Date: 2022-08-02T03:15:16+00:00

Actual source code: tomography.c

      1: /* XH:
      2:     Todo: add cs1f.F90 and adjust makefile.
      3:     Todo: maybe provide code template to generate 1D/2D/3D gradient, DCT transform matrix for D etc.
      4: */
      5: /*
      6:    Include "petsctao.h" so that we can use TAO solvers.  Note that this
      7:    file automatically includes libraries such as:
      8:      petsc.h       - base PETSc routines   petscvec.h - vectors
      9:      petscsys.h    - system routines        petscmat.h - matrices
     10:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     11:      petscviewer.h - viewers               petscpc.h  - preconditioners

     13: */

     15: #include <petsctao.h>

     17: /*
     18: Description:   BRGN tomography reconstruction example .
     19:                0.5*||Ax-b||^2 + lambda*g(x)
     20: Reference:     None
     21: */

     23: static char help[] = "Finds the least-squares solution to the under constraint linear model Ax = b, with regularizer. \n\
     24:             A is a M*N real matrix (M<N), x is sparse. A good regularizer is an L1 regularizer. \n\
     25:             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\
     26:             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";

     28: /* User-defined application context */
     29: typedef struct {
     30:   /* Working space. linear least square:  res(x) = A*x - b */
     31:   PetscInt  M,N,K;            /* Problem dimension: A is M*N Matrix, D is K*N Matrix */
     32:   Mat       A,D;              /* Coefficients, Dictionary Transform of size M*N and K*N respectively. For linear least square, Jacobian Matrix J = A. For nonlinear least square, it is different from A */
     33:   Vec       b,xGT,xlb,xub;    /* observation b, ground truth xGT, the lower bound and upper bound of x*/
     34: } AppCtx;

     36: /* User provided Routines */
     37: PetscErrorCode InitializeUserData(AppCtx *);
     38: PetscErrorCode FormStartingPoint(Vec,AppCtx *);
     39: PetscErrorCode EvaluateResidual(Tao,Vec,Vec,void *);
     40: PetscErrorCode EvaluateJacobian(Tao,Vec,Mat,Mat,void *);
     41: PetscErrorCode EvaluateRegularizerObjectiveAndGradient(Tao,Vec,PetscReal *,Vec,void*);
     42: PetscErrorCode EvaluateRegularizerHessian(Tao,Vec,Mat,void*);
     43: PetscErrorCode EvaluateRegularizerHessianProd(Mat,Vec,Vec);

     45: /*--------------------------------------------------------------------*/
     46: int main(int argc,char **argv)
     47: {
     48:   Vec            x,res;              /* solution, function res(x) = A*x-b */
     49:   Mat            Hreg;               /* regularizer Hessian matrix for user specified regularizer*/
     50:   Tao            tao;                /* Tao solver context */
     51:   PetscReal      hist[100],resid[100],v1,v2;
     52:   PetscInt       lits[100];
     53:   AppCtx         user;               /* user-defined work context */
     54:   PetscViewer    fd;   /* used to save result to file */
     55:   char           resultFile[] = "tomographyResult_x";  /* Debug: change from "tomographyResult_x" to "cs1Result_x" */

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

     59:   /* Create TAO solver and set desired solution method */
     60:   TaoCreate(PETSC_COMM_SELF,&tao);
     61:   TaoSetType(tao,TAOBRGN);

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

     66:   /* Allocate solution vector x,  and function vectors Ax-b, */
     67:   VecCreateSeq(PETSC_COMM_SELF,user.N,&x);
     68:   VecCreateSeq(PETSC_COMM_SELF,user.M,&res);

     70:   /* Set initial guess */
     71:   FormStartingPoint(x,&user);

     73:   /* Bind x to tao->solution. */
     74:   TaoSetSolution(tao,x);
     75:   /* Sets the upper and lower bounds of x */
     76:   TaoSetVariableBounds(tao,user.xlb,user.xub);

     78:   /* Bind user.D to tao->data->D */
     79:   TaoBRGNSetDictionaryMatrix(tao,user.D);

     81:   /* Set the residual function and Jacobian routines for least squares. */
     82:   TaoSetResidualRoutine(tao,res,EvaluateResidual,(void*)&user);
     83:   /* Jacobian matrix fixed as user.A for Linear least square problem. */
     84:   TaoSetJacobianResidualRoutine(tao,user.A,user.A,EvaluateJacobian,(void*)&user);

