Date: 2021-03-03T22:28:15+00:00

Actual source code: tomography.c
petsc-3.14.5 2021-03-03
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      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    - sysem 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";
     27: /*T
     28:    Concepts: TAO^Solving a system of nonlinear equations, nonlinear least squares
     29:    Routines: TaoCreate();
     30:    Routines: TaoSetType();
     31:    Routines: TaoSetSeparableObjectiveRoutine();
     32:    Routines: TaoSetJacobianRoutine();
     33:    Routines: TaoSetInitialVector();
     34:    Routines: TaoSetFromOptions();
     35:    Routines: TaoSetConvergenceHistory(); TaoGetConvergenceHistory();
     36:    Routines: TaoSolve();
     37:    Routines: TaoView(); TaoDestroy();
     38:    Processors: 1
     39: T*/

     41: /* User-defined application context */
     42: typedef struct {
     43:   /* Working space. linear least square:  res(x) = A*x - b */
     44:   PetscInt  M,N,K;            /* Problem dimension: A is M*N Matrix, D is K*N Matrix */
     45:   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 */
     46:   Vec       b,xGT,xlb,xub;    /* observation b, ground truth xGT, the lower bound and upper bound of x*/
     47: } AppCtx;

     49: /* User provided Routines */
     50: PetscErrorCode InitializeUserData(AppCtx *);
     51: PetscErrorCode FormStartingPoint(Vec,AppCtx *);
     52: PetscErrorCode EvaluateResidual(Tao,Vec,Vec,void *);
     53: PetscErrorCode EvaluateJacobian(Tao,Vec,Mat,Mat,void *);
     54: PetscErrorCode EvaluateRegularizerObjectiveAndGradient(Tao,Vec,PetscReal *,Vec,void*);
     55: PetscErrorCode EvaluateRegularizerHessian(Tao,Vec,Mat,void*);
     56: PetscErrorCode EvaluateRegularizerHessianProd(Mat,Vec,Vec);

     58: /*--------------------------------------------------------------------*/
     59: int main(int argc,char **argv)
     60: {
     62:   Vec            x,res;              /* solution, function res(x) = A*x-b */
     63:   Mat            Hreg;               /* regularizer Hessian matrix for user specified regularizer*/
     64:   Tao            tao;                /* Tao solver context */
     65:   PetscReal      hist[100],resid[100],v1,v2;
     66:   PetscInt       lits[100];
     67:   AppCtx         user;               /* user-defined work context */
     68:   PetscViewer    fd;   /* used to save result to file */
     69:   char           resultFile[] = "tomographyResult_x";  /* Debug: change from "tomographyResult_x" to "cs1Result_x" */

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

     73:   /* Create TAO solver and set desired solution method */
     74:   TaoCreate(PETSC_COMM_SELF,&tao);
     75:   TaoSetType(tao,TAOBRGN);

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

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

     84:   /* Set initial guess */
     85:   FormStartingPoint(x,&user);

     87:   /* Bind x to tao->solution. */
     88:   TaoSetInitialVector(tao,x);
     89:   /* Sets the upper and lower bounds of x */
     90:   TaoSetVariableBounds(tao,user.xlb,user.xub);

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

     95:   /* Set the residual function and Jacobian routines for least squares. */
     96:   TaoSetResidualRoutine(tao,res,EvaluateResidual,(void*)&user);
     97:   /* Jacobian matrix fixed as user.A for Linear least sqaure problem. */
     98:   TaoSetJacobianResidualRoutine(tao,user.A,user.A,EvaluateJacobian,(void*)&user);

