xref: /petsc/src/tao/constrained/tutorials/tomographyADMM.c (revision 3ba1676111f5c958fe6c2729b46ca4d523958bb3)

#include <petsctao.h>
/*
Description:   ADMM tomography reconstruction example .
               0.5*||Ax-b||^2 + lambda*g(x)
Reference:     BRGN Tomography Example
*/

static char help[] = "Finds the ADMM solution to the under constraint linear model Ax = b, with regularizer. \n\
                      A is a M*N real matrix (M<N), x is sparse. A good regularizer is an L1 regularizer. \n\
                      We first split the operator into 0.5*||Ax-b||^2, f(x), and lambda*||x||_1, g(z), where lambda is user specified weight. \n\
                      g(z) could be either ||z||_1, or ||z||_2^2. Default closed form solution for NORM1 would be soft-threshold, which is \n\
                      natively supported in admm.c with -tao_admm_regularizer_type soft-threshold. Or user can use regular TAO solver for  \n\
                      either NORM1 or NORM2 or TAOSHELL, with -reg {1,2,3} \n\
                      Then, we augment both f and g, and solve it via ADMM. \n\
                      D is the M*N transform matrix so that D*x is sparse. \n";

typedef struct {
  PetscInt  M, N, K, reg;
  PetscReal lambda, eps, mumin;
  Mat       A, ATA, H, Hx, D, Hz, DTD, HF;
  Vec       c, xlb, xub, x, b, workM, workN, workN2, workN3, xGT; /* observation b, ground truth xGT, the lower bound and upper bound of x*/
} AppCtx;

/*------------------------------------------------------------*/

PetscErrorCode NullJacobian(Tao tao, Vec X, Mat J, Mat Jpre, void *ptr)
{
  PetscFunctionBegin;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*------------------------------------------------------------*/

static PetscErrorCode TaoShellSolve_SoftThreshold(Tao tao)
{
  PetscReal lambda, mu;
  AppCtx   *user;
  Vec       out, work, y, x;
  Tao       admm_tao, misfit;

  PetscFunctionBegin;
  user = NULL;
  mu   = 0;
  PetscCall(TaoGetADMMParentTao(tao, &admm_tao));
  PetscCall(TaoADMMGetMisfitSubsolver(admm_tao, &misfit));
  PetscCall(TaoADMMGetSpectralPenalty(admm_tao, &mu));
  PetscCall(TaoShellGetContext(tao, &user));

  lambda = user->lambda;
  work   = user->workN;
  PetscCall(TaoGetSolution(tao, &out));
  PetscCall(TaoGetSolution(misfit, &x));
  PetscCall(TaoADMMGetDualVector(admm_tao, &y));

  /* Dx + y/mu */
  PetscCall(MatMult(user->D, x, work));
  PetscCall(VecAXPY(work, 1 / mu, y));

  /* soft thresholding */
  PetscCall(TaoSoftThreshold(work, -lambda / mu, lambda / mu, out));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*------------------------------------------------------------*/

PetscErrorCode MisfitObjectiveAndGradient(Tao tao, Vec X, PetscReal *f, Vec g, void *ptr)
{
  AppCtx *user = (AppCtx *)ptr;

  PetscFunctionBegin;
  /* Objective  0.5*||Ax-b||_2^2 */
  PetscCall(MatMult(user->A, X, user->workM));
  PetscCall(VecAXPY(user->workM, -1, user->b));
  PetscCall(VecDot(user->workM, user->workM, f));
  *f *= 0.5;
  /* Gradient. ATAx-ATb */
  PetscCall(MatMult(user->ATA, X, user->workN));
  PetscCall(MatMultTranspose(user->A, user->b, user->workN2));
  PetscCall(VecWAXPY(g, -1., user->workN2, user->workN));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*------------------------------------------------------------*/

PetscErrorCode RegularizerObjectiveAndGradient1(Tao tao, Vec X, PetscReal *f_reg, Vec G_reg, void *ptr)
{
  AppCtx *user = (AppCtx *)ptr;