     86:   /* User set the regularizer objective, gradient, and hessian. Set it the same as using l2prox choice, for testing purpose.  */
     87:   TaoBRGNSetRegularizerObjectiveAndGradientRoutine(tao,EvaluateRegularizerObjectiveAndGradient,(void*)&user);
     88:   /* User defined regularizer Hessian setup, here is identiy shell matrix */
     89:   MatCreate(PETSC_COMM_SELF,&Hreg);
     90:   MatSetSizes(Hreg,PETSC_DECIDE,PETSC_DECIDE,user.N,user.N);
     91:   MatSetType(Hreg,MATSHELL);
     92:   MatSetUp(Hreg);
     93:   MatShellSetOperation(Hreg,MATOP_MULT,(void (*)(void))EvaluateRegularizerHessianProd);
     94:   TaoBRGNSetRegularizerHessianRoutine(tao,Hreg,EvaluateRegularizerHessian,(void*)&user);

     96:   /* Check for any TAO command line arguments */
     97:   TaoSetFromOptions(tao);

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

    101:   /* Perform the Solve */
    102:   TaoSolve(tao);

    104:   /* Save x (reconstruction of object) vector to a binary file, which maybe read from Matlab and convert to a 2D image for comparison. */
    105:   PetscViewerBinaryOpen(PETSC_COMM_SELF,resultFile,FILE_MODE_WRITE,&fd);
    106:   VecView(x,fd);
    107:   PetscViewerDestroy(&fd);

    109:   /* compute the error */
    110:   VecAXPY(x,-1,user.xGT);
    111:   VecNorm(x,NORM_2,&v1);
    112:   VecNorm(user.xGT,NORM_2,&v2);
    113:   PetscPrintf(PETSC_COMM_SELF, "relative reconstruction error: ||x-xGT||/||xGT|| = %6.4e.\n", (double)(v1/v2));

    115:   /* Free TAO data structures */
    116:   TaoDestroy(&tao);

    118:    /* Free PETSc data structures */
    119:   VecDestroy(&x);
    120:   VecDestroy(&res);
    121:   MatDestroy(&Hreg);
    122:   /* Free user data structures */
    123:   MatDestroy(&user.A);
    124:   MatDestroy(&user.D);
    125:   VecDestroy(&user.b);
    126:   VecDestroy(&user.xGT);
    127:   VecDestroy(&user.xlb);
    128:   VecDestroy(&user.xub);
    129:   PetscFinalize();
    130:   return 0;
    131: }

    133: /*--------------------------------------------------------------------*/
    134: /* Evaluate residual function A(x)-b in least square problem ||A(x)-b||^2 */
    135: PetscErrorCode EvaluateResidual(Tao tao,Vec X,Vec F,void *ptr)
    136: {
    137:   AppCtx         *user = (AppCtx *)ptr;

    139:   /* Compute Ax - b */
    140:   MatMult(user->A,X,F);
    141:   VecAXPY(F,-1,user->b);
    142:   PetscLogFlops(2.0*user->M*user->N);
    143:   return 0;
    144: }

    146: /*------------------------------------------------------------*/
    147: PetscErrorCode EvaluateJacobian(Tao tao,Vec X,Mat J,Mat Jpre,void *ptr)
    148: {
    149:   /* Jacobian is not changing here, so use a empty dummy function here.  J[m][n] = df[m]/dx[n] = A[m][n] for linear least square */
    150:   return 0;
    151: }

    153: /* ------------------------------------------------------------ */
    154: PetscErrorCode EvaluateRegularizerObjectiveAndGradient(Tao tao,Vec X,PetscReal *f_reg,Vec G_reg,void *ptr)
    155: {
    156:   /* compute regularizer objective = 0.5*x'*x */
    157:   VecDot(X,X,f_reg);
    158:   *f_reg *= 0.5;
    159:   /* compute regularizer gradient = x */
    160:   VecCopy(X,G_reg);
    161:   return 0;
    162: }

    164: PetscErrorCode EvaluateRegularizerHessianProd(Mat Hreg,Vec in,Vec out)
    165: {
    166:   VecCopy(in,out);
    167:   return 0;
    168: }

    170: /* ------------------------------------------------------------ */
    171: PetscErrorCode EvaluateRegularizerHessian(Tao tao,Vec X,Mat Hreg,void *ptr)
    172: {
    173:   /* Hessian for regularizer objective = 0.5*x'*x is identity matrix, and is not changing*/
    174:   return 0;
    175: }

    177: /* ------------------------------------------------------------ */
    178: PetscErrorCode FormStartingPoint(Vec X,AppCtx *user)
    179: {
    180:   VecSet(X,0.0);
    181:   return 0;
    182: }

