xref: /petsc/src/tao/unconstrained/tutorials/rosenbrock4.h (revision d8e47b638cf8f604a99e9678e1df24f82d959cd7)

#pragma once

#include <petsctao.h>
#include <petscsf.h>
#include <petscdevice.h>
#include <petscdevice_cupm.h>

/*
   User-defined application context - contains data needed by the
   application-provided call-back routines that evaluate the function,
   gradient, and hessian.
*/

typedef struct _Rosenbrock {
  PetscInt  bs; // each block of bs variables is one chained multidimensional rosenbrock problem
  PetscInt  i_start, i_end;
  PetscInt  c_start, c_end;
  PetscReal alpha; // condition parameter
} Rosenbrock;

typedef struct _AppCtx *AppCtx;
struct _AppCtx {
  MPI_Comm      comm;
  PetscInt      n; /* dimension */
  PetscInt      n_local;
  PetscInt      n_local_comp;
  Rosenbrock    problem;
  Vec           Hvalues; /* vector for writing COO values of this MPI process */
  Vec           gvalues; /* vector for writing gradient values of this mpi process */
  Vec           fvector;
  PetscSF       off_process_scatter;
  PetscSF       gscatter;
  Vec           off_process_values; /* buffer for off-process values if chained */
  PetscBool     test_lmvm;
  PetscLogEvent event_f, event_g, event_fg;
};

/* -------------- User-defined routines ---------- */

static PETSC_HOSTDEVICE_INLINE_DECL PetscReal RosenbrockObjective(PetscScalar alpha, PetscScalar x_1, PetscScalar x_2)
{
  PetscScalar d = x_2 - x_1 * x_1;
  PetscScalar e = 1.0 - x_1;
  return alpha * d * d + e * e;
}

static const PetscLogDouble RosenbrockObjectiveFlops = 7.0;

static PETSC_HOSTDEVICE_INLINE_DECL void RosenbrockGradient(PetscScalar alpha, PetscScalar x_1, PetscScalar x_2, PetscScalar g[2])
{
  PetscScalar d  = x_2 - x_1 * x_1;
  PetscScalar e  = 1.0 - x_1;
  PetscScalar g2 = alpha * d * 2.0;

  g[0] = -2.0 * x_1 * g2 - 2.0 * e;
  g[1] = g2;
}

static const PetscInt RosenbrockGradientFlops = 9.0;

static PETSC_HOSTDEVICE_INLINE_DECL PetscReal RosenbrockObjectiveGradient(PetscScalar alpha, PetscScalar x_1, PetscScalar x_2, PetscScalar g[2])
{
  PetscScalar d  = x_2 - x_1 * x_1;
  PetscScalar e  = 1.0 - x_1;
  PetscScalar ad = alpha * d;
  PetscScalar g2 = ad * 2.0;

  g[0] = -2.0 * x_1 * g2 - 2.0 * e;
  g[1] = g2;
  return ad * d + e * e;
}

static const PetscLogDouble RosenbrockObjectiveGradientFlops = 12.0;

static PETSC_HOSTDEVICE_INLINE_DECL void RosenbrockHessian(PetscScalar alpha, PetscScalar x_1, PetscScalar x_2, PetscScalar h[4])
{
  PetscScalar d  = x_2 - x_1 * x_1;
  PetscScalar g2 = alpha * d * 2.0;
  PetscScalar h2 = -4.0 * alpha * x_1;

  h[0] = -2.0 * (g2 + x_1 * h2) + 2.0;
  h[1] = h[2] = h2;
  h[3]        = 2.0 * alpha;
}

static const PetscLogDouble RosenbrockHessianFlops = 11.0;

static PetscErrorCode AppCtxCreate(MPI_Comm comm, AppCtx *ctx)
{
  AppCtx             user;
  PetscDeviceContext dctx;

  PetscFunctionBegin;
  PetscCall(PetscNew(ctx));
  user       = *ctx;
  user->comm = PETSC_COMM_WORLD;

