LBPM/common/Array.h

/*
  Copyright 2013--2018 James E. McClure, Virginia Polytechnic & State University
  Copyright Equnior ASA

  This file is part of the Open Porous Media project (OPM).
  OPM is free software: you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published by
  the Free Software Foundation, either version 3 of the License, or
  (at your option) any later version.
  OPM is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.
  You should have received a copy of the GNU General Public License
  along with OPM.  If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef included_ArrayClass
#define included_ArrayClass

#include "common/ArraySize.h"

#include <array>
#include <cstdint>
#include <functional>
#include <initializer_list>
#include <iostream>
#include <memory>
#include <stdint.h>
#include <string>
#include <vector>

/*!
 * Class Array is a multi-dimensional array class written by Mark Berrill
 */
template <class TYPE, class FUN, class Allocator> class Array final {
public: // Constructors / assignment operators
    /*!
     * Create a new empty Array
     */
    Array();

    /*!
     * Create an Array with the given size
     * @param N             Size of the array
     */
    explicit Array(const ArraySize &N);

    /*!
     * Create a new 1D Array with the given number of elements
     * @param N             Number of elements in the array
     */
    explicit Array(size_t N);

    /*!
     * Create a new 2D Array with the given number of rows and columns
     * @param N_rows        Number of rows
     * @param N_columns     Number of columns
     */
    explicit Array(size_t N_rows, size_t N_columns);

    /*!
     * Create a new 3D Array with the given number of rows and columns
     * @param N1            Number of rows
     * @param N2            Number of columns
     * @param N3            Number of elements in the third dimension
     */
    explicit Array(size_t N1, size_t N2, size_t N3);

    /*!
     * Create a new 4D Array with the given number of rows and columns
     * @param N1            Number of elements in the first dimension
     * @param N2            Number of elements in the second dimension
     * @param N3            Number of elements in the third dimension
     * @param N4            Number of elements in the fourth dimension
     */
    explicit Array(size_t N1, size_t N2, size_t N3, size_t N4);

    /*!
     * Create a new 4D Array with the given number of rows and columns
     * @param N1            Number of elements in the first dimension
     * @param N2            Number of elements in the second dimension
     * @param N3            Number of elements in the third dimension
     * @param N4            Number of elements in the fourth dimension
     * @param N5            Number of elements in the fifth dimension
     */
    explicit Array(size_t N1, size_t N2, size_t N3, size_t N4, size_t N5);

    /*!
     * Create a multi-dimensional Array with the given number of elements
     * @param N             Number of elements in each dimension
     * @param data          Optional raw array to copy the src data
     */
    explicit Array(const std::vector<size_t> &N, const TYPE *data = nullptr);

    /*!
     * Create a 1D Array using a string that mimic's MATLAB
     * @param range         Range of the data
     */
    explicit Array(std::string range);

    /*!
     * Create a 1D Array with the given initializer list
     * @param data          Input data
     */
    Array(std::initializer_list<TYPE> data);

    /*!
     * Create a 2D Array with the given initializer lists
     * @param data          Input data
     */
    Array(std::initializer_list<std::initializer_list<TYPE>> data);

    /*!
     * Copy constructor
     * @param rhs           Array to copy
     */
    Array(const Array &rhs);

    /*!
     * Move constructor
     * @param rhs           Array to copy
     */
    Array(Array &&rhs);

    /*!
     * Assignment operator
     * @param rhs           Array to copy
     */
    Array &operator=(const Array &rhs);

    /*!
     * Move assignment operator
     * @param rhs           Array to copy
     */
    Array &operator=(Array &&rhs);

    /*!
     * Assignment operator
     * @param rhs           std::vector to copy
     */
    Array &operator=(const std::vector<TYPE> &rhs);

    //! Is copyable?
    inline bool isCopyable() const { return d_isCopyable; }

    //! Set is copyable
    inline void setCopyable(bool flag) { d_isCopyable = flag; }

