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

 75:   PetscInitialize(&argc,&argv,(char *)0,help);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

135:   PetscFinalize();
136:   return 0;
137: }

139: /*--------------------------------------------------------------------*/
140: PetscErrorCode EvaluateFunction(Tao tao, Vec X, Vec F, void *ptr)
141: {
142:   AppCtx         *user = (AppCtx *)ptr;
143:   PetscInt       m,n;
144:   const PetscReal *x;
145:   PetscReal      *b=user->b,*f;

147:   VecGetArrayRead(X,&x);
148:   VecGetArray(F,&f);

150:   /* 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 */
151:   for (m=0;m<M;m++) {
152:     f[m] = -b[m];
153:     for (n=0;n<N;n++) {
154:       f[m] += user->A[m][n]*x[n];
155:     }
156:   }
157:   VecRestoreArrayRead(X,&x);
158:   VecRestoreArray(F,&f);
159:   PetscLogFlops(2.0*M*N);
160:   return 0;
161: }

163: /*------------------------------------------------------------*/
164: /* J[m][n] = df[m]/dx[n] */
165: PetscErrorCode EvaluateJacobian(Tao tao, Vec X, Mat J, Mat Jpre, void *ptr)
166: {
167:   AppCtx         *user = (AppCtx *)ptr;
168:   PetscInt       m,n;
169:   const PetscReal *x;

171:   VecGetArrayRead(X,&x); /* not used for linear least square, but keep for future nonlinear least square) */
172:   /* 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?
173:     For nonlinear least square, we require x to compute J, keep codes here for future nonlinear least square*/
174:   for (m=0; m<M; ++m) {
175:     for (n=0; n<N; ++n) {
176:       user->J[m][n] = user->A[m][n];
177:     }
178:   }

180:   MatSetValues(J,M,user->idm,N,user->idn,(PetscReal *)user->J,INSERT_VALUES);
181:   MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
182:   MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);

184:   VecRestoreArrayRead(X,&x);/* not used for linear least square, but keep for future nonlinear least square) */
185:   PetscLogFlops(0);  /* 0 for linear least square, >0 for nonlinear least square */
186:   return 0;
187: }

189: /* ------------------------------------------------------------ */
190: /* Currently fixed matrix, in future may be dynamic for D(x)? */
191: PetscErrorCode FormDictionaryMatrix(Mat D,AppCtx *user)
192: {
193:   MatSetValues(D,K,user->idk,N,user->idn,(PetscReal *)user->D,INSERT_VALUES);
194:   MatAssemblyBegin(D,MAT_FINAL_ASSEMBLY);
195:   MatAssemblyEnd(D,MAT_FINAL_ASSEMBLY);

197:   PetscLogFlops(0); /* 0 for fixed dictionary matrix, >0 for varying dictionary matrix */
198:   return 0;
199: }

201: /* ------------------------------------------------------------ */
202: PetscErrorCode FormStartingPoint(Vec X)
203: {
204:   VecSet(X,0.0);
205:   return 0;
206: }

208: /* ---------------------------------------------------------------------- */
209: PetscErrorCode InitializeUserData(AppCtx *user)
210: {
211:   PetscReal *b=user->b; /* **A=user->A, but we don't kown the dimension of A in this way, how to fix? */
212:   PetscInt  m,n,k; /* loop index for M,N,K dimension. */

214:   /* b = A*x while x = [0;0;1;0;0] here*/
215:   m = 0;
216:   b[m++] = 0.28;
217:   b[m++] = 0.55;
218:   b[m++] = 0.96;

220:   /* matlab generated random matrix, uniformly distributed in [0,1] with 2 digits accuracy. rng(0); A = rand(M, N); A = round(A*100)/100;
221:   A = [0.81  0.91  0.28  0.96  0.96
222:        0.91  0.63  0.55  0.16  0.49
223:        0.13  0.10  0.96  0.97  0.80]
224:   */
225:   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;
226:   ++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;
227:   ++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;

229:   /* initialize to 0 */
230:   for (k=0; k<K; k++) {
231:     for (n=0; n<N; n++) {
232:       user->D[k][n] = 0.0;
233:     }
234:   }
235:   /* Choice I: set D to identity matrix of size N*N for testing */
236:   /* for (k=0; k<K; k++) user->D[k][k] = 1.0; */
237:   /* Choice II: set D to Backward difference matrix of size (N-1)*N, with zero extended boundary assumption */
238:   for (k=0;k<K;k++) {
239:       user->D[k][k]   = -1.0;
240:       user->D[k][k+1] = 1.0;
241:   }

243:   return 0;
244: }

246: /*TEST

248:    build:
249:       requires: !complex !single !quad !defined(PETSC_USE_64BIT_INDICES)

251:    test:
252:       localrunfiles: cs1Data_A_b_xGT
253:       args: -tao_smonitor -tao_max_it 100 -tao_type pounders -tao_gatol 1.e-6

255:    test:
256:       suffix: 2
257:       localrunfiles: cs1Data_A_b_xGT
258:       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

260:    test:
261:       suffix: 3
262:       localrunfiles: cs1Data_A_b_xGT
263:       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

265:    test:
266:       suffix: 4
267:       localrunfiles: cs1Data_A_b_xGT
268:       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

270:    test:
271:       suffix: 5
272:       localrunfiles: cs1Data_A_b_xGT
273:       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

275: TEST*/