    184: /* ---------------------------------------------------------------------- */
    185: PetscErrorCode InitializeUserData(AppCtx *user)
    186: {
    187:   PetscInt       k,n; /* indices for row and columns of D. */
    188:   char           dataFile[] = "tomographyData_A_b_xGT";   /* Matrix A and vectors b, xGT(ground truth) binary files generated by Matlab. Debug: change from "tomographyData_A_b_xGT" to "cs1Data_A_b_xGT". */
    189:   PetscInt       dictChoice = 1; /* choose from 0:identity, 1:gradient1D, 2:gradient2D, 3:DCT etc */
    190:   PetscViewer    fd;   /* used to load data from file */
    191:   PetscReal      v;

    194:   /*
    195:   Matrix Vector read and write refer to:
    196:   https://petsc.org/release/src/mat/tutorials/ex10.c
    197:   https://petsc.org/release/src/mat/tutorials/ex12.c
    198:  */
    199:   /* Load the A matrix, b vector, and xGT vector from a binary file. */
    200:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,dataFile,FILE_MODE_READ,&fd);
    201:   MatCreate(PETSC_COMM_WORLD,&user->A);
    202:   MatSetType(user->A,MATSEQAIJ);
    203:   MatLoad(user->A,fd);
    204:   VecCreate(PETSC_COMM_WORLD,&user->b);
    205:   VecLoad(user->b,fd);
    206:   VecCreate(PETSC_COMM_WORLD,&user->xGT);
    207:   VecLoad(user->xGT,fd);
    208:   PetscViewerDestroy(&fd);
    209:   VecDuplicate(user->xGT,&(user->xlb));
    210:   VecSet(user->xlb,0.0);
    211:   VecDuplicate(user->xGT,&(user->xub));
    212:   VecSet(user->xub,PETSC_INFINITY);

    214:   /* Specify the size */
    215:   MatGetSize(user->A,&user->M,&user->N);

    217:   /* shortcut, when D is identity matrix, we may just specify it as NULL, and brgn will treat D*x as x without actually computing D*x.
    218:   if (dictChoice == 0) {
    219:     user->D = NULL;
    220:     return 0;
    221:   }
    222:   */

    224:   /* Speficy D */
    225:   /* (1) Specify D Size */
    226:   switch (dictChoice) {
    227:     case 0: /* 0:identity */
    228:       user->K = user->N;
    229:       break;
    230:     case 1: /* 1:gradient1D */
    231:       user->K = user->N-1;
    232:       break;
    233:   }

    235:   MatCreate(PETSC_COMM_SELF,&user->D);
    236:   MatSetSizes(user->D,PETSC_DECIDE,PETSC_DECIDE,user->K,user->N);
    237:   MatSetFromOptions(user->D);
    238:   MatSetUp(user->D);

    240:   /* (2) Specify D Content */
    241:   switch (dictChoice) {
    242:     case 0: /* 0:identity */
    243:       for (k=0; k<user->K; k++) {
    244:         v = 1.0;
    245:         MatSetValues(user->D,1,&k,1,&k,&v,INSERT_VALUES);
    246:       }
    247:       break;
    248:     case 1: /* 1:gradient1D.  [-1, 1, 0,...; 0, -1, 1, 0, ...] */
    249:       for (k=0; k<user->K; k++) {
    250:         v = 1.0;
    251:         n = k+1;
    252:         MatSetValues(user->D,1,&k,1,&n,&v,INSERT_VALUES);
    253:         v = -1.0;
    254:         MatSetValues(user->D,1,&k,1,&k,&v,INSERT_VALUES);
    255:       }
    256:       break;
    257:   }
    258:   MatAssemblyBegin(user->D,MAT_FINAL_ASSEMBLY);
    259:   MatAssemblyEnd(user->D,MAT_FINAL_ASSEMBLY);

    261:   return 0;
    262: }

    264: /*TEST

    266:    build:
    267:       requires: !complex !single !__float128 !defined(PETSC_USE_64BIT_INDICES)

    269:    test:
    270:       localrunfiles: tomographyData_A_b_xGT
    271:       args: -tao_max_it 1000 -tao_brgn_regularization_type l1dict -tao_brgn_regularizer_weight 1e-8 -tao_brgn_l1_smooth_epsilon 1e-6 -tao_gatol 1.e-8

    273:    test:
    274:       suffix: 2
    275:       localrunfiles: tomographyData_A_b_xGT
    276:       args: -tao_monitor -tao_max_it 1000 -tao_brgn_regularization_type l2prox -tao_brgn_regularizer_weight 1e-8 -tao_gatol 1.e-6

    278:    test:
    279:       suffix: 3
    280:       localrunfiles: tomographyData_A_b_xGT
    281:       args: -tao_monitor -tao_max_it 1000 -tao_brgn_regularization_type user -tao_brgn_regularizer_weight 1e-8 -tao_gatol 1.e-6

    283: TEST*/