// This file is triangularView of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
// SPDX-License-Identifier: MPL-2.0

#include "main.h"

template <typename MatrixType>
void bandmatrix(const MatrixType& _m) {
  typedef typename MatrixType::Scalar Scalar;
  typedef typename NumTraits<Scalar>::Real RealScalar;
  typedef Matrix<Scalar, Dynamic, Dynamic> DenseMatrixType;

  Index rows = _m.rows();
  Index cols = _m.cols();
  Index supers = _m.supers();
  Index subs = _m.subs();

  MatrixType m(rows, cols, supers, subs);

  DenseMatrixType dm1(rows, cols);
  dm1.setZero();

  m.diagonal().setConstant(123);
  dm1.diagonal().setConstant(123);
  for (int i = 1; i <= m.supers(); ++i) {
    m.diagonal(i).setConstant(static_cast<RealScalar>(i));
    dm1.diagonal(i).setConstant(static_cast<RealScalar>(i));
  }
  for (int i = 1; i <= m.subs(); ++i) {
    m.diagonal(-i).setConstant(-static_cast<RealScalar>(i));
    dm1.diagonal(-i).setConstant(-static_cast<RealScalar>(i));
  }
  // std::cerr << m.m_data << "\n\n" << m.toDense() << "\n\n" << dm1 << "\n\n\n\n";
  VERIFY_IS_APPROX(dm1, m.toDenseMatrix());

  for (int i = 0; i < cols; ++i) {
    m.col(i).setConstant(static_cast<RealScalar>(i + 1));
    dm1.col(i).setConstant(static_cast<RealScalar>(i + 1));
  }
  Index d = (std::min)(rows, cols);
  Index a = std::max<Index>(0, cols - d - supers);
  Index b = std::max<Index>(0, rows - d - subs);
  if (a > 0) dm1.block(0, d + supers, rows, a).setZero();
  dm1.block(0, supers + 1, cols - supers - 1 - a, cols - supers - 1 - a).template triangularView<Upper>().setZero();
  dm1.block(subs + 1, 0, rows - subs - 1 - b, rows - subs - 1 - b).template triangularView<Lower>().setZero();
  if (b > 0) dm1.block(d + subs, 0, b, cols).setZero();
  // std::cerr << m.m_data << "\n\n" << m.toDense() << "\n\n" << dm1 << "\n\n";
  VERIFY_IS_APPROX(dm1, m.toDenseMatrix());
}

using Eigen::internal::BandMatrix;

// diagonal<N>() of a const band matrix, and the sub and super diagonals of a const tridiagonal one.
template <int>
void bandmatrix_const_diagonals() {
  BandMatrix<double, Dynamic, Dynamic, 2, 1> band(6, 7, 2, 1);
  band.coeffs().setRandom();
  const BandMatrix<double, Dynamic, Dynamic, 2, 1>& constBand = band;
  VERIFY_IS_EQUAL(RowVectorXd(constBand.diagonal<2>()), RowVectorXd(band.diagonal(2)));
  VERIFY_IS_EQUAL(RowVectorXd(constBand.diagonal<-1>()), RowVectorXd(band.diagonal(-1)));

  Eigen::internal::TridiagonalMatrix<double, Dynamic, 0> tri(5);
  tri.coeffs().setRandom();
  const Eigen::internal::TridiagonalMatrix<double, Dynamic, 0>& constTri = tri;
  VERIFY_IS_EQUAL(RowVectorXd(constTri.super()), RowVectorXd(tri.diagonal(1)));
  VERIFY_IS_EQUAL(RowVectorXd(constTri.sub()), RowVectorXd(tri.diagonal(-1)));
}

// A self-adjoint tridiagonal matrix stores the subdiagonal only; its superdiagonal is the conjugate.
template <typename Scalar>
void bandmatrix_selfadjoint_diagonals() {
  using RowVector = Matrix<Scalar, 1, Dynamic>;
  Eigen::internal::TridiagonalMatrix<Scalar, Dynamic, SelfAdjoint> tri(5);
  tri.coeffs().setRandom();
  const Eigen::internal::TridiagonalMatrix<Scalar, Dynamic, SelfAdjoint>& constTri = tri;
  const RowVector sub = tri.diagonal(-1);
  VERIFY_IS_EQUAL(RowVector(tri.sub()), sub);
  VERIFY_IS_EQUAL(RowVector(tri.super()), RowVector(sub.conjugate()));
  VERIFY_IS_EQUAL(RowVector(constTri.super()), RowVector(sub.conjugate()));
}

EIGEN_DECLARE_TEST(bandmatrix) {
  CALL_SUBTEST(bandmatrix_const_diagonals<0>());
  CALL_SUBTEST(bandmatrix_selfadjoint_diagonals<double>());
  CALL_SUBTEST(bandmatrix_selfadjoint_diagonals<std::complex<double>>());
  for (int i = 0; i < 10 * g_repeat; i++) {
    Index rows = internal::random<Index>(1, 10);
    Index cols = internal::random<Index>(1, 10);
    Index sups = internal::random<Index>(0, cols - 1);
    Index subs = internal::random<Index>(0, rows - 1);
    CALL_SUBTEST(bandmatrix(BandMatrix<float>(rows, cols, sups, subs)));
  }
}