    100:   /* User set the regularizer objective, gradient, and hessian. Set it the same as using l2prox choice, for testing purpose.  */
    101:   TaoBRGNSetRegularizerObjectiveAndGradientRoutine(tao,EvaluateRegularizerObjectiveAndGradient,(void*)&user);
    102:   /* User defined regularizer Hessian setup, here is identiy shell matrix */
    103:   MatCreate(PETSC_COMM_SELF,&Hreg);
    104:   MatSetSizes(Hreg,PETSC_DECIDE,PETSC_DECIDE,user.N,user.N);
    105:   MatSetType(Hreg,MATSHELL);
    106:   MatSetUp(Hreg);
    107:   MatShellSetOperation(Hreg,MATOP_MULT,(void (*)(void))EvaluateRegularizerHessianProd);
    108:   TaoBRGNSetRegularizerHessianRoutine(tao,Hreg,EvaluateRegularizerHessian,(void*)&user);

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

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

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

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

    123:   /* compute the error */
    124:   VecAXPY(x,-1,user.xGT);
    125:   VecNorm(x,NORM_2,&v1);
    126:   VecNorm(user.xGT,NORM_2,&v2);
    127:   PetscPrintf(PETSC_COMM_SELF, "relative reconstruction error: ||x-xGT||/||xGT|| = %6.4e.\n", (double)(v1/v2));

    129:   /* Free TAO data structures */
    130:   TaoDestroy(&tao);

    132:    /* Free PETSc data structures */
    133:   VecDestroy(&x);
    134:   VecDestroy(&res);
    135:   MatDestroy(&Hreg);
    136:   /* Free user data structures */
    137:   MatDestroy(&user.A);
    138:   MatDestroy(&user.D);
    139:   VecDestroy(&user.b);
    140:   VecDestroy(&user.xGT);
    141:   VecDestroy(&user.xlb);
    142:   VecDestroy(&user.xub);
    143:   PetscFinalize();
    144:   return ierr;
    145: }

    147: /*--------------------------------------------------------------------*/
    148: /* Evaluate residual function A(x)-b in least square problem ||A(x)-b||^2 */
    149: PetscErrorCode EvaluateResidual(Tao tao,Vec X,Vec F,void *ptr)
    150: {
    151:   AppCtx         *user = (AppCtx *)ptr;

    155:   /* Compute Ax - b */
    156:   MatMult(user->A,X,F);
    157:   VecAXPY(F,-1,user->b);
    158:   PetscLogFlops(2.0*user->M*user->N);
    159:   return(0);
    160: }

    162: /*------------------------------------------------------------*/
    163: PetscErrorCode EvaluateJacobian(Tao tao,Vec X,Mat J,Mat Jpre,void *ptr)
    164: {
    165:   /* 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 */
    167:   return(0);
    168: }

    170: /* ------------------------------------------------------------ */
    171: PetscErrorCode EvaluateRegularizerObjectiveAndGradient(Tao tao,Vec X,PetscReal *f_reg,Vec G_reg,void *ptr)
    172: {

    176:   /* compute regularizer objective = 0.5*x'*x */
    177:   VecDot(X,X,f_reg);
    178:   *f_reg *= 0.5;
    179:   /* compute regularizer gradient = x */
    180:   VecCopy(X,G_reg);
    181:   return(0);
    182: }

    184: PetscErrorCode EvaluateRegularizerHessianProd(Mat Hreg,Vec in,Vec out)
    185: {
    188:   VecCopy(in,out);
    189:   return(0);
    190: }

    192: /* ------------------------------------------------------------ */
    193: PetscErrorCode EvaluateRegularizerHessian(Tao tao,Vec X,Mat Hreg,void *ptr)
    194: {
    195:   /* Hessian for regularizer objective = 0.5*x'*x is identity matrix, and is not changing*/
    197:   return(0);
    198: }

    200: /* ------------------------------------------------------------ */
    201: PetscErrorCode FormStartingPoint(Vec X,AppCtx *user)
    202: {
    205:   VecSet(X,0.0);
    206:   return(0);
    207: }

    209: /* ---------------------------------------------------------------------- */
    210: PetscErrorCode InitializeUserData(AppCtx *user)
    211: {
    212:   PetscInt       k,n; /* indices for row and columns of D. */
    213:   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". */
    214:   PetscInt       dictChoice = 1; /* choose from 0:identity, 1:gradient1D, 2:gradient2D, 3:DCT etc */
    215:   PetscViewer    fd;   /* used to load data from file */
    217:   PetscReal      v;