    //! Is fixed size?
    inline bool isFixedSize() const { return d_isFixedSize; }

    //! Set is copyable
    inline void setFixedSize(bool flag) { d_isFixedSize = flag; }

public: // Views/copies/subset
    /*!
     * Create a multi-dimensional Array view to a raw block of data
     * @param N             Number of elements in each dimension
     * @param data          Pointer to the data
     */
    static std::unique_ptr<Array> view(const ArraySize &N,
                                       std::shared_ptr<TYPE> data);

    /*!
     * Create a multi-dimensional Array view to a raw block of data
     * @param N             Number of elements in each dimension
     * @param data          Pointer to the data
     */
    static std::unique_ptr<const Array>
    constView(const ArraySize &N, std::shared_ptr<const TYPE> const &data);

    /*!
     * Make this object a view of the src
     * @param src           Source vector to take the view of
     */
    void view2(Array &src);

    /*!
     * Make this object a view of the data
     * @param N             Number of elements in each dimension
     * @param data          Pointer to the data
     */
    void view2(const ArraySize &N, std::shared_ptr<TYPE> data);

    /*!
     * Make this object a view of the raw data (expert use only).
     * Use view2( N, shared_ptr(data,[](TYPE*){}) ) instead.
     *   Note: this interface is not recommended as it does not protect from
     *   the src data being deleted while still being used by the Array.
     *   Additionally for maximum performance it does not set the internal shared_ptr
     *   so functions like getPtr and resize will not work correctly.
     * @param ndim          Number of dimensions
     * @param dims          Number of elements in each dimension
     * @param data          Pointer to the data
     * @param isCopyable    Once the view is created, can the array be copied
     * @param isFixedSize   Once the view is created, is the array size fixed
     */
    inline void viewRaw(int ndim, const size_t *dims, TYPE *data,
                        bool isCopyable = true, bool isFixedSize = true) {
        viewRaw(ArraySize(ndim, dims), data, isCopyable, isFixedSize);
    }

    /*!
     * Make this object a view of the raw data (expert use only).
     * Use view2( N, shared_ptr(data,[](TYPE*){}) ) instead.
     *   Note: this interface is not recommended as it does not protect from
     *   the src data being deleted while still being used by the Array.
     *   Additionally for maximum performance it does not set the internal shared_ptr
     *   so functions like getPtr and resize will not work correctly.
     * @param N             Number of elements in each dimension
     * @param data          Pointer to the data
     * @param isCopyable    Once the view is created, can the array be copied
     * @param isFixedSize   Once the view is created, is the array size fixed
     */
    void viewRaw(const ArraySize &N, TYPE *data, bool isCopyable = true,
                 bool isFixedSize = true);

    /*!
     * Create an array view of the given data (expert use only).
     * Use view2( N, shared_ptr(data,[](TYPE*){}) ) instead.
     *   Note: this interface is not recommended as it does not protect from
     *   the src data being deleted while still being used by the Array.
     *   Additionally for maximum performance it does not set the internal shared_ptr
     *   so functions like getPtr and resize will not work correctly.
     * @param N             Number of elements in each dimension
     * @param data          Pointer to the data
     */
    static inline Array staticView(const ArraySize &N, TYPE *data) {
        Array x;
        x.viewRaw(N, data, true, true);
        return x;
    }

    /*!
     * Convert an array of one type to another.  This may or may not allocate new memory.
     * @param array         Input array
     */
    template <class TYPE2>
    static inline std::unique_ptr<Array<TYPE2, FUN, Allocator>>
    convert(std::shared_ptr<Array<TYPE, FUN, Allocator>> array) {
        auto array2 = std::make_unique<Array<TYPE2>>(array->size());
        array2.copy(*array);
        return array2;
    }

