Jpre, void *ptr)
169: {
170:   AppCtx         *user = (AppCtx *)ptr;
171:   PetscInt       m,n;
172:   const PetscReal *x;

176:   VecGetArrayRead(X,&x); /* not used for linear least square, but keep for future nonlinear least square) */
177:   /* 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?
178:     For nonlinear least square, we require x to compute J, keep codes here for future nonlinear least square*/
179:   for (m=0; m<M; ++m) {
180:     for (n=0; n<N; ++n) {
181:       user->J[m][n] = user->A[m][n];
182:     }
183:   }

185:   MatSetValues(J,M,user->idm,N,user->idn,(PetscReal *)user->J,INSERT_VALUES);
186:   MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
187:   MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);

189:   VecRestoreArrayRead(X,&x);/* not used for linear least square, but keep for future nonlinear least square) */
190:   PetscLogFlops(0);  /* 0 for linear least square, >0 for nonlinear least square */
191:   return(0);
192: }

194: /* ------------------------------------------------------------ */
195: /* Currently fixed matrix, in future may be dynamic for D(x)? */
196: PetscErrorCode FormDictionaryMatrix(Mat D,AppCtx *user)
197: {

201:   MatSetValues(D,K,user->idk,N,user->idn,(PetscReal *)user->D,INSERT_VALUES);
202:   MatAssemblyBegin(D,MAT_FINAL_ASSEMBLY);
203:   MatAssemblyEnd(D,MAT_FINAL_ASSEMBLY);

205:   PetscLogFlops(0); /* 0 for fixed dictionary matrix, >0 for varying dictionary matrix */
206:   return(0);
207: }

209: /* ------------------------------------------------------------ */
210: PetscErrorCode FormStartingPoint(Vec X)
211: {
214:   VecSet(X,0.0);
215:   return(0);
216: }

218: /* ---------------------------------------------------------------------- */
219: PetscErrorCode InitializeUserData(AppCtx *user)
220: {
221:   PetscReal *b=user->b; /* **A=user->A, but we don't kown the dimension of A in this way, how to fix? */
222:   PetscInt  m,n,k; /* loop index for M,N,K dimension. */

225:   /* b = A*x while x = [0;0;1;0;0] here*/
226:   m = 0;
227:   b[m++] = 0.28;
228:   b[m++] = 0.55;
229:   b[m++] = 0.96;

231:   /* matlab generated random matrix, uniformly distributed in [0,1] with 2 digits accuracy. rng(0); A = rand(M, N); A = round(A*100)/100;
232:   A = [0.81  0.91  0.28  0.96  0.96
233:        0.91  0.63  0.55  0.16  0.49
234:        0.13  0.10  0.96  0.97  0.80]
235:   */
236:   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;
237:   ++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;
238:   ++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;

240:   /* initialize to 0 */
241:   for (k=0; k<K; k++) {
242:     for (n=0; n<N; n++) {
243:       user->D[k][n] = 0.0;
244:     }
245:   }
246:   /* Choice I: set D to identity matrix of size N*N for testing */
247:   /* for (k=0; k<K; k++) user->D[k][k] = 1.0; */
248:   /* Choice II: set D to Backward difference matrix of size (N-1)*N, with zero extended boundary assumption */
249:   for (k=0;k<K;k++) {
250:       user->D[k][k]   = -1.0;
251:       user->D[k][k+1] = 1.0;
252:   }

254:   return(0);
255: }

257: /*TEST

259:    build:
260:       requires: !complex !single !quad !define(PETSC_USE_64BIT_INDICES)

262:    test:
263:       localrunfiles: cs1Data_A_b_xGT
264:       args: -tao_smonitor -tao_max_it 100 -tao_type pounders -tao_gatol 1.e-6

266:    test:
267:       suffix: 2
268:       localrunfiles: cs1Data_A_b_xGT
269:       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

271:    test:
272:       suffix: 3
273:       localrunfiles: cs1Data_A_b_xGT
274:       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

276:    test:
277:       suffix: 4
278:       localrunfiles: cs1Data_A_b_xGT
279:       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

281: TEST*/