251 lines
6.1 KiB
Python
251 lines
6.1 KiB
Python
import numpy as np
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# UTILITY {{{1
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F = lambda a: np.array(a, np.float64)
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A = lambda *args: F(args)
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and1 = lambda a: A(*a.T, np.ones_like(a.T[0])).T # appends a column of 1s
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# (works for both vectors and matrices thanks to some transposition magic)
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def either1d2d(fun):
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from functools import wraps
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@wraps(fun)
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def wrap(a, *args, **kwargs):
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a = np.asfarray(a)
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assert a.ndim in (1, 2), f"expected a 1D or 2D array, got {a.ndim}"
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return fun(a, *args, **kwargs)
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return wrap
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# DATA {{{1
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d65 = A(95.0489, 100.0000, 108.8840)
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d50 = A(96.4212, 100.0000, +82.5188)
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mat_alt_xyz = A( # for SRLAB2
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(0.320530, 0.636920, 0.042560),
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(0.161987, 0.756636, 0.081376),
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(0.017228, 0.108660, 0.874112),
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)
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mat_alt_lab = A( # for SRLAB2
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(37.0950, +62.9054, -0.0008),
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(663.4684, -750.5078, +87.0328),
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(63.9569, +108.4576, -172.4152),
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)
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lab_magic = A(
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[0, 116, 0],
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[500, -500, 0],
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[0, 200, -200],
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)
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lab_offset = A(-16, 0, 0)
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bradford = A(
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[+0.8951, +0.2664, -0.1614],
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[-0.7502, +1.7135, +0.0367],
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[+0.0389, -0.0685, +1.0296],
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)
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mat_BFD = bradford
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mat_97 = A(
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[+0.8562, +0.3372, -0.1934],
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[-0.8360, +1.8327, +0.0033],
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[+0.0357, -0.0469, +1.0112],
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)
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mat_02 = A(
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[+0.7328, +0.4296, -0.1624],
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[-0.7036, +1.6975, +0.0061],
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[+0.0030, +0.0136, +0.9834],
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)
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mat_16 = A(
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[+0.401288, +0.650173, -0.051461],
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[-0.250268, +1.204414, +0.045854],
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[-0.002079, +0.048952, +0.953127],
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)
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# REC709_PRI
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sRGB_primaries = A( # strangely, these seem to be missing a digit of significance.
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# actually, this might be ITU-R BT.709-5 which is naturally less accurate?
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[+0.64000, +0.33000], # +0.03000
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[+0.30000, +0.60000], # +0.10000
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[+0.15000, +0.06000], # +0.79000
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[+0.31270, +0.32900], # +0.35830
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)
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# AP0
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AP0_primaries = A(
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[+0.73470, +0.26530], # +0.00000
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[+0.00000, +1.00000], # +0.00000
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[+0.00010, -0.07700], # +1.07690
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[+0.32168, +0.33767], # +0.34065
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)
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# AP1
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AP1_primaries = A(
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[+0.71300, +0.29300], # -0.00600
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[+0.16500, +0.83000], # +0.00500
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[+0.12800, +0.04400], # +0.82800
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[+0.32168, +0.33767], # +0.34065
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)
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ref_XYZ = A( # sRGB -> XYZ (still needs to be converted from D65)
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[506752 / 1228815, 87881 / 245763, 12673 / 70218], # sum: 3127/3290
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[87098 / 409605, 175762 / 245763, 12673 / 175545], # sum: 1/1
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[7918 / 409605, 87881 / 737289, 1001167 / 1053270], # sum: 3583/3290
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)
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_Zify = A( # goes *after* input vector, not before.
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[1, 0, -1],
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[0, 1, -1],
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[0, 0, +1],
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)
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# DATA (INVERSES) {{{1
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inv_alt_xyz = np.linalg.inv(mat_alt_xyz)
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inv_alt_lab = np.linalg.inv(mat_alt_lab)
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inv_lab_magic = np.linalg.inv(lab_magic)
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inv_BFD = np.linalg.inv(mat_BFD) # TODO: use this!
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inv_97 = np.linalg.inv(mat_97) # TODO: rename to _CAT97?
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inv_02 = np.linalg.inv(mat_02) # TODO: rename to _CAT02?
