def psy_scale(data,
scale_factor=[1.0 / 55.0, 3.0 / 2.0, 2.0],
scale_max=100.0): # defaults for cri2012
"""
Psychometric based color rendering index scale from CRI2012:
| Rfi,a = 100 * (2 / (exp(c1*abs(DEi,a)**(c2) + 1))) ** c3.
Args:
:data:
| float or list[floats] or ndarray
:scale_factor:
| [1/55, 3/2, 2.0] or list[float] or ndarray, optional
| Rescales color differences before subtracting them from :scale_max:
| Note that the default value is the one from (Smet et al. 2013, LRT).
:scale_max:
| 100.0, optional
| Maximum value of linear scale
Returns:
:returns:
| float or list[floats] or ndarray
References:
1. `Smet, K., Schanda, J., Whitehead, L., & Luo, R. (2013).
CRI2012: A proposal for updating the CIE colour rendering index.
Lighting Research and Technology, 45, 689–709.
<http://lrt.sagepub.com/content/45/6/689>`_
"""
return scale_max * np.power(
2.0 /
(np.exp(scale_factor[0] * np.power(np.abs(data), scale_factor[1])) +
1.0), scale_factor[2])
def get_xyz(self, *args):
""" get cartesian coordinates """
theta, phi, r = args
x = r * np.sin(theta) * np.cos(phi)
y = r * np.sin(theta) * np.sin(phi)
z = r * np.cos(theta)
z[np.abs(z) < self._TINY] = 0.0
return x, y, z
def naka_rushton(data, sig=2.0, n=0.73, scaling=1.0, noise=0.0, forward=True):
"""
Apply a Naka-Rushton response compression (n) and an adaptive shift (sig).
| NK(x) = sign(x) * scaling * ((abs(x)**n) / ((abs(x)**n) + (sig**n))) + noise
Args:
:data:
| float or ndarray
:sig:
| 2.0, optional
| Semi-saturation constant. Value for which NK(:data:) is 1/2
:n:
| 0.73, optional
| Compression power.
:scaling:
| 1.0, optional
| Maximum value of NK-function.
:noise:
| 0.0, optional
| Cone excitation noise.
:forward:
| True, optional
| True: do NK(x)
| False: do NK(x)**(-1).
Returns:
:returns:
| float or ndarray with NK-(de)compressed input :x:
"""
if forward:
return np.sign(data) * scaling * ((np.abs(data)**n) /
((np.abs(data)**n) +
(sig**n))) + noise
elif forward == False:
Ip = sig * (((np.abs(np.abs(data) - noise)) /
(scaling - np.abs(np.abs(data) - noise))))**(1 / n)
if not np.isscalar(Ip):
p = np.where(np.abs(data) < noise)
Ip[p] = -Ip[p]
else:
if np.abs(data) < noise:
Ip = -Ip
return Ip
def polyarea(x,y):
"""
Calculates area of polygon.
| First coordinate should also be last.
Args:
:x:
| ndarray of x-coordinates of polygon vertices.
:y:
| ndarray of x-coordinates of polygon vertices.
Returns:
:returns:
| float (area or polygon)
"""
return 0.5*np.abs(np.dot(x,np.roll(y,1).T)-np.dot(y,np.roll(x,1).T))
def xyz_to_cct_ohno2011(xyz):
"""
Calculate cct and Duv from CIE 1931 2° xyz following Ohno (2011).
Args:
:xyz:
| ndarray with CIE 1931 2° X,Y,Z tristimulus values
Returns:
:cct, duv:
| ndarrays with correlated color temperatures and distance to blackbody locus in CIE 1960 uv
References:
