JUCE/modules/juce_dsp/maths/juce_Matrix.h

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

   This file is part of the JUCE library.
   Copyright (c) 2017 - ROLI Ltd.

   JUCE is an open source library subject to commercial or open-source
   licensing.

   By using JUCE, you agree to the terms of both the JUCE 5 End-User License
   Agreement and JUCE 5 Privacy Policy (both updated and effective as of the
   27th April 2017).

   End User License Agreement: www.juce.com/juce-5-licence
   Privacy Policy: www.juce.com/juce-5-privacy-policy

   Or: You may also use this code under the terms of the GPL v3 (see
   www.gnu.org/licenses).

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

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

/**
    General matrix and vectors class, meant for classic math manipulation such as
    additions, multiplications, and linear systems of equations solving.

    @see LinearAlgebra
*/
template<typename ElementType>
class Matrix
{
public:
    //==============================================================================
    /** Creates a new matrix with a given number of rows and columns. */
    Matrix (size_t numRows, size_t numColumns)
        : rows (numRows), columns (numColumns)
    {
        resize();
        clear();
    }

    /** Creates a new matrix with a given number of rows and columns, with initial
        data coming from an array, stored in row-major order.
    */
    Matrix (size_t numRows, size_t numColumns, const ElementType* dataPointer)
        : rows (numRows), columns (numColumns)
    {
        resize();
        memcpy (data.getRawDataPointer(), dataPointer, rows * columns * sizeof (ElementType));
    }

    /** Creates a copy of another matrix. */
    Matrix (const Matrix&) = default;

    /** Moves a copy of another matrix. */
    Matrix (Matrix&&) noexcept = default;

    /** Creates a copy of another matrix. */
    Matrix& operator= (const Matrix&) = default;

    /** Moves another matrix into this one */
    Matrix& operator= (Matrix&&) noexcept = default;

    //==============================================================================
    /** Creates the identity matrix */
    static Matrix identity (size_t size);

    /** Creates a Toeplitz Matrix from a vector with a given squared size */
    static Matrix toeplitz (const Matrix& vector, size_t size);

    /** Creates a squared size x size Hankel Matrix from a vector with an optional offset.

        @param vector    The vector from which the Hankel matrix should be generated.
                         Its number of rows should be at least 2 * (size - 1) + 1
        @param size      The size of resulting square matrix.
        @param offset    An optional offset into the given vector.
    */
    static Matrix hankel (const Matrix& vector, size_t size, size_t offset = 0);

    //==============================================================================
    /** Returns the number of rows in the matrix. */
    size_t getNumRows() const noexcept                 { return rows; }

    /** Returns the number of columns in the matrix. */
    size_t getNumColumns() const noexcept              { return columns; }

    /** Returns an Array of 2 integers with the number of rows and columns in the
        matrix.
    */
    Array<size_t> getSize() const noexcept             { return {{ rows, columns }}; }

    /** Fills the contents of the matrix with zeroes. */
    void clear() noexcept                              { zeromem (data.begin(), sizeof (ElementType) * (size_t) data.size()); }

    //==============================================================================
    /** Swaps the contents of two rows in the matrix and returns a reference to itself. */
    Matrix& swapRows (size_t rowOne, size_t rowTwo) noexcept;

    /** Swaps the contents of two columns in the matrix and returns a reference to itself. */
    Matrix& swapColumns (size_t columnOne, size_t columnTwo) noexcept;

    //==============================================================================
    /** Returns the value of the matrix at a given row and column (for reading). */
    inline ElementType operator() (size_t row, size_t column) const noexcept
    {
        jassert (row < rows && column < columns);
        return data.getReference (static_cast<int> (dataAcceleration.getReference (static_cast<int> (row))) + static_cast<int> (column));
    }

    /** Returns the value of the matrix at a given row and column (for modifying). */
    inline ElementType& operator() (size_t row, size_t column) noexcept
    {
        jassert (row < rows && column < columns);
        return data.getReference (static_cast<int> (dataAcceleration.getReference (static_cast<int> (row))) + static_cast<int> (column));
    }

    /** Returns a pointer to the raw data of the matrix object, ordered in row-major
        order (for modifying).
    */
    inline ElementType* getRawDataPointer() noexcept                    { return data.getRawDataPointer(); }

