#include <petsc/private/snesimpl.h> /*I  "petscsnes.h"  I*/
#include <petsc/private/vecimpl.h>  /* for Vec->ops->setvalues */
#include <petscdm.h>

/*@
  SNESComputeJacobianDefault - Computes the Jacobian using finite differences.

  Collective

  Input Parameters:
+ snes - the `SNES` context
. x1   - compute Jacobian at this point
- ctx  - application's function context, as set with `SNESSetFunction()`

  Output Parameters:
+ J - Jacobian matrix (not altered in this routine)
- B - newly computed Jacobian matrix to use with preconditioner (generally the same as `J`)

  Options Database Keys:
+ -snes_fd             - Activates `SNESComputeJacobianDefault()`
. -snes_fd_coloring    - Activates a faster computation that uses a graph coloring of the matrix
. -snes_test_err etol  - Square root of function error tolerance, default square root of machine
                         epsilon (1.e-8 in double, 3.e-4 in single)
- -mat_fd_type (wp|ds) - See `MATMFFD_WP` and `MATMFFD_DS`

  Level: intermediate

  Notes:
  This routine is slow and expensive, and is not currently optimized
  to take advantage of sparsity in the problem.  Although
  `SNESComputeJacobianDefault()` is not recommended for general use
  in large-scale applications, It can be useful in checking the
  correctness of a user-provided Jacobian.

  An alternative routine that uses coloring to exploit matrix sparsity is
  `SNESComputeJacobianDefaultColor()`.

  This routine ignores the maximum number of function evaluations set with `SNESSetTolerances()` and the function
  evaluations it performs are not counted in what is returned by of `SNESGetNumberFunctionEvals()`.

  This function can be provided to `SNESSetJacobian()` along with a dense matrix to hold the Jacobian

  Developer Note:
  The function has a poorly chosen name since it does not mention the use of finite differences

.seealso: [](ch_snes), `SNES`, `SNESSetJacobian()`, `SNESComputeJacobianDefaultColor()`, `MatCreateSNESMF()`
@*/
PetscErrorCode SNESComputeJacobianDefault(SNES snes, Vec x1, Mat J, Mat B, PetscCtx ctx)
{
  Vec                j1a, j2a, x2;
  PetscInt           i, N, start, end, j, value, max_funcs = snes->max_funcs;
  PetscScalar        dx, *y, wscale;
  const PetscScalar *xx;
  PetscReal          amax, epsilon = PETSC_SQRT_MACHINE_EPSILON;
  PetscReal          dx_min = 1.e-16, dx_par = 1.e-1, unorm;
  MPI_Comm           comm;
  PetscBool          assembled, use_wp = PETSC_TRUE, flg;
  const char        *list[2] = {"ds", "wp"};
  PetscMPIInt        size, root;
  const PetscInt    *ranges;
  DM                 dm;
  DMSNES             dms;

  PetscFunctionBegin;
  snes->max_funcs = PETSC_INT_MAX;
  /* Since this Jacobian will possibly have "extra" nonzero locations just turn off errors for these locations */
  PetscCall(MatSetOption(B, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));
  PetscCall(PetscOptionsGetReal(((PetscObject)snes)->options, ((PetscObject)snes)->prefix, "-snes_test_err", &epsilon, NULL));

  PetscCall(PetscObjectGetComm((PetscObject)x1, &comm));
  PetscCallMPI(MPI_Comm_size(comm, &size));
  PetscCall(MatAssembled(B, &assembled));
  if (assembled) PetscCall(MatZeroEntries(B));
  if (!snes->nvwork) {
    if (snes->dm) {
      PetscCall(DMGetGlobalVector(snes->dm, &j1a));
      PetscCall(DMGetGlobalVector(snes->dm, &j2a));
      PetscCall(DMGetGlobalVector(snes->dm, &x2));
    } else {
      snes->nvwork = 3;
      PetscCall(VecDuplicateVecs(x1, snes->nvwork, &snes->vwork));
      j1a = snes->vwork[0];
      j2a = snes->vwork[1];
      x2  = snes->vwork[2];
    }
  }

