def check_dimensions(data, xyzw, caller='cat.apply()'):
"""
Check if dimensions of data and xyzw match.
| Does nothing when they do, but raises error if dimensions don't match.
Args:
:data:
| ndarray with color data.
:xyzw:
| ndarray with white point tristimulus values.
:caller:
| str with caller function for error handling, optional
Returns:
:returns:
| ndarray with input color data,
| Raises error if dimensions don't match.
"""
xyzw = np2d(xyzw)
data = np2d(data)
if ((xyzw.shape[0] > 1) & (data.shape[0] != xyzw.shape[0]) &
(data.ndim == 2)):
raise Exception(
'{}: Cannot match dim of xyzw with data: xyzw.shape[0]>1 & != data.shape[0]'
.format(caller))
def xyz_to_wuv(xyz, xyzw = _COLORTF_DEFAULT_WHITE_POINT, **kwargs):
"""
Convert XYZ tristimulus values CIE 1964 U*V*W* color space.
Args:
:xyz:
| ndarray with tristimulus values
:xyzw:
| ndarray with tristimulus values of white point, optional
(Defaults to luxpy._COLORTF_DEFAULT_WHITE_POINT)
Returns:
:wuv:
| ndarray with W*U*V* values
"""
xyz = np2d(xyz)
xyzw = np2d(xyzw)
Yuv = xyz_to_Yuv(xyz) # convert to cie 1976 u'v'
Yuvw = xyz_to_Yuv(xyzw)
Y, u, v = asplit(Yuv)
Yw, uw, vw = asplit(Yuvw)
W = 25.0*(Y**(1/3)) - 17.0
U = 13.0*W*(u - uw)
V = 13.0*W*(v - vw)*(2.0/3.0) # *(2/3) to convert to cie 1960 u, v
return ajoin((W,U,V))
def wuv_to_xyz(wuv,xyzw = _COLORTF_DEFAULT_WHITE_POINT, **kwargs):
"""
Convert CIE 1964 U*V*W* color space coordinates to XYZ tristimulus values.
Args:
:wuv:
| ndarray with W*U*V* values
:xyzw:
| ndarray with tristimulus values of white point, optional
(Defaults to luxpy._COLORTF_DEFAULT_WHITE_POINT)
Returns:
:xyz:
| ndarray with tristimulus values
"""
wuv = np2d(wuv)
xyzw = np2d(xyzw)
Yuvw = xyz_to_Yuv(xyzw) # convert to cie 1976 u'v'
Yw, uw, vw = asplit(Yuvw)
vw = (2.0/3.0)*vw # convert to cie 1960 u, v
W,U,V = asplit(wuv)
Y = ((W + 17.0) / 25.0)**3.0
u = uw + U/(13.0*W)
v = (vw + V/(13.0*W)) * (3.0/2.0)
Yuv = ajoin((Y,u,v)) # = 1976 u',v'
return Yuv_to_xyz(Yuv)
def objfcn(uv_offset, uv0, cct, duv, out = 1):#, cieobs = cieobs, wl = wl, mode = mode):
uv0 = np2d(uv0 + uv_offset)
Yuv0 = np.concatenate((np2d([100.0]), uv0),axis=1)
cct_min, duv_min = xyz_to_cct(Yuv_to_xyz(Yuv0),cieobs = cieobs, out = 'cct,duv',wl = wl, mode = mode, accuracy = accuracy, force_out_of_lut = force_out_of_lut, upper_cct_max = upper_cct_max, approx_cct_temp = approx_cct_temp)
F = np.sqrt(((100.0*(cct_min[0] - cct[0])/(cct[0]))**2.0) + (((duv_min[0] - duv[0])/(duv[0]))**2.0))
if out == 'F':
return F
else:
return np.concatenate((cct_min, duv_min, np2d(F)),axis = 1)
def normalize_3x3_matrix(M, xyz0=np.array([[1.0, 1.0, 1.0]])):
"""
Normalize 3x3 matrix M to xyz0 -- > [1,1,1]
If M.shape == (1,9): M is reshaped to (3,3)
Args:
:M:
| ndarray((3,3) or ndarray((1,9))
:xyz0:
| 2darray, optional
Returns:
:returns:
| normalized matrix such that M*xyz0 = [1,1,1]
"""
M = np2d(M)
if M.shape[-1] == 9:
M = M.reshape(3, 3)
if xyz0.shape[0] == 1:
return np.dot(np.diagflat(1 / (np.dot(M, xyz0.T))), M)
else:
return np.concatenate([
np.dot(np.diagflat(1 / (np.dot(M, xyz0[1].T))), M)
for i in range(xyz0.shape[0])
],
axis=0).reshape(xyz0.shape[0], 3, 3)
def xyz_to_lms(xyz, cieobs=_CIEOBS, M=None, **kwargs):
"""
Convert XYZ tristimulus values to LMS cone fundamental responses.