  PetscFunctionBegin;
  /* compute regularizer objective
   * f = f + lambda*sum(sqrt(y.^2+epsilon^2) - epsilon), where y = D*x */
  PetscCall(VecCopy(X, user->workN2));
  PetscCall(VecPow(user->workN2, 2.));
  PetscCall(VecShift(user->workN2, user->eps * user->eps));
  PetscCall(VecSqrtAbs(user->workN2));
  PetscCall(VecCopy(user->workN2, user->workN3));
  PetscCall(VecShift(user->workN2, -user->eps));
  PetscCall(VecSum(user->workN2, f_reg));
  *f_reg *= user->lambda;
  /* compute regularizer gradient = lambda*x */
  PetscCall(VecPointwiseDivide(G_reg, X, user->workN3));
  PetscCall(VecScale(G_reg, user->lambda));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*------------------------------------------------------------*/

PetscErrorCode RegularizerObjectiveAndGradient2(Tao tao, Vec X, PetscReal *f_reg, Vec G_reg, void *ptr)
{
  AppCtx   *user = (AppCtx *)ptr;
  PetscReal temp;

  PetscFunctionBegin;
  /* compute regularizer objective = lambda*|z|_2^2 */
  PetscCall(VecDot(X, X, &temp));
  *f_reg = 0.5 * user->lambda * temp;
  /* compute regularizer gradient = lambda*z */
  PetscCall(VecCopy(X, G_reg));
  PetscCall(VecScale(G_reg, user->lambda));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*------------------------------------------------------------*/

static PetscErrorCode HessianMisfit(Tao tao, Vec x, Mat H, Mat Hpre, void *ptr)
{
  PetscFunctionBegin;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*------------------------------------------------------------*/

static PetscErrorCode HessianReg(Tao tao, Vec x, Mat H, Mat Hpre, void *ptr)
{
  AppCtx *user = (AppCtx *)ptr;

  PetscFunctionBegin;
  PetscCall(MatMult(user->D, x, user->workN));
  PetscCall(VecPow(user->workN2, 2.));
  PetscCall(VecShift(user->workN2, user->eps * user->eps));
  PetscCall(VecSqrtAbs(user->workN2));
  PetscCall(VecShift(user->workN2, -user->eps));
  PetscCall(VecReciprocal(user->workN2));
  PetscCall(VecScale(user->workN2, user->eps * user->eps));
  PetscCall(MatDiagonalSet(H, user->workN2, INSERT_VALUES));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*------------------------------------------------------------*/

PetscErrorCode FullObjGrad(Tao tao, Vec X, PetscReal *f, Vec g, void *ptr)
{
  AppCtx   *user = (AppCtx *)ptr;
  PetscReal f_reg;

  PetscFunctionBegin;
  /* Objective  0.5*||Ax-b||_2^2 + lambda*||x||_2^2*/
  PetscCall(MatMult(user->A, X, user->workM));
  PetscCall(VecAXPY(user->workM, -1, user->b));
  PetscCall(VecDot(user->workM, user->workM, f));
  PetscCall(VecNorm(X, NORM_2, &f_reg));
  *f *= 0.5;
  *f += user->lambda * f_reg * f_reg;
  /* Gradient. ATAx-ATb + 2*lambda*x */
  PetscCall(MatMult(user->ATA, X, user->workN));
  PetscCall(MatMultTranspose(user->A, user->b, user->workN2));
  PetscCall(VecWAXPY(g, -1., user->workN2, user->workN));
  PetscCall(VecAXPY(g, 2 * user->lambda, X));
  PetscFunctionReturn(PETSC_SUCCESS);
}
/*------------------------------------------------------------*/

static PetscErrorCode HessianFull(Tao tao, Vec x, Mat H, Mat Hpre, void *ptr)
{
  PetscFunctionBegin;
  PetscFunctionReturn(PETSC_SUCCESS);
}
/*------------------------------------------------------------*/

PetscErrorCode InitializeUserData(AppCtx *user)
{
  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". */
  PetscViewer fd;                                    /* used to load data from file */
  PetscInt    k, n;
  PetscScalar v;

  PetscFunctionBegin;
  /* Load the A matrix, b vector, and xGT vector from a binary file. */
  PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD, dataFile, FILE_MODE_READ, &fd));
  PetscCall(MatCreate(PETSC_COMM_WORLD, &user->A));
  PetscCall(MatSetType(user->A, MATAIJ));
  PetscCall(MatLoad(user->A, fd));
  PetscCall(VecCreate(PETSC_COMM_WORLD, &user->b));
  PetscCall(VecLoad(user->b, fd));
  PetscCall(VecCreate(PETSC_COMM_WORLD, &user->xGT));
  PetscCall(VecLoad(user->xGT, fd));
  PetscCall(PetscViewerDestroy(&fd));