  PetscCall(VecGetSize(x1, &N));
  PetscCall(VecGetOwnershipRange(x1, &start, &end));
  PetscCall(SNESGetDM(snes, &dm));
  PetscCall(DMGetDMSNES(dm, &dms));
  if (dms->ops->computemffunction) PetscCall(SNESComputeMFFunction(snes, x1, j1a));
  else PetscCall(SNESComputeFunction(snes, x1, j1a)); /* does not handle use of SNESSetFunctionDomainError() correctly */

  PetscOptionsBegin(PetscObjectComm((PetscObject)snes), ((PetscObject)snes)->prefix, "Differencing options", "SNES");
  PetscCall(PetscOptionsEList("-mat_fd_type", "Algorithm to compute difference parameter", "SNESComputeJacobianDefault", list, 2, "wp", &value, &flg));
  PetscOptionsEnd();
  if (flg && !value) use_wp = PETSC_FALSE;

  if (use_wp) PetscCall(VecNorm(x1, NORM_2, &unorm));
  /* Compute Jacobian approximation, 1 column at a time.
      x1 = current iterate, j1a = F(x1)
      x2 = perturbed iterate, j2a = F(x2)
   */
  for (i = 0; i < N; i++) {
    PetscCall(VecCopy(x1, x2));
    if (i >= start && i < end) {
      PetscCall(VecGetArrayRead(x1, &xx));
      if (use_wp) dx = PetscSqrtReal(1.0 + unorm);
      else dx = xx[i - start];
      PetscCall(VecRestoreArrayRead(x1, &xx));
      if (PetscAbsScalar(dx) < dx_min) dx = (PetscRealPart(dx) < 0. ? -1. : 1.) * dx_par;
      dx *= epsilon;
      wscale = 1.0 / dx;
      if (x2->ops->setvalues) PetscCall(VecSetValues(x2, 1, &i, &dx, ADD_VALUES));
      else {
        PetscCall(VecGetArray(x2, &y));
        y[i - start] += dx;
        PetscCall(VecRestoreArray(x2, &y));
      }
    } else {
      wscale = 0.0;
    }
    PetscCall(VecAssemblyBegin(x2));
    PetscCall(VecAssemblyEnd(x2));
    if (dms->ops->computemffunction) PetscCall(SNESComputeMFFunction(snes, x2, j2a));
    else PetscCall(SNESComputeFunction(snes, x2, j2a)); /* does not handle use of SNESSetFunctionDomainError() correctly */
    PetscCall(VecAXPY(j2a, -1.0, j1a));
    /* Communicate scale=1/dx_i to all processors */
    PetscCall(VecGetOwnershipRanges(x1, &ranges));
    root = size;
    for (j = size - 1; j > -1; j--) {
      root--;
      if (i >= ranges[j]) break;
    }
    PetscCallMPI(MPI_Bcast(&wscale, 1, MPIU_SCALAR, root, comm));
    PetscCall(VecScale(j2a, wscale));
    PetscCall(VecNorm(j2a, NORM_INFINITY, &amax));
    amax *= 1.e-14;
    PetscCall(VecGetArray(j2a, &y));
    for (j = start; j < end; j++) {
      if (PetscAbsScalar(y[j - start]) > amax || j == i) PetscCall(MatSetValues(B, 1, &j, 1, &i, y + j - start, INSERT_VALUES));
    }
    PetscCall(VecRestoreArray(j2a, &y));
  }
  if (snes->dm) {
    PetscCall(DMRestoreGlobalVector(snes->dm, &j1a));
    PetscCall(DMRestoreGlobalVector(snes->dm, &j2a));
    PetscCall(DMRestoreGlobalVector(snes->dm, &x2));
  }
  PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
  if (B != J) {
    PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
  }
  snes->max_funcs = max_funcs;
  snes->nfuncs -= N;
  PetscFunctionReturn(PETSC_SUCCESS);
}
