// @HEADER
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//
//                           MiniTensor Package
//                 Copyright (2016) Sandia Corporation
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
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// 1. Redistributions of source code must retain the above copyright
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//
// 2. Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
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// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// Questions: Alejandro Mota (amota@sandia.gov)
//
// ************************************************************************
// @HEADER

#include <ctime>
#include <vector>

#include "gtest/gtest.h"
#include "MiniTensor.h"

int
main(int ac, char* av[])
{
  Kokkos::initialize();

  ::testing::GTEST_FLAG(print_time) = (ac > 1) ? true : false;

  ::testing::InitGoogleTest(&ac, av);

  auto const
  retval = RUN_ALL_TESTS();

  Kokkos::finalize();

  return retval;
}

namespace minitensor {

namespace {

template<typename T>
std::vector<T>
generate_sequence(
    Index const number_elements, T const & start, T const & increment)
{
  std::vector<T>
  v(number_elements);

  for (Index i = 0; i < number_elements; ++i) {
    v[i] = start + i * increment;
  }

  return v;
}

template<typename Tensor, typename Scalar>
bool
test_fundamentals(Index const dimension)
{
  bool
  passed = true;

  Index const
  number_components = integer_power(dimension, Tensor::ORDER);

  std::vector<Scalar> const
  X = generate_sequence<Scalar>(number_components, 1.0, 1.0);

  // Test constructor with pointer
  Tensor const
  A(dimension, &X[0]);

  // Test copy constructor
  Tensor
  B = A;

  Tensor
  C;

  // Test copy assignment
  C = B - A;

  Scalar
  error = norm_f(C);

  bool const
  copy_assigned = error <= machine_epsilon<Scalar>();
  passed = passed && copy_assigned;

  // Test fill with pointer
  B.fill(&X[0]);

  C = B - A;

  error = norm_f(C);

  bool const
  filled_pointer = error <= machine_epsilon<Scalar>();
  passed = passed && filled_pointer;

  std::vector<Scalar> const
  Y = generate_sequence<Scalar>(number_components, -1.0, -1.0);

  C.fill(&Y[0]);

  // Test increment
  C += A;

  error = norm_f(C);

  bool const
  incremented = error <= machine_epsilon<Scalar>();
  passed = passed && incremented;

  C.fill(&X[0]);

  // Test decrement
  C -= A;

  error = norm_f(C);

  bool const
  decremented = error <= machine_epsilon<Scalar>();
  passed = passed && decremented;

  //test Tensor fill and create for Kokkos data types
  Kokkos::View<Scalar *, Kokkos::DefaultHostExecutionSpace>
  X1("X1_kokkos", dimension);

  Kokkos::View<Scalar **, Kokkos::DefaultHostExecutionSpace>
  X2("X2_kokkos", dimension, dimension);

  Kokkos::View<Scalar ***, Kokkos::DefaultHostExecutionSpace>
  X3("X3_kokkos", dimension, dimension, dimension);

  Kokkos::View<Scalar ****, Kokkos::DefaultHostExecutionSpace>
  X4("X4_kokkos", dimension, dimension, dimension, dimension);

  Kokkos::deep_copy(X1, 3.1);
  Kokkos::deep_copy(X2, 3.2);
  Kokkos::deep_copy(X3, 3.3);
  Kokkos::deep_copy(X4, 3.4);

  Tensor
  Z(dimension);

  Index
  rank = 0;

  Index
  temp = number_components;

  while (temp != 1) {
    temp = temp / dimension;
    rank = rank + 1;
    assert(temp > 0);
  }

  switch (rank) {
  default:
    assert(false);
    break;

  case 1:
    Z.fill(X1, 0);
    break;

  case 2:
    Z.fill(X2, 0, 0);
    break;

  case 3:
    Z.fill(X3, 0, 0, 0);
    break;

  case 4:
    Z.fill(X4, 0, 0, 0, 0);
    break;
  }

  // Test copy constructor.
  Tensor const
  U = Z;

  // Test copy assignment.
  Tensor
  V;

  V = U - Z;

  error = norm_f(V);

  bool const
  passed_copy = error <= machine_epsilon<Scalar>();
  passed = passed && passed_copy;

  return passed;
}

template<typename Tensor, typename Scalar>
bool
test_filling(Index const dimension)
{
  bool
  passed = true;

  Index const
  number_components = integer_power(dimension, Tensor::ORDER);

  // Test construct with zeros
  Tensor
  A(dimension, Filler::ZEROS);

  Real
  error = norm_f_square(A);

  bool const
  zeros_constructed = error <= machine_epsilon<Scalar>();
  passed = passed && zeros_constructed;

  // Test construct with ones
  Tensor
  B(dimension, Filler::ONES);

  error = norm_f_square(B) - number_components;

  bool const
  ones_constructed = error <= machine_epsilon<Scalar>();
  passed = passed && ones_constructed;