  /* Initialize problem parameters */
  user->n             = 2;
  user->problem.alpha = 99.0;
  user->problem.bs    = 2; // bs = 2 is block Rosenbrock, bs = n is chained Rosenbrock
  user->test_lmvm     = PETSC_FALSE;
  /* Check for command line arguments to override defaults */
  PetscOptionsBegin(user->comm, NULL, "Rosenbrock example", NULL);
  PetscCall(PetscOptionsInt("-n", "Rosenbrock problem size", NULL, user->n, &user->n, NULL));
  PetscCall(PetscOptionsInt("-bs", "Rosenbrock block size (2 <= bs <= n)", NULL, user->problem.bs, &user->problem.bs, NULL));
  PetscCall(PetscOptionsReal("-alpha", "Rosenbrock off-diagonal coefficient", NULL, user->problem.alpha, &user->problem.alpha, NULL));
  PetscCall(PetscOptionsBool("-test_lmvm", "Test LMVM solve against LMVM mult", NULL, user->test_lmvm, &user->test_lmvm, NULL));
  PetscOptionsEnd();
  PetscCheck(user->problem.bs >= 1, comm, PETSC_ERR_ARG_INCOMP, "Block size %" PetscInt_FMT " is not bigger than 1", user->problem.bs);
  PetscCheck((user->n % user->problem.bs) == 0, comm, PETSC_ERR_ARG_INCOMP, "Block size %" PetscInt_FMT " does not divide problem size % " PetscInt_FMT, user->problem.bs, user->n);
  PetscCall(PetscLogEventRegister("Rbock_Obj", TAO_CLASSID, &user->event_f));
  PetscCall(PetscLogEventRegister("Rbock_Grad", TAO_CLASSID, &user->event_g));
  PetscCall(PetscLogEventRegister("Rbock_ObjGrad", TAO_CLASSID, &user->event_fg));
  PetscCall(PetscDeviceContextGetCurrentContext(&dctx));
  PetscCall(PetscDeviceContextSetUp(dctx));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode AppCtxDestroy(AppCtx *ctx)
{
  AppCtx user;

  PetscFunctionBegin;
  user = *ctx;
  *ctx = NULL;
  PetscCall(VecDestroy(&user->Hvalues));
  PetscCall(VecDestroy(&user->gvalues));
  PetscCall(VecDestroy(&user->fvector));
  PetscCall(VecDestroy(&user->off_process_values));
  PetscCall(PetscSFDestroy(&user->off_process_scatter));
  PetscCall(PetscSFDestroy(&user->gscatter));
  PetscCall(PetscFree(user));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode CreateHessian(AppCtx user, Mat *Hessian)
{
  Mat         H;
  PetscLayout layout;
  PetscInt    i_start, i_end, n_local_comp, nnz_local;
  PetscInt    c_start, c_end;
  PetscInt   *coo_i;
  PetscInt   *coo_j;
  PetscInt    bs = user->problem.bs;
  VecType     vec_type;

  PetscFunctionBegin;
  /* Partition the optimization variables and the computations.
     There are (bs - 1) contributions to the objective function for every (bs)
     degrees of freedom. */
  PetscCall(PetscLayoutCreateFromSizes(user->comm, PETSC_DECIDE, user->n, 1, &layout));
  PetscCall(PetscLayoutSetUp(layout));
  PetscCall(PetscLayoutGetRange(layout, &i_start, &i_end));
  user->problem.i_start = i_start;
  user->problem.i_end   = i_end;
  user->n_local         = i_end - i_start;
  user->problem.c_start = c_start = (i_start / bs) * (bs - 1) + (i_start % bs);
  user->problem.c_end = c_end = (i_end / bs) * (bs - 1) + (i_end % bs);
  user->n_local_comp = n_local_comp = c_end - c_start;

  PetscCall(MatCreate(user->comm, Hessian));
  H = *Hessian;
  PetscCall(MatSetLayouts(H, layout, layout));
  PetscCall(PetscLayoutDestroy(&layout));
  PetscCall(MatSetType(H, MATAIJ));
  PetscCall(MatSetOption(H, MAT_HERMITIAN, PETSC_TRUE));
  PetscCall(MatSetOption(H, MAT_SYMMETRIC, PETSC_TRUE));
  PetscCall(MatSetOption(H, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
  PetscCall(MatSetOption(H, MAT_STRUCTURALLY_SYMMETRIC, PETSC_TRUE));
  PetscCall(MatSetOption(H, MAT_STRUCTURAL_SYMMETRY_ETERNAL, PETSC_TRUE));
  PetscCall(MatSetFromOptions(H)); /* set from options so that we can change the underlying matrix type */

  nnz_local = n_local_comp * 4;
  PetscCall(PetscMalloc2(nnz_local, &coo_i, nnz_local, &coo_j));
  /* Instead of having one computation thread per row of the matrix,
     this example uses one thread per contribution to the objective
     function.  Each contribution to the objective function relates
     two adjacent degrees of freedom, so each contribution to
     the objective function adds a 2x2 block into the matrix.
     We describe these 2x2 blocks in COO format. */
  for (PetscInt c = c_start, k = 0; c < c_end; c++, k += 4) {
    PetscInt i = (c / (bs - 1)) * bs + c % (bs - 1);

    coo_i[k + 0] = i;
    coo_i[k + 1] = i;
    coo_i[k + 2] = i + 1;
    coo_i[k + 3] = i + 1;

    coo_j[k + 0] = i;
    coo_j[k + 1] = i + 1;
    coo_j[k + 2] = i;
    coo_j[k + 3] = i + 1;
  }
  PetscCall(MatSetPreallocationCOO(H, nnz_local, coo_i, coo_j));
  PetscCall(PetscFree2(coo_i, coo_j));

