# Source code for colour.models.derivation

#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""
RGB Colourspace Derivation
==========================

Defines objects related to *RGB* colourspace derivation, essentially
calculating the normalised primary matrix for given *RGB* colourspace primaries
and whitepoint.

--------
RGB Colourspaces IPython Notebook
<http://nbviewer.ipython.org/github/colour-science/colour-ipython/blob/master/notebooks/models/rgb.ipynb>_  # noqa

References
----------
.. [1]  SMPTE. (1993). Derivation of Basic Television Color Equations. In
RP 177:1993 (Vol. RP 177:199). doi:10.5594/S9781614821915
"""

from __future__ import division, unicode_literals

import numpy as np

from colour.models import xy_to_XYZ

__author__ = 'Colour Developers'
__maintainer__ = 'Colour Developers'
__status__ = 'Production'

__all__ = ['xy_to_z',
'normalised_primary_matrix',
'RGB_luminance_equation',
'RGB_luminance']

[docs]def xy_to_z(xy):
"""
Returns the *z* coordinate using given *xy* chromaticity coordinates.

Parameters
----------
xy : array_like
*xy* chromaticity coordinates.

Returns
-------
numeric
*z* coordinate.

Examples
--------
>>> xy_to_z((0.25, 0.25))
0.5
"""

return 1 - xy[0] - xy[1]

[docs]def normalised_primary_matrix(primaries, whitepoint):
"""
Returns the *normalised primary matrix* using given *primaries* and
*whitepoint* matrices.

Parameters
----------
primaries : array_like
Primaries chromaticity coordinate matrix, (3, 2).
whitepoint : array_like
Illuminant / whitepoint chromaticity coordinates.

Returns
-------
ndarray, (3, 3)
Normalised primary matrix.

Examples
--------
>>> pms = np.array([0.73470, 0.26530, 0.00000, 1.00000, 0.00010, -0.07700])
>>> whitepoint = (0.32168, 0.33767)
>>> normalised_primary_matrix(pms, whitepoint)  # doctest: +ELLIPSIS
array([[  9.5255239...e-01,   0.0000000...e+00,   9.3678631...e-05],
[  3.4396645...e-01,   7.2816609...e-01,  -7.2132546...e-02],
[  0.0000000...e+00,   0.0000000...e+00,   1.0088251...e+00]])
"""

# Add *z* coordinates to the primaries and transposing the matrix.
primaries = primaries.reshape((3, 2))
z = np.array([xy_to_z(np.ravel(primary)) for primary in primaries])
primaries = np.hstack((primaries, z.reshape((3, 1))))

primaries = np.transpose(primaries)

whitepoint = xy_to_XYZ(whitepoint).reshape((3, 1))

coefficients = np.dot(np.linalg.inv(primaries), whitepoint)
coefficients = np.diagflat(coefficients)

npm = np.dot(primaries, coefficients)

return npm

[docs]def RGB_luminance_equation(primaries, whitepoint):
"""
Returns the *luminance equation* from given *primaries* and *whitepoint*
matrices.

Parameters
----------
primaries : array_like, (3, 2)
Primaries chromaticity coordinate matrix.
whitepoint : array_like
Illuminant / whitepoint chromaticity coordinates.

Returns
-------
unicode
*Luminance* equation.

Examples
--------
>>> pms = np.array([0.73470, 0.26530, 0.00000, 1.00000, 0.00010, -0.07700])
>>> whitepoint = (0.32168, 0.33767)
>>> # Doctests skip for Python 2.x compatibility.
>>> RGB_luminance_equation(pms, whitepoint)  # doctest: +SKIP
'Y = 0.3439664...(R) + 0.7281660...(G) + -0.0721325...(B)'
"""

return 'Y = {0}(R) + {1}(G) + {2}(B)'.format(
*np.ravel(normalised_primary_matrix(primaries, whitepoint))[3:6])

[docs]def RGB_luminance(RGB, primaries, whitepoint):
"""
Returns the *luminance* :math:y of given *RGB* components from given
*primaries* and *whitepoint* matrices.

Parameters
----------
RGB : array_like, (3,)
*RGB* chromaticity coordinate matrix.
primaries : array_like, (3, 2)
Primaries chromaticity coordinate matrix.
whitepoint : array_like
Illuminant / whitepoint chromaticity coordinates.

Returns
-------
numeric
*Luminance* :math:y.

Examples
--------
>>> RGB = np.array([40.6, 4.2, 67.4])
>>> pms = np.array([0.73470, 0.26530, 0.00000, 1.00000, 0.00010, -0.07700])
>>> whitepoint = (0.32168, 0.33767)
>>> RGB_luminance(RGB, pms, whitepoint)  # doctest: +ELLIPSIS
12.1616018...
"""

R, G, B = np.ravel(RGB)
X, Y, Z = np.ravel(normalised_primary_matrix(primaries,
whitepoint))[3:6]

return X * R + Y * G + Z * B