  // Test construct with random entries
  Tensor
  C(dimension, Filler::RANDOM_UNIFORM);

  error = norm_f(C);

  bool const
  random_constructed = error > 0.0 && error < number_components;
  passed = passed && random_constructed;

  // Test fill with random components
  A.fill(Filler::RANDOM_UNIFORM);

  error = norm_f(A);

  bool const
  random_filled = error > 0.0 && error < number_components;
  passed = passed && random_filled;

  // Test fill with zeros
  B.fill(Filler::ZEROS);

  error = norm_f_square(B);

  bool const
  zeros_filled = error <= machine_epsilon<Scalar>();
  passed = passed && zeros_filled;

  // Test fill with ones
  C.fill(Filler::ZEROS);

  error = norm_f_square(C) - number_components;

  bool const
  ones_filled = error <= machine_epsilon<Scalar>();
  passed = passed && ones_filled;

  return passed;
}

template<typename Tensor, typename Scalar>
bool
test_arithmetic(Index const dimension)
{
  bool
  passed = true;

  Index const
  number_components = integer_power(dimension, Tensor::ORDER);

  std::vector<Scalar> const
  X = generate_sequence<Scalar>(number_components, 1.0, 1.0);

  Real const
  sum_squares = number_components * (number_components + 1) *
      (2 * number_components + 1) / 6;

  // Test addition
  Tensor const
  A(dimension, &X[0]);

  Tensor const
  B = -1.0 * A;

  Tensor const
  C = -1.0 * B;

  Tensor const
  D = A + B;

  Real
  error = norm_f_square(D);

  bool const
  added = error <= machine_epsilon<Scalar>();
  passed = passed && added;

  // Test subtraction
  Tensor const
  E = A - C;

  error = norm_f_square(E);

  bool const
  subtracted = error <= machine_epsilon<Scalar>();
  passed = passed && subtracted;

  // Test scaling
  error = norm_f_square(C) - sum_squares;

  bool const
  scaled = error <= machine_epsilon<Scalar>();
  passed = passed && scaled;

  Tensor const
  F = C / -1.0;

  error = norm_f_square(F) - sum_squares;

  bool const
  divided = error <= machine_epsilon<Scalar>();
  passed = passed && divided;

  Tensor const
  G = 1.0 / C;

  error = norm_f_square(G) - sum_squares;

  bool const
  split = error <= machine_epsilon<Scalar>();
  passed = passed && split;

  return passed;
}

template<typename Matrix, typename Scalar>
bool
test_fundamentals(Index const rows, Index const cols)
{
  bool
  passed = true;

  Index const
  number_components = rows * cols;

  std::vector<Scalar> const
  X = generate_sequence<Scalar>(number_components, 1.0, 1.0);

  // Test constructor with pointer
  Matrix const
  A(rows, cols, &X[0]);

  // Test copy constructor
  Matrix
  B = A;

  Matrix
  C;

  // Test copy assignment
  C = B - A;

  Scalar
  error = norm_f(C);

  bool const
  copy_assigned = error <= machine_epsilon<Scalar>();
  passed = passed && copy_assigned;

  // Test fill with pointer
  B.fill(&X[0]);

  C = B - A;

  error = norm_f(C);

  bool const
  filled_pointer = error <= machine_epsilon<Scalar>();
  passed = passed && filled_pointer;

  std::vector<Scalar> const
  Y = generate_sequence<Scalar>(number_components, -1.0, -1.0);

  C.fill(&Y[0]);

  // Test increment
  C += A;

  error = norm_f(C);

  bool const
  incremented = error <= machine_epsilon<Scalar>();
  passed = passed && incremented;

  C.fill(&X[0]);

  // Test decrement
  C -= A;

  error = norm_f(C);

  bool const
  decremented = error <= machine_epsilon<Scalar>();
  passed = passed && decremented;

  return passed;
}

template<typename Matrix, typename Scalar>
bool
test_filling(Index const rows, Index const cols)
{
  bool
  passed = true;

  Index const
  number_components = rows * cols;

  // Test construct with zeros
  Matrix
  A(rows, cols, Filler::ZEROS);

  Real
  error = norm_f_square(A);

  bool const
  zeros_constructed = error <= machine_epsilon<Scalar>();
  passed = passed && zeros_constructed;

  // Test construct with ones
  Matrix
  B(rows, cols, Filler::ONES);

  error = norm_f_square(B) - number_components;

  bool const
  ones_constructed = error <= machine_epsilon<Scalar>();
  passed = passed && ones_constructed;

  // Test construct with random entries
  Matrix
  C(rows, cols, Filler::RANDOM_UNIFORM);

  error = norm_f(C);

  bool const
  random_constructed = error > 0.0 && error < number_components;
  passed = passed && random_constructed;

  // Test fill with random components
  A.fill(Filler::RANDOM_UNIFORM);

  error = norm_f(A);

  bool const
  random_filled = error > 0.0 && error < number_components;
  passed = passed && random_filled;