  PetscCall(MatGetVecType(H, &vec_type));
  PetscCall(VecCreate(user->comm, &user->Hvalues));
  PetscCall(VecSetSizes(user->Hvalues, nnz_local, PETSC_DETERMINE));
  PetscCall(VecSetType(user->Hvalues, vec_type));

  // vector to collect contributions to the objective
  PetscCall(VecCreate(user->comm, &user->fvector));
  PetscCall(VecSetSizes(user->fvector, user->n_local_comp, PETSC_DETERMINE));
  PetscCall(VecSetType(user->fvector, vec_type));

  { /* If we are using a device (such as a GPU), run some computations that will
       warm up its linear algebra runtime before the problem we actually want
       to profile */

    PetscMemType       memtype;
    const PetscScalar *a;

    PetscCall(VecGetArrayReadAndMemType(user->fvector, &a, &memtype));
    PetscCall(VecRestoreArrayReadAndMemType(user->fvector, &a));

    if (memtype == PETSC_MEMTYPE_DEVICE) {
      PetscLogStage      warmup;
      Mat                A, AtA;
      Vec                x, b;
      PetscInt           warmup_size = 1000;
      PetscDeviceContext dctx;

      PetscCall(PetscLogStageRegister("Device Warmup", &warmup));
      PetscCall(PetscLogStageSetActive(warmup, PETSC_FALSE));

      PetscCall(PetscLogStagePush(warmup));
      PetscCall(MatCreateDenseFromVecType(PETSC_COMM_SELF, vec_type, warmup_size, warmup_size, warmup_size, warmup_size, PETSC_DEFAULT, NULL, &A));
      PetscCall(MatSetRandom(A, NULL));
      PetscCall(MatCreateVecs(A, &x, &b));
      PetscCall(VecSetRandom(x, NULL));

      PetscCall(MatMult(A, x, b));
      PetscCall(MatTransposeMatMult(A, A, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &AtA));
      PetscCall(MatShift(AtA, (PetscScalar)warmup_size));
      PetscCall(MatSetOption(AtA, MAT_SPD, PETSC_TRUE));
      PetscCall(MatCholeskyFactor(AtA, NULL, NULL));
      PetscCall(MatDestroy(&AtA));
      PetscCall(VecDestroy(&b));
      PetscCall(VecDestroy(&x));
      PetscCall(MatDestroy(&A));
      PetscCall(PetscDeviceContextGetCurrentContext(&dctx));
      PetscCall(PetscDeviceContextSynchronize(dctx));
      PetscCall(PetscLogStagePop());
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode CreateVectors(AppCtx user, Mat H, Vec *solution, Vec *gradient)
{
  VecType     vec_type;
  PetscInt    n_coo, *coo_i, i_start, i_end;
  Vec         x;
  PetscInt    n_recv;
  PetscSFNode recv;
  PetscLayout layout;
  PetscInt    c_start = user->problem.c_start, c_end = user->problem.c_end, bs = user->problem.bs;

  PetscFunctionBegin;
  PetscCall(MatCreateVecs(H, solution, gradient));
  x = *solution;
  PetscCall(VecGetOwnershipRange(x, &i_start, &i_end));
  PetscCall(VecGetType(x, &vec_type));
  // create scatter for communicating values
  PetscCall(VecGetLayout(x, &layout));
  n_recv = 0;
  if (user->n_local_comp && i_end < user->n) {
    PetscMPIInt rank;
    PetscInt    index;

    n_recv = 1;
    PetscCall(PetscLayoutFindOwnerIndex(layout, i_end, &rank, &index));
    recv.rank  = rank;
    recv.index = index;
  }
  PetscCall(PetscSFCreate(user->comm, &user->off_process_scatter));
  PetscCall(PetscSFSetGraph(user->off_process_scatter, user->n_local, n_recv, NULL, PETSC_USE_POINTER, &recv, PETSC_COPY_VALUES));
  PetscCall(VecCreate(user->comm, &user->off_process_values));
  PetscCall(VecSetSizes(user->off_process_values, 1, PETSC_DETERMINE));
  PetscCall(VecSetType(user->off_process_values, vec_type));
  PetscCall(VecZeroEntries(user->off_process_values));