  PetscCall(MatGetSize(user->A, &user->M, &user->N));

  PetscCall(MatCreate(PETSC_COMM_WORLD, &user->D));
  PetscCall(MatSetSizes(user->D, PETSC_DECIDE, PETSC_DECIDE, user->N, user->N));
  PetscCall(MatSetFromOptions(user->D));
  PetscCall(MatSetUp(user->D));
  for (k = 0; k < user->N; k++) {
    v = 1.0;
    n = k + 1;
    if (k < user->N - 1) PetscCall(MatSetValues(user->D, 1, &k, 1, &n, &v, INSERT_VALUES));
    v = -1.0;
    PetscCall(MatSetValues(user->D, 1, &k, 1, &k, &v, INSERT_VALUES));
  }
  PetscCall(MatAssemblyBegin(user->D, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(user->D, MAT_FINAL_ASSEMBLY));

  PetscCall(MatTransposeMatMult(user->D, user->D, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &user->DTD));

  PetscCall(MatCreate(PETSC_COMM_WORLD, &user->Hz));
  PetscCall(MatSetSizes(user->Hz, PETSC_DECIDE, PETSC_DECIDE, user->N, user->N));
  PetscCall(MatSetFromOptions(user->Hz));
  PetscCall(MatSetUp(user->Hz));
  PetscCall(MatAssemblyBegin(user->Hz, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(user->Hz, MAT_FINAL_ASSEMBLY));

  PetscCall(VecCreate(PETSC_COMM_WORLD, &(user->x)));
  PetscCall(VecCreate(PETSC_COMM_WORLD, &(user->workM)));
  PetscCall(VecCreate(PETSC_COMM_WORLD, &(user->workN)));
  PetscCall(VecCreate(PETSC_COMM_WORLD, &(user->workN2)));
  PetscCall(VecSetSizes(user->x, PETSC_DECIDE, user->N));
  PetscCall(VecSetSizes(user->workM, PETSC_DECIDE, user->M));
  PetscCall(VecSetSizes(user->workN, PETSC_DECIDE, user->N));
  PetscCall(VecSetSizes(user->workN2, PETSC_DECIDE, user->N));
  PetscCall(VecSetFromOptions(user->x));
  PetscCall(VecSetFromOptions(user->workM));
  PetscCall(VecSetFromOptions(user->workN));
  PetscCall(VecSetFromOptions(user->workN2));

  PetscCall(VecDuplicate(user->workN, &(user->workN3)));
  PetscCall(VecDuplicate(user->x, &(user->xlb)));
  PetscCall(VecDuplicate(user->x, &(user->xub)));
  PetscCall(VecDuplicate(user->x, &(user->c)));
  PetscCall(VecSet(user->xlb, 0.0));
  PetscCall(VecSet(user->c, 0.0));
  PetscCall(VecSet(user->xub, PETSC_INFINITY));

  PetscCall(MatTransposeMatMult(user->A, user->A, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &(user->ATA)));
  PetscCall(MatTransposeMatMult(user->A, user->A, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &(user->Hx)));
  PetscCall(MatTransposeMatMult(user->A, user->A, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &(user->HF)));

  PetscCall(MatAssemblyBegin(user->ATA, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(user->ATA, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyBegin(user->Hx, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(user->Hx, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyBegin(user->HF, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(user->HF, MAT_FINAL_ASSEMBLY));

  user->lambda = 1.e-8;
  user->eps    = 1.e-3;
  user->reg    = 2;
  user->mumin  = 5.e-6;

  PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Configure separable objection example", "tomographyADMM.c");
  PetscCall(PetscOptionsInt("-reg", "Regularization scheme for z solver (1,2)", "tomographyADMM.c", user->reg, &(user->reg), NULL));
  PetscCall(PetscOptionsReal("-lambda", "The regularization multiplier. 1 default", "tomographyADMM.c", user->lambda, &(user->lambda), NULL));
  PetscCall(PetscOptionsReal("-eps", "L1 norm epsilon padding", "tomographyADMM.c", user->eps, &(user->eps), NULL));
  PetscCall(PetscOptionsReal("-mumin", "Minimum value for ADMM spectral penalty", "tomographyADMM.c", user->mumin, &(user->mumin), NULL));
  PetscOptionsEnd();
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*------------------------------------------------------------*/