  // Test fill with zeros
  B.fill(Filler::ZEROS);

  error = norm_f_square(B);

  bool const
  zeros_filled = error <= machine_epsilon<Scalar>();
  passed = passed && zeros_filled;

  // Test fill with ones
  C.fill(Filler::ZEROS);

  error = norm_f_square(C) - number_components;

  bool const
  ones_filled = error <= machine_epsilon<Scalar>();
  passed = passed && ones_filled;

  return passed;
}

template<typename Matrix, typename Scalar>
bool
test_arithmetic(Index const rows, Index const cols)
{
  bool
  passed = true;

  Index const
  number_components = rows * cols;

  std::vector<Scalar> const
  X = generate_sequence<Scalar>(number_components, 1.0, 1.0);

  Real const
  sum_squares = number_components * (number_components + 1) *
      (2 * number_components + 1) / 6;

  // Test addition
  Matrix const
  A(rows, cols, &X[0]);

  Matrix const
  B = -1.0 * A;

  Matrix const
  C = -1.0 * B;

  Matrix const
  D = A + B;

  Real
  error = norm_f_square(D);

  bool const
  added = error <= machine_epsilon<Scalar>();
  passed = passed && added;

  // Test subtraction
  Matrix const
  E = A - C;

  error = norm_f_square(E);

  bool const
  subtracted = error <= machine_epsilon<Scalar>();
  passed = passed && subtracted;

  // Test scaling
  error = norm_f_square(C) - sum_squares;

  bool const
  scaled = error <= machine_epsilon<Scalar>();
  passed = passed && scaled;

  Matrix const
  F = C / -1.0;

  error = norm_f_square(F) - sum_squares;

  bool const
  divided = error <= machine_epsilon<Scalar>();
  passed = passed && divided;

  Matrix const
  G = 1.0 / C;

  error = norm_f_square(G) - sum_squares;

  bool const
  split = error <= machine_epsilon<Scalar>();
  passed = passed && split;

  return passed;
}

} // anonymous namespace

TEST(MiniTensor, Fundamentals)
{
  bool const
  vector_dynamic_passed = test_fundamentals<Vector<Real>, Real>(3);

  ASSERT_EQ(vector_dynamic_passed, true);

  bool const
  vector_static_passed = test_fundamentals<Vector<Real, 3>, Real>(3);

  ASSERT_EQ(vector_static_passed, true);

  bool const
  tensor_dynamic_passed = test_fundamentals<Tensor<Real>, Real>(3);

  ASSERT_EQ(tensor_dynamic_passed, true);

  bool const
  tensor_static_passed = test_fundamentals<Tensor<Real, 3>, Real>(3);

  ASSERT_EQ(tensor_static_passed, true);

  bool const
  tensor3_dynamic_passed = test_fundamentals<Tensor3<Real>, Real>(3);

  ASSERT_EQ(tensor3_dynamic_passed, true);

  bool const
  tensor3_static_passed = test_fundamentals<Tensor3<Real, 3>, Real>(3);

  ASSERT_EQ(tensor3_static_passed, true);

  bool const
  tensor4_dynamic_passed = test_fundamentals<Tensor4<Real>, Real>(3);

  ASSERT_EQ(tensor4_dynamic_passed, true);

  bool const
  tensor4_static_passed = test_fundamentals<Tensor4<Real, 3>, Real>(3);

  ASSERT_EQ(tensor4_static_passed, true);

  bool const
  matrix_dynamic_passed = test_fundamentals<Matrix<Real>, Real>(4, 3);

  ASSERT_EQ(matrix_dynamic_passed, true);

  bool const
  matrix_static_passed = test_fundamentals<Matrix<Real, 4, 3>, Real>(4, 3);

  ASSERT_EQ(matrix_static_passed, true);
}

TEST(MiniTensor, Filling)
{
  bool const
  vector_dynamic_passed = test_filling<Vector<Real>, Real>(3);

  ASSERT_EQ(vector_dynamic_passed, true);

  bool const
  vector_static_passed = test_filling<Vector<Real, 3>, Real>(3);

  ASSERT_EQ(vector_static_passed, true);

  bool const
  tensor_dynamic_passed = test_filling<Tensor<Real>, Real>(3);

  ASSERT_EQ(tensor_dynamic_passed, true);

  bool const
  tensor_static_passed = test_filling<Tensor<Real, 3>, Real>(3);

  ASSERT_EQ(tensor_static_passed, true);

  bool const
  tensor3_dynamic_passed = test_filling<Tensor3<Real>, Real>(3);

  ASSERT_EQ(tensor3_dynamic_passed, true);

  bool const
  tensor3_static_passed = test_filling<Tensor3<Real, 3>, Real>(3);

  ASSERT_EQ(tensor3_static_passed, true);

  bool const
  tensor4_dynamic_passed = test_filling<Tensor4<Real>, Real>(3);

