gradient.hpp

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#pragma once
 
#include <complex>
#include <string>
 
#include "NumCpp/Core/Internal/Error.hpp"
#include "NumCpp/Core/Internal/StaticAsserts.hpp"
#include "NumCpp/Core/Internal/StdComplexOperators.hpp"
#include "NumCpp/Core/Internal/StlAlgorithms.hpp"
#include "NumCpp/Core/Shape.hpp"
#include "NumCpp/Core/Types.hpp"
#include "NumCpp/NdArray.hpp"
 
namespace nc
{
    //============================================================================
    // Method Description:
    template<typename dtype>
    NdArray<double> gradient(const NdArray<dtype>& inArray, Axis inAxis = Axis::ROW)
    {
        STATIC_ASSERT_ARITHMETIC(dtype);
 
        switch (inAxis)
        {
            case Axis::ROW:
            {
                const auto inShape = inArray.shape();
                if (inShape.rows < 2)
                {
                    THROW_INVALID_ARGUMENT_ERROR("input array must have more than 1 row.");
                }
 
                // first do the first and last rows
                auto returnArray = NdArray<double>(inShape);
                for (uint32 col = 0; col < inShape.cols; ++col)
                {
                    returnArray(0, col) = static_cast<double>(inArray(1, col)) - static_cast<double>(inArray(0, col));
                    returnArray(-1, col) =
                        static_cast<double>(inArray(-1, col)) - static_cast<double>(inArray(-2, col));
                }
 
                // then rip through the rest of the array
                for (uint32 col = 0; col < inShape.cols; ++col)
                {
                    for (uint32 row = 1; row < inShape.rows - 1; ++row)
                    {
                        returnArray(row, col) =
                            (static_cast<double>(inArray(row + 1, col)) - static_cast<double>(inArray(row - 1, col))) /
                            2.;
                    }
                }
 
                return returnArray;
            }
            case Axis::COL:
            {
                const auto inShape = inArray.shape();
                if (inShape.cols < 2)
                {
                    THROW_INVALID_ARGUMENT_ERROR("input array must have more than 1 columns.");
                }
 
                // first do the first and last columns
                auto returnArray = NdArray<double>(inShape);
                for (uint32 row = 0; row < inShape.rows; ++row)
                {
                    returnArray(row, 0) = static_cast<double>(inArray(row, 1)) - static_cast<double>(inArray(row, 0));
                    returnArray(row, -1) =
                        static_cast<double>(inArray(row, -1)) - static_cast<double>(inArray(row, -2));
                }
 
                // then rip through the rest of the array
                for (uint32 row = 0; row < inShape.rows; ++row)
                {
                    for (uint32 col = 1; col < inShape.cols - 1; ++col)
                    {
                        returnArray(row, col) =
                            (static_cast<double>(inArray(row, col + 1)) - static_cast<double>(inArray(row, col - 1))) /
                            2.;
                    }
                }
 
                return returnArray;
            }
            default:
            {
                // will return the gradient of the flattened array
                if (inArray.size() < 2)
                {
                    THROW_INVALID_ARGUMENT_ERROR("input array must have more than 1 element.");
                }
 
                auto returnArray = NdArray<double>(1, inArray.size());
                returnArray[0]   = static_cast<double>(inArray[1]) - static_cast<double>(inArray[0]);
                returnArray[-1]  = static_cast<double>(inArray[-1]) - static_cast<double>(inArray[-2]);
 
                stl_algorithms::transform(inArray.cbegin() + 2,
                                          inArray.cend(),
                                          inArray.cbegin(),
                                          returnArray.begin() + 1,
                                          [](dtype value1, dtype value2) -> double
                                          { return (static_cast<double>(value1) - static_cast<double>(value2)) / 2.; });
 
                return returnArray;
            }
        }
    }
 
    //============================================================================
    // Method Description:
    template<typename dtype>
    NdArray<std::complex<double>> gradient(const NdArray<std::complex<dtype>>& inArray, Axis inAxis = Axis::ROW)
    {
        STATIC_ASSERT_ARITHMETIC(dtype);
 
        switch (inAxis)
        {
            case Axis::ROW:
            {
                const auto inShape = inArray.shape();
                if (inShape.rows < 2)
                {
                    THROW_INVALID_ARGUMENT_ERROR("input array must have more than 1 row.");
                }
 
                // first do the first and last rows
                auto returnArray = NdArray<std::complex<double>>(inShape);
                for (uint32 col = 0; col < inShape.cols; ++col)
                {
                    returnArray(0, col) = complex_cast<double>(inArray(1, col)) - complex_cast<double>(inArray(0, col));
                    returnArray(-1, col) =
                        complex_cast<double>(inArray(-1, col)) - complex_cast<double>(inArray(-2, col));
                }
 
                // then rip through the rest of the array
                for (uint32 col = 0; col < inShape.cols; ++col)
                {
                    for (uint32 row = 1; row < inShape.rows - 1; ++row)
                    {
                        returnArray(row, col) = (complex_cast<double>(inArray(row + 1, col)) -
                                                 complex_cast<double>(inArray(row - 1, col))) /
                                                2.;
                    }
                }
 
                return returnArray;
            }
            case Axis::COL:
            {
                const auto inShape = inArray.shape();
                if (inShape.cols < 2)
                {
                    THROW_INVALID_ARGUMENT_ERROR("input array must have more than 1 columns.");
                }
 
                // first do the first and last columns
                auto returnArray = NdArray<std::complex<double>>(inShape);
                for (uint32 row = 0; row < inShape.rows; ++row)
                {
                    returnArray(row, 0) = complex_cast<double>(inArray(row, 1)) - complex_cast<double>(inArray(row, 0));
                    returnArray(row, -1) =
                        complex_cast<double>(inArray(row, -1)) - complex_cast<double>(inArray(row, -2));
                }
 
                // then rip through the rest of the array
                for (uint32 row = 0; row < inShape.rows; ++row)
                {
                    for (uint32 col = 1; col < inShape.cols - 1; ++col)
                    {
                        returnArray(row, col) = (complex_cast<double>(inArray(row, col + 1)) -
                                                 complex_cast<double>(inArray(row, col - 1))) /
                                                2.;
                    }
                }
 
                return returnArray;
            }
            default:
            {
                // will return the gradient of the flattened array
                if (inArray.size() < 2)
                {
                    THROW_INVALID_ARGUMENT_ERROR("input array must have more than 1 element.");
                }
 
                auto returnArray = NdArray<std::complex<double>>(1, inArray.size());
                returnArray[0]   = complex_cast<double>(inArray[1]) - complex_cast<double>(inArray[0]);
                returnArray[-1]  = complex_cast<double>(inArray[-1]) - complex_cast<double>(inArray[-2]);
 
                stl_algorithms::transform(
                    inArray.cbegin() + 2,
                    inArray.cend(),
                    inArray.cbegin(),
                    returnArray.begin() + 1,
                    [](const std::complex<dtype>& value1, const std::complex<dtype>& value2) -> std::complex<double>
                    { return (complex_cast<double>(value1) - complex_cast<double>(value2)) / 2.; });
 
                return returnArray;
            }
        }
    }
} // namespace nc