1. Ohno, Y. (2011). Calculation of CCT and Duv and Practical Conversion Formulae.
CORM 2011 Conference, Gaithersburg, MD, May 3-5, 2011
"""
uvp = xyz_to_Yuv(xyz)[..., 1:]
uv = uvp * np.array([[1, 2 / 3]])
Lfp = ((uv[..., 0] - 0.292)**2 + (uv[..., 1] - 0.24)**2)**0.5
a = np.arctan((uv[..., 1] - 0.24) / (uv[..., 0] - 0.292))
a[a < 0] = a[a < 0] + np.pi
Lbb = np.polyval(_KIJ[0, :], a)
Duv = Lfp - Lbb
T1 = 1 / np.polyval(_KIJ[1, :], a)
T1[a >= 2.54] = 1 / np.polyval(_KIJ[2, :], a[a >= 2.54])
dTc1 = np.polyval(_KIJ[3, :], a) * (Lbb + 0.01) / Lfp * Duv / 0.01
dTc1[a >= 2.54] = 1 / np.polyval(_KIJ[4, :], a[a >= 2.54]) * (
Lbb[a >= 2.54] + 0.01) / Lfp[a >= 2.54] * Duv[a >= 2.54] / 0.01
T2 = T1 - dTc1
c = np.log10(T2)
c[T2 == 0] = -np.inf
dTc2 = np.polyval(_KIJ[5, :], c)
dTc2[Duv < 0] = np.polyval(_KIJ[6, :], c[Duv < 0]) * np.abs(
Duv[Duv < 0] / 0.03)**2
Tfinal = T2 - dTc2
return Tfinal, Duv
def xyz_to_Ydlep(xyz,
cieobs=_CIEOBS,
xyzw=_COLORTF_DEFAULT_WHITE_POINT,
flip_axes=False,
SL_max_lambda=None,
**kwargs):
"""
Convert XYZ tristimulus values to Y, dominant (complementary) wavelength
and excitation purity.
Args:
:xyz:
| ndarray with tristimulus values
:xyzw:
| None or ndarray with tristimulus values of a single (!) native white point, optional
| None defaults to xyz of CIE D65 using the :cieobs: observer.
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when calculating spectrum locus coordinates.
:flip_axes:
| False, optional
| If True: flip axis 0 and axis 1 in Ydelep to increase speed of loop in function.
| (single xyzw with is not flipped!)
:SL_max_lambda:
| None or float, optional
| Maximum wavelength of spectrum locus before it turns back on itelf in the high wavelength range (~700 nm)
Returns:
:Ydlep:
| ndarray with Y, dominant (complementary) wavelength
| and excitation purity
"""
xyz3 = np3d(xyz).copy().astype(np.float)
# flip axis so that shortest dim is on axis0 (save time in looping):
if (xyz3.shape[0] < xyz3.shape[1]) & (flip_axes == True):
axes12flipped = True
xyz3 = xyz3.transpose((1, 0, 2))
else:
axes12flipped = False
# convert xyz to Yxy:
Yxy = xyz_to_Yxy(xyz3)
Yxyw = xyz_to_Yxy(xyzw)
# get spectrum locus Y,x,y and wavelengths:
SL = _CMF[cieobs]['bar']
SL = SL[:, SL[1:].sum(axis=0) >
0] # avoid div by zero in xyz-to-Yxy conversion
wlsl = SL[0]
Yxysl = xyz_to_Yxy(SL[1:4].T)[:, None]
# Get maximum wavelength of spectrum locus (before it turns back on itself)
if SL_max_lambda is None:
pmaxlambda = Yxysl[..., 1].argmax() # lambda with largest x value
dwl = np.diff(
Yxysl[:, 0,
1]) # spectrumlocus in that range should have increasing x
dwl[wlsl[:-1] < 600] = 10000
pmaxlambda = np.where(
dwl <= 0)[0][0] # Take first element with zero or <zero slope
else:
pmaxlambda = np.abs(wlsl - SL_max_lambda).argmin()
Yxysl = Yxysl[:(pmaxlambda + 1), :]
wlsl = wlsl[:(pmaxlambda + 1)]
# center on xyzw:
Yxy = Yxy - Yxyw
Yxysl = Yxysl - Yxyw
Yxyw = Yxyw - Yxyw
#split:
Y, x, y = asplit(Yxy)
Yw, xw, yw = asplit(Yxyw)
Ysl, xsl, ysl = asplit(Yxysl)
# calculate hue:
h = math.positive_arctan(x, y, htype='deg')
hsl = math.positive_arctan(xsl, ysl, htype='deg')