  ASSERT_EQ(tensor4_dynamic_passed, true);

  bool const
  tensor4_static_passed = test_filling<Tensor4<Real, 3>, Real>(3);

  ASSERT_EQ(tensor4_static_passed, true);

  bool const
  matrix_dynamic_passed = test_filling<Matrix<Real>, Real>(4, 3);

  ASSERT_EQ(matrix_dynamic_passed, true);

  bool const
  matrix_static_passed = test_filling<Matrix<Real, 4, 3>, Real>(4, 3);

  ASSERT_EQ(matrix_static_passed, true);
}

TEST(MiniTensor, Arithmetic)
{
  bool const
  vector_dynamic_passed = test_arithmetic<Vector<Real>, Real>(3);

  ASSERT_EQ(vector_dynamic_passed, true);

  bool const
  vector_static_passed = test_arithmetic<Vector<Real, 3>, Real>(3);

  ASSERT_EQ(vector_static_passed, true);

  bool const
  tensor_dynamic_passed = test_arithmetic<Tensor<Real>, Real>(3);

  ASSERT_EQ(tensor_dynamic_passed, true);

  bool const
  tensor_static_passed = test_arithmetic<Tensor<Real, 3>, Real>(3);

  ASSERT_EQ(tensor_static_passed, true);

  bool const
  tensor3_dynamic_passed = test_arithmetic<Tensor3<Real>, Real>(3);

  ASSERT_EQ(tensor3_dynamic_passed, true);

  bool const
  tensor3_static_passed = test_arithmetic<Tensor3<Real, 3>, Real>(3);

  ASSERT_EQ(tensor3_static_passed, true);

  bool const
  tensor4_dynamic_passed = test_arithmetic<Tensor4<Real>, Real>(3);

  ASSERT_EQ(tensor4_dynamic_passed, true);

  bool const
  tensor4_static_passed = test_arithmetic<Tensor4<Real, 3>, Real>(3);

  ASSERT_EQ(tensor4_static_passed, true);

  bool const
  matrix_dynamic_passed = test_arithmetic<Matrix<Real>, Real>(4, 3);

  ASSERT_EQ(matrix_dynamic_passed, true);

  bool const
  matrix_static_passed = test_arithmetic<Matrix<Real, 4, 3>, Real>(4, 3);

  ASSERT_EQ(matrix_static_passed, true);
}

TEST(MiniTensor, Inverse2x2)
{
  Index const
  N = 2;

  Tensor<Real, N> const
  A = 2.0 * eye<Real, N>() + Tensor<Real, N>(Filler::RANDOM_UNIFORM);

  Tensor<Real, N> const
  B = inverse(A);

  Tensor<Real, N> const
  C = A * B;

  Real const
  error = norm(C - eye<Real, N>()) / norm(A);

  // See Golub & Van Loan, Matrix Computations 4th Ed., pp 122-123
  Real const
  tolerance = 2 * (N - 1) * machine_epsilon<Real>();

  ASSERT_LE(error, tolerance);
}

TEST(MiniTensor, Inverse3x3)
{
  Index const
  N = 3;

  Tensor<Real, N> const
  A = 2.0 * eye<Real, N>() + Tensor<Real, N>(Filler::RANDOM_UNIFORM);

  Tensor<Real, N> const
  B = inverse(A);

  Tensor<Real, N> const
  C = A * B;

  Real const
  error = norm(C - eye<Real, N>()) / norm(A);

  // See Golub & Van Loan, Matrix Computations 4th Ed., pp 122-123
  Real const
  tolerance = 2 * (N - 1) * machine_epsilon<Real>();

  ASSERT_LE(error, tolerance);
}

TEST(MiniTensor, InverseNxN)
{
  Index const
  N = 11;

  Tensor<Real, N> const
  A = 2.0 * eye<Real, N>() + Tensor<Real, N>(Filler::RANDOM_UNIFORM);

  Tensor<Real, N> const
  B = inverse(A);

  Tensor<Real, N> const
  C = A * B;

  Real const
  error = norm(C - eye<Real, N>()) / norm(A);

  // See Golub & Van Loan, Matrix Computations 4th Ed., pp 122-123
  Real const
  tolerance = 2 * (N - 1) * machine_epsilon<Real>();

  ASSERT_LE(error, tolerance);
}

TEST(MiniTensor, Inverse_4th_NxN)
{
  Index const
  N = 4;

  Tensor4<Real, N> const
  A = 2.0 * identity_1<Real, N>() + Tensor4<Real, N>(Filler::RANDOM_UNIFORM);

  Tensor4<Real, N> const
  B = inverse(A);

  Tensor4<Real, N> const
  C = dotdot(A, B);

  Real const
  error = norm_f(C - identity_1<Real, N>()) / norm_f(A);

  // See Golub & Van Loan, Matrix Computations 4th Ed., pp 122-123
  Real const
  tolerance = 2 * (2 * N - 1) * machine_epsilon<Real>();