Args:
:xyz:
| ndarray with tristimulus values
:cieobs:
| _CIEOBS or str, optional
:M:
| None, optional
| Conversion matrix for xyz to lms.
| If None: use the one defined by :cieobs:
Returns:
:lms:
| ndarray with LMS cone fundamental responses
"""
xyz = np2d(xyz)
if M is None:
M = _CMF[cieobs]['M']
# convert xyz to lms:
if len(xyz.shape) == 3:
lms = np.einsum('ij,klj->kli', M, xyz)
else:
lms = np.einsum('ij,lj->li', M, xyz)
return lms
def lms_to_xyz(lms, cieobs=_CIEOBS, M=None, **kwargs):
"""
Convert LMS cone fundamental responses to XYZ tristimulus values.
Args:
:lms:
| ndarray with LMS cone fundamental responses
:cieobs:
| _CIEOBS or str, optional
:M:
| None, optional
| Conversion matrix for xyz to lms.
| If None: use the one defined by :cieobs:
Returns:
:xyz:
| ndarray with tristimulus values
"""
lms = np2d(lms)
if M is None:
M = _CMF[cieobs]['M']
# convert from lms to xyz:
if len(lms.shape) == 3:
xyz = np.einsum('ij,klj->kli', np.linalg.inv(M), lms)
else:
xyz = np.einsum('ij,lj->li', np.linalg.inv(M), lms)
return xyz
def xyz_to_cct_mcamy(xyzw):
"""
Convert XYZ tristimulus values to correlated color temperature (CCT) using
the mccamy approximation.
| Only valid for approx. 3000 < T < 9000, if < 6500, error < 2 K.
Args:
:xyzw:
| ndarray of tristimulus values
Returns:
:cct:
| ndarray of correlated color temperatures estimates
References:
1. `McCamy, Calvin S. (April 1992).
"Correlated color temperature as an explicit function of
chromaticity coordinates".
Color Research & Application. 17 (2): 142–144.
<http://onlinelibrary.wiley.com/doi/10.1002/col.5080170211/abstract>`_
"""
Yxy = xyz_to_Yxy(xyzw)
#axis_of_v3 = len(xyzw.shape)-1
n = (Yxy[:, 1] - 0.3320) / (Yxy[:, 2] - 0.1858)
return np2d(-449.0 * (n**3) + 3525.0 * (n**2) - 6823.3 * n + 5520.33).T
def parse_x1x2_parameters(x,
target_shape,
catmode,
expand_2d_to_3d=None,
default=[1.0, 1.0]):
"""
Parse input parameters x and make them the target_shape for easy calculation.
| Input in main function can now be a single value valid for all xyzw or
an array with a different value for each xyzw.
Args:
:x:
| list[float, float] or ndarray
:target_shape:
| tuple with shape information
:catmode:
| '1>0>2, optional
| -'1>0>2': Two-step CAT
| from illuminant 1 to baseline illuminant 0 to illuminant 2.
| -'1>0': One-step CAT
| from illuminant 1 to baseline illuminant 0.
| -'0>2': One-step CAT
| from baseline illuminant 0 to illuminant 2.
