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*/