  ASSERT_LE(error, tolerance);
}

TEST(MiniTensor, TensorManipulation)
{
  Tensor<Real> A = eye<Real>(3);
  Tensor<Real> B(3);
  Tensor<Real> C(3);
  Vector<Real> u(3);

  A = 2.0 * A;
  A(1, 0) = A(0, 1) = 1.0;
  A(2, 1) = A(1, 2) = 1.0;

  B = inverse(A);

  C = A * B;

  ASSERT_LE(norm(C - eye<Real>(3)), machine_epsilon<Real>());

  Real I1_A = I1(A);
  Real I2_A = I2(A);
  Real I3_A = I3(A);

  u(0) = I1_A - 6;
  u(1) = I2_A - 10;
  u(2) = I3_A - 4;

  Real const error = norm(u);

  ASSERT_LE(error, machine_epsilon<Real>());
}

TEST(MiniTensor, Exponential)
{
  Tensor<Real> const A = eye<Real>(3) + Tensor<Real>(3, Filler::ONES);

  Tensor<Real> const B = exp_pade(A);

  Tensor<Real> const C = exp_taylor(A);

  Tensor<Real> const D = B - C;

  Real const error = norm(D) / norm(B);

  ASSERT_LE(error, 2.0 * machine_epsilon<Real>());
}

TEST(MiniTensor, SymmetricEigen)
{
  Tensor<Real> A = eye<Real>(3);
  A(0, 1) = 0.1;
  A(1, 0) = 0.1;

  Tensor<Real> V(3);
  Tensor<Real> D(3);

  std::tie(V, D) = eig_sym(A);

  ASSERT_LE(std::abs(D(0, 0) - 1.1), machine_epsilon<Real>());
  ASSERT_LE(std::abs(D(1, 1) - 1.0), machine_epsilon<Real>());
  ASSERT_LE(std::abs(D(2, 2) - 0.9), machine_epsilon<Real>());
}

TEST(MiniTensor, LeftPolarDecomposition)
{
  Tensor<Real> const X(1.1, 0.2, 0.0, 0.2, 1.0, 0.0, 0.0, 0.0, 1.2);

  Real const
  c = sqrt(2.0) / 2.0;

  Tensor<Real> const Y(c, -c, 0.0, c, c, 0.0, 0.0, 0.0, 1.0);

  Tensor<Real> const F = X * Y;
  Tensor<Real> V(3);
  Tensor<Real> R(3);

  std::tie(V, R) = polar_left(F);

  Real const
  error_x = norm(V - X) / norm(X);

  Real const
  error_y = norm(R - Y) / norm(Y);

  ASSERT_LE(error_x, machine_epsilon<Real>());
  ASSERT_LE(error_y, machine_epsilon<Real>());
}

TEST(MiniTensor, LogRotation)
{
  // Identity rotation
  Tensor<Real>
  I = identity<Real>(3);

  Tensor<Real>
  i = log_rotation(I);

  Real const
  error_I = norm(i) / norm(I);

  ASSERT_LE(error_I, machine_epsilon<Real>());

  // Pi / 4 rotation about Z.
  Real const
  c = sqrt(2.0) / 2.0;

  Tensor<Real> const R(c, -c, 0.0, c, c, 0.0, 0.0, 0.0, 1.0);

  Tensor<Real> const r = log_rotation(R);

  Real const
  Pi = std::acos(-1.0);

  Real const
  error_R = std::abs(r(0,1) + Pi / 4.0);

  ASSERT_LE(error_R, machine_epsilon<Real>());

  Real const
  error_r = std::abs(r(0,1) + r(1,0));

  ASSERT_LE(error_r, machine_epsilon<Real>());

  // Pi rotation about Z
  I(0, 0) = -1.0;
  I(1, 1) = -1.0;

  i = log_rotation(I);

  Real const
  error_pi = 0.5 * (std::abs(i(0, 1) + Pi) + std::abs(i(1, 0) - Pi));

  ASSERT_LE(error_pi, machine_epsilon<Real>());
}

TEST(MiniTensor, BakerCampbellHausdorff)
{
  Real const
  Pi = std::acos(-1.0);

  Real const
  gamma = 0.1;

  Tensor<Real> const u(0, gamma, 0, gamma, 0, 0, 0, 0, 0);

  Tensor<Real> const r(0, -Pi/4, 0, Pi/4, 0, 0, 0, 0, 0);

  Tensor<Real> const f_bch = bch(r, u);

  Tensor<Real> const U = exp(u);

  Tensor<Real> const R = exp(r);

  Tensor<Real> const F = R * U;

  Tensor<Real> const f = log(F);

  Real const
  error = norm(f_bch - f) / norm(F);

  // Our implementation of the Baker-Campbell-Hausdorff
  // formula uses only 4 terms, so we expect some error here.
  Real const
  tolerance = 1.0e-3;

