Official GIST feidmath (feidlambda-math) v0.1

feidmath_v0_1.scala

/*
feidmath v0.1.0 - MATH FUNCTIONS BY FIAKO ENGINEERING
OFFICIAL GIST (feidmath v0.1.x): 
    https://gist.github.com/taruma/8b0978227dffbee50c3a9d56e31d34f3
REPOSITORY: 
    https://github.com/fiakoenjiniring/feidlambda
CONTRIBUTOR: @taruma, @iingLK
TESTED: Microsoft Excel 365 v2304
*/

// BATAS MAKSMIMUM LAYAR EDITOR -------------------------------------------#

/*
---- INTERPOLATION ----
*/

// NONE ---> _INTERPOLATION_LINEAR
_INTERPOLATION_LINEAR = LAMBDA(x, known_ys, known_xs,
    LET(
        known_xs, TOCOL(known_xs),
        known_ys, TOCOL(known_ys),
        nrow, ROWS(known_ys),
        known_table, HSTACK(known_xs, known_ys),
        sorted_table, SORT(known_table, 1),
        sorted_xs, CHOOSECOLS(sorted_table, 1),
        sorted_ys, CHOOSECOLS(sorted_table, 2),
        nearest_x, IFS(
            x > MAX(sorted_xs),
            XMATCH(x, sorted_xs, -1),
            x < MIN(sorted_xs),
            XMATCH(x, sorted_xs, 1),
            TRUE,
            XMATCH(x, sorted_xs, -1)
        ),
        index_ys, IF(
            nearest_x < nrow,
            VSTACK(nearest_x, nearest_x + 1),
            VSTACK(nearest_x - 1, nearest_x)
        ),
        select_ys, CHOOSEROWS(sorted_ys, index_ys),
        select_xs, CHOOSEROWS(sorted_xs, index_ys),
        FORECAST.LINEAR(x, select_ys, select_xs)
    )
);

// _INTERPOLATION_LINEAR ---> INTERPOLATION_LINEAR
INTERPOLATION_LINEAR = LAMBDA(x_vector, known_ys, known_xs,
    LET(
        x_vector, TOCOL(x_vector),
        y_vector, BYROW(
            x_vector,
            LAMBDA(x, _INTERPOLATION_LINEAR(x, known_ys, known_xs))
        ),
        y_vector
    )
);

/*
---- LINEAR ALGEBRA (LINALG) ----
*/

// NONE ---> LINALG_ROTATION_MATRIX
LINALG_ROTATION_MATRIX = LAMBDA(theta_x, theta_y, theta_z, [num_digits],
    LET(
        round_number, IF(ISOMITTED(num_digits), 0, num_digits),
        angle_x, RADIANS(theta_x),
        angle_y, RADIANS(theta_y),
        angle_z, RADIANS(theta_z),
        cos_x, COS(angle_x),
        sin_x, SIN(angle_x),
        rotation_x, VSTACK(
            HSTACK(1, 0, 0),
            HSTACK(0, cos_x, -sin_x),
            HSTACK(0, sin_x, cos_x)
        ),
        cos_y, COS(angle_y),
        sin_y, SIN(angle_y),
        rotation_y, VSTACK(
            HSTACK(cos_y, 0, sin_y),
            HSTACK(0, 1, 0),
            HSTACK(-sin_y, 0, cos_y)
        ),
        cos_z, COS(angle_z),
        sin_z, SIN(angle_z),
        rotation_z, VSTACK(
            HSTACK(cos_z, -sin_z, 0),
            HSTACK(sin_z, cos_z, 0),
            HSTACK(0, 0, 1)
        ),
        rotation_matrix, MMULT(rotation_z, MMULT(rotation_y, rotation_x)),
        IF(
            round_number,
            ROUND(rotation_matrix, round_number),
            rotation_matrix
        )
    )
);

