// Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at
// the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights
// reserved. See files LICENSE and NOTICE for details.
//
// This file is part of CEED, a collection of benchmarks, miniapps, software
// libraries and APIs for efficient high-order finite element and spectral
// element discretizations for exascale applications. For more information and
// source code availability see http://github.com/ceed.
//
// The CEED research is supported by the Exascale Computing Project 17-SC-20-SC,
// a collaborative effort of two U.S. Department of Energy organizations (Office
// of Science and the National Nuclear Security Administration) responsible for
// the planning and preparation of a capable exascale ecosystem, including
// software, applications, hardware, advanced system engineering and early
// testbed platforms, in support of the nation's exascale computing imperative.

/// @file
/// libCEED QFunctions for mass operator example for a scalar field on the sphere using PETSc

#ifndef bp1sphere_h
#define bp1sphere_h

#ifndef __CUDACC__
#  include <math.h>
#endif

// -----------------------------------------------------------------------------
// This QFunction sets up the geometric factors required for integration and
//   coordinate transformations when reference coordinates have a different
//   dimension than the one of physical coordinates
//
// Reference (parent) 2D coordinates: X \in [-1, 1]^2
//
// Global 3D physical coordinates given by the mesh: xx \in [-R, R]^3
//   with R radius of the sphere
//
// Local 3D physical coordinates on the 2D manifold: x \in [-l, l]^3
//   with l half edge of the cube inscribed in the sphere
//
// Change of coordinates matrix computed by the library:
//   (physical 3D coords relative to reference 2D coords)
//   dxx_j/dX_i (indicial notation) [3 * 2]
//
// Change of coordinates x (on the 2D manifold) relative to xx (phyisical 3D):
//   dx_i/dxx_j (indicial notation) [3 * 3]
//
// Change of coordinates x (on the 2D manifold) relative to X (reference 2D):
//   (by chain rule)
//   dx_i/dX_j [3 * 2] = dx_i/dxx_k [3 * 3] * dxx_k/dX_j [3 * 2]
//
// mod_J is given by the magnitude of the cross product of the columns of dx_i/dX_j
//
// The quadrature data is stored in the array q_data.
//
// We require the determinant of the Jacobian to properly compute integrals of
//   the form: int( u v )
//
// Qdata: mod_J * w
//
// -----------------------------------------------------------------------------
CEED_QFUNCTION(SetupMassGeo)(void *ctx, const CeedInt Q,
                             const CeedScalar *const *in,
                             CeedScalar *const *out) {
  // Inputs
  const CeedScalar *X = in[0], *J = in[1], *w = in[2];
  // Outputs
  CeedScalar *q_data = out[0];

  // Quadrature Point Loop
  CeedPragmaSIMD
  for (CeedInt i=0; i<Q; i++) {
    // Read global Cartesian coordinates
    const CeedScalar xx[3] = {X[i+0*Q],
                              X[i+1*Q],
                              X[i+2*Q]
                             };

    // Read dxxdX Jacobian entries, stored as
    // 0 3
    // 1 4
    // 2 5
    const CeedScalar dxxdX[3][2] = {{J[i+Q*0],
                                     J[i+Q*3]},
                                    {J[i+Q*1],
                                     J[i+Q*4]},
                                    {J[i+Q*2],
                                     J[i+Q*5]}
                                   };

    // Setup
    // x = xx (xx^T xx)^{-1/2}
    // dx/dxx = I (xx^T xx)^{-1/2} - xx xx^T (xx^T xx)^{-3/2}
    const CeedScalar mod_xx_sq = xx[0]*xx[0]+xx[1]*xx[1]+xx[2]*xx[2];
    CeedScalar xx_sq[3][3];
    for (int j=0; j<3; j++)
      for (int k=0; k<3; k++)
        xx_sq[j][k] = xx[j]*xx[k] / (sqrt(mod_xx_sq) * mod_xx_sq);

    const CeedScalar dxdxx[3][3] = {{1./sqrt(mod_xx_sq) - xx_sq[0][0],
                                     -xx_sq[0][1],
                                     -xx_sq[0][2]},
                                    {-xx_sq[1][0],
                                     1./sqrt(mod_xx_sq) - xx_sq[1][1],
                                     -xx_sq[1][2]},
                                    {-xx_sq[2][0],
                                     -xx_sq[2][1],
                                     1./sqrt(mod_xx_sq) - xx_sq[2][2]}
                                   };

    CeedScalar dxdX[3][2];
    for (int j=0; j<3; j++)
      for (int k=0; k<2; k++) {
        dxdX[j][k] = 0;
        for (int l=0; l<3; l++)
          dxdX[j][k] += dxdxx[j][l]*dxxdX[l][k];
      }

    // J is given by the cross product of the columns of dxdX
    const CeedScalar J[3] = {dxdX[1][0]*dxdX[2][1] - dxdX[2][0]*dxdX[1][1],
                             dxdX[2][0]*dxdX[0][1] - dxdX[0][0]*dxdX[2][1],
                             dxdX[0][0]*dxdX[1][1] - dxdX[1][0]*dxdX[0][1]
                            };

    // Use the magnitude of J as our detJ (volume scaling factor)
    const CeedScalar mod_J = sqrt(J[0]*J[0]+J[1]*J[1]+J[2]*J[2]);

    // Interp-to-Interp q_data
    q_data[i+Q*0] = mod_J * w[i];
  } // End of Quadrature Point Loop

  return 0;
}

// -----------------------------------------------------------------------------
// This QFunction sets up the rhs and true solution for the problem
// -----------------------------------------------------------------------------
CEED_QFUNCTION(SetupMassRhs)(void *ctx, const CeedInt Q,
                             const CeedScalar *const *in,
                             CeedScalar *const *out) {
  // Inputs
  const CeedScalar *X = in[0], *q_data = in[1];
  // Outputs
  CeedScalar *true_soln = out[0], *rhs = out[1];

  // Context
  const CeedScalar *context = (const CeedScalar*)ctx;
  const CeedScalar R        = context[0];

  // Quadrature Point Loop
  CeedPragmaSIMD
  for (CeedInt i=0; i<Q; i++) {
    // Compute latitude
    const CeedScalar theta =  asin(X[i+2*Q] / R);

    // Use absolute value of latitude for true solution
    true_soln[i] = fabs(theta);

    rhs[i] = q_data[i] * true_soln[i];
  } // End of Quadrature Point Loop

  return 0;
}

// -----------------------------------------------------------------------------
// This QFunction applies the mass operator for a scalar field.
//
// Inputs:
//   u     - Input vector at quadrature points
//   q_data - Geometric factors
//
// Output:
//   v     - Output vector (test functions) at quadrature points
//
// -----------------------------------------------------------------------------
CEED_QFUNCTION(Mass)(void *ctx, const CeedInt Q,
                     const CeedScalar *const *in, CeedScalar *const *out) {
  // Inputs
  const CeedScalar *u = in[0], *q_data = in[1];
  // Outputs
  CeedScalar *v = out[0];

  // Quadrature Point Loop
  CeedPragmaSIMD
  for (CeedInt i=0; i<Q; i++)
    v[i] = q_data[i] * u[i];

  return 0;
}
// -----------------------------------------------------------------------------

#endif // bp1sphere_h