    /*!
     * Convert an array of one type to another.  This may or may not allocate new memory.
     * @param array         Input array
     */
    template <class TYPE2>
    static inline std::unique_ptr<const Array<TYPE2, FUN, Allocator>>
    convert(std::shared_ptr<const Array<TYPE, FUN, Allocator>> array) {
        auto array2 = std::make_unique<Array<TYPE2>>(array->size());
        array2.copy(*array);
        return array2;
    }

    /*!
     * Copy and convert data from another array to this array
     * @param array         Source array
     */
    template <class TYPE2, class FUN2, class Allocator2>
    void inline copy(const Array<TYPE2, FUN2, Allocator2> &array) {
        resize(array.size());
        copy(array.data());
    }

    /*!
     * Copy and convert data from a raw vector to this array.
     *    Note: The current array must be allocated to the proper size first.
     * @param data          Source data
     */
    template <class TYPE2> inline void copy(const TYPE2 *data);

    /*!
     * Copy and convert data from this array to a raw vector.
     * @param data          Source data
     */
    template <class TYPE2> inline void copyTo(TYPE2 *data) const;

    /*!
     * Copy and convert data from this array to a new array
     */
    template <class TYPE2>
    Array<TYPE2, FUN, std::allocator<TYPE2>> inline cloneTo() const {
        Array<TYPE2, FUN, std::allocator<TYPE2>> dst(this->size());
        copyTo(dst.data());
        return dst;
    }

    /*! swap the raw data pointers for the Arrays after checking for compatibility */
    void swap(Array &other);

    /*!
     * Fill the array with the given value
     * @param y         Value to fill
     */
    inline void fill(const TYPE &y) {
        for (auto &x : *this)
            x = y;
    }

    /*!
     * Scale the array by the given value
     * @param y         Value to scale by
     */
    template <class TYPE2> inline void scale(const TYPE2 &y) {
        for (auto &x : *this)
            x *= y;
    }

    /*!
     * Set the values of this array to pow(base, exp)
     * @param base        Base array
     * @param exp         Exponent value
     */
    void pow(const Array &base, const TYPE &exp);

    //! Destructor
    ~Array();

    //! Clear the data in the array
    void clear();

    //! Return the size of the Array
    inline int ndim() const { return d_size.ndim(); }

    //! Return the size of the Array
    inline const ArraySize &size() const { return d_size; }

    //! Return the size of the Array
    inline size_t size(int d) const { return d_size[d]; }

    //! Return the size of the Array
    inline size_t length() const { return d_size.length(); }

    //! Return true if the Array is empty
    inline bool empty() const { return d_size.length() == 0; }

    //! Return true if the Array is not empty
    inline operator bool() const { return d_size.length() != 0; }

    /*!
     * Resize the Array
     * @param N             NUmber of elements
     */
    inline void resize(size_t N) { resize(ArraySize(N)); }

    /*!
     * Resize the Array
     * @param N_row         Number of rows
     * @param N_col         Number of columns
     */
    inline void resize(size_t N_row, size_t N_col) {
        resize(ArraySize(N_row, N_col));
    }

    /*!
     * Resize the Array
     * @param N1            Number of rows
     * @param N2            Number of columns
     * @param N3            Number of elements in the third dimension
     */
    inline void resize(size_t N1, size_t N2, size_t N3) {
        resize(ArraySize(N1, N2, N3));
    }

    /*!
     * Resize the Array
     * @param N             Number of elements in each dimension
     */
    void resize(const ArraySize &N);

    /*!
     * Resize the given dimension of the array
     * @param dim           The dimension to resize
     * @param N             Number of elements for the given dimension
     * @param value         Value to initialize new elements
     */
    void resizeDim(int dim, size_t N, const TYPE &value);

    /*!
     * Reshape the Array (total size of array will not change)
     * @param N             Number of elements in each dimension
     */
    void reshape(const ArraySize &N);

    /*!
     * Remove singleton dimensions.
     */
    void squeeze();

    /*!
     * Reshape the Array so that the number of dimensions is the
     *    max of ndim and the largest dim>1.
     * @param ndim          Desired number of dimensions
     */
    inline void setNdim(int ndim) { d_size.setNdim(ndim); }

