Source code for colour.colorimetry.dominant

"""
Dominant Wavelength and Purity
==============================

Defines the objects to compute the *dominant wavelength* and *purity* of a
colour and related quantities:

-   :func:`colour.dominant_wavelength`
-   :func:`colour.complementary_wavelength`
-   :func:`colour.excitation_purity`
-   :func:`colour.colorimetric_purity`

References
----------
-   :cite:`CIETC1-482004o` : CIE TC 1-48. (2004). 9.1 Dominant wavelength and
    purity. In CIE 015:2004 Colorimetry, 3rd Edition (pp. 32-33).
    ISBN:978-3-901906-33-6
-   :cite:`Erdogana` : Erdogan, T. (n.d.). How to Calculate Luminosity,
    Dominant Wavelength, and Excitation Purity (p. 7).
    http://www.semrock.com/Data/Sites/1/semrockpdfs/\
whitepaper_howtocalculateluminositywavelengthandpurity.pdf
"""

from __future__ import annotations

import numpy as np
import scipy.spatial.distance

from colour.algebra import (
    euclidean_distance,
    extend_line_segment,
    intersect_line_segments,
    sdiv,
    sdiv_mode,
)
from colour.colorimetry import (
    MultiSpectralDistributions,
    handle_spectral_arguments,
)
from colour.hints import (
    ArrayLike,
    Boolean,
    FloatingOrNDArray,
    NDArray,
    Optional,
    Tuple,
)
from colour.models import XYZ_to_xy
from colour.utilities import as_float_array

__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 Colour Developers"
__license__ = "New BSD License - https://opensource.org/licenses/BSD-3-Clause"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__status__ = "Production"

__all__ = [
    "closest_spectral_locus_wavelength",
    "dominant_wavelength",
    "complementary_wavelength",
    "excitation_purity",
    "colorimetric_purity",
]


def closest_spectral_locus_wavelength(
    xy: ArrayLike, xy_n: ArrayLike, xy_s: ArrayLike, inverse: Boolean = False
) -> Tuple[NDArray, NDArray]:
    """
    Return the coordinates and closest spectral locus wavelength index to the
    point where the line defined by the given achromatic stimulus :math:`xy_n`
    to colour stimulus :math:`xy_n` *CIE xy* chromaticity coordinates
    intersects the spectral locus.

    Parameters
    ----------
    xy
        Colour stimulus *CIE xy* chromaticity coordinates.
    xy_n
        Achromatic stimulus *CIE xy* chromaticity coordinates.
    xy_s
        Spectral locus *CIE xy* chromaticity coordinates.
    inverse
        The intersection will be computed using the colour stimulus :math:`xy`
        to achromatic stimulus :math:`xy_n` inverse direction.

    Returns
    -------
    :class:`tuple`
        Closest wavelength index, intersection point *CIE xy* chromaticity
        coordinates.

    Raises
    ------
    ValueError
        If no closest spectral locus wavelength index and coordinates found.

    Examples
    --------
    >>> from colour.colorimetry import MSDS_CMFS
    >>> cmfs = MSDS_CMFS['CIE 1931 2 Degree Standard Observer']
    >>> xy = np.array([0.54369557, 0.32107944])
    >>> xy_n = np.array([0.31270000, 0.32900000])
    >>> xy_s = XYZ_to_xy(cmfs.values)
    >>> ix, intersect = closest_spectral_locus_wavelength(xy, xy_n, xy_s)
    >>> print(ix) #
    256
    >>> print(intersect) # doctest: +ELLIPSIS
    [ 0.6835474...  0.3162840...]
    """

    xy = as_float_array(xy)
    xy_n = np.resize(xy_n, xy.shape)
    xy_s = as_float_array(xy_s)

    xy_e = (
        extend_line_segment(xy, xy_n)
        if inverse
        else extend_line_segment(xy_n, xy)
    )