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inv_16 = np.linalg.inv(mat_16)
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# FUNCTIONS {{{1
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@either1d2d
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def cartesian_to_polar(a):
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return A(a.T[0], np.hypot(a.T[1], a.T[2]), np.arctan2(a.T[2], a.T[1])).T
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@either1d2d
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def polar_to_cartesian(a):
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return A(a.T[0], a.T[1] * np.cos(a.T[2]), a.T[1] * np.sin(a.T[2])).T
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def rgb2lin(a):
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a = np.asfarray(a)
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return np.where(a > 0.04045, ((a + 0.055) / 1.055) ** 2.4, a / 12.92)
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def lin2rgb(a):
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a = np.asfarray(a)
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return np.where(a > 0.04045 / 12.92, (a ** (1 / 2.4) * 1.055) - 0.055, a * 12.92)
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@either1d2d
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def xyY_2_XYZ(xyY):
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# transposition allows this function to be vectorized (over vectors).
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x, y, Y = xyY.T
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y = np.maximum(y, 1e-10)
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return (Y / y * A(x, y, 1.0 - x - y)).T
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@either1d2d
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def lab_to_xyz(lab, *, ref):
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ijk = (lab - lab_offset) @ inv_lab_magic.T
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xyz = np.where(ijk > np.cbrt(0.008856), ijk**3, (ijk - 16 / 116) / 7.787)
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xyz = xyz * ref
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return xyz
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@either1d2d
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def xyz_to_lab(xyz, *, ref):
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xyz = xyz / ref
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# absolute value just to shut up numpy:
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ijk = np.where(xyz > 0.008856, np.cbrt(np.abs(xyz)), 7.787 * xyz + 16 / 116)
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lab = ijk @ lab_magic.T + lab_offset
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return lab
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# print(xyz_to_lab((30, 50, 20), ref=d50))
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# print("[ 76.06926101 -58.04284385 34.04319485]")
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# print(lab_to_xyz(( 76.06926101, -58.04284385, 34.04319485), ref=d50))
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# stop
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@either1d2d
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def xyz_to_srlab2(xyz):
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rgb = xyz @ inv_XYZ.T
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xyz = rgb @ mat_alt_xyz.T
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ijk = np.where(
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xyz <= 216.0 / 24389.0, 24389.0 / 2700.0 * xyz, 1.16 * np.cbrt(xyz) - 0.16
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)
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lab = ijk @ mat_alt_lab.T
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return lab
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@either1d2d
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def srlab2_to_xyz(lab):
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ijk = lab @ inv_alt_lab.T
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xyz = np.where(ijk <= 0.08, 2700.0 / 24389.0 * ijk, ((ijk + 0.16) / 1.16) ** 3)
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rgb = xyz @ inv_alt_xyz.T
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xyz = rgb @ mat_XYZ.T
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return xyz
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# print(srlab2_to_xyz(xyz_to_srlab2((0.3, 0.4, 0.5))))
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# print(srlab2_to_xyz(xyz_to_srlab2((0.3, 0.4, 0.5))))
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# stop
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def ref_to_uv(ref):
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# NOTE: this assumes that ref is valid i.e. won't cause a division by zero.
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xt, yt, zt = ref # tristimulus values (CIE 1931 XYZ)
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den = xt + yt + zt # denominator
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xc, yc = xt / den, yt / den # chromaticity values (still CIE 1931)
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den = xc + 15 * yc + 3 * (1 - xc - yc)
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u, v = 4 * xc / den, 6 * yc / den # u, v coordinates (CIE 1960 UCS)
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return u, v
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@either1d2d
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def xyz_to_uvw(xyz, *, ref):
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u0, v0 = ref_to_uv(ref)
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x, y, z = xyz.T
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den = np.maximum(x + 15 * y + 3 * z, 1e-12)
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u = 4 * x / den
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v = 6 * y / den
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W = 25 * np.cbrt(y) - 17
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U = 13 * W * (u - u0)
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V = 13 * W * (v - v0)
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return A(U, V, W).T
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@either1d2d
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def uvw_to_xyz(uvw, *, ref):
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u0, v0 = ref_to_uv(ref)
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U, V, W = uvw.T
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Y = ((W + 17) / 25) ** 3
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u = U / (13 * W) + u0
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v = V / (13 * W) + v0
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den = Y * 6 / np.maximum(v, 1e-12)
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X = u / 4 * den
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Z = (den - X - 15 * Y) / 3
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return A(X, Y, Z).T
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def makemat(prim, normalize=True):
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primz, white = and1(prim[:3]) @ _Zify, xyY_2_XYZ(and1(prim[3]))
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rescalant = np.cross(primz[((1, 2, 0),)], primz[((2, 0, 1),)]) @ white
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mat = (primz * rescalant[:, None]).T
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# normalize such that max inputs (1.0, 1.0, 1.0) yields (any, 1.0, any)
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return mat / np.sum(mat[1, :]) if normalize else mat
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# GENERATED DATA {{{1
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mat_XYZ = makemat(sRGB_primaries)
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inv_XYZ = np.linalg.inv(mat_XYZ)
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