    /*!
     * Subset the Array
     * @param index         Index to subset (imin,imax,jmin,jmax,kmin,kmax,...)
     */
    Array subset(const std::vector<size_t> &index) const;

    /*!
     * Subset the Array
     * @param index         Index to subset (ix:kx:jx,iy:ky:jy,...)
     */
    Array subset(const std::vector<Range<size_t>> &index) const;

    /*!
     * Copy data from an array into a subset of this array
     * @param index         Index of the subset (imin,imax,jmin,jmax,kmin,kmax,...)
     * @param subset        The subset array to copy from
     */
    void copySubset(const std::vector<size_t> &index, const Array &subset);

    /*!
     * Copy data from an array into a subset of this array
     * @param index         Index of the subset
     * @param subset        The subset array to copy from
     */
    void copySubset(const std::vector<Range<size_t>> &index,
                    const Array &subset);

    /*!
     * Add data from an array into a subset of this array
     * @param index         Index of the subset (imin,imax,jmin,jmax,kmin,kmax,...)
     * @param subset        The subset array to add from
     */
    void addSubset(const std::vector<size_t> &index, const Array &subset);

    /*!
     * Add data from an array into a subset of this array
     * @param index         Index of the subset
     * @param subset        The subset array to add from
     */
    void addSubset(const std::vector<Range<size_t>> &index,
                   const Array &subset);

public: // Accessors
    /*!
     * Access the desired element
     * @param i             The row index
     */
    ARRAY_ATTRIBUTE inline TYPE &operator()(size_t i) {
        return d_data[d_size.index(i)];
    }

    /*!
     * Access the desired element
     * @param i             The row index
     */
    ARRAY_ATTRIBUTE inline const TYPE &operator()(size_t i) const {
        return d_data[d_size.index(i)];
    }

    /*!
     * Access the desired element
     * @param i             The row index
     * @param j             The column index
     */
    ARRAY_ATTRIBUTE inline TYPE &operator()(size_t i, size_t j) {
        return d_data[d_size.index(i, j)];
    }

    /*!
     * Access the desired element
     * @param i             The row index
     * @param j             The column index
     */
    ARRAY_ATTRIBUTE inline const TYPE &operator()(size_t i, size_t j) const {
        return d_data[d_size.index(i, j)];
    }

    /*!
     * Access the desired element
     * @param i             The row index
     * @param j             The column index
     * @param k             The third index
     */
    ARRAY_ATTRIBUTE inline TYPE &operator()(size_t i, size_t j, size_t k) {
        return d_data[d_size.index(i, j, k)];
    }

    /*!
     * Access the desired element
     * @param i             The row index
     * @param j             The column index
     * @param k             The third index
     */
    ARRAY_ATTRIBUTE inline const TYPE &operator()(size_t i, size_t j,
                                                  size_t k) const {
        return d_data[d_size.index(i, j, k)];
    }

    /*!
     * Access the desired element
     * @param i1            The first index
     * @param i2            The second index
     * @param i3            The third index
     * @param i4            The fourth index
     */
    ARRAY_ATTRIBUTE inline TYPE &operator()(size_t i1, size_t i2, size_t i3,
                                            size_t i4) {
        return d_data[d_size.index(i1, i2, i3, i4)];
    }

    /*!
     * Access the desired element
     * @param i1            The first index
     * @param i2            The second index
     * @param i3            The third index
     * @param i4            The fourth index
     */
    ARRAY_ATTRIBUTE inline const TYPE &operator()(size_t i1, size_t i2,
                                                  size_t i3, size_t i4) const {
        return d_data[d_size.index(i1, i2, i3, i4)];
    }