:expand_2d_to_3d:
| None, optional
| [will be removed in future, serves no purpose]
| Expand :x: from 2 to 3 dimensions.
:default:
| [1.0,1.0], optional
| Default values for :x:
Returns:
:returns:
| (ndarray, ndarray) for x10 and x20
"""
if x is None:
x10 = np.ones(target_shape) * default[0]
if (catmode == '1>0>2') | (catmode == '1>2'):
x20 = np.ones(target_shape) * default[1]
else:
x20 = np.ones(target_shape) * np.nan
else:
x = np2d(x)
if (catmode == '1>0>2') | (catmode == '1>2'):
if x.shape[-1] == 2:
x10 = np.ones(target_shape) * x[..., 0]
x20 = np.ones(target_shape) * x[..., 1]
else:
x10 = np.ones(target_shape) * x
x20 = x10.copy()
elif catmode == '1>0':
x10 = np.ones(target_shape) * x[..., 0]
x10 = np.ones(target_shape) * np.nan
return x10, x20
def mahalanobis2(x, y=None, mu=None, sigmainv=None):
"""
Evaluate the squared mahalanobis distance with center mu and shape
and orientation determined by sigmainv.
Args:
:x:
| scalar or list or ndarray (.ndim = 1 or 2) with x(y)-coordinates
at which to evaluate the mahalanobis distance squared.
:y:
| None or scalar or list or ndarray (.ndim = 1) with y-coordinates
at which to evaluate the mahalanobis distance squared, optional.
| If :y: is None, :x: should be a 2d array.
:mu:
| None or ndarray (.ndim = 2) with center coordinates of the
mahalanobis ellipse, optional.
| None defaults to ndarray([0,0]).
:sigmainv:
| None or ndarray with 'inverse covariance matrix', optional
| Determines the shape and orientation of the PD.
| None default to np.eye(2).
Returns:
:returns:
| ndarray with magnitude of mahalanobis2(x,y)
"""
if mu is None:
mu = np.zeros(2)
if sigmainv is None:
sigmainv = np.eye(2)
x = np2d(x)
if y is not None:
x = x - mu[0] # center data on mu
y = np2d(y) - mu[1] # center data on mu
else:
x = x - mu # center data on mu
x, y = asplit(x)
return (sigmainv[0, 0] * (x**2.0) + sigmainv[1, 1] * (y**2.0) +
2.0 * sigmainv[0, 1] * (x * y))
def Vrb_mb_to_xyz(Vrb,
cieobs=_CIEOBS,
scaling=[1, 1],
M=None,
Minverted=False,
**kwargs):
"""
Convert V,r,b (Macleod-Boynton) color coordinates to XYZ tristimulus values.
| Macleod Boynton: V = R+G, r = R/V, b = B/V
| Note that R,G,B ~ L,M,S
Args:
:Vrb:
| ndarray with V,r,b (Macleod-Boynton) color coordinates
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when getting the default M, which is
the xyz to lms conversion matrix.
:scaling:
| list of scaling factors for r and b dimensions.
:M:
| None, optional
| Conversion matrix for going from XYZ to RGB (LMS)
| If None, :cieobs: determines the M (function does inversion)
:Minverted:
| False, optional
| Bool that determines whether M should be inverted.
Returns:
:xyz:
| ndarray with tristimulus values
Reference:
1. `MacLeod DI, and Boynton RM (1979).
Chromaticity diagram showing cone excitation by stimuli of equal luminance.
J. Opt. Soc. Am. 69, 1183–1186.
<https://www.osapublishing.org/josa/abstract.cfm?uri=josa-69-8-1183>`_
"""
Vrb = np2d(Vrb)
RGB = np.empty(Vrb.shape)
RGB[..., 0] = Vrb[..., 1] * Vrb[..., 0] / scaling[0]
RGB[..., 2] = Vrb[..., 2] * Vrb[..., 0] / scaling[1]
RGB[..., 1] = Vrb[..., 0] - RGB[..., 0]
if M is None:
M = _CMF[cieobs]['M']
if Minverted == False:
M = np.linalg.inv(M)
if len(RGB.shape) == 3:
return np.einsum('ij,klj->kli', M, RGB)
else:
return np.einsum('ij,lj->li', M, RGB)
def xyz_to_cct_HA(xyzw):
"""
Convert XYZ tristimulus values to correlated color temperature (CCT).