hsl_max = hsl[0] # max hue angle at min wavelength
hsl_min = hsl[-1] # min hue angle at max wavelength
if hsl_min < hsl_max: hsl_min += 360
dominantwavelength = np.empty(Y.shape)
purity = np.empty(Y.shape)
for i in range(xyz3.shape[1]):
# find index of complementary wavelengths/hues:
pc = np.where(
(h[:, i] > hsl_max) & (h[:, i] < hsl_min)
) # hue's requiring complementary wavelength (purple line)
h[:, i][pc] = h[:, i][pc] - np.sign(
h[:, i][pc] - 180.0
) * 180.0 # add/subtract 180° to get positive complementary wavelength
# find 2 closest enclosing hues in sl:
#hslb,hib = meshblock(hsl,h[:,i:i+1])
hib, hslb = np.meshgrid(h[:, i:i + 1], hsl)
dh = (hslb - hib)
q1 = np.abs(dh).argmin(axis=0) # index of closest hue
sign_q1 = np.sign(dh[q1])[0]
dh[np.sign(dh) ==
sign_q1] = 1000000 # set all dh on the same side as q1 to a very large value
q2 = np.abs(dh).argmin(
axis=0) # index of second closest (enclosing) hue
# # Test changes to code:
# print('wls',i, wlsl[q1],wlsl[q2])
# import matplotlib.pyplot as plt
# plt.figure()
# plt.plot(wlsl[:-1],np.diff(xsl[:,0]),'k.-')
# plt.figure()
# plt.plot(x[0,i],y[0,i],'k.'); plt.plot(xsl,ysl,'r.-');plt.plot(xsl[q1],ysl[q1],'b.');plt.plot(xsl[q2],ysl[q2],'g.');plt.plot(xsl[-1],ysl[-1],'c+')
dominantwavelength[:, i] = wlsl[q1] + np.multiply(
(h[:, i] - hsl[q1, 0]),
np.divide((wlsl[q2] - wlsl[q1]), (hsl[q2, 0] - hsl[q1, 0]))
) # calculate wl corresponding to h: y = y1 + (x-x1)*(y2-y1)/(x2-x1)
dominantwavelength[:, i][pc] = -dominantwavelength[:, i][
pc] #complementary wavelengths are specified by '-' sign
# calculate excitation purity:
x_dom_wl = xsl[q1, 0] + (xsl[q2, 0] - xsl[q1, 0]) * (h[:, i] - hsl[
q1, 0]) / (hsl[q2, 0] - hsl[q1, 0]) # calculate x of dom. wl
y_dom_wl = ysl[q1, 0] + (ysl[q2, 0] - ysl[q1, 0]) * (h[:, i] - hsl[
q1, 0]) / (hsl[q2, 0] - hsl[q1, 0]) # calculate y of dom. wl
d_wl = (x_dom_wl**2.0 +
y_dom_wl**2.0)**0.5 # distance from white point to sl
d = (x[:, i]**2.0 +
y[:, i]**2.0)**0.5 # distance from white point to test point
purity[:, i] = d / d_wl
# correct for those test points that have a complementary wavelength
# calculate intersection of line through white point and test point and purple line:
xy = np.vstack((x[:, i], y[:, i])).T
xyw = np.hstack((xw, yw))
xypl1 = np.hstack((xsl[0, None], ysl[0, None]))
xypl2 = np.hstack((xsl[-1, None], ysl[-1, None]))
da = (xy - xyw)
db = (xypl2 - xypl1)
dp = (xyw - xypl1)
T = np.array([[0.0, -1.0], [1.0, 0.0]])
dap = np.dot(da, T)
denom = np.sum(dap * db, axis=1, keepdims=True)
num = np.sum(dap * dp, axis=1, keepdims=True)
xy_linecross = (num / denom) * db + xypl1
d_linecross = np.atleast_2d(
(xy_linecross[:, 0]**2.0 + xy_linecross[:, 1]**2.0)**0.5).T #[0]
purity[:, i][pc] = d[pc] / d_linecross[pc][:, 0]
Ydlep = np.dstack((xyz3[:, :, 1], dominantwavelength, purity))
if axes12flipped == True:
Ydlep = Ydlep.transpose((1, 0, 2))
else:
Ydlep = Ydlep.transpose((0, 1, 2))
return Ydlep.reshape(xyz.shape)
def DE2000(xyzt,
xyzr,
dtype='xyz',
DEtype='jab',
avg=None,
avg_axis=0,
out='DEi',
xyzwt=None,
xyzwr=None,
KLCH=None):
"""
Calculate DE2000 color difference.