  // create COO data for writing the gradient
  n_coo = user->n_local_comp * 2;
  PetscCall(PetscMalloc1(n_coo, &coo_i));
  for (PetscInt c = c_start, k = 0; c < c_end; c++, k += 2) {
    PetscInt i = (c / (bs - 1)) * bs + (c % (bs - 1));

    coo_i[k + 0] = i;
    coo_i[k + 1] = i + 1;
  }
  PetscCall(PetscSFCreate(user->comm, &user->gscatter));
  PetscCall(PetscSFSetGraphLayout(user->gscatter, layout, n_coo, NULL, PETSC_USE_POINTER, coo_i));
  PetscCall(PetscSFSetUp(user->gscatter));
  PetscCall(PetscFree(coo_i));
  PetscCall(VecCreate(user->comm, &user->gvalues));
  PetscCall(VecSetSizes(user->gvalues, n_coo, PETSC_DETERMINE));
  PetscCall(VecSetType(user->gvalues, vec_type));
  PetscFunctionReturn(PETSC_SUCCESS);
}

#if PetscDefined(USING_CUPMCC)

  #if PetscDefined(USING_NVCC)
typedef cudaStream_t cupmStream_t;
    #define PetscCUPMLaunch(...) \
      do { \
        __VA_ARGS__; \
        PetscCallCUDA(cudaGetLastError()); \
      } while (0)
  #elif PetscDefined(USING_HCC)
    #define PetscCUPMLaunch(...) \
      do { \
        __VA_ARGS__; \
        PetscCallHIP(hipGetLastError()); \
      } while (0)
typedef hipStream_t cupmStream_t;
  #endif

// x: on-process optimization variables
// o: buffer that contains the next optimization variable after the variables on this process
template <typename T>
PETSC_DEVICE_INLINE_DECL static void rosenbrock_for_loop(Rosenbrock r, const PetscScalar x[], const PetscScalar o[], T &&func) noexcept
{
  PetscInt idx         = blockIdx.x * blockDim.x + threadIdx.x; // 1D grid
  PetscInt num_threads = gridDim.x * blockDim.x;

  for (PetscInt c = r.c_start + idx, k = idx; c < r.c_end; c += num_threads, k += num_threads) {
    PetscInt    i   = (c / (r.bs - 1)) * r.bs + (c % (r.bs - 1));
    PetscScalar x_a = x[i - r.i_start];
    PetscScalar x_b = ((i + 1) < r.i_end) ? x[i + 1 - r.i_start] : o[0];

    func(k, x_a, x_b);
  }
  return;
}

PETSC_KERNEL_DECL void RosenbrockObjective_Kernel(Rosenbrock r, const PetscScalar x[], const PetscScalar o[], PetscScalar f_vec[])
{
  rosenbrock_for_loop(r, x, o, [&](PetscInt k, PetscScalar x_a, PetscScalar x_b) { f_vec[k] = RosenbrockObjective(r.alpha, x_a, x_b); });
}

PETSC_KERNEL_DECL void RosenbrockGradient_Kernel(Rosenbrock r, const PetscScalar x[], const PetscScalar o[], PetscScalar g[])
{
  rosenbrock_for_loop(r, x, o, [&](PetscInt k, PetscScalar x_a, PetscScalar x_b) { RosenbrockGradient(r.alpha, x_a, x_b, &g[2 * k]); });
}

PETSC_KERNEL_DECL void RosenbrockObjectiveGradient_Kernel(Rosenbrock r, const PetscScalar x[], const PetscScalar o[], PetscScalar f_vec[], PetscScalar g[])
{
  rosenbrock_for_loop(r, x, o, [&](PetscInt k, PetscScalar x_a, PetscScalar x_b) { f_vec[k] = RosenbrockObjectiveGradient(r.alpha, x_a, x_b, &g[2 * k]); });
}

PETSC_KERNEL_DECL void RosenbrockHessian_Kernel(Rosenbrock r, const PetscScalar x[], const PetscScalar o[], PetscScalar h[])
{
  rosenbrock_for_loop(r, x, o, [&](PetscInt k, PetscScalar x_a, PetscScalar x_b) { RosenbrockHessian(r.alpha, x_a, x_b, &h[4 * k]); });
}

static PetscErrorCode RosenbrockObjective_Device(cupmStream_t stream, Rosenbrock r, const PetscScalar x[], const PetscScalar o[], PetscScalar f_vec[])
{
  PetscInt n_comp = r.c_end - r.c_start;

  PetscFunctionBegin;
  if (n_comp) PetscCUPMLaunch(RosenbrockObjective_Kernel<<<(n_comp + 255) / 256, 256, 0, stream>>>(r, x, o, f_vec));
  PetscCall(PetscLogGpuFlops(RosenbrockObjectiveFlops * n_comp));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode RosenbrockGradient_Device(cupmStream_t stream, Rosenbrock r, const PetscScalar x[], const PetscScalar o[], PetscScalar g[])
{
  PetscInt n_comp = r.c_end - r.c_start;