Args:
:xyzw:
| ndarray of tristimulus values
Returns:
:cct:
| ndarray of correlated color temperatures estimates
References:
1. `Hernández-Andrés, Javier; Lee, RL; Romero, J (September 20, 1999).
Calculating Correlated Color Temperatures Across the Entire Gamut
of Daylight and Skylight Chromaticities.
Applied Optics. 38 (27), 5703–5709. P
<https://www.osapublishing.org/ao/abstract.cfm?uri=ao-38-27-5703>`_
Notes:
According to paper small error from 3000 - 800 000 K, but a test with
Planckians showed errors up to 20% around 500 000 K;
e>0.05 for T>200 000, e>0.1 for T>300 000, ...
"""
if len(xyzw.shape)>2:
raise Exception('xyz_to_cct_HA(): Input xyzw.ndim must be <= 2 !')
out_of_range_code = np.nan
xe = [0.3366, 0.3356]
ye = [0.1735, 0.1691]
A0 = [-949.86315, 36284.48953]
A1 = [6253.80338, 0.00228]
t1 = [0.92159, 0.07861]
A2 = [28.70599, 5.4535*1e-36]
t2 = [0.20039, 0.01543]
A3 = [0.00004, 0.0]
t3 = [0.07125,1.0]
cct_ranges = np.array([[3000.0,50000.0],[50000.0,800000.0]])
Yxy = xyz_to_Yxy(xyzw)
CCT = np.ones((1,Yxy.shape[0]))*out_of_range_code
for i in range(2):
n = (Yxy[:,1]-xe[i])/(Yxy[:,2]-ye[i])
CCT_i = np2d(np.array(A0[i] + A1[i]*np.exp(np.divide(-n,t1[i])) + A2[i]*np.exp(np.divide(-n,t2[i])) + A3[i]*np.exp(np.divide(-n,t3[i]))))
p = (CCT_i >= (1.0-0.05*(i == 0))*cct_ranges[i][0]) & (CCT_i < (1.0+0.05*(i == 0))*cct_ranges[i][1])
CCT[p] = CCT_i[p]
p = (CCT_i < (1.0-0.05)*cct_ranges[0][0]) #smaller than smallest valid CCT value
CCT[p] = -1
if (np.isnan(CCT.sum()) == True) | (np.any(CCT == -1)):
print("Warning: xyz_to_cct_HA(): one or more CCTs out of range! --> (CCT < 3 kK, CCT >800 kK) coded as (-1, NaN) 's")
return CCT.T
def xyz_to_xyz(xyz, **kwargs):
"""
Convert XYZ tristimulus values to XYZ tristimulus values.
Args:
:xyz:
| ndarray with tristimulus values
Returns:
:xyz:
| ndarray with tristimulus values
"""
return np2d(xyz)
def xyz_to_wuv(xyz, xyzw=_COLORTF_DEFAULT_WHITE_POINT, **kwargs):
"""
Convert XYZ tristimulus values CIE 1964 U*V*W* color space.
Args:
:xyz:
| ndarray with tristimulus values
:xyzw:
| ndarray with tristimulus values of white point, optional
(Defaults to luxpy._COLORTF_DEFAULT_WHITE_POINT)
Returns:
:wuv:
| ndarray with W*U*V* values
"""
Yuv = xyz_to_Yuv(np2d(xyz)) # convert to cie 1976 u'v'
Yuvw = xyz_to_Yuv(np2d(xyzw))
wuv = np.empty(xyz.shape)
wuv[..., 0] = 25.0 * (Yuv[..., 0]**(1 / 3)) - 17.0
wuv[..., 1] = 13.0 * wuv[..., 0] * (Yuv[..., 1] - Yuvw[..., 1])
wuv[..., 2] = 13.0 * wuv[..., 0] * (Yuv[..., 2] - Yuvw[..., 2]) * (
2.0 / 3.0) #*(2/3) to convert to cie 1960 u, v
return wuv
def xyz_to_srgb(xyz, gamma=2.4, **kwargs):
"""
Calculates IEC:61966 sRGB values from xyz.