PetscErrorCode DestroyContext(AppCtx *user)
{
  PetscFunctionBegin;
  PetscCall(MatDestroy(&user->A));
  PetscCall(MatDestroy(&user->ATA));
  PetscCall(MatDestroy(&user->Hx));
  PetscCall(MatDestroy(&user->Hz));
  PetscCall(MatDestroy(&user->HF));
  PetscCall(MatDestroy(&user->D));
  PetscCall(MatDestroy(&user->DTD));
  PetscCall(VecDestroy(&user->xGT));
  PetscCall(VecDestroy(&user->xlb));
  PetscCall(VecDestroy(&user->xub));
  PetscCall(VecDestroy(&user->b));
  PetscCall(VecDestroy(&user->x));
  PetscCall(VecDestroy(&user->c));
  PetscCall(VecDestroy(&user->workN3));
  PetscCall(VecDestroy(&user->workN2));
  PetscCall(VecDestroy(&user->workN));
  PetscCall(VecDestroy(&user->workM));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*------------------------------------------------------------*/

int main(int argc, char **argv)
{
  Tao         tao, misfit, reg;
  PetscReal   v1, v2;
  AppCtx     *user;
  PetscViewer fd;
  char        resultFile[] = "tomographyResult_x";

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
  PetscCall(PetscNew(&user));
  PetscCall(InitializeUserData(user));

  PetscCall(TaoCreate(PETSC_COMM_WORLD, &tao));
  PetscCall(TaoSetType(tao, TAOADMM));
  PetscCall(TaoSetSolution(tao, user->x));
  /* f(x) + g(x) for parent tao */
  PetscCall(TaoADMMSetSpectralPenalty(tao, 1.));
  PetscCall(TaoSetObjectiveAndGradient(tao, NULL, FullObjGrad, (void *)user));
  PetscCall(MatShift(user->HF, user->lambda));
  PetscCall(TaoSetHessian(tao, user->HF, user->HF, HessianFull, (void *)user));

  /* f(x) for misfit tao */
  PetscCall(TaoADMMSetMisfitObjectiveAndGradientRoutine(tao, MisfitObjectiveAndGradient, (void *)user));
  PetscCall(TaoADMMSetMisfitHessianRoutine(tao, user->Hx, user->Hx, HessianMisfit, (void *)user));
  PetscCall(TaoADMMSetMisfitHessianChangeStatus(tao, PETSC_FALSE));
  PetscCall(TaoADMMSetMisfitConstraintJacobian(tao, user->D, user->D, NullJacobian, (void *)user));

  /* g(x) for regularizer tao */
  if (user->reg == 1) {
    PetscCall(TaoADMMSetRegularizerObjectiveAndGradientRoutine(tao, RegularizerObjectiveAndGradient1, (void *)user));
    PetscCall(TaoADMMSetRegularizerHessianRoutine(tao, user->Hz, user->Hz, HessianReg, (void *)user));
    PetscCall(TaoADMMSetRegHessianChangeStatus(tao, PETSC_TRUE));
  } else if (user->reg == 2) {
    PetscCall(TaoADMMSetRegularizerObjectiveAndGradientRoutine(tao, RegularizerObjectiveAndGradient2, (void *)user));
    PetscCall(MatShift(user->Hz, 1));
    PetscCall(MatScale(user->Hz, user->lambda));
    PetscCall(TaoADMMSetRegularizerHessianRoutine(tao, user->Hz, user->Hz, HessianMisfit, (void *)user));
    PetscCall(TaoADMMSetRegHessianChangeStatus(tao, PETSC_TRUE));
  } else PetscCheck(user->reg == 3, PETSC_COMM_WORLD, PETSC_ERR_ARG_UNKNOWN_TYPE, "Incorrect Reg type"); /* TaoShell case */

