// Copyright (c) 2017-2018, 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.

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

// *****************************************************************************
//   BP 1
// *****************************************************************************
CEED_QFUNCTION(masssetupf)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
  CeedScalar *rho = out[0], *rhs = out[1];
  const CeedScalar *x = in[0];
  const CeedScalar *J = in[1];
  const CeedScalar *w = in[2];

  // Quadrature Point Loop
  for (CeedInt i=0; i<Q; i++) {
    CeedScalar det = (J[i+Q*0]*(J[i+Q*4]*J[i+Q*8] - J[i+Q*5]*J[i+Q*7]) -
                      J[i+Q*1]*(J[i+Q*3]*J[i+Q*8] - J[i+Q*5]*J[i+Q*6]) +
                      J[i+Q*2]*(J[i+Q*3]*J[i+Q*7] - J[i+Q*4]*J[i+Q*6]));
    rho[i] = det * w[i];
    rhs[i] = rho[i] * w[i] * 
               sqrt(x[i]*x[i] + x[i+Q]*x[i+Q] + x[i+2*Q]*x[i+2*Q]);
  } // End of Quadrature Point Loop
  return 0;
}

CEED_QFUNCTION int massf(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
  const CeedScalar *u = in[0];
  const CeedScalar *rho = in[1];
  CeedScalar *v = out[0];

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

  return 0;
}
// *****************************************************************************
//   BP 3
// *****************************************************************************
CEED_QFUNCTION(diffsetupf)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
  #ifndef M_PI
  #define M_PI    3.14159265358979323846
  #endif
  const CeedScalar *x = in[0];
  const CeedScalar *J = in[1];
  const CeedScalar *w = in[2];
  CeedScalar *qd = out[0], *rhs = out[1];

  // Quadrature Point Loop
  for (CeedInt i=0; i<Q; i++) {
    // Stored in Voigt convention
    // 0 5 4
    // 5 1 3
    // 4 3 2
    const CeedScalar J11 = J[i+Q*0];
    const CeedScalar J21 = J[i+Q*1];
    const CeedScalar J31 = J[i+Q*2];
    const CeedScalar J12 = J[i+Q*3];
    const CeedScalar J22 = J[i+Q*4];
    const CeedScalar J32 = J[i+Q*5];
    const CeedScalar J13 = J[i+Q*6];
    const CeedScalar J23 = J[i+Q*7];
    const CeedScalar J33 = J[i+Q*8];
    const CeedScalar A11 = J22*J33 - J23*J32;
    const CeedScalar A12 = J13*J32 - J12*J33;
    const CeedScalar A13 = J12*J23 - J13*J22;
    const CeedScalar A21 = J23*J31 - J21*J33;
    const CeedScalar A22 = J11*J33 - J13*J31;
    const CeedScalar A23 = J13*J21 - J11*J23;
    const CeedScalar A31 = J21*J32 - J22*J31;
    const CeedScalar A32 = J12*J31 - J11*J32;
    const CeedScalar A33 = J11*J22 - J12*J21;
    const CeedScalar qw = w[i] / (J11*A11 + J21*A12 + J31*A13);
    qd[i+Q*0] = qw * (A11*A11 + A12*A12 + A13*A13);
    qd[i+Q*1] = qw * (A21*A21 + A22*A22 + A23*A23);
    qd[i+Q*2] = qw * (A31*A31 + A32*A32 + A33*A33);
    qd[i+Q*3] = qw * (A21*A31 + A22*A32 + A23*A33);
    qd[i+Q*4] = qw * (A11*A31 + A12*A32 + A13*A33);
    qd[i+Q*5] = qw * (A11*A21 + A12*A22 + A13*A23);
    const CeedScalar c[3] = { 0, 1., 2. };
    const CeedScalar k[3] = { 1., 2., 3. };
    const CeedScalar rho = w[i] * (J11*A11 + J21*A12 + J31*A13);
    rhs[i] = rho * M_PI*M_PI * (k[0]*k[0] + k[1]*k[1] + k[2]*k[2]) * 
               sin(M_PI*(c[0] + k[0]*x[i+Q*0])) *
               sin(M_PI*(c[1] + k[1]*x[i+Q*1])) *
               sin(M_PI*(c[2] + k[2]*x[i+Q*2]));
  } // End of Quadrature Point Loop
  return 0;
}

CEED_QFUNCTION int diffusionf(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
  const CeedScalar *ug = in[0];
  const CeedScalar *qd = in[1];
  CeedScalar *vg = out[0];

  // Quadrature Point Loop
  for (CeedInt i=0; i<Q; i++) {
    const CeedScalar ug0 = ug[i+Q*0];
    const CeedScalar ug1 = ug[i+Q*1];
    const CeedScalar ug2 = ug[i+Q*2];
    vg[i+Q*0] = qd[i+Q*0]*ug0 + qd[i+Q*5]*ug1 + qd[i+Q*4]*ug2;
    vg[i+Q*1] = qd[i+Q*5]*ug0 + qd[i+Q*1]*ug1 + qd[i+Q*3]*ug2;
    vg[i+Q*2] = qd[i+Q*4]*ug0 + qd[i+Q*3]*ug1 + qd[i+Q*2]*ug2;
  } // End of Quadrature Point Loop
  return 0;
}