Args:
:xyzt:
| ndarray with tristimulus values of test data.
:xyzr:
| ndarray with tristimulus values of reference data.
:dtype:
| 'xyz' or 'lab', optional
| Specifies data type in :xyzt: and :xyzr:.
:xyzwt:
| None or ndarray, optional
| White point tristimulus values of test data
| None defaults to the one set in lx.xyz_to_lab()
:xyzwr:
| None or ndarray, optional
| Whitepoint tristimulus values of reference data
| None defaults to the one set in lx.xyz_to_lab()
:DEtype:
| 'jab' or str, optional
| Options:
| - 'jab' : calculates full color difference over all 3 dimensions.
| - 'ab' : calculates chromaticity difference.
| - 'j' : calculates lightness or brightness difference
| (depending on :outin:).
| - 'j,ab': calculates both 'j' and 'ab' options
| and returns them as a tuple.
:KLCH:
| None, optional
| Weigths for L, C, H
| None: default to [1,1,1]
:avg:
| None, optional
| None: don't calculate average DE,
| otherwise use function handle in :avg:.
:avg_axis:
| axis to calculate average over, optional
:out:
| 'DEi' or str, optional
| Requested output.
Note:
For the other input arguments, see specific color space used.
Returns:
:returns:
| ndarray with DEi [, DEa] or other as specified by :out:
References:
1. `Sharma, G., Wu, W., & Dalal, E. N. (2005).
The CIEDE2000 color‐difference formula: Implementation notes,
supplementary test data, and mathematical observations.
Color Research & Application, 30(1), 21–30.
<https://doi.org/10.1002/col.20070>`_
"""
if KLCH is None:
KLCH = [1, 1, 1]
if dtype == 'xyz':
labt = xyz_to_lab(xyzt, xyzw=xyzwt)
labr = xyz_to_lab(xyzr, xyzw=xyzwr)
else:
labt = xyzt
labr = xyzr
Lt = labt[..., 0:1]
at = labt[..., 1:2]
bt = labt[..., 2:3]
Ct = np.sqrt(at**2 + bt**2)
#ht = cam.hue_angle(at,bt,htype = 'rad')
Lr = labr[..., 0:1]
ar = labr[..., 1:2]
br = labr[..., 2:3]
Cr = np.sqrt(ar**2 + br**2)
#hr = cam.hue_angle(at,bt,htype = 'rad')
# Step 1:
Cavg = (Ct + Cr) / 2
G = 0.5 * (1 - np.sqrt((Cavg**7.0) / ((Cavg**7.0) + (25.0**7))))
apt = (1 + G) * at
apr = (1 + G) * ar
Cpt = np.sqrt(apt**2 + bt**2)
Cpr = np.sqrt(apr**2 + br**2)
Cpprod = Cpt * Cpr
hpt = cam.hue_angle(apt, bt, htype='deg')
hpr = cam.hue_angle(apr, br, htype='deg')
hpt[(apt == 0) * (bt == 0)] = 0
hpr[(apr == 0) * (br == 0)] = 0
# Step 2:
dL = np.abs(Lr - Lt)
dCp = np.abs(Cpr - Cpt)
dhp_ = hpr - hpt
dhp = dhp_.copy()
dhp[np.where(np.abs(dhp_) > 180)] = dhp[np.where(np.abs(dhp_) > 180)] - 360
dhp[np.where(
np.abs(dhp_) < -180)] = dhp[np.where(np.abs(dhp_) < -180)] + 360
dhp[np.where(Cpprod == 0)] = 0
#dH = 2*np.sqrt(Cpprod)*np.sin(dhp/2*np.pi/180)
dH = deltaH(dhp, Cpprod, htype='deg')
# Step 3:
Lp = (Lr + Lt) / 2
Cp = (Cpr + Cpt) / 2
hps = hpt + hpr
hp = (hpt + hpr) / 2
hp[np.where((np.abs(dhp_) > 180)
& (hps < 360))] = hp[np.where((np.abs(dhp_) > 180)
& (hps < 360))] + 180
hp[np.where((np.abs(dhp_) > 180)