  /* Set type for the misfit solver */
  PetscCall(TaoADMMGetMisfitSubsolver(tao, &misfit));
  PetscCall(TaoADMMGetRegularizationSubsolver(tao, &reg));
  PetscCall(TaoSetType(misfit, TAONLS));
  if (user->reg == 3) {
    PetscCall(TaoSetType(reg, TAOSHELL));
    PetscCall(TaoShellSetContext(reg, (void *)user));
    PetscCall(TaoShellSetSolve(reg, TaoShellSolve_SoftThreshold));
  } else {
    PetscCall(TaoSetType(reg, TAONLS));
  }
  PetscCall(TaoSetVariableBounds(misfit, user->xlb, user->xub));

  /* Soft Thresholding solves the ADMM problem with the L1 regularizer lambda*||z||_1 and the x-z=0 constraint */
  PetscCall(TaoADMMSetRegularizerCoefficient(tao, user->lambda));
  PetscCall(TaoADMMSetRegularizerConstraintJacobian(tao, NULL, NULL, NullJacobian, (void *)user));
  PetscCall(TaoADMMSetMinimumSpectralPenalty(tao, user->mumin));

  PetscCall(TaoADMMSetConstraintVectorRHS(tao, user->c));
  PetscCall(TaoSetFromOptions(tao));
  PetscCall(TaoSolve(tao));

  /* Save x (reconstruction of object) vector to a binary file, which maybe read from Matlab and convert to a 2D image for comparison. */
  PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD, resultFile, FILE_MODE_WRITE, &fd));
  PetscCall(VecView(user->x, fd));
  PetscCall(PetscViewerDestroy(&fd));

  /* compute the error */
  PetscCall(VecAXPY(user->x, -1, user->xGT));
  PetscCall(VecNorm(user->x, NORM_2, &v1));
  PetscCall(VecNorm(user->xGT, NORM_2, &v2));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "relative reconstruction error: ||x-xGT||/||xGT|| = %6.4e.\n", (double)(v1 / v2)));

  /* Free TAO data structures */
  PetscCall(TaoDestroy(&tao));
  PetscCall(DestroyContext(user));
  PetscCall(PetscFree(user));
  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

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

   test:
      suffix: 1
      localrunfiles: tomographyData_A_b_xGT
      args:  -lambda 1.e-8 -tao_monitor -tao_type nls -tao_nls_pc_type icc

   test:
      suffix: 2
      localrunfiles: tomographyData_A_b_xGT
      args:  -reg 2 -lambda 1.e-8 -tao_admm_dual_update update_basic -tao_admm_regularizer_type regularizer_user -tao_max_it 20 -tao_monitor -tao_admm_tolerance_update_factor 1.e-8  -misfit_tao_nls_pc_type icc -misfit_tao_monitor -reg_tao_monitor

   test:
      suffix: 3
      localrunfiles: tomographyData_A_b_xGT
      args:  -lambda 1.e-8 -tao_admm_dual_update update_basic -tao_admm_regularizer_type regularizer_soft_thresh -tao_max_it 20 -tao_monitor -tao_admm_tolerance_update_factor 1.e-8 -misfit_tao_nls_pc_type icc -misfit_tao_monitor

   test:
      suffix: 4
      localrunfiles: tomographyData_A_b_xGT
      args:  -lambda 1.e-8 -tao_admm_dual_update update_adaptive -tao_admm_regularizer_type regularizer_soft_thresh -tao_max_it 20 -tao_monitor -misfit_tao_monitor -misfit_tao_nls_pc_type icc

   test:
      suffix: 5
      localrunfiles: tomographyData_A_b_xGT
      args:  -reg 2 -lambda 1.e-8 -tao_admm_dual_update update_adaptive -tao_admm_regularizer_type regularizer_user -tao_max_it 20 -tao_monitor -tao_admm_tolerance_update_factor 1.e-8 -misfit_tao_monitor -reg_tao_monitor -misfit_tao_nls_pc_type icc

   test:
      suffix: 6
      localrunfiles: tomographyData_A_b_xGT
      args:  -reg 3 -lambda 1.e-8 -tao_admm_dual_update update_adaptive -tao_admm_regularizer_type regularizer_user -tao_max_it 20 -tao_monitor -tao_admm_tolerance_update_factor 1.e-8 -misfit_tao_monitor -reg_tao_monitor -misfit_tao_nls_pc_type icc

TEST*/