// Copyright (c) 2017-2022, Lawrence Livermore National Security, LLC and other CEED contributors.
// All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
//
// SPDX-License-Identifier: BSD-2-Clause
//
// This file is part of CEED:  http://github.com/ceed

/// @file
/// Geometric factors (2D) for Navier-Stokes example using PETSc

#ifndef setup_geo_2d_h
#define setup_geo_2d_h

#include <ceed.h>
#include <math.h>

// *****************************************************************************
// This QFunction sets up the geometric factors required for integration and
//   coordinate transformations
//
// Reference (parent) coordinates: X
// Physical (current) coordinates: x
// Change of coordinate matrix: dxdX_{i,j} = x_{i,j} (indicial notation)
// Inverse of change of coordinate matrix: dXdx_{i,j} = (detJ^-1) * X_{i,j}
//
// All quadrature data is stored in 10 field vector of quadrature data.
//
// We require the determinant of the Jacobian to properly compute integrals of
//   the form: int( v u )
//
// Determinant of Jacobian:
//   detJ = J11*J22 - J21*J12
//     Jij = Jacobian entry ij
//
// Stored: w detJ
//   in q_data[0]
//
// We require the transpose of the inverse of the Jacobian to properly compute
//   integrals of the form: int( gradv u )
//
// Inverse of Jacobian:
//   dXdx_i,j = Aij / detJ
//   Aij = Adjoint ij
//
// Stored: Aij / detJ
//   in q_data[1:4] as
//   (detJ^-1) * [A11 A12]
//               [A21 A22]
//
// *****************************************************************************
CEED_QFUNCTION(Setup2d)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
  // Inputs
  const CeedScalar(*J)[2][CEED_Q_VLA] = (const CeedScalar(*)[2][CEED_Q_VLA])in[0];
  const CeedScalar(*w)                = in[1];

  // Outputs
  CeedScalar(*q_data)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];

  CeedPragmaSIMD
      // Quadrature Point Loop
      for (CeedInt i = 0; i < Q; i++) {
    // Setup
    const CeedScalar J11  = J[0][0][i];
    const CeedScalar J21  = J[0][1][i];
    const CeedScalar J12  = J[1][0][i];
    const CeedScalar J22  = J[1][1][i];
    const CeedScalar detJ = J11 * J22 - J21 * J12;

    // Qdata
    // -- Interp-to-Interp q_data
    q_data[0][i] = w[i] * detJ;
    // -- Interp-to-Grad q_data
    // Inverse of change of coordinate matrix: X_i,j
    q_data[1][i] = J22 / detJ;
    q_data[2][i] = -J12 / detJ;
    q_data[3][i] = -J21 / detJ;
    q_data[4][i] = J11 / detJ;
  }  // End of Quadrature Point Loop

  // Return
  return 0;
}

// *****************************************************************************
// This QFunction sets up the geometric factor required for integration when
//   reference coordinates are in 1D and the physical coordinates are in 2D
//
// Reference (parent) 1D coordinates: X
// Physical (current) 2D coordinates: x
// Change of coordinate vector:
//           J1 = dx_1/dX
//           J2 = dx_2/dX
//
// detJb is the magnitude of (J1,J2)
//
// All quadrature data is stored in 3 field vector of quadrature data.
//
// We require the determinant of the Jacobian to properly compute integrals of
//   the form: int( u v )
//
// Stored: w detJb
//   in q_data_sur[0]
//
// Normal vector is given by the cross product of (J1,J2)/detJ and ẑ
//
// Stored: (J1,J2,0) x (0,0,1) / detJb
//   in q_data_sur[1:2] as
//   (detJb^-1) * [ J2 ]
//                [-J1 ]
//
// *****************************************************************************
CEED_QFUNCTION(SetupBoundary2d)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
  // Inputs
  const CeedScalar(*J)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0];
  const CeedScalar(*w)             = in[1];

  // Outputs
  CeedScalar(*q_data_sur)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0];

  CeedPragmaSIMD
      // Quadrature Point Loop
      for (CeedInt i = 0; i < Q; i++) {
    // Setup
    const CeedScalar J1 = J[0][i];
    const CeedScalar J2 = J[1][i];

    const CeedScalar detJb = sqrt(J1 * J1 + J2 * J2);

    q_data_sur[0][i] = w[i] * detJb;
    q_data_sur[1][i] = J2 / detJb;
    q_data_sur[2][i] = -J1 / detJb;
  }  // End of Quadrature Point Loop

  // Return
  return 0;
}

// *****************************************************************************

#endif  // setup_geo_2d_h