Args:
:xyz:
| ndarray with relative tristimulus values.
:gamma:
| 2.4, optional
| compression in sRGB
Returns:
:rgb:
| ndarray with R,G,B values (uint8).
"""
xyz = np2d(xyz)
# define 3x3 matrix
M = np.array([[3.2404542, -1.5371385, -0.4985314],
[-0.9692660, 1.8760108, 0.0415560],
[0.0556434, -0.2040259, 1.0572252]])
if len(xyz.shape) == 3:
srgb = np.einsum('ij,klj->kli', M, xyz / 100)
else:
srgb = np.einsum('ij,lj->li', M, xyz / 100)
# perform clipping:
srgb[np.where(srgb > 1)] = 1
srgb[np.where(srgb < 0)] = 0
# test for the dark colours in the non-linear part of the function:
dark = np.where(srgb <= 0.0031308)
# apply gamma function:
g = 1 / gamma
# and scale to range 0-255:
rgb = srgb.copy()
rgb = (1.055 * rgb**g - 0.055) * 255
# non-linear bit for dark colours
rgb[dark] = (srgb[dark].copy() * 12.92) * 255
# clip to range:
rgb[rgb > 255] = 255
rgb[rgb < 0] = 0
return rgb
def Vrb_mb_to_xyz(Vrb,cieobs = _CIEOBS, scaling = [1,1], M = None, Minverted = False, **kwargs):
"""
Convert V,r,b (Macleod-Boynton) color coordinates to XYZ tristimulus values.
| Macleod Boynton: V = R+G, r = R/V, b = B/V
| Note that R,G,B ~ L,M,S
Args:
:Vrb:
| ndarray with V,r,b (Macleod-Boynton) color coordinates
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when getting the default M, which is
the xyz to lms conversion matrix.
:scaling:
| list of scaling factors for r and b dimensions.
:M:
| None, optional
| Conversion matrix for going from XYZ to RGB (LMS)
| If None, :cieobs: determines the M (function does inversion)
:Minverted:
| False, optional
| Bool that determines whether M should be inverted.
Returns:
:xyz:
| ndarray with tristimulus values
Reference:
1. `MacLeod DI, and Boynton RM (1979).
Chromaticity diagram showing cone excitation by stimuli of equal luminance.
J. Opt. Soc. Am. 69, 1183–1186.
<https://www.osapublishing.org/josa/abstract.cfm?uri=josa-69-8-1183>`_
"""
Vrb = np2d(Vrb)
V,r,b = asplit(Vrb)
R = r*V / scaling[0]
B = b*V / scaling[1]
G = V-R
if M is None:
M = _CMF[cieobs]['M']
if Minverted == False:
M = np.linalg.inv(M)
X, Y, Z = [M[i,0]*R + M[i,1]*G + M[i,2]*B for i in range(3)]
return ajoin((X,Y,Z))
def xyz_to_Vrb_mb(xyz, cieobs=_CIEOBS, scaling=[1, 1], M=None, **kwargs):
"""
Convert XYZ tristimulus values to V,r,b (Macleod-Boynton) color coordinates.
| Macleod Boynton: V = R+G, r = R/V, b = B/V
| Note that R,G,B ~ L,M,S
Args:
:xyz:
| ndarray with tristimulus values
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when getting the default M, which is
the xyz to lms conversion matrix.
:scaling:
| list of scaling factors for r and b dimensions.
:M:
| None, optional
| Conversion matrix for going from XYZ to RGB (LMS)
| If None, :cieobs: determines the M (function does inversion)
Returns:
:Vrb:
| ndarray with V,r,b (Macleod-Boynton) color coordinates
Reference:
1. `MacLeod DI, and Boynton RM (1979).
