/*
  ==============================================================================

   This file is part of the JUCE framework.
   Copyright (c) Raw Material Software Limited

   JUCE is an open source framework subject to commercial or open source
   licensing.

   By downloading, installing, or using the JUCE framework, or combining the
   JUCE framework with any other source code, object code, content or any other
   copyrightable work, you agree to the terms of the JUCE End User Licence
   Agreement, and all incorporated terms including the JUCE Privacy Policy and
   the JUCE Website Terms of Service, as applicable, which will bind you. If you
   do not agree to the terms of these agreements, we will not license the JUCE
   framework to you, and you must discontinue the installation or download
   process and cease use of the JUCE framework.

   JUCE End User Licence Agreement: https://juce.com/legal/juce-8-licence/
   JUCE Privacy Policy: https://juce.com/juce-privacy-policy
   JUCE Website Terms of Service: https://juce.com/juce-website-terms-of-service/

   Or:

   You may also use this code under the terms of the AGPLv3:
   https://www.gnu.org/licenses/agpl-3.0.en.html

   THE JUCE FRAMEWORK IS PROVIDED "AS IS" WITHOUT ANY WARRANTY, AND ALL
   WARRANTIES, WHETHER EXPRESSED OR IMPLIED, INCLUDING WARRANTY OF
   MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE, ARE DISCLAIMED.

  ==============================================================================
*/

namespace juce::dsp
{

template <typename ElementType>
Matrix<ElementType> Matrix<ElementType>::identity (size_t size)
{
    Matrix result (size, size);

    for (size_t i = 0; i < size; ++i)
        result (i, i) = 1;

    return result;
}

template <typename ElementType>
Matrix<ElementType> Matrix<ElementType>::toeplitz (const Matrix& vector, size_t size)
{
    jassert (vector.isOneColumnVector());
    jassert (size <= vector.rows);

    Matrix result (size, size);

    for (size_t i = 0; i < size; ++i)
        result (i, i) = vector (0, 0);

    for (size_t i = 1; i < size; ++i)
        for (size_t j = i; j < size; ++j)
            result (j, j - i) = result (j - i, j) = vector (i, 0);

    return result;
}

template <typename ElementType>
Matrix<ElementType> Matrix<ElementType>::hankel (const Matrix& vector, size_t size, size_t offset)
{
    jassert (vector.isOneColumnVector());
    jassert (vector.rows >= (2 * (size - 1) + 1));

    Matrix result (size, size);

    for (size_t i = 0; i < size; ++i)
        result (i, i) = vector ((2 * i) + offset, 0);

    for (size_t i = 1; i < size; ++i)
        for (size_t j = i; j < size; ++j)
            result (j, j - i) = result (j - i, j) = vector (i + 2 * (j - i) + offset, 0);

    return result;
}

//==============================================================================
template <typename ElementType>
Matrix<ElementType>& Matrix<ElementType>::swapColumns (size_t columnOne, size_t columnTwo) noexcept
{
    jassert (columnOne < columns && columnTwo < columns);

    auto* p = data.getRawDataPointer();

    for (size_t i = 0; i < rows; ++i)
    {
        auto offset = dataAcceleration.getUnchecked (static_cast<int> (i));
        std::swap (p[offset + columnOne], p[offset + columnTwo]);
    }

    return *this;
}

template <typename ElementType>
Matrix<ElementType>& Matrix<ElementType>::swapRows (size_t rowOne, size_t rowTwo) noexcept
{
    jassert (rowOne < rows && rowTwo < rows);

    auto offset1 = rowOne * columns;
    auto offset2 = rowTwo * columns;

    auto* p = data.getRawDataPointer();

    for (size_t i = 0; i < columns; ++i)
        std::swap (p[offset1 + i], p[offset2 + i]);

    return *this;
}

//==============================================================================
template <typename ElementType>
Matrix<ElementType> Matrix<ElementType>::operator* (const Matrix<ElementType>& other) const
{
    auto n = getNumRows(), m = other.getNumColumns(), p = getNumColumns();
    Matrix result (n, m);

    jassert (p == other.getNumRows());

    size_t offsetMat = 0, offsetlhs = 0;

    auto* dst = result.getRawDataPointer();
    auto* a = getRawDataPointer();
    auto* b = other.getRawDataPointer();

    for (size_t i = 0; i < n; ++i)
    {
        size_t offsetrhs = 0;

        for (size_t k = 0; k < p; ++k)
        {
            auto ak = a[offsetlhs++];

            for (size_t j = 0; j < m; ++j)
                dst[offsetMat + j] += ak * b[offsetrhs + j];

            offsetrhs += m;
        }

        offsetMat += m;
    }

    return result;
}

//==============================================================================
template <typename ElementType>
bool Matrix<ElementType>::compare (const Matrix& a, const Matrix& b, ElementType tolerance) noexcept
{
    if (a.rows != b.rows || a.columns != b.columns)
        return false;