  PetscFunctionBegin;
  if (n_comp) PetscCUPMLaunch(RosenbrockGradient_Kernel<<<(n_comp + 255) / 256, 256, 0, stream>>>(r, x, o, g));
  PetscCall(PetscLogGpuFlops(RosenbrockGradientFlops * n_comp));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode RosenbrockObjectiveGradient_Device(cupmStream_t stream, Rosenbrock r, const PetscScalar x[], const PetscScalar o[], PetscScalar f_vec[], PetscScalar g[])
{
  PetscInt n_comp = r.c_end - r.c_start;

  PetscFunctionBegin;
  if (n_comp) PetscCUPMLaunch(RosenbrockObjectiveGradient_Kernel<<<(n_comp + 255) / 256, 256, 0, stream>>>(r, x, o, f_vec, g));
  PetscCall(PetscLogGpuFlops(RosenbrockObjectiveGradientFlops * n_comp));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode RosenbrockHessian_Device(cupmStream_t stream, Rosenbrock r, const PetscScalar x[], const PetscScalar o[], PetscScalar h[])
{
  PetscInt n_comp = r.c_end - r.c_start;

  PetscFunctionBegin;
  if (n_comp) PetscCUPMLaunch(RosenbrockHessian_Kernel<<<(n_comp + 255) / 256, 256, 0, stream>>>(r, x, o, h));
  PetscCall(PetscLogGpuFlops(RosenbrockHessianFlops * n_comp));
  PetscFunctionReturn(PETSC_SUCCESS);
}
#endif

static PetscErrorCode RosenbrockObjective_Host(Rosenbrock r, const PetscScalar x[], const PetscScalar o[], PetscReal *f)
{
  PetscReal _f = 0.0;

  PetscFunctionBegin;
  for (PetscInt c = r.c_start; c < r.c_end; c++) {
    PetscInt    i   = (c / (r.bs - 1)) * r.bs + (c % (r.bs - 1));
    PetscScalar x_a = x[i - r.i_start];
    PetscScalar x_b = ((i + 1) < r.i_end) ? x[i + 1 - r.i_start] : o[0];

    _f += RosenbrockObjective(r.alpha, x_a, x_b);
  }
  *f = _f;
  PetscCall(PetscLogFlops((RosenbrockObjectiveFlops + 1.0) * (r.c_end - r.c_start)));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode RosenbrockGradient_Host(Rosenbrock r, const PetscScalar x[], const PetscScalar o[], PetscScalar g[])
{
  PetscFunctionBegin;
  for (PetscInt c = r.c_start, k = 0; c < r.c_end; c++, k++) {
    PetscInt    i   = (c / (r.bs - 1)) * r.bs + (c % (r.bs - 1));
    PetscScalar x_a = x[i - r.i_start];
    PetscScalar x_b = ((i + 1) < r.i_end) ? x[i + 1 - r.i_start] : o[0];

    RosenbrockGradient(r.alpha, x_a, x_b, &g[2 * k]);
  }
  PetscCall(PetscLogFlops(RosenbrockGradientFlops * (r.c_end - r.c_start)));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode RosenbrockObjectiveGradient_Host(Rosenbrock r, const PetscScalar x[], const PetscScalar o[], PetscReal *f, PetscScalar g[])
{
  PetscReal _f = 0.0;

  PetscFunctionBegin;
  for (PetscInt c = r.c_start, k = 0; c < r.c_end; c++, k++) {
    PetscInt    i   = (c / (r.bs - 1)) * r.bs + (c % (r.bs - 1));
    PetscScalar x_a = x[i - r.i_start];
    PetscScalar x_b = ((i + 1) < r.i_end) ? x[i + 1 - r.i_start] : o[0];

    _f += RosenbrockObjectiveGradient(r.alpha, x_a, x_b, &g[2 * k]);
  }
  *f = _f;
  PetscCall(PetscLogFlops(RosenbrockObjectiveGradientFlops * (r.c_end - r.c_start)));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode RosenbrockHessian_Host(Rosenbrock r, const PetscScalar x[], const PetscScalar o[], PetscScalar h[])
{
  PetscFunctionBegin;
  for (PetscInt c = r.c_start, k = 0; c < r.c_end; c++, k++) {
    PetscInt    i   = (c / (r.bs - 1)) * r.bs + (c % (r.bs - 1));
    PetscScalar x_a = x[i - r.i_start];
    PetscScalar x_b = ((i + 1) < r.i_end) ? x[i + 1 - r.i_start] : o[0];

    RosenbrockHessian(r.alpha, x_a, x_b, &h[4 * k]);
  }
  PetscCall(PetscLogFlops(RosenbrockHessianFlops * (r.c_end - r.c_start)));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

static PetscErrorCode FormObjective(Tao tao, Vec X, PetscReal *f, void *ptr)
{
  AppCtx             user    = (AppCtx)ptr;
  PetscReal          f_local = 0.0;
  const PetscScalar *x;
  const PetscScalar *o = NULL;
  PetscMemType       memtype_x;

