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    - 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;

    150:   VecGetArrayRead(X,&x);
    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:   }
    160:   VecRestoreArrayRead(X,&x);
    161:   VecRestoreArray(F,&f);
    162:   PetscLogFlops(2.0*M*N);
    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 -tao_brgn_subsolver_ksp_converged_reason

    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:
    282:       suffix: 5
    283:       localrunfiles: cs1Data_A_b_xGT
    284:       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

    286: TEST*/