    # Closing horse-shoe shape to handle line of purples intersections.
    xy_s = np.vstack([xy_s, xy_s[0, :]])

    xy_wl = intersect_line_segments(
        np.concatenate((xy_n, xy_e), -1),
        np.hstack([xy_s, np.roll(xy_s, 1, axis=0)]),
    ).xy
    # Extracting the first intersection per-wavelength.
    xy_wl = np.sort(xy_wl, 1)[:, 0, :]

    if not len(xy_wl):
        raise ValueError(
            f"No closest spectral locus wavelength index and coordinates "
            f'found for "{xy}" colour stimulus and "{xy_n}" achromatic '
            f'stimulus "xy" chromaticity coordinates!'
        )

    i_wl = np.argmin(scipy.spatial.distance.cdist(xy_wl, xy_s), axis=-1)

    i_wl = np.reshape(i_wl, xy.shape[0:-1])
    xy_wl = np.reshape(xy_wl, xy.shape)

    return i_wl, xy_wl


[docs]def dominant_wavelength( xy: ArrayLike, xy_n: ArrayLike, cmfs: Optional[MultiSpectralDistributions] = None, inverse: bool = False, ) -> Tuple[NDArray, NDArray, NDArray]: """ Return the *dominant wavelength* :math:`\\lambda_d` for given colour stimulus :math:`xy` and the related :math:`xy_wl` first and :math:`xy_{cw}` second intersection coordinates with the spectral locus. In the eventuality where the :math:`xy_wl` first intersection coordinates are on the line of purples, the *complementary wavelength* will be computed in lieu. The *complementary wavelength* is indicated by a negative sign and the :math:`xy_{cw}` second intersection coordinates which are set by default to the same value than :math:`xy_wl` first intersection coordinates will be set to the *complementary dominant wavelength* intersection coordinates with the spectral locus. Parameters ---------- xy Colour stimulus *CIE xy* chromaticity coordinates. xy_n Achromatic stimulus *CIE xy* chromaticity coordinates. cmfs Standard observer colour matching functions, default to the *CIE 1931 2 Degree Standard Observer*. inverse Inverse the computation direction to retrieve the *complementary wavelength*. Returns ------- :class:`tuple` *Dominant wavelength*, first intersection point *CIE xy* chromaticity coordinates, second intersection point *CIE xy* chromaticity coordinates. References ---------- :cite:`CIETC1-482004o`, :cite:`Erdogana` Examples -------- *Dominant wavelength* computation: >>> from colour.colorimetry import MSDS_CMFS >>> from pprint import pprint >>> cmfs = MSDS_CMFS['CIE 1931 2 Degree Standard Observer'] >>> xy = np.array([0.54369557, 0.32107944]) >>> xy_n = np.array([0.31270000, 0.32900000]) >>> pprint(dominant_wavelength(xy, xy_n, cmfs)) # doctest: +ELLIPSIS (array(616...), array([ 0.6835474..., 0.3162840...]), array([ 0.6835474..., 0.3162840...])) *Complementary dominant wavelength* is returned if the first intersection is located on the line of purples: >>> xy = np.array([0.37605506, 0.24452225]) >>> pprint(dominant_wavelength(xy, xy_n)) # doctest: +ELLIPSIS (array(-509.0), array([ 0.4572314..., 0.1362814...]), array([ 0.0104096..., 0.7320745...])) """ cmfs, _illuminant = handle_spectral_arguments(cmfs) xy = as_float_array(xy) xy_n = np.resize(xy_n, xy.shape) xy_s = XYZ_to_xy(cmfs.values) i_wl, xy_wl = closest_spectral_locus_wavelength(xy, xy_n, xy_s, inverse) xy_cwl = xy_wl wl = cmfs.wavelengths[i_wl] xy_e = ( extend_line_segment(xy, xy_n) if inverse else extend_line_segment(xy_n, xy) ) intersect = intersect_line_segments( np.concatenate((xy_n, xy_e), -1), np.hstack([xy_s[0], xy_s[-1]]) ).intersect intersect = np.reshape(intersect, wl.shape) i_wl_r, xy_cwl_r = closest_spectral_locus_wavelength( xy, xy_n, xy_s, not inverse ) wl_r = -cmfs.wavelengths[i_wl_r] wl = np.where(intersect, wl_r, wl) xy_cwl = np.where(intersect[..., None], xy_cwl_r, xy_cwl) return wl, np.squeeze(xy_wl), np.squeeze(xy_cwl)