  ASSERT_LE(error, tolerance);
}

TEST(MiniTensor, PolarLeftLog)
{
  Real const
  gamma = 0.1;

  Tensor<Real> const x(0, gamma, 0, gamma, 0, 0, 0, 0, 0);

  Tensor<Real> const X = exp(x);

  Real const
  c = sqrt(2.0) / 2.0;

  Tensor<Real> const Y(c, -c, 0.0, c, c, 0.0, 0.0, 0.0, 1.0);

  Tensor<Real> const F = X * Y;

  Tensor<Real> V(3), R(3), v(3);

  std::tie(V, R, v) = polar_left_logV(F);

  Real const error = norm(v - x) / norm(x);

  Real const
  tolerance = 16.0 * machine_epsilon<Real>();

  ASSERT_LE(error, tolerance);
}

TEST(MiniTensor, VolumetricDeviatoric)
{
  Tensor<Real> A = 3.0 * eye<Real>(3);

  ASSERT_LE(norm(A - vol(A)), machine_epsilon<Real>());

  Tensor<Real> const B = dev(A);

  A(0, 0) = 0.0;
  A(1, 1) = 0.0;
  A(2, 2) = 0.0;

  ASSERT_LE(norm(A - B), machine_epsilon<Real>());
}

TEST(MiniTensor, SVD2x2)
{
  Real const phi = 1.0;

  Real const psi = 2.0;

  Real const s0 = sqrt(3.0);

  Real const s1 = sqrt(2.0);

  Real const cl = cos(phi);

  Real const sl = sin(phi);

  Real const cr = cos(psi);

  Real const sr = sin(psi);

  Tensor<Real> const X(cl, -sl, sl, cl);

  Tensor<Real> const Y(cr, -sr, sr, cr);

  Tensor<Real> const D(s0, 0.0, 0.0, s1);

  Tensor<Real> const A = X * D * transpose(Y);

  Tensor<Real> U(2), S(2), V(2);

  std::tie(U, S, V) = svd(A);

  Tensor<Real> B = U * S * transpose(V);

  Real const error = norm(A - B) / norm(A);

  ASSERT_LE(error, 2.0 * machine_epsilon<Real>());
}

TEST(MiniTensor, SVD3x3)
{
  Tensor<Real> const A(1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0);

  Tensor<Real> U(3), S(3), V(3);

  std::tie(U, S, V) = svd(A);

  Tensor<Real> const B = U * S * transpose(V);

  Real const error = norm(A - B) / norm(A);

  ASSERT_LE(error, 2.0 * machine_epsilon<Real>());
}

TEST(MiniTensor, SVD3x3Fad)
{
  Tensor<Sacado::Fad::DFad<Real>> const
  A(1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0);

  Tensor<Sacado::Fad::DFad<Real>> U(3), S(3), V(3);

  std::tie(U, S, V) = svd(A);

  Tensor<Sacado::Fad::DFad<Real>> const
  B = U * S * transpose(V);

  Sacado::Fad::DFad<Real> const
  error = norm(B - A) / norm(A);

  ASSERT_LE(error, 2.0 * machine_epsilon<Real>());
}

TEST(MiniTensor, MixedTypes)
{
  Tensor<Sacado::Fad::DFad<Real>>
  A(1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0);

  Tensor<Sacado::Fad::DFad<Real>> const
  B(3, Filler::ONES);

  Tensor<Real> const
  C(3, Filler::ONES);

  Real const
  b = 1.0;

  Sacado::Fad::DFad<Real> const
  c = 1.0;

  A += b * B;

  A -= c * C;

  Sacado::Fad::DFad<Real>
  error = norm_f_square(A) - 3.0;

  ASSERT_LE(error, machine_epsilon<Real>());

  A = B + C;

  error = norm_f(A) - 6.0;

  ASSERT_LE(error, machine_epsilon<Real>());

  A = C - B;

  error = norm_f(A);

  ASSERT_LE(error, machine_epsilon<Real>());

  A += C;

  error = norm_f(A) - 3.0;

  ASSERT_LE(error, machine_epsilon<Real>());

  A -= C;

  error = norm_f(A);

  ASSERT_LE(error, machine_epsilon<Real>());
}

TEST(MiniTensor, SymmetricEigen2x2)
{
  Tensor<Real> const A(2.0, 1.0, 1.0, 2.0);

  Tensor<Real> V(2), D(2);

  std::tie(V, D) = eig_sym(A);

  Tensor<Real> const B = V * D * transpose(V);

  Real const error = norm(A - B) / norm(A);

  ASSERT_LE(error, machine_epsilon<Real>());
}

TEST(MiniTensor, SymmetricEigen3x3)
{
  Tensor<Real> const A(2.0, 1.0, 0.0, 1.0, 2.0, 1.0, 0.0, 1.0, 2.0);

  Tensor<Real> V(3), D(3);

  std::tie(V, D) = eig_sym(A);