    /*!
     * Access the desired element
     * @param i1            The first index
     * @param i2            The second index
     * @param i3            The third index
     * @param i4            The fourth index
     * @param i5            The fifth index
     */
    ARRAY_ATTRIBUTE inline TYPE &operator()(size_t i1, size_t i2, size_t i3,
                                            size_t i4, size_t i5) {
        return d_data[d_size.index(i1, i2, i3, i4, i5)];
    }

    /*!
     * Access the desired element
     * @param i1            The first index
     * @param i2            The second index
     * @param i3            The third index
     * @param i4            The fourth index
     * @param i5            The fifth index
     */
    ARRAY_ATTRIBUTE inline const TYPE &
    operator()(size_t i1, size_t i2, size_t i3, size_t i4, size_t i5) const {
        return d_data[d_size.index(i1, i2, i3, i4, i5)];
    }

    /*!
     * Access the desired element as a raw pointer
     * @param i             The global index
     */
    ARRAY_ATTRIBUTE inline TYPE *ptr(size_t i) {
        return i >= d_size.length() ? nullptr : &d_data[i];
    }

    /*!
     * Access the desired element as a raw pointer
     * @param i             The global index
     */
    ARRAY_ATTRIBUTE inline const TYPE *ptr(size_t i) const {
        return i >= d_size.length() ? nullptr : &d_data[i];
    }

    //! Get iterator to beginning of data
    inline TYPE *begin() { return d_data; }

    //! Get iterator to beginning of data
    inline const TYPE *begin() const { return d_data; }

    //! Get iterator to beginning of data
    inline TYPE *end() { return d_data + d_size.length(); }

    //! Get iterator to beginning of data
    inline const TYPE *end() const { return d_data + d_size.length(); }

    //! Return the pointer to the raw data
    inline std::shared_ptr<TYPE> getPtr() { return d_ptr; }

    //! Return the pointer to the raw data
    inline std::shared_ptr<const TYPE> getPtr() const { return d_ptr; }

    //! Return the pointer to the raw data
    ARRAY_ATTRIBUTE inline TYPE *data() { return d_data; }

    //! Return the pointer to the raw data
    ARRAY_ATTRIBUTE inline const TYPE *data() const { return d_data; }

public: // Operator overloading
    //! Check if two matrices are equal
    // Equality means the dimensions and data have to be identical
    bool operator==(const Array &rhs) const;

    //! Check if two matrices are not equal
    inline bool operator!=(const Array &rhs) const {
        return !this->operator==(rhs);
    }

    //! Add another array
    Array &operator+=(const Array &rhs);

    //! Subtract another array
    Array &operator-=(const Array &rhs);

    //! Add a scalar
    Array &operator+=(const TYPE &rhs);

    //! Subtract a scalar
    Array &operator-=(const TYPE &rhs);

public: // Math operations
    //! Concatenates the arrays along the dimension dim.
    static Array cat(const std::vector<Array> &x, int dim = 0);

    //! Concatenates the arrays along the dimension dim.
    static Array cat(const std::initializer_list<Array> &x, int dim = 0);

    //! Concatenates the arrays along the dimension dim.
    static Array cat(size_t N_array, const Array *x, int dim);

    //! Concatenates a given array with the current array
    void cat(const Array &x, int dim = 0);

    //! Initialize the array with random values (defined from the function table)
    //void rand();

    //! Return true if NaNs are present
    bool NaNs() const;

    //! Return the smallest value
    TYPE min() const;

    //! Return the largest value
    TYPE max() const;

    //! Return the sum of all elements
    TYPE sum() const;

    //! Return the mean of all elements
    TYPE mean() const;

    //! Return the min of all elements in a given direction
    Array min(int dir) const;

    //! Return the max of all elements in a given direction
    Array max(int dir) const;

    //! Return the sum of all elements in a given direction
    Array sum(int dir) const;

    //! Return the smallest value
    TYPE min(const std::vector<size_t> &index) const;

    //! Return the largest value
    TYPE max(const std::vector<size_t> &index) const;

    //! Return the sum of all elements
    TYPE sum(const std::vector<size_t> &index) const;