[docs]def complementary_wavelength( xy: ArrayLike, xy_n: ArrayLike, cmfs: Optional[MultiSpectralDistributions] = None, ) -> Tuple[NDArray, NDArray, NDArray]: """ Return the *complementary wavelength* :math:`\\lambda_c` for given colour stimulus :math:`xy` and the related :math:`xy_wl` first and :math:`xy_{cw}` second intersection coordinates with the spectral locus. In the eventuality where the :math:`xy_wl` first intersection coordinates are on the line of purples, the *dominant wavelength* will be computed in lieu. The *dominant wavelength* is indicated by a negative sign and the :math:`xy_{cw}` second intersection coordinates which are set by default to the same value than :math:`xy_wl` first intersection coordinates will be set to the *dominant wavelength* intersection coordinates with the spectral locus. Parameters ---------- xy Colour stimulus *CIE xy* chromaticity coordinates. xy_n Achromatic stimulus *CIE xy* chromaticity coordinates. cmfs Standard observer colour matching functions, default to the *CIE 1931 2 Degree Standard Observer*. Returns ------- :class:`tuple` *Complementary wavelength*, first intersection point *CIE xy* chromaticity coordinates, second intersection point *CIE xy* chromaticity coordinates. References ---------- :cite:`CIETC1-482004o`, :cite:`Erdogana` Examples -------- *Complementary wavelength* computation: >>> from colour.colorimetry import MSDS_CMFS >>> from pprint import pprint >>> cmfs = MSDS_CMFS['CIE 1931 2 Degree Standard Observer'] >>> xy = np.array([0.37605506, 0.24452225]) >>> xy_n = np.array([0.31270000, 0.32900000]) >>> pprint(complementary_wavelength(xy, xy_n, cmfs)) # doctest: +ELLIPSIS (array(509.0), array([ 0.0104096..., 0.7320745...]), array([ 0.0104096..., 0.7320745...])) *Dominant wavelength* is returned if the first intersection is located on the line of purples: >>> xy = np.array([0.54369557, 0.32107944]) >>> pprint(complementary_wavelength(xy, xy_n)) # doctest: +ELLIPSIS (array(492.0), array([ 0.0364795 , 0.3384712...]), array([ 0.0364795 , 0.3384712...])) """ return dominant_wavelength(xy, xy_n, cmfs, True)
[docs]def excitation_purity( xy: ArrayLike, xy_n: ArrayLike, cmfs: Optional[MultiSpectralDistributions] = None, ) -> FloatingOrNDArray: """ Return the *excitation purity* :math:`P_e` for given colour stimulus :math:`xy`. Parameters ---------- xy Colour stimulus *CIE xy* chromaticity coordinates. xy_n Achromatic stimulus *CIE xy* chromaticity coordinates. cmfs Standard observer colour matching functions, default to the *CIE 1931 2 Degree Standard Observer*. Returns ------- :class:`np.floating` or :class:`numpy.ndarray` *Excitation purity* :math:`P_e`. References ---------- :cite:`CIETC1-482004o`, :cite:`Erdogana` Examples -------- >>> from colour.colorimetry import MSDS_CMFS >>> cmfs = MSDS_CMFS['CIE 1931 2 Degree Standard Observer'] >>> xy = np.array([0.54369557, 0.32107944]) >>> xy_n = np.array([0.31270000, 0.32900000]) >>> excitation_purity(xy, xy_n, cmfs) # doctest: +ELLIPSIS 0.6228856... """ _wl, xy_wl, _xy_cwl = dominant_wavelength(xy, xy_n, cmfs) with sdiv_mode(): P_e = sdiv( euclidean_distance(xy_n, xy), euclidean_distance(xy_n, xy_wl), ) return P_e
[docs]def colorimetric_purity( xy: ArrayLike, xy_n: ArrayLike, cmfs: Optional[MultiSpectralDistributions] = None, ) -> FloatingOrNDArray: """ Return the *colorimetric purity* :math:`P_c` for given colour stimulus :math:`xy`. Parameters ---------- xy Colour stimulus *CIE xy* chromaticity coordinates. xy_n Achromatic stimulus *CIE xy* chromaticity coordinates. cmfs Standard observer colour matching functions, default to the *CIE 1931 2 Degree Standard Observer*. Returns ------- :class:`np.floating` or :class:`numpy.ndarray` *Colorimetric purity* :math:`P_c`. References ---------- :cite:`CIETC1-482004o`, :cite:`Erdogana` Examples -------- >>> from colour.colorimetry import MSDS_CMFS >>> cmfs = MSDS_CMFS['CIE 1931 2 Degree Standard Observer'] >>> xy = np.array([0.54369557, 0.32107944]) >>> xy_n = np.array([0.31270000, 0.32900000]) >>> colorimetric_purity(xy, xy_n, cmfs) # doctest: +ELLIPSIS 0.6135828... """ xy = as_float_array(xy) _wl, xy_wl, _xy_cwl = dominant_wavelength(xy, xy_n, cmfs) P_e = excitation_purity(xy, xy_n, cmfs) with sdiv_mode(): P_c = P_e * sdiv(xy_wl[..., 1], xy[..., 1]) return P_c