kev/Drawer/GVision/SurfaceGrid/lib/functions/Triangle.h

/*------------------------------------------------------------------------------
 *	Copyright (c) 2023 by Bai Bing (seread@163.com)
 *	S++ COPYING file for copying and redistribution conditions.
 *
 *  Alians IT Studio.
 *----------------------------------------------------------------------------*/
#pragma once

#include "core/StaticAsserts.h"
#include "ASShape.h"
#include "ASMatrix.h"

namespace ais
{
    //============================================================================
    // Method Description:
    /// An array with ones at and below the given diagonal and zeros elsewhere.
    ///
    /// @param num: number of rows and cols
    /// @param offset: (the sub-diagonal at and below which the array is filled.
    /// k = 0 is the main diagonal, while k < 0 is below it,
    /// and k > 0 is above. The default is 0.)
    ///
    /// @return Matrix
    ///
    template <typename dtype>
    Matrix<dtype> tril(uint32_t num, int32_t offset = 0)
    {
        STATIC_ASSERT_ARITHMETIC_OR_COMPLEX(dtype);

        uint32_t rowStart = 0;
        uint32_t colStart = 0;
        if (offset > 0)
        {
            colStart = offset;
        }
        else
        {
            rowStart = offset * -1;
        }

        Matrix<dtype> returnArray(num);
        returnArray.zeros();
        for (uint32_t row = rowStart; row < num; ++row)
        {
            for (uint32_t col = 0; col < row + colStart + 1 - rowStart; ++col)
            {
                if (col == num)
                {
                    break;
                }

                returnArray(row, col) = dtype{1};
            }
        }

        return returnArray;
    }

    //============================================================================
    // Method Description:
    /// An array with ones at and below the given diagonal and zeros elsewhere.
    ///
    /// @param num: number of rows
    /// @param inM: number of columns
    /// @param offset: (the sub-diagonal at and below which the array is filled.
    /// k = 0 is the main diagonal, while k < 0 is below it,
    /// and k > 0 is above. The default is 0.)
    ///
    ///
    /// @return Matrix
    ///
    template <typename dtype>
    Matrix<dtype> tril(uint32_t num, uint32_t inM, int32_t offset = 0)
    {
        STATIC_ASSERT_ARITHMETIC_OR_COMPLEX(dtype);

        uint32_t rowStart = 0;
        uint32_t colStart = 0;
        if (offset > 0)
        {
            colStart = offset;
        }
        else if (offset < 0)
        {
            rowStart = offset * -1;
        }

        Matrix<dtype> returnArray(num, inM);
        returnArray.zeros();
        for (uint32_t row = rowStart; row < num; ++row)
        {
            for (uint32_t col = 0; col < row + colStart + 1 - rowStart; ++col)
            {
                if (col == inM)
                {
                    break;
                }

                returnArray(row, col) = dtype{1};
            }
        }

        return returnArray;
    }

    // forward declare
    template <typename dtype>
    Matrix<dtype> triu(uint32_t num, uint32_t inM, int32_t offset = 0);

    //============================================================================
    // Method Description:
    /// Lower triangle of an array.
    ///
    /// Return a copy of an array with elements above the k - th diagonal zeroed.
    ///
    /// @param array: number of rows and cols
    /// @param offset: (the sub-diagonal at and below which the array is filled.
    /// k = 0 is the main diagonal, while k < 0 is below it,
    /// and k > 0 is above. The default is 0.)
    ///
    ///
    /// @return Matrix
    ///
    template <typename dtype>
    Matrix<dtype> tril(const Matrix<dtype> &array, size_t offset = 0)
    {
        STATIC_ASSERT_ARITHMETIC_OR_COMPLEX(dtype);

        const Shape inShape = array.shape();
        auto outArray = array.copy();
        outArray.put_mask(triu<bool>(inShape.rows, inShape.cols, offset + 1), 0);
        return outArray;
    }

    //============================================================================
    // Method Description:
    /// An array with ones at and above the given diagonal and zeros elsewhere.
    ///
    /// @param num: number of rows
    /// @param inM: number of columns
    /// @param offset: (the sub-diagonal at and above which the array is filled.
    /// k = 0 is the main diagonal, while k < 0 is below it,
    /// and k > 0 is above. The default is 0.)
    ///
    ///
    /// @return Matrix
    ///
    template <typename dtype>
    Matrix<dtype> triu(uint32_t num, uint32_t inM, int32_t offset)
    {
        STATIC_ASSERT_ARITHMETIC_OR_COMPLEX(dtype);

        // because i'm stealing the lines of code from tril and reversing it, this is necessary
        offset -= 1;

        uint32_t rowStart = 0;
        uint32_t colStart = 0;
        if (offset > 0)
        {
            colStart = offset;
        }
        else if (offset < 0)
        {
            rowStart = offset * -1;
        }

        Matrix<dtype> returnArray(num, inM);
        returnArray.ones();
        for (uint32_t row = rowStart; row < num; ++row)
        {
            for (uint32_t col = 0; col < row + colStart + 1 - rowStart; ++col)
            {
                if (col == inM)
                {
                    break;
                }

                returnArray(row, col) = dtype{0};
            }
        }

        return returnArray;
    }

    //============================================================================
    // Method Description:
    /// An array with ones at and above the given diagonal and zeros elsewhere.
    ///
    /// @param num: number of rows and cols
    /// @param offset: (the sub-diagonal at and above which the array is filled.
    /// k = 0 is the main diagonal, while k < 0 is below it,
    /// and k > 0 is above. The default is 0.)
    ///
    ///
    /// @return Matrix
    ///
    template <typename dtype>
    Matrix<dtype> triu(uint32_t num, int32_t offset = 0)
    {
        STATIC_ASSERT_ARITHMETIC_OR_COMPLEX(dtype);

        return tril<dtype>(num, -offset).transpose();
    }

    //============================================================================
    // Method Description:
    /// Upper triangle of an array.
    ///
    /// Return a copy of an array with elements below the k - th diagonal zeroed.
    ///
    /// @param array: number of rows and cols
    /// @param offset: (the sub-diagonal at and below which the array is filled.
    /// k = 0 is the main diagonal, while k < 0 is below it,
    /// and k > 0 is above. The default is 0.)
    ///
    ///
    /// @return Matrix
    ///
    template <typename dtype>
    Matrix<dtype> triu(const Matrix<dtype> &array, size_t offset = 0)
    {
        STATIC_ASSERT_ARITHMETIC_OR_COMPLEX(dtype);

        const Shape inShape = array.shape();
        auto outArray = array.copy();
        outArray.put_mask(tril<bool>(inShape.rows, inShape.cols, offset - 1), 0);
        return outArray;
    }
} // namespace ais