& (hps >= 360))] = hp[np.where((np.abs(dhp_) > 180)
& (hps >= 360))] - 180
hp[np.where(Cpprod == 0)] = 0
T = 1 - 0.17*np.cos((hp - 30)*np.pi/180) + 0.24*np.cos(2*hp*np.pi/180) +\
0.32*np.cos((3*hp + 6)*np.pi/180) - 0.20*np.cos((4*hp - 63)*np.pi/180)
dtheta = 30 * np.exp(-((hp - 275) / 25)**2)
RC = 2 * np.sqrt((Cp**7) / ((Cp**7) + (25**7)))
SL = 1 + ((0.015 * (Lp - 50)**2) / np.sqrt(20 + (Lp - 50)**2))
SC = 1 + 0.045 * Cp
SH = 1 + 0.015 * Cp * T
RT = -np.sin(2 * dtheta * np.pi / 180) * RC
kL, kC, kH = KLCH
DEi = ((dL / (kL * SL))**2, (dCp / (kC * SC))**2 + (dH / (kH * SH))**2 +
RT * (dCp / (kC * SC)) * (dH / (kH * SH)))
return _process_DEi(DEi,
DEtype=DEtype,
avg=avg,
avg_axis=avg_axis,
out=out)
def _xyz_to_jab_cam02ucs(xyz, xyzw, ucs=True, conditions=None):
"""
Calculate CAM02-UCS J'a'b' coordinates from xyz tristimulus values of sample and white point.
Args:
:xyz:
| ndarray with sample tristimulus values
:xyzw:
| ndarray with white point tristimulus values
:conditions:
| None, optional
| Dictionary with viewing conditions.
| None results in:
| {'La':100, 'Yb':20, 'D':1, 'surround':'avg'}
| For more info see luxpy.cam.ciecam02()?
Returns:
:jab:
| ndarray with J'a'b' coordinates.
"""
#--------------------------------------------
# Get/ set conditions parameters:
if conditions is not None:
surround_parameters = {
'surrounds': ['avg', 'dim', 'dark'],
'avg': {
'c': 0.69,
'Nc': 1.0,
'F': 1.0,
'FLL': 1.0
},
'dim': {
'c': 0.59,
'Nc': 0.9,
'F': 0.9,
'FLL': 1.0
},
'dark': {
'c': 0.525,
'Nc': 0.8,
'F': 0.8,
'FLL': 1.0
}
}
La = conditions['La']
Yb = conditions['Yb']
D = conditions['D']
surround = conditions['surround']
if isinstance(surround, str):
surround = surround_parameters[conditions['surround']]
F, FLL, Nc, c = [surround[x] for x in sorted(surround.keys())]
else:
# set defaults:
La, Yb, D, F, FLL, Nc, c = 100, 20, 1, 1, 1, 1, 0.69
#--------------------------------------------
# Define sensor space and cat matrices:
mhpe = np.array([[0.38971, 0.68898, -0.07868], [-0.22981, 1.1834, 0.04641],
[0.0, 0.0, 1.0]
]) # Hunt-Pointer-Estevez sensors (cone fundamentals)
mcat = np.array([[0.7328, 0.4296, -0.1624], [-0.7036, 1.6975, 0.0061],
[0.0030, 0.0136, 0.9834]]) # CAT02 sensor space
#--------------------------------------------
# pre-calculate some matrices:
invmcat = np.linalg.inv(mcat)
mhpe_x_invmcat = np.dot(mhpe, invmcat)
#--------------------------------------------
# calculate condition dependent parameters:
Yw = xyzw[..., 1:2].T
k = 1.0 / (5.0 * La + 1.0)
FL = 0.2 * (k**4.0) * (5.0 * La) + 0.1 * ((1.0 - k**4.0)**2.0) * (
(5.0 * La)**(1.0 / 3.0)) # luminance adaptation factor
n = Yb / Yw
Nbb = 0.725 * (1 / n)**0.2
Ncb = Nbb
z = 1.48 + FLL * n**0.5
if D is None:
D = F * (1.0 - (1.0 / 3.6) * np.exp((-La - 42.0) / 92.0))
#--------------------------------------------
