/// @file
/// Test grad in multiple dimensions
/// \test Test grad in multiple dimensions
#include <ceed.h>
#include <math.h>

static CeedScalar Eval(CeedInt dim, const CeedScalar x[]) {
  CeedScalar result = tanh(x[0] + 0.1);
  if (dim > 1) result += atan(x[1] + 0.2);
  if (dim > 2) result += exp(-(x[2] + 0.3)*(x[2] + 0.3));
  return result;
}

int main(int argc, char **argv) {
  Ceed ceed;

  CeedInit(argv[1], &ceed);

  for (CeedInt dim=1; dim<=3; dim++) {
    CeedVector X, X_q, U, U_q, ones, grad_T_ones;
    CeedBasis basis_x_lobatto, basis_u_gauss;
    CeedInt P = 8, Q = 10, P_dim = CeedIntPow(P, dim), Q_dim = CeedIntPow(Q, dim),
            X_dim = CeedIntPow(2, dim);
    CeedScalar x[X_dim*dim], u[P_dim];
    const CeedScalar *x_q, *u_q, *grad_t_ones_array;
    CeedScalar sum_1 = 0, sum_2 = 0;

    for (CeedInt d=0; d<dim; d++)
      for (CeedInt i=0; i<X_dim; i++)
        x[d*X_dim + i] = (i % CeedIntPow(2, dim-d)) /
                         CeedIntPow(2, dim-d-1) ? 1 : -1;

    CeedVectorCreate(ceed, X_dim*dim, &X);
    CeedVectorSetArray(X, CEED_MEM_HOST, CEED_USE_POINTER, x);
    CeedVectorCreate(ceed, P_dim*dim, &X_q);
    CeedVectorSetValue(X_q, 0);
    CeedVectorCreate(ceed, P_dim, &U);
    CeedVectorCreate(ceed, Q_dim*dim, &U_q);
    CeedVectorSetValue(U_q, 0);
    CeedVectorCreate(ceed, Q_dim*dim, &ones);
    CeedVectorSetValue(ones, 1);
    CeedVectorCreate(ceed, P_dim, &grad_T_ones);
    CeedVectorSetValue(grad_T_ones, 0);

    // Get function values at quadrature points
    CeedBasisCreateTensorH1Lagrange(ceed, dim, dim, 2, P,
                                    CEED_GAUSS_LOBATTO, &basis_x_lobatto);
    CeedBasisApply(basis_x_lobatto, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, X, X_q);

    CeedVectorGetArrayRead(X_q, CEED_MEM_HOST, &x_q);
    for (CeedInt i=0; i<P_dim; i++) {
      CeedScalar xx[dim];
      for (CeedInt d=0; d<dim; d++)
        xx[d] = x_q[d*P_dim + i];
      u[i] = Eval(dim, xx);
    }
    CeedVectorRestoreArrayRead(X_q, &x_q);
    CeedVectorSetArray(U, CEED_MEM_HOST, CEED_USE_POINTER, u);

    // Calculate G u at quadrature points, G' * 1 at dofs
    CeedBasisCreateTensorH1Lagrange(ceed, dim, 1, P, Q, CEED_GAUSS, &basis_u_gauss);
    CeedBasisApply(basis_u_gauss, 1, CEED_NOTRANSPOSE, CEED_EVAL_GRAD, U, U_q);
    CeedBasisApply(basis_u_gauss, 1, CEED_TRANSPOSE, CEED_EVAL_GRAD, ones,
                   grad_T_ones);

    // Check if 1' * G * u = u' * (G' * 1)
    CeedVectorGetArrayRead(grad_T_ones, CEED_MEM_HOST, &grad_t_ones_array);
    CeedVectorGetArrayRead(U_q, CEED_MEM_HOST, &u_q);
    for (CeedInt i=0; i<P_dim; i++)
      sum_1 += grad_t_ones_array[i]*u[i];
    for (CeedInt i=0; i<dim*Q_dim; i++)
      sum_2 += u_q[i];
    CeedVectorRestoreArrayRead(grad_T_ones, &grad_t_ones_array);
    CeedVectorRestoreArrayRead(U_q, &u_q);
    if (fabs(sum_1 - sum_2) > 1E-10)
      // LCOV_EXCL_START
      printf("[%d] %f != %f\n", dim, sum_1, sum_2);
    // LCOV_EXCL_STOP

    CeedVectorDestroy(&X);
    CeedVectorDestroy(&X_q);
    CeedVectorDestroy(&U);
    CeedVectorDestroy(&U_q);
    CeedVectorDestroy(&ones);
    CeedVectorDestroy(&grad_T_ones);
    CeedBasisDestroy(&basis_x_lobatto);
    CeedBasisDestroy(&basis_u_gauss);
  }
  CeedDestroy(&ceed);
  return 0;
}