  PetscFunctionBeginUser;
  PetscCall(PetscLogEventBegin(user->event_f, tao, NULL, NULL, NULL));
  PetscCall(VecScatterBegin(user->off_process_scatter, X, user->off_process_values, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(VecScatterEnd(user->off_process_scatter, X, user->off_process_values, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(VecGetArrayReadAndMemType(user->off_process_values, &o, NULL));
  PetscCall(VecGetArrayReadAndMemType(X, &x, &memtype_x));
  if (memtype_x == PETSC_MEMTYPE_HOST) {
    PetscCall(RosenbrockObjective_Host(user->problem, x, o, &f_local));
    PetscCallMPI(MPIU_Allreduce(&f_local, f, 1, MPI_DOUBLE, MPI_SUM, user->comm));
#if PetscDefined(USING_CUPMCC)
  } else if (memtype_x == PETSC_MEMTYPE_DEVICE) {
    PetscScalar       *_fvec;
    PetscScalar        f_scalar;
    cupmStream_t      *stream;
    PetscDeviceContext dctx;

    PetscCall(PetscDeviceContextGetCurrentContext(&dctx));
    PetscCall(PetscDeviceContextGetStreamHandle(dctx, (void **)&stream));
    PetscCall(VecGetArrayWriteAndMemType(user->fvector, &_fvec, NULL));
    PetscCall(RosenbrockObjective_Device(*stream, user->problem, x, o, _fvec));
    PetscCall(VecRestoreArrayWriteAndMemType(user->fvector, &_fvec));
    PetscCall(VecSum(user->fvector, &f_scalar));
    *f = PetscRealPart(f_scalar);
#endif
  } else SETERRQ(user->comm, PETSC_ERR_SUP, "Unsupported memtype %d", (int)memtype_x);
  PetscCall(VecRestoreArrayReadAndMemType(X, &x));
  PetscCall(VecRestoreArrayReadAndMemType(user->off_process_values, &o));
  PetscCall(PetscLogEventEnd(user->event_f, tao, NULL, NULL, NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode FormGradient(Tao tao, Vec X, Vec G, void *ptr)
{
  AppCtx             user = (AppCtx)ptr;
  PetscScalar       *g;
  const PetscScalar *x;
  const PetscScalar *o = NULL;
  PetscMemType       memtype_x, memtype_g;

  PetscFunctionBeginUser;
  PetscCall(PetscLogEventBegin(user->event_g, tao, NULL, NULL, NULL));
  PetscCall(VecScatterBegin(user->off_process_scatter, X, user->off_process_values, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(VecScatterEnd(user->off_process_scatter, X, user->off_process_values, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(VecGetArrayReadAndMemType(user->off_process_values, &o, NULL));
  PetscCall(VecGetArrayReadAndMemType(X, &x, &memtype_x));
  PetscCall(VecGetArrayWriteAndMemType(user->gvalues, &g, &memtype_g));
  PetscAssert(memtype_x == memtype_g, user->comm, PETSC_ERR_ARG_INCOMP, "solution vector and gradient must have save memtype");
  if (memtype_x == PETSC_MEMTYPE_HOST) {
    PetscCall(RosenbrockGradient_Host(user->problem, x, o, g));
#if PetscDefined(USING_CUPMCC)
  } else if (memtype_x == PETSC_MEMTYPE_DEVICE) {
    cupmStream_t      *stream;
    PetscDeviceContext dctx;

    PetscCall(PetscDeviceContextGetCurrentContext(&dctx));
    PetscCall(PetscDeviceContextGetStreamHandle(dctx, (void **)&stream));
    PetscCall(RosenbrockGradient_Device(*stream, user->problem, x, o, g));
#endif
  } else SETERRQ(user->comm, PETSC_ERR_SUP, "Unsupported memtype %d", (int)memtype_x);
  PetscCall(VecRestoreArrayWriteAndMemType(user->gvalues, &g));
  PetscCall(VecRestoreArrayReadAndMemType(X, &x));
  PetscCall(VecRestoreArrayReadAndMemType(user->off_process_values, &o));
  PetscCall(VecZeroEntries(G));
  PetscCall(VecScatterBegin(user->gscatter, user->gvalues, G, ADD_VALUES, SCATTER_REVERSE));
  PetscCall(VecScatterEnd(user->gscatter, user->gvalues, G, ADD_VALUES, SCATTER_REVERSE));
  PetscCall(PetscLogEventEnd(user->event_g, tao, NULL, NULL, NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
    FormObjectiveGradient - Evaluates the function, f(X), and gradient, G(X).