# transform from xyz, xyzw to cat sensor space:
rgb = math.dot23(mcat, xyz.T)
rgbw = mcat @ xyzw.T
#--------------------------------------------
# apply von Kries cat:
rgbc = (
(D * Yw / rgbw)[..., None] + (1 - D)
) * rgb # factor 100 from ciecam02 is replaced with Yw[i] in ciecam16, but see 'note' in Fairchild's "Color Appearance Models" (p291 ni 3ed.)
rgbwc = (
(D * Yw / rgbw) + (1 - D)
) * rgbw # factor 100 from ciecam02 is replaced with Yw[i] in ciecam16, but see 'note' in Fairchild's "Color Appearance Models" (p291 ni 3ed.)
#--------------------------------------------
# convert from cat02 sensor space to cone sensors (hpe):
rgbp = math.dot23(mhpe_x_invmcat, rgbc).T
rgbwp = (mhpe_x_invmcat @ rgbwc).T
#--------------------------------------------
# apply Naka_rushton repsonse compression:
naka_rushton = lambda x: 400 * x**0.42 / (x**0.42 + 27.13) + 0.1
rgbpa = naka_rushton(FL * rgbp / 100.0)
p = np.where(rgbp < 0)
rgbpa[p] = 0.1 - (naka_rushton(FL * np.abs(rgbp[p]) / 100.0) - 0.1)
rgbwpa = naka_rushton(FL * rgbwp / 100.0)
pw = np.where(rgbwp < 0)
rgbwpa[pw] = 0.1 - (naka_rushton(FL * np.abs(rgbwp[pw]) / 100.0) - 0.1)
#--------------------------------------------
# Calculate achromatic signal:
A = (2.0 * rgbpa[..., 0] + rgbpa[..., 1] +
(1.0 / 20.0) * rgbpa[..., 2] - 0.305) * Nbb
Aw = (2.0 * rgbwpa[..., 0] + rgbwpa[..., 1] +
(1.0 / 20.0) * rgbwpa[..., 2] - 0.305) * Nbb
#--------------------------------------------
# calculate initial opponent channels:
a = rgbpa[..., 0] - 12.0 * rgbpa[..., 1] / 11.0 + rgbpa[..., 2] / 11.0
b = (1.0 / 9.0) * (rgbpa[..., 0] + rgbpa[..., 1] - 2.0 * rgbpa[..., 2])
#--------------------------------------------
# calculate hue h and eccentricity factor, et:
h = np.arctan2(b, a)
et = (1.0 / 4.0) * (np.cos(h + 2.0) + 3.8)
#--------------------------------------------
# calculate lightness, J:
J = 100.0 * (A / Aw)**(c * z)
#--------------------------------------------
# calculate chroma, C:
t = ((50000.0 / 13.0) * Nc * Ncb * et *
((a**2.0 + b**2.0)**0.5)) / (rgbpa[..., 0] + rgbpa[..., 1] +
(21.0 / 20.0 * rgbpa[..., 2]))
C = (t**0.9) * ((J / 100.0)**0.5) * (1.64 - 0.29**n)**0.73
#--------------------------------------------
# Calculate colorfulness, M:
M = C * FL**0.25
#--------------------------------------------
# convert to cam02ucs J', aM', bM':
if ucs == True:
KL, c1, c2 = 1.0, 0.007, 0.0228
Jp = (1.0 + 100.0 * c1) * J / (1.0 + c1 * J)
Mp = (1.0 / c2) * np.log(1.0 + c2 * M)
else:
Jp = J
Mp = M
aMp = Mp * np.cos(h)
bMp = Mp * np.sin(h)
return np.dstack((Jp, aMp, bMp))
def plot_spectrum_colors(spd = None, spdmax = None,\
wavelength_height = -0.05, wavelength_opacity = 1.0, wavelength_lightness = 1.0,\
cieobs = _CIEOBS, show = True, axh = None,\
show_grid = False,ylabel = 'Spectral intensity (a.u.)',xlim=None,\
**kwargs):
"""
Plot the spectrum colors.