    221:   /*
    222:   Matrix Vector read and write refer to:
    223:   https://www.mcs.anl.gov/petsc/petsc-current/src/mat/tutorials/ex10.c
    224:   https://www.mcs.anl.gov/petsc/petsc-current/src/mat/tutorials/ex12.c
    225:  */
    226:   /* Load the A matrix, b vector, and xGT vector from a binary file. */
    227:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,dataFile,FILE_MODE_READ,&fd);
    228:   MatCreate(PETSC_COMM_WORLD,&user->A);
    229:   MatSetType(user->A,MATSEQAIJ);
    230:   MatLoad(user->A,fd);
    231:   VecCreate(PETSC_COMM_WORLD,&user->b);
    232:   VecLoad(user->b,fd);
    233:   VecCreate(PETSC_COMM_WORLD,&user->xGT);
    234:   VecLoad(user->xGT,fd);
    235:   PetscViewerDestroy(&fd);
    236:   VecDuplicate(user->xGT,&(user->xlb));
    237:   VecSet(user->xlb,0.0);
    238:   VecDuplicate(user->xGT,&(user->xub));
    239:   VecSet(user->xub,PETSC_INFINITY);

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

    244:   /* 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.
    245:   if (dictChoice == 0) {
    246:     user->D = NULL;
    247:     return(0);
    248:   }
    249:   */

    251:   /* Speficy D */
    252:   /* (1) Specify D Size */
    253:   switch (dictChoice) {
    254:     case 0: /* 0:identity */
    255:       user->K = user->N;
    256:       break;
    257:     case 1: /* 1:gradient1D */
    258:       user->K = user->N-1;
    259:       break;
    260:   }

    262:   MatCreate(PETSC_COMM_SELF,&user->D);
    263:   MatSetSizes(user->D,PETSC_DECIDE,PETSC_DECIDE,user->K,user->N);
    264:   MatSetFromOptions(user->D);
    265:   MatSetUp(user->D);

    267:   /* (2) Specify D Content */
    268:   switch (dictChoice) {
    269:     case 0: /* 0:identity */
    270:       for (k=0; k<user->K; k++) {
    271:         v = 1.0;
    272:         MatSetValues(user->D,1,&k,1,&k,&v,INSERT_VALUES);
    273:       }
    274:       break;
    275:     case 1: /* 1:gradient1D.  [-1, 1, 0,...; 0, -1, 1, 0, ...] */
    276:       for (k=0; k<user->K; k++) {
    277:         v = 1.0;
    278:         n = k+1;
    279:         MatSetValues(user->D,1,&k,1,&n,&v,INSERT_VALUES);
    280:         v = -1.0;
    281:         MatSetValues(user->D,1,&k,1,&k,&v,INSERT_VALUES);
    282:       }
    283:       break;
    284:   }
    285:   MatAssemblyBegin(user->D,MAT_FINAL_ASSEMBLY);
    286:   MatAssemblyEnd(user->D,MAT_FINAL_ASSEMBLY);

    288:   return(0);
    289: }

    291: /*TEST

    293:    build:
    294:       requires: !complex !single !__float128 !define(PETSC_USE_64BIT_INDICES)

    296:    test:
    297:       localrunfiles: tomographyData_A_b_xGT
    298:       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

    300:    test:
    301:       suffix: 2
    302:       localrunfiles: tomographyData_A_b_xGT
    303:       args: -tao_monitor -tao_max_it 1000 -tao_brgn_regularization_type l2prox -tao_brgn_regularizer_weight 1e-8 -tao_gatol 1.e-6

    305:    test:
    306:       suffix: 3
    307:       localrunfiles: tomographyData_A_b_xGT
    308:       args: -tao_monitor -tao_max_it 1000 -tao_brgn_regularization_type user -tao_brgn_regularizer_weight 1e-8 -tao_gatol 1.e-6

    310: TEST*/