Chromaticity diagram showing cone excitation by stimuli of equal luminance.
J. Opt. Soc. Am. 69, 1183–1186.
<https://www.osapublishing.org/josa/abstract.cfm?uri=josa-69-8-1183>`_
"""
xyz = np2d(xyz)
if M is None:
M = _CMF[cieobs]['M']
if len(xyz.shape) == 3:
RGB = np.einsum('ij,klj->kli', M, xyz)
else:
RGB = np.einsum('ij,lj->li', M, xyz)
Vrb = np.empty(xyz.shape)
Vrb[..., 0] = RGB[..., 0] + RGB[..., 1]
Vrb[..., 1] = RGB[..., 0] / Vrb[..., 0] * scaling[0]
Vrb[..., 2] = RGB[..., 2] / Vrb[..., 0] * scaling[1]
return Vrb
def lab_to_xyz(lab, xyzw = None, cieobs = _CIEOBS, **kwargs):
"""
Convert CIE 1976 L*a*b* (CIELAB) color coordinates to XYZ tristimulus values.
Args:
:lab:
| ndarray with CIE 1976 L*a*b* (CIELAB) color coordinates
:xyzw:
| None or ndarray with tristimulus values of white point, optional
| None defaults to xyz of CIE D65 using the :cieobs: observer.
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when calculating xyzw.
Returns:
:xyz:
| ndarray with tristimulus values
"""
lab = np2d(lab)
if xyzw is None:
xyzw = spd_to_xyz(_CIE_ILLUMINANTS['D65'],cieobs = cieobs)
# make xyzw same shape as data:
xyzw = xyzw*np.ones(lab.shape)
# set knee point of function:
k=(24/116) #(24/116)**3**(1/3)
# get L*, a*, b* and Xw, Yw, Zw:
L,a,b = asplit(lab)
Xw,Yw,Zw = asplit(xyzw)
fy = (L + 16.0) / 116.0
fx = a / 500.0 + fy
fz = fy - b/200.0
# apply 3rd power:
X,Y,Z = [xw*(x**3.0) for (x,xw) in ((fx,Xw),(fy,Yw),(fz,Zw))]
# Now calculate T where T/Tn is below the knee point:
p,q,r = [np.where(x<k) for x in (fx,fy,fz)]
X[p],Y[q],Z[r] = [np.squeeze(xw[xp]*((x[xp] - 16.0/116.0) / (841/108))) for (x,xw,xp) in ((fx,Xw,p),(fy,Yw,q),(fz,Zw,r))]
return ajoin((X,Y,Z))
def normalize_3x3_matrix(M, xyz0 = np.array([[1.0,1.0,1.0]])):
"""
Normalize 3x3 matrix M to xyz0 -- > [1,1,1]
If M.shape == (1,9): M is reshaped to (3,3)
Args:
:M:
| ndarray((3,3) or ndarray((1,9))
:xyz0:
| 2darray, optional
Returns:
:returns:
| normalized matrix such that M*xyz0 = [1,1,1]
"""
M = np2d(M)
if M.shape[-1]==9:
M = M.reshape(3,3)
return np.dot(np.diagflat(1/(np.dot(M,xyz0.T))),M)
def xyz_to_Yxy(xyz, **kwargs):
"""
Convert XYZ tristimulus values CIE Yxy chromaticity values.
Args:
:xyz:
| ndarray with tristimulus values
Returns:
:Yxy:
| ndarray with Yxy chromaticity values
(Y value refers to luminance or luminance factor)
"""
xyz = np2d(xyz)
X,Y,Z = asplit(xyz)
sumxyz = X + Y + Z
x = X / sumxyz
y = Y / sumxyz
return ajoin((Y,x,y))
def Yxy_to_xyz(Yxy, **kwargs):
"""
Convert CIE Yxy chromaticity values to XYZ tristimulus values.