  Tensor<Real> const B = V * D * transpose(V);

  Real const error = norm(A - B) / norm(A);

  ASSERT_LE(error, 4.0 * machine_epsilon<Real>());
}

TEST(MiniTensor, Polar3x3)
{
  Tensor<Real> const A(2.0, 1.0, 0.0, 0.0, 2.0, 1.0, 0.0, 0.0, 2.0);

  Tensor<Real> R(3), U(3);

  std::tie(R, U) = polar_right(A);

  Tensor<Real> X(3), D(3), Y(3);

  std::tie(X, D, Y) = svd(A);

  Tensor<Real> const B = R - X * transpose(Y) + U - Y * D * transpose(Y);

  Real const error = norm(B) / norm(A);

  ASSERT_LE(error, 8.0 * machine_epsilon<Real>());
}

TEST(MiniTensor, Cholesky)
{
  Tensor<Real> const A(1.0, 1.0, 1.0, 1.0, 5.0, 3.0, 1.0, 3.0, 3.0);

  Tensor<Real> G(3);

  bool is_spd;

  std::tie(G, is_spd) = cholesky(A);

  Tensor<Real> const B(1.0, 0.0, 0.0, 1.0, 2.0, 0.0, 1.0, 1.0, 1.0);

  Real const error = norm(G - B) / norm(A);

  ASSERT_LE(error, machine_epsilon<Real>());
}

TEST(MiniTensor, MechanicsTransforms)
{
  Tensor<Real> const F(0.0, -6.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 1.0 / 3.0);

  Tensor<Real> sigma(0.0, 0.0, 0.0, 0.0, 50.0, 0.0, 0.0, 0.0, 0.0);

  Tensor<Real> const P = piola(F, sigma);

  Real error = std::abs(P(1, 0) - 100.0) / 100.0;

  ASSERT_LE(error, machine_epsilon<Real>());

  sigma = piola_inverse(F, P);

  error = std::abs(sigma(1, 1) - 50.0) / 50.0;

  ASSERT_LE(error, machine_epsilon<Real>());

  Tensor<Real> const E = 0.5 * (t_dot(F, F) - eye<Real>(3));

  Tensor<Real> const e = 0.5 * (eye<Real>(3) - inverse(dot_t(F, F)));

  Tensor<Real> const g = push_forward_covariant(F, E);

  error = norm(g - e) / norm(e);

  ASSERT_LE(error, machine_epsilon<Real>());

  Tensor<Real> const G = pull_back_covariant(F, e);

  error = norm(G - E) / norm(E);

  ASSERT_LE(error, machine_epsilon<Real>());
}

TEST(MiniTensor, KroneckerProduct)
{
  Tensor4<Real> const A = identity_3<Real>(3);

  Tensor<Real> const Q = eye<Real>(3);

  Tensor4<Real> const B = kronecker(Q, A);

  Real const error = norm_f(B - A) / norm_f(A);

  ASSERT_LE(error, machine_epsilon<Real>());
}

TEST(MiniTensor, SegmentLength)
{
  Vector<Real, 3> const u(0.0, 0.0, 0.0);
  Vector<Real, 3> const v(1.0, 2.0, 3.0);

  Real const l = length(u, v);
  Real const n = norm(v);
  Real const error = std::abs(l - n);

  ASSERT_LE(error, machine_epsilon<Real>());
}

TEST(MiniTensor, TriangleArea)
{
  Vector<Real, 3> const a(0.0, 0.0, 0.0);
  Vector<Real, 3> const b(1.0, 0.0, 0.0);
  Vector<Real, 3> const c(0.0, 1.0, 0.0);

  Real const A = area(a, b, c);
  Real const error = std::abs(A - 0.5);

  ASSERT_LE(error, machine_epsilon<Real>());
}

TEST(MiniTensor, QuadArea)
{
  Vector<Real, 3> const a(1.0, 0.0, 0.0);
  Vector<Real, 3> const b(2.0, 1.0, 0.0);
  Vector<Real, 3> const c(1.0, 2.0, 0.0);
  Vector<Real, 3> const d(0.0, 1.0, 0.0);

  Real const A = area(a, b, c, d);
  Real const error = std::abs(A - 2.0);

  ASSERT_LE(error, machine_epsilon<Real>());
}

TEST(MiniTensor, TetVolume)
{
  Vector<Real, 3> const a(0.0, 0.0, 0.0);
  Vector<Real, 3> const b(1.0, 0.0, 0.0);
  Vector<Real, 3> const c(0.0, 1.0, 0.0);
  Vector<Real, 3> const d(0.0, 0.0, 1.0);

  Real const V = volume(a, b, c, d);
  Real const error = std::abs(V - 1.0 / 6.0);