// LINALG_ROTATION_MATRIX ---> LINALG_ROTATE_POINT
LINALG_ROTATE_POINT = LAMBDA(
    point_vector,
    theta_x,
    theta_y,
    theta_z,
    [active_rotation],
    [num_digits],
    LET(
        active_rotation, IF(
            ISOMITTED(active_rotation),
            TRUE,
            active_rotation
        ),
        rotation_matrix, LINALG_ROTATION_MATRIX(
            theta_x,
            theta_y,
            theta_z,
            num_digits
        ),
        point_vector, TOCOL(point_vector),
        final_rotation, IF(
            active_rotation,
            rotation_matrix,
            TRANSPOSE(rotation_matrix)
        ),
        point_rotation, MMULT(final_rotation, point_vector),
        TOROW(point_rotation)
    )
);

// LINALG_ROTATE_POINT ---> _RECURSIVE_ROTATE_POINTS
// _RECURSIVE_ROTATE_POINTS ---> _RECURSIVE_ROTATE_POINTS
_RECURSIVE_ROTATE_POINTS = LAMBDA(
    ntry,
    data_points,
    theta_x,
    theta_y,
    theta_z,
    [active_rotation],
    [num_digits],
    LET(
        selected_row, CHOOSEROWS(data_points, ntry),
        IF(
            ntry = 1,
            LINALG_ROTATE_POINT(
                selected_row,
                theta_x,
                theta_y,
                theta_z,
                active_rotation,
                num_digits
            ),
            LET(
                next_try, ntry - 1,
                result, LINALG_ROTATE_POINT(
                    selected_row,
                    theta_x,
                    theta_y,
                    theta_z,
                    active_rotation,
                    num_digits
                ),
                VSTACK(
                    _RECURSIVE_ROTATE_POINTS(
                        next_try,
                        data_points,
                        theta_x,
                        theta_y,
                        theta_z,
                        active_rotation,
                        num_digits
                    ),
                    result
                )
            )
        )
    )
);

// _RECURSIVE_ROTATE_POINTS ---> LINALG_ROTATE_POINT_ARRAY
LINALG_ROTATE_POINT_ARRAY = LAMBDA(
    data_points,
    theta_x,
    theta_y,
    theta_z,
    [active_rotation],
    [num_digits],
    _RECURSIVE_ROTATE_POINTS(
        ROWS(data_points),
        data_points,
        theta_x,
        theta_y,
        theta_z,
        active_rotation,
        num_digits
    )
);

/*
---- GEOMETRY ----
*/

// NONE ---> GEOMETRY_IS_POINT_IN_POLYGON
GEOMETRY_IS_POINT_IN_POLYGON = LAMBDA(point_vector, data_polygon,
    LET(
        point_vector, TOCOL(point_vector),
        xp, INDEX(point_vector, 1),
        yp, INDEX(point_vector, 2),
        data_1, DROP(data_polygon, -1),
        data_2, DROP(data_polygon, 1),
        data_joined, HSTACK(data_1, data_2),
        _x1, CHOOSECOLS(data_joined, 1),
        _y1, CHOOSECOLS(data_joined, 2),
        _x2, CHOOSECOLS(data_joined, 3),
        _y2, CHOOSECOLS(data_joined, 4),
        first_condition, (yp < _y1) <> (yp < _y2),
        second_condition, xp <
            (_x1 + (((yp - _y1) / (_y2 - _y1)) * (_x2 - _x1))),
        final_condition, IFERROR(
            (first_condition * second_condition) = 1,
            FALSE
        ),
        is_inside, MOD(SUM(INT(final_condition)), 2) = 1,
        is_inside
    )
);

// GEOMETRY_IS_POINT_IN_POLYGON ---> GEOMETRY_ARE_POINTS_IN_POLYGON
GEOMETRY_ARE_POINTS_IN_POLYGON = LAMBDA(data_points, polygon_points,
    BYROW(
        data_points,
        LAMBDA(row, GEOMETRY_IS_POINT_IN_POLYGON(row, polygon_points))
    )
);

/*
MIT License

Copyright (c) 2023 PT. FIAKO ENJINIRING INDONESIA

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/