Args:
:Yxy:
| ndarray with Yxy chromaticity values
(Y value refers to luminance or luminance factor)
Returns:
:xyz:
| ndarray with tristimulus values
"""
Yxy = np2d(Yxy)
Y,x,y = asplit(Yxy)
X = Y*x/y
Z = Y*(1.0-x-y)/y
return ajoin((X,Y,Z))
def Yuv_to_xyz2(Yuv, **kwargs):
"""
Convert CIE 1976 Yu'v' chromaticity values to XYZ tristimulus values.
Args:
:Yuv:
| ndarray with CIE 1976 Yu'v' chromaticity values
(Y value refers to luminance or luminance factor)
Returns:
:xyz:
| ndarray with tristimulus values
"""
Yuv = np2d(Yuv)
xyz = Yuv.astype(np.float)
xyz[...,1] = Yuv[...,0]
xyz[...,0] = Yuv[...,0]*(9.0*Yuv[...,1])/(4.0*Yuv[...,2])
xyz[...,2] = Yuv[...,0]*(12.0 - 3.0*Yuv[...,1] - 20.0*Yuv[...,2])/(4.0*Yuv[...,2])
return xyz
def Yxy_to_xyz(Yxy, **kwargs):
"""
Convert CIE Yxy chromaticity values to XYZ tristimulus values.
Args:
:Yxy:
| ndarray with Yxy chromaticity values
(Y value refers to luminance or luminance factor)
Returns:
:xyz:
| ndarray with tristimulus values
"""
Yxy = np2d(Yxy)
xyz = np.empty(Yxy.shape)
xyz[..., 1] = Yxy[..., 0]
xyz[..., 0] = Yxy[..., 0] * Yxy[..., 1] / Yxy[..., 2]
xyz[..., 2] = Yxy[..., 0] * (1.0 - Yxy[..., 1] - Yxy[..., 2]) / Yxy[..., 2]
return xyz
def Yuv_to_xyz(Yuv, **kwargs):
"""
Convert CIE 1976 Yu'v' chromaticity values to XYZ tristimulus values.
Args:
:Yuv:
| ndarray with CIE 1976 Yu'v' chromaticity values
(Y value refers to luminance or luminance factor)
Returns:
:xyz:
| ndarray with tristimulus values
"""
Yuv = np2d(Yuv)
Y,u,v = asplit(Yuv)
X = Y*(9.0*u)/(4.0*v)
Z = Y*(12.0 - 3.0*u - 20.0*v)/(4.0*v)
return ajoin((X,Y,Z))
def xyz_to_lab(xyz, xyzw=None, cieobs=_CIEOBS, **kwargs):
"""
Convert XYZ tristimulus values to CIE 1976 L*a*b* (CIELAB) coordinates.
Args:
:xyz:
| ndarray with tristimulus values
:xyzw:
| None or ndarray with tristimulus values of white point, optional
| None defaults to xyz of CIE D65 using the :cieobs: observer.
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when calculating xyzw.
Returns:
:lab:
| ndarray with CIE 1976 L*a*b* (CIELAB) color coordinates
"""
xyz = np2d(xyz)
if xyzw is None:
xyzw = spd_to_xyz(_CIE_ILLUMINANTS['D65'], cieobs=cieobs)
# get and normalize (X,Y,Z) to white point:
XYZr = xyz / xyzw
# Apply cube-root compression:
fXYZr = XYZr**(1.0 / 3.0)
# Check for T/Tn <= 0.008856: (Note (24/116)**3 = 0.008856)
pqr = XYZr <= (24 / 116)**3
# calculate f(T) for T/Tn <= 0.008856: (Note:(1/3)*((116/24)**2) = 841/108 = 7.787)
fXYZr[pqr] = ((841 / 108) * XYZr[pqr] + 16.0 / 116.0)
# calculate L*, a*, b*:
Lab = np.empty(xyz.shape)
Lab[..., 0] = 116.0 * (fXYZr[..., 1]) - 16.0
Lab[pqr[..., 1], 0] = 903.3 * XYZr[pqr[..., 1], 1]
Lab[..., 1] = 500.0 * (fXYZr[..., 0] - fXYZr[..., 1])
Lab[..., 2] = 200.0 * (fXYZr[..., 1] - fXYZr[..., 2])
return Lab
def luv_to_xyz(luv, xyzw = None, cieobs = _CIEOBS, **kwargs):
"""
Convert CIE 1976 L*u*v* (CIELUVB) coordinates to XYZ tristimulus values.