    /** Returns a pointer to the raw data of the matrix object, ordered in row-major
        order (for reading).
     */
    inline const ElementType* getRawDataPointer() const noexcept        { return data.begin(); }

    //==============================================================================
    /** Addition of two matrices */
    inline Matrix& operator+= (const Matrix& other) noexcept            { return apply (other, std::plus<ElementType>()); }

    /** Subtraction of two matrices */
    inline Matrix& operator-= (const Matrix& other) noexcept            { return apply (other, std::minus<ElementType>()); }

    /** Scalar multiplication */
    inline Matrix& operator*= (ElementType scalar) noexcept
    {
        std::for_each (begin(), end(), [scalar] (ElementType& x) { x*= scalar; });
        return *this;
    }

    /** Addition of two matrices */
    inline Matrix operator+ (const Matrix& other) const                 { Matrix result (*this); result += other;  return result; }

    /** Addition of two matrices */
    inline Matrix operator- (const Matrix& other) const                 { Matrix result (*this); result -= other;  return result; }

    /** Scalar multiplication */
    inline Matrix operator* (ElementType scalar) const                  { Matrix result (*this); result *= scalar; return result; }

    /** Matrix multiplication */
    Matrix operator* (const Matrix& other) const;

    /** Does a hadarmard product with the receiver and other and stores the result in the receiver */
    inline Matrix& hadarmard (const Matrix& other) noexcept             { return apply (other, std::multiplies<ElementType>()); }

    /** Does a hadarmard product with a and b returns the result. */
    static inline Matrix hadarmard (const Matrix& a, const Matrix& b)   { Matrix result (a); result.hadarmard (b); return result; }

    //==============================================================================
    /** Compare to matrices with a given tolerance */
    static bool compare (const Matrix& a, const Matrix& b, ElementType tolerance = 0) noexcept;

    /* Comparison operator */
    inline bool operator== (const Matrix& other) const noexcept      { return compare (*this, other); }

    //==============================================================================
    /** Tells if the matrix is a square matrix */
    bool isSquare() const noexcept                                   { return rows == columns; }

    /** Tells if the matrix is a vector */
    bool isVector() const noexcept                                   { return isOneColumnVector() || isOneRowVector(); }

    /** Tells if the matrix is a one column vector */
    bool isOneColumnVector() const noexcept                          { return columns == 1; }

    /** Tells if the matrix is a one row vector */
    bool isOneRowVector() const noexcept                             { return rows == 1; }

    /** Tells if the matrix is a null matrix */
    bool isNullMatrix() const noexcept                               { return rows == 0 || columns == 0; }

    //==============================================================================
    /** Solves a linear system of equations represented by this object and the argument b,
        using various algorithms depending on the size of the arguments.

        The matrix must be a square matrix N times N, and b must be a vector N times 1,
        with the coefficients of b. After the execution of the algorithm,
        the vector b will contain the solution.

        Returns true if the linear system of euqations was successfully solved.
     */
    bool solve (Matrix& b) const noexcept;

    //==============================================================================
    /** Returns a String displaying in a convenient way the matrix contents. */
    String toString() const;

    //==============================================================================
    ElementType* begin() noexcept                   { return data.begin(); }
    ElementType* end() noexcept                     { return data.end(); }

    const ElementType* begin() const noexcept       { return &data.getReference (0); }
    const ElementType* end()   const noexcept       { return begin() + data.size(); }

private:
    //==============================================================================
    /** Resizes the matrix. */
    void resize()
    {
        data.resize (static_cast<int> (columns * rows));
        dataAcceleration.resize (static_cast<int> (rows));

        for (size_t i = 0; i < rows; ++i)
            dataAcceleration.setUnchecked (static_cast<int> (i), i * columns);
    }

    template <typename BinaryOperation>
    Matrix& apply (const Matrix& other, BinaryOperation binaryOp)
    {
        jassert (rows == other.rows && columns == other.columns);

        auto* dst = getRawDataPointer();

        for (auto src : other)
        {
            *dst = binaryOp (*dst, src);
            ++dst;
        }

        return *this;
    }

    //==============================================================================
    Array<ElementType> data;
    Array<size_t> dataAcceleration;

    size_t rows, columns;

    //==============================================================================
    JUCE_LEAK_DETECTOR (Matrix)
};