    //! Return the mean of all elements
    TYPE mean(const std::vector<size_t> &index) const;

    //! Return the smallest value
    TYPE min(const std::vector<Range<size_t>> &index) const;

    //! Return the largest value
    TYPE max(const std::vector<Range<size_t>> &index) const;

    //! Return the sum of all elements
    TYPE sum(const std::vector<Range<size_t>> &index) const;

    //! Return the mean of all elements
    TYPE mean(const std::vector<Range<size_t>> &index) const;

    //! Find all elements that match the operator
    std::vector<size_t>
    find(const TYPE &value,
         std::function<bool(const TYPE &, const TYPE &)> compare) const;

    //! Print an array
    void print(std::ostream &os, const std::string &name = "A",
               const std::string &prefix = "") const;

    //! Transpose an array
    Array reverseDim() const;

    /*!
     * @brief  Shift dimensions
     * @details  Shifts the dimensions of the array by N.  When N is positive,
     *    shiftDim shifts the dimensions to the left and wraps the
     *    N leading dimensions to the end.  When N is negative,
     *    shiftDim shifts the dimensions to the right and pads with singletons.
     * @param N             Desired shift
     */
    Array shiftDim(int N) const;

    /*!
     * @brief   Permute array dimensions
     * @details  Rearranges the dimensions of the array so that they
     *    are in the order specified by the vector index.
     *    The array produced has the same values as A but the order of the subscripts
     *    needed to access any particular element are rearranged as specified.
     * @param index        Desired order of the subscripts
     */
    Array permute(const std::vector<uint8_t> &index) const;

    //! Replicate an array a given number of times in each direction
    Array repmat(const std::vector<size_t> &N) const;

    //! Coarsen an array using the given filter
    Array coarsen(const Array &filter) const;

    //! Coarsen an array using the given filter
    Array coarsen(const std::vector<size_t> &ratio,
                  std::function<TYPE(const Array &)> filter) const;

    /*!
     * Perform a element-wise operation y = f(x)
     * @param[in] fun           The function operation
     * @param[in] x             The input array
     */
    static Array transform(std::function<TYPE(const TYPE &)> fun,
                           const Array &x);

    /*!
     * Perform a element-wise operation z = f(x,y)
     * @param[in] fun           The function operation
     * @param[in] x             The first array
     * @param[in] y             The second array
     */
    static Array transform(std::function<TYPE(const TYPE &, const TYPE &)> fun,
                           const Array &x, const Array &y);

    /*!
     * axpby operation: this = alpha*x + beta*this
     * @param[in] alpha         alpha
     * @param[in] x             x
     * @param[in] beta          beta
     */
    void axpby(const TYPE &alpha, const Array &x, const TYPE &beta);

    /*!
     * Linear interpolation
     * @param[in] x             Position as a decimal index
     */
    inline TYPE interp(const std::vector<double> &x) const {
        return interp(x.data());
    }

    /*!
     * Linear interpolation
     * @param[in] x             Position as a decimal index
     */
    TYPE interp(const double *x) const;

    /**
     * \fn equals (Array & const rhs, TYPE tol )
     * \brief  Determine if two Arrays are equal using an absolute tolerance
     * \param[in] rhs Vector to compare to
     * \param[in] tol Tolerance of comparison
     * \return  True iff \f$||\mathit{rhs} - x||_\infty < \mathit{tol}\f$
     */
    bool equals(const Array &rhs, TYPE tol = 0.000001) const;

private:
    bool d_isCopyable;           // Can the array be copied
    bool d_isFixedSize;          // Can the array be resized
    ArraySize d_size;            // Size of each dimension
    TYPE *d_data;                // Raw pointer to data in array
    std::shared_ptr<TYPE> d_ptr; // Shared pointer to data in array
    void allocate(const ArraySize &N);

private:
    inline void checkSubsetIndex(const std::vector<Range<size_t>> &range) const;
    inline std::vector<Range<size_t>>
    convert(const std::vector<size_t> &index) const;
    static inline void getSubsetArrays(const std::vector<Range<size_t>> &range,
                                       std::array<size_t, 5> &first,
                                       std::array<size_t, 5> &last,
                                       std::array<size_t, 5> &inc,
                                       std::array<size_t, 5> &N);
};