Args:
:luv:
| ndarray with CIE 1976 L*u*v* (CIELUV) color coordinates
:xyzw:
| None or ndarray with tristimulus values of white point, optional
| None defaults to xyz of CIE D65 using the :cieobs: observer.
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when calculating xyzw.
Returns:
:xyz:
| ndarray with tristimulus values
"""
luv = np2d(luv)
if xyzw is None:
xyzw = spd_to_xyz(_CIE_ILLUMINANTS['D65'],cieobs = cieobs)
# Make xyzw same shape as luv:
Yuvw = todim(xyz_to_Yuv(xyzw), luv.shape, equal_shape = True)
# Get Yw, uw,vw:
Yw,uw,vw = asplit(Yuvw)
# calculate u'v' from u*,v*:
L,u,v = asplit(luv)
up,vp = [(x / (13*L)) + xw for (x,xw) in ((u,uw),(v,vw))]
up[np.where(L == 0.0)] = 0.0
vp[np.where(L == 0.0)] = 0.0
fy = (L + 16.0) / 116.0
Y = Yw*(fy**3.0)
p = np.where((Y/Yw) < ((6.0/29.0)**3.0))
Y[p] = Yw[p]*(L[p]/((29.0/3.0)**3.0))
return Yuv_to_xyz(ajoin((Y,up,vp)))
def rms(data,axis = 0, keepdims = False):
"""
Calculate root-mean-square along axis.
Args:
:data:
| list of values or ndarray
:axis:
| 0, optional
| Axis along which to calculate rms.
:keepdims:
| False or True, optional
| Keep original dimensions of array.
Returns:
:returns:
| ndarray with rms values.
"""
data = np2d(data)
return np.sqrt(np.power(data,2).mean(axis=axis, keepdims = keepdims))
def geomean(data, axis = 0, keepdims = False):
"""
Calculate geometric mean along axis.
Args:
:data:
| list of values or ndarray
:axis:
| 0, optional
| Axis along which to calculate geomean.
:keepdims:
| False or True, optional
| Keep original dimensions of array.
Returns:
:returns:
| ndarray with geomean values.
"""
data = np2d(data)
return np.power(data.prod(axis=axis, keepdims = keepdims),1/data.shape[axis])
def xyz_to_Yuv(xyz, **kwargs):
"""
Convert XYZ tristimulus values CIE 1976 Yu'v' chromaticity values.
Args:
:xyz:
| ndarray with tristimulus values
Returns:
:Yuv:
| ndarray with CIE 1976 Yu'v' chromaticity values
(Y value refers to luminance or luminance factor)
"""
xyz = np2d(xyz)
Yuv = np.empty(xyz.shape)
denom = xyz[..., 0] + 15.0 * xyz[..., 1] + 3.0 * xyz[..., 2]
Yuv[..., 0] = xyz[..., 1]
Yuv[..., 1] = 4.0 * xyz[..., 0] / denom
Yuv[..., 2] = 9.0 * xyz[..., 1] / denom
return Yuv
def xyz_to_Yxy(xyz, **kwargs):
"""
Convert XYZ tristimulus values CIE Yxy chromaticity values.
Args:
:xyz:
| ndarray with tristimulus values
Returns:
:Yxy:
| ndarray with Yxy chromaticity values
(Y value refers to luminance or luminance factor)
"""
xyz = np2d(xyz)
Yxy = np.empty(xyz.shape)
sumxyz = xyz[..., 0] + xyz[..., 1] + xyz[..., 2]
Yxy[..., 0] = xyz[..., 1]
Yxy[..., 1] = xyz[..., 0] / sumxyz
Yxy[..., 2] = xyz[..., 1] / sumxyz
return Yxy