    Input Parameters:
.   tao  - the Tao context
.   X    - input vector
.   ptr  - optional user-defined context, as set by TaoSetObjectiveGradient()

    Output Parameters:
.   G - vector containing the newly evaluated gradient
.   f - function value

    Note:
    Some optimization methods ask for the function and the gradient evaluation
    at the same time.  Evaluating both at once may be more efficient that
    evaluating each separately.
*/
static PetscErrorCode FormObjectiveGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
{
  AppCtx             user    = (AppCtx)ptr;
  PetscReal          f_local = 0.0;
  PetscScalar       *g;
  const PetscScalar *x;
  const PetscScalar *o = NULL;
  PetscMemType       memtype_x, memtype_g;

  PetscFunctionBeginUser;
  PetscCall(PetscLogEventBegin(user->event_fg, tao, NULL, NULL, NULL));
  PetscCall(VecScatterBegin(user->off_process_scatter, X, user->off_process_values, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(VecScatterEnd(user->off_process_scatter, X, user->off_process_values, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(VecGetArrayReadAndMemType(user->off_process_values, &o, NULL));
  PetscCall(VecGetArrayReadAndMemType(X, &x, &memtype_x));
  PetscCall(VecGetArrayWriteAndMemType(user->gvalues, &g, &memtype_g));
  PetscAssert(memtype_x == memtype_g, user->comm, PETSC_ERR_ARG_INCOMP, "solution vector and gradient must have save memtype");
  if (memtype_x == PETSC_MEMTYPE_HOST) {
    PetscCall(RosenbrockObjectiveGradient_Host(user->problem, x, o, &f_local, g));
    PetscCallMPI(MPIU_Allreduce((void *)&f_local, (void *)f, 1, MPI_DOUBLE, MPI_SUM, PETSC_COMM_WORLD));
#if PetscDefined(USING_CUPMCC)
  } else if (memtype_x == PETSC_MEMTYPE_DEVICE) {
    PetscScalar       *_fvec;
    PetscScalar        f_scalar;
    cupmStream_t      *stream;
    PetscDeviceContext dctx;

    PetscCall(PetscDeviceContextGetCurrentContext(&dctx));
    PetscCall(PetscDeviceContextGetStreamHandle(dctx, (void **)&stream));
    PetscCall(VecGetArrayWriteAndMemType(user->fvector, &_fvec, NULL));
    PetscCall(RosenbrockObjectiveGradient_Device(*stream, user->problem, x, o, _fvec, g));
    PetscCall(VecRestoreArrayWriteAndMemType(user->fvector, &_fvec));
    PetscCall(VecSum(user->fvector, &f_scalar));
    *f = PetscRealPart(f_scalar);
#endif
  } else SETERRQ(user->comm, PETSC_ERR_SUP, "Unsupported memtype %d", (int)memtype_x);

  PetscCall(VecRestoreArrayWriteAndMemType(user->gvalues, &g));
  PetscCall(VecRestoreArrayReadAndMemType(X, &x));
  PetscCall(VecRestoreArrayReadAndMemType(user->off_process_values, &o));
  PetscCall(VecZeroEntries(G));
  PetscCall(VecScatterBegin(user->gscatter, user->gvalues, G, ADD_VALUES, SCATTER_REVERSE));
  PetscCall(VecScatterEnd(user->gscatter, user->gvalues, G, ADD_VALUES, SCATTER_REVERSE));
  PetscCall(PetscLogEventEnd(user->event_fg, tao, NULL, NULL, NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* ------------------------------------------------------------------- */
/*
   FormHessian - Evaluates Hessian matrix.

   Input Parameters:
.  tao   - the Tao context
.  x     - input vector
.  ptr   - optional user-defined context, as set by TaoSetHessian()

   Output Parameters:
.  H     - Hessian matrix

   Note:  Providing the Hessian may not be necessary.  Only some solvers
   require this matrix.
*/
static PetscErrorCode FormHessian(Tao tao, Vec X, Mat H, Mat Hpre, void *ptr)
{
  AppCtx             user = (AppCtx)ptr;
  PetscScalar       *h;
  const PetscScalar *x;
  const PetscScalar *o = NULL;
  PetscMemType       memtype_x, memtype_h;

  PetscFunctionBeginUser;
  PetscCall(VecScatterBegin(user->off_process_scatter, X, user->off_process_values, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(VecScatterEnd(user->off_process_scatter, X, user->off_process_values, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(VecGetArrayReadAndMemType(user->off_process_values, &o, NULL));
  PetscCall(VecGetArrayReadAndMemType(X, &x, &memtype_x));
  PetscCall(VecGetArrayWriteAndMemType(user->Hvalues, &h, &memtype_h));
  PetscAssert(memtype_x == memtype_h, user->comm, PETSC_ERR_ARG_INCOMP, "solution vector and hessian must have save memtype");
  if (memtype_x == PETSC_MEMTYPE_HOST) {
    PetscCall(RosenbrockHessian_Host(user->problem, x, o, h));
#if PetscDefined(USING_CUPMCC)
  } else if (memtype_x == PETSC_MEMTYPE_DEVICE) {
    cupmStream_t      *stream;
    PetscDeviceContext dctx;