/********************************************************
 *  ostream operator                                     *
 ********************************************************/
inline std::ostream &operator<<(std::ostream &out, const ArraySize &s) {
    out << "[" << s[0];
    for (size_t i = 1; i < s.ndim(); i++)
        out << "," << s[i];
    out << "]";
    return out;
}

/********************************************************
 *  Math operations                                      *
 ********************************************************/
template <class TYPE, class FUN, class Allocator>
inline Array<TYPE, FUN, Allocator>
operator+(const Array<TYPE, FUN, Allocator> &a,
          const Array<TYPE, FUN, Allocator> &b) {
    Array<TYPE, FUN, Allocator> c;
    const auto &op = [](const TYPE &a, const TYPE &b) { return a + b; };
    FUN::transform(op, a, b, c);
    return c;
}
template <class TYPE, class FUN, class Allocator>
inline Array<TYPE, FUN, Allocator>
operator-(const Array<TYPE, FUN, Allocator> &a,
          const Array<TYPE, FUN, Allocator> &b) {
    Array<TYPE, FUN, Allocator> c;
    const auto &op = [](const TYPE &a, const TYPE &b) { return a - b; };
    FUN::transform(op, a, b, c);
    return c;
}
template <class TYPE, class FUN, class Allocator>
inline Array<TYPE, FUN, Allocator>
operator*(const Array<TYPE, FUN, Allocator> &a,
          const Array<TYPE, FUN, Allocator> &b) {
    Array<TYPE, FUN, Allocator> c;
    FUN::multiply(a, b, c);
    return c;
}
template <class TYPE, class FUN, class Allocator>
inline Array<TYPE, FUN, Allocator>
operator*(const Array<TYPE, FUN, Allocator> &a, const std::vector<TYPE> &b) {
    Array<TYPE, FUN, Allocator> b2, c;
    b2.viewRaw({b.size()}, const_cast<TYPE *>(b.data()));
    FUN::multiply(a, b2, c);
    return c;
}
template <class TYPE, class FUN, class Allocator>
inline Array<TYPE, FUN, Allocator>
operator*(const TYPE &a, const Array<TYPE, FUN, Allocator> &b) {
    auto c = b;
    c.scale(a);
    return c;
}
template <class TYPE, class FUN, class Allocator>
inline Array<TYPE, FUN, Allocator>
operator*(const Array<TYPE, FUN, Allocator> &a, const TYPE &b) {
    auto c = a;
    c.scale(b);
    return c;
}

/********************************************************
 *  Copy array                                           *
 ********************************************************/
template <class TYPE, class FUN, class Allocator>
template <class TYPE2>
inline void Array<TYPE, FUN, Allocator>::copy(const TYPE2 *data) {
    if (std::is_same<TYPE, TYPE2>::value) {
        std::copy(data, data + d_size.length(), d_data);
    } else {
        for (size_t i = 0; i < d_size.length(); i++)
            d_data[i] = static_cast<TYPE>(data[i]);
    }
}
template <class TYPE, class FUN, class Allocator>
template <class TYPE2>
inline void Array<TYPE, FUN, Allocator>::copyTo(TYPE2 *data) const {
    if (std::is_same<TYPE, TYPE2>::value) {
        std::copy(d_data, d_data + d_size.length(), data);
    } else {
        for (size_t i = 0; i < d_size.length(); i++)
            data[i] = static_cast<TYPE2>(d_data[i]);
    }
}

/********************************************************
 *  Convience typedefs                                   *
 *  Copy array                                           *
 ********************************************************/
typedef Array<double> DoubleArray;
typedef Array<int> IntArray;

#endif