  ASSERT_LE(error, machine_epsilon<Real>());
}

TEST(MiniTensor, HexVolume)
{
  Vector<Real, 3> const a(0.0, 0.0, 0.0);
  Vector<Real, 3> const b(1.0, 0.0, 0.0);
  Vector<Real, 3> const c(1.0, 1.0, 0.0);
  Vector<Real, 3> const d(0.0, 1.0, 0.0);
  Vector<Real, 3> const e(0.0, 0.0, 1.0);
  Vector<Real, 3> const f(1.0, 0.0, 1.0);
  Vector<Real, 3> const g(1.0, 1.0, 1.0);
  Vector<Real, 3> const h(0.0, 1.0, 1.0);

  Real const V = volume(a, b, c, d, e, f, g, h);
  Real const error = std::abs(V - 1.0);

  ASSERT_LE(error, machine_epsilon<Real>());
}

TEST(MiniTensor, TemplateMetaProgramming)
{
  {
    Real
    a = 0.0;

    Sacado::Fad::DFad<Real>
    b = 0.0;

    Real
    c = Sacado::ScalarValue<Real>::eval(a);

    //std::cout << c << '\n';

    Real
    d = Sacado::ScalarValue<Sacado::Fad::DFad<Real>>::eval(b);

    //std::cout << d << '\n';

    bool const
    is_equal = c == d;

    ASSERT_EQ(is_equal, true);
  }

  {
    Vector<Real>
    A(3, Filler::ZEROS);

    Vector<Sacado::Fad::DFad<Real>>
    B(3, Filler::ZEROS);

    Vector<Real>
    C = Sacado::ScalarValue<Vector<Real>>::eval(A);

    //std::cout << C << '\n';

    Vector<Real>
    D = Sacado::ScalarValue<Vector<Sacado::Fad::DFad<Real>>>::eval(B);

    //std::cout << D << '\n';

    bool const
    is_equal = C == D;

    ASSERT_EQ(is_equal, true);
  }

  {
    Tensor<Real>
    A(3, Filler::ZEROS);

    Tensor<Sacado::Fad::DFad<Real>>
    B(3, Filler::ZEROS);

    Tensor<Real>
    C = Sacado::ScalarValue<Tensor<Real>>::eval(A);

    //std::cout << C << '\n';

    Tensor<Real>
    D = Sacado::ScalarValue<Tensor<Sacado::Fad::DFad<Real>>>::eval(B);

    //std::cout << D << '\n';

    bool const
    is_equal = C == D;

    ASSERT_EQ(is_equal, true);
  }

  {
    Tensor3<Real>
    A(3, Filler::ZEROS);

    Tensor3<Sacado::Fad::DFad<Real>>
    B(3, Filler::ZEROS);

    Tensor3<Real>
    C = Sacado::ScalarValue<Tensor3<Real>>::eval(A);

    //std::cout << C << '\n';

    Tensor3<Real>
    D = Sacado::ScalarValue<Tensor3<Sacado::Fad::DFad<Real>>>::eval(B);

    //std::cout << D << '\n';

    bool const
    is_equal = C == D;

    ASSERT_EQ(is_equal, true);
  }

  {
    Tensor4<Real>
    A(3, Filler::ZEROS);

    Tensor4<Sacado::Fad::DFad<Real>>
    B(3, Filler::ZEROS);

    Tensor4<Real>
    C = Sacado::ScalarValue<Tensor4<Real>>::eval(A);

    //std::cout << C << '\n';

    Tensor4<Real>
    D = Sacado::ScalarValue<Tensor4<Sacado::Fad::DFad<Real>>>::eval(B);

    //std::cout << D << '\n';

    bool const
    is_equal = C == D;

    ASSERT_EQ(is_equal, true);
  }

#if !defined(KOKKOS_ENABLE_CUDA)
  {
    //
    // use double explicitly
    //
    using A = Vector<double>;

    using B = Vector<Sacado::Fad::DFad<double>>;

    using C = Vector<Sacado::Fad::DFad<Sacado::Fad::DFad<double>>>;

    std::string const
    double_string = "double";

    std::string const
    fad_string = "Sacado::Fad::DFad< double >";

    std::string
    type_string =
        Sacado::StringName<Sacado::ScalarType<A>::type>::eval();

    ASSERT_EQ(type_string, double_string);

    type_string =
        Sacado::StringName<Sacado::ValueType<A>::type>::eval();

    ASSERT_EQ(type_string, double_string);

    type_string =
        Sacado::StringName<Sacado::ScalarType<B>::type>::eval();

    ASSERT_EQ(type_string, double_string);

    type_string =
        Sacado::StringName<Sacado::ValueType<B>::type>::eval();

    ASSERT_EQ(type_string, double_string);

    type_string =
        Sacado::StringName<Sacado::ScalarType<C>::type>::eval();

    ASSERT_EQ(type_string, double_string);

    type_string =
        Sacado::StringName<Sacado::ValueType<C>::type>::eval();

    ASSERT_EQ(type_string, fad_string);
  }
#endif // KOKKOS_ENABLE_CUDA

}

} // namespace minitensor