    PetscCall(PetscDeviceContextGetCurrentContext(&dctx));
    PetscCall(PetscDeviceContextGetStreamHandle(dctx, (void **)&stream));
    PetscCall(RosenbrockHessian_Device(*stream, user->problem, x, o, h));
#endif
  } else SETERRQ(user->comm, PETSC_ERR_SUP, "Unsupported memtype %d", (int)memtype_x);

  PetscCall(MatSetValuesCOO(H, h, INSERT_VALUES));
  PetscCall(VecRestoreArrayWriteAndMemType(user->Hvalues, &h));

  PetscCall(VecRestoreArrayReadAndMemType(X, &x));
  PetscCall(VecRestoreArrayReadAndMemType(user->off_process_values, &o));

  if (Hpre != H) PetscCall(MatCopy(H, Hpre, SAME_NONZERO_PATTERN));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TestLMVM(Tao tao)
{
  KSP       ksp;
  PC        pc;
  PetscBool is_lmvm;

  PetscFunctionBegin;
  PetscCall(TaoGetKSP(tao, &ksp));
  if (!ksp) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(KSPGetPC(ksp, &pc));
  PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCLMVM, &is_lmvm));
  if (is_lmvm) {
    Mat       M;
    Vec       in, out, out2;
    PetscReal mult_solve_dist;
    Vec       x;

    PetscCall(PCLMVMGetMatLMVM(pc, &M));
    PetscCall(TaoGetSolution(tao, &x));
    PetscCall(VecDuplicate(x, &in));
    PetscCall(VecDuplicate(x, &out));
    PetscCall(VecDuplicate(x, &out2));
    PetscCall(VecSetRandom(in, NULL));
    PetscCall(MatMult(M, in, out));
    PetscCall(MatSolve(M, out, out2));

    PetscCall(VecAXPY(out2, -1.0, in));
    PetscCall(VecNorm(out2, NORM_2, &mult_solve_dist));
    if (mult_solve_dist < 1.e-11) {
      PetscCall(PetscPrintf(PetscObjectComm((PetscObject)tao), "Inverse error of LMVM MatMult and MatSolve: < 1.e-11\n"));
    } else if (mult_solve_dist < 1.e-6) {
      PetscCall(PetscPrintf(PetscObjectComm((PetscObject)tao), "Inverse error of LMVM MatMult and MatSolve: < 1.e-6\n"));
    } else {
      PetscCall(PetscPrintf(PetscObjectComm((PetscObject)tao), "Inverse error of LMVM MatMult and MatSolve is not small: %e\n", (double)mult_solve_dist));
    }
    PetscCall(VecDestroy(&in));
    PetscCall(VecDestroy(&out));
    PetscCall(VecDestroy(&out2));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode RosenbrockMain(void)
{
  Vec           x;    /* solution vector */
  Vec           g;    /* gradient vector */
  Mat           H;    /* Hessian matrix */
  Tao           tao;  /* Tao solver context */
  AppCtx        user; /* user-defined application context */
  PetscLogStage solve;

  /* Initialize TAO and PETSc */
  PetscFunctionBegin;
  PetscCall(PetscLogStageRegister("Rosenbrock solve", &solve));

  PetscCall(AppCtxCreate(PETSC_COMM_WORLD, &user));
  PetscCall(CreateHessian(user, &H));
  PetscCall(CreateVectors(user, H, &x, &g));

  /* The TAO code begins here */

  PetscCall(TaoCreate(user->comm, &tao));
  PetscCall(VecZeroEntries(x));
  PetscCall(TaoSetSolution(tao, x));

  /* Set routines for function, gradient, hessian evaluation */
  PetscCall(TaoSetObjective(tao, FormObjective, user));
  PetscCall(TaoSetObjectiveAndGradient(tao, g, FormObjectiveGradient, user));
  PetscCall(TaoSetGradient(tao, g, FormGradient, user));
  PetscCall(TaoSetHessian(tao, H, H, FormHessian, user));

  PetscCall(TaoSetFromOptions(tao));

  /* SOLVE THE APPLICATION */
  PetscCall(PetscLogStagePush(solve));
  PetscCall(TaoSolve(tao));
  PetscCall(PetscLogStagePop());

  if (user->test_lmvm) PetscCall(TestLMVM(tao));

  PetscCall(TaoDestroy(&tao));
  PetscCall(VecDestroy(&g));
  PetscCall(VecDestroy(&x));
  PetscCall(MatDestroy(&H));
  PetscCall(AppCtxDestroy(&user));
  PetscFunctionReturn(PETSC_SUCCESS);
}