Args:
:spd:
| None, optional
| Spectrum
:spdmax:
| None, optional
| max ylim is set at 1.05 or (1+abs(wavelength_height)*spdmax)
:wavelength_opacity:
| 1.0, optional
| Sets opacity of wavelength rectangle.
:wavelength_lightness:
| 1.0, optional
| Sets lightness of wavelength rectangle.
:wavelength_height:
| -0.05 or 'spd', optional
| Determine wavelength bar height
| if not 'spd': x% of spd.max()
:axh:
| None or axes handle, optional
| Determines axes to plot data in.
| None: make new figure.
:show:
| True or False, optional
| Invoke matplotlib.pyplot.show() right after plotting
:cieobs:
| luxpy._CIEOBS or str, optional
| Determines CMF set to calculate spectrum locus or other.
:show_grid:
| False, optional
| Show grid (True) or not (False)
:ylabel:
| 'Spectral intensity (a.u.)' or str, optional
| Set y-axis label.
:xlim:
| None, optional
| list or ndarray with xlimits.
:kwargs:
| additional keyword arguments for use with matplotlib.pyplot.
Returns:
"""
if isinstance(cieobs, str):
cmfs = _CMF[cieobs]['bar']
else:
cmfs = cieobs
cmfs = cmfs[:, cmfs[1:].sum(axis=0) >
0] # avoid div by zero in xyz-to-Yxy conversion
wavs = cmfs[0:1].T
SL = cmfs[1:4].T
srgb = xyz_to_srgb(wavelength_lightness * 100 * SL)
srgb = srgb / srgb.max()
if show == True:
if axh is None:
fig = plt.figure()
axh = fig.add_subplot(111)
if (wavelength_height == 'spd') & (spd is not None):
if spdmax is None:
spdmax = np.nanmax(spd[1:, :])
y_min, y_max = 0.0, spdmax * (1.05)
if xlim is None:
x_min, x_max = spd[0, :].min(), spd[0, :].max()
else:
x_min, x_max = xlim
SLrect = np.vstack([
(x_min, 0.0),
spd.T,
(x_max, 0.0),
])
wavelength_height = y_max
spdmax = 1
else:
if (spdmax is None) & (spd is not None):
spdmax = np.nanmax(spd[1:, :])
y_min, y_max = wavelength_height * spdmax, spdmax * (
1 + np.abs(wavelength_height))
elif (spdmax is None) & (spd is None):
spdmax = 1
y_min, y_max = wavelength_height, 0
elif (spdmax is not None):
y_min, y_max = wavelength_height * spdmax, spdmax #*(1 + np.abs(wavelength_height))
if xlim is None:
x_min, x_max = wavs.min(), wavs.max()
else:
x_min, x_max = xlim
SLrect = np.vstack([
(x_min, 0.0),
(x_min, wavelength_height * spdmax),
(x_max, wavelength_height * spdmax),
(x_max, 0.0),
])
axh.set_xlim([x_min, x_max])
axh.set_ylim([y_min, y_max])
polygon = Polygon(SLrect, facecolor=None, edgecolor=None)
axh.add_patch(polygon)
padding = 0.1
axh.bar(x=wavs - padding,
height=wavelength_height * spdmax,
width=1 + padding,
color=srgb,
align='edge',
linewidth=0,
clip_path=polygon)
if spd is not None:
axh.plot(spd[0:1, :].T, spd[1:, :].T, color='k', label='spd')
if show_grid == True:
plt.grid(True)
axh.set_xlabel('Wavelength (nm)', kwargs)
axh.set_ylabel(ylabel, kwargs)
#plt.show()
return axh
else:
return None
def get_macadam_ellipse(xy = None, k_neighbours = 3, nsteps = 10, average_cik = True):
"""
Estimate n-step MacAdam ellipse at CIE x,y coordinates xy by calculating
average inverse covariance ellipse of the k_neighbours closest ellipses.