    tolerance = std::abs (tolerance);

    auto* bPtr = b.begin();
    for (auto aValue : a)
        if (std::abs (aValue - *bPtr++) > tolerance)
            return false;

    return true;
}

//==============================================================================
template <typename ElementType>
bool Matrix<ElementType>::solve (Matrix& b) const noexcept
{
    auto n = columns;
    jassert (n == n && n == b.rows && b.isOneColumnVector());

    auto* x = b.getRawDataPointer();
    const auto& A = *this;

    switch (n)
    {
        case 1:
        {
            auto denominator = A (0,0);

            if (approximatelyEqual (denominator, (ElementType) 0))
                return false;

            b (0, 0) /= denominator;
        }
        break;

        case 2:
        {
            auto denominator = A (0, 0) * A (1, 1) - A (0, 1) * A (1, 0);

            if (approximatelyEqual (denominator, (ElementType) 0))
                return false;

            auto factor = (1 / denominator);
            auto b0 = x[0], b1 = x[1];

            x[0] = factor * (A (1, 1) * b0 - A (0, 1) * b1);
            x[1] = factor * (A (0, 0) * b1 - A (1, 0) * b0);
        }
        break;

        case 3:
        {
            auto denominator = A (0, 0) * (A (1, 1) * A (2, 2) - A (1, 2) * A (2, 1))
                             + A (0, 1) * (A (1, 2) * A (2, 0) - A (1, 0) * A (2, 2))
                             + A (0, 2) * (A (1, 0) * A (2, 1) - A (1, 1) * A (2, 0));

            if (approximatelyEqual (denominator, (ElementType) 0))
                return false;

            auto factor = 1 / denominator;
            auto b0 = x[0], b1 = x[1], b2 = x[2];

            x[0] =  ( ( A (0, 1) * A (1, 2) - A (0, 2) * A (1, 1)) * b2
                    + (-A (0, 1) * A (2, 2) + A (0, 2) * A (2, 1)) * b1
                    + ( A (1, 1) * A (2, 2) - A (1, 2) * A (2, 1)) * b0) * factor;

            x[1] = -( ( A (0, 0) * A (1, 2) - A (0, 2) * A (1, 0)) * b2
                    + (-A (0, 0) * A (2, 2) + A (0, 2) * A (2, 0)) * b1
                    + ( A (1, 0) * A (2, 2) - A (1, 2) * A (2, 0)) * b0) * factor;

            x[2] =  ( ( A (0, 0) * A (1, 1) - A (0, 1) * A (1, 0)) * b2
                    + (-A (0, 0) * A (2, 1) + A (0, 1) * A (2, 0)) * b1
                    + ( A (1, 0) * A (2, 1) - A (1, 1) * A (2, 0)) * b0) * factor;
        }
        break;


        default:
        {
            Matrix<ElementType> M (A);

            for (size_t j = 0; j < n; ++j)
            {
                if (approximatelyEqual (M (j, j), (ElementType) 0))
                {
                    auto i = j;
                    while (i < n && approximatelyEqual (M (i, j), (ElementType) 0))
                        ++i;

                    if (i == n)
                        return false;

                    for (size_t k = 0; k < n; ++k)
                        M (j, k) += M (i, k);

                    x[j] += x[i];
                }

                auto t = 1 / M (j, j);

                for (size_t k = 0; k < n; ++k)
                    M (j, k) *= t;

                x[j] *= t;

                for (size_t k = j + 1; k < n; ++k)
                {
                    auto u = -M (k, j);

                    for (size_t l = 0; l < n; ++l)
                        M (k, l) += u * M (j, l);

                    x[k] += u * x[j];
                }
            }

            for (int k = static_cast<int> (n) - 2; k >= 0; --k)
                for (size_t i = static_cast<size_t> (k) + 1; i < n; ++i)
                    x[k] -= M (static_cast<size_t> (k), i) * x[i];
        }
    }

    return true;
}

//==============================================================================
template <typename ElementType>
String Matrix<ElementType>::toString() const
{
    StringArray entries;
    int sizeMax = 0;

    auto* p = data.begin();

    for (size_t i = 0; i < rows; ++i)
    {
        for (size_t j = 0; j < columns; ++j)
        {
            String entry (*p++, 4);
            sizeMax = jmax (sizeMax, entry.length());

            entries.add (entry);
        }
    }

    sizeMax = ((sizeMax + 1) / 4 + 1) * 4;

    MemoryOutputStream result;

    auto n = static_cast<size_t> (entries.size());

    for (size_t i = 0; i < n; ++i)
    {
        result << entries[(int) i].paddedRight (' ', sizeMax);

        if (i % columns == (columns - 1))
            result << newLine;
    }

    return result.toString();
}

template class Matrix<float>;
template class Matrix<double>;

} // namespace juce::dsp