Args:
:xy:
| None or ndarray, optional
| If None: output Macadam ellipses, if not None: xy are the
| CIE xy coordinates for which ellipses will be estimated.
:k_neighbours:
| 3, optional
| Number of nearest ellipses to use to calculate ellipse at xy
:nsteps:
| 10, optional
| Set number of MacAdam steps of ellipse.
:average_cik:
| True, optional
| If True: take distance weighted average of inverse
| 'covariance ellipse' elements cik.
| If False: average major & minor axis lengths and
| ellipse orientation angles directly.
Returns:
:v_mac_est:
| estimated MacAdam ellipse(s) in v-format [Rmax,Rmin,xc,yc,theta]
References:
1. MacAdam DL. Visual Sensitivities to Color Differences in Daylight*. J Opt Soc Am. 1942;32(5):247-274.
"""
# list of MacAdam ellipses (x10)
v_mac = np.atleast_2d([
[0.16, 0.057, 0.0085, 0.0035, 62.5],
[0.187, 0.118, 0.022, 0.0055, 77],
[0.253, 0.125, 0.025, 0.005, 55.5],
[0.15, 0.68, 0.096, 0.023, 105],
[0.131, 0.521, 0.047, 0.02, 112.5],
[0.212, 0.55, 0.058, 0.023, 100],
[0.258, 0.45, 0.05, 0.02, 92],
[0.152, 0.365, 0.038, 0.019, 110],
[0.28, 0.385, 0.04, 0.015, 75.5],
[0.38, 0.498, 0.044, 0.012, 70],
[0.16, 0.2, 0.021, 0.0095, 104],
[0.228, 0.25, 0.031, 0.009, 72],
[0.305, 0.323, 0.023, 0.009, 58],
[0.385, 0.393, 0.038, 0.016, 65.5],
[0.472, 0.399, 0.032, 0.014, 51],
[0.527, 0.35, 0.026, 0.013, 20],
[0.475, 0.3, 0.029, 0.011, 28.5],
[0.51, 0.236, 0.024, 0.012, 29.5],
[0.596, 0.283, 0.026, 0.013, 13],
[0.344, 0.284, 0.023, 0.009, 60],
[0.39, 0.237, 0.025, 0.01, 47],
[0.441, 0.198, 0.028, 0.0095, 34.5],
[0.278, 0.223, 0.024, 0.0055, 57.5],
[0.3, 0.163, 0.029, 0.006, 54],
[0.365, 0.153, 0.036, 0.0095, 40]
])
# convert to v-format ([a,b, xc, yc, theta]):
v_mac = v_mac[:,[2,3,0,1,4]]
# convert last column to rad.:
v_mac[:,-1] = v_mac[:,-1]*np.pi/180
# convert to desired number of MacAdam-steps:
v_mac[:,0:2] = v_mac[:,0:2]/10*nsteps
if xy is not None:
#calculate inverse covariance matrices:
cik = math.v_to_cik(v_mac, inverse = True)
if average_cik == True:
cik_long = np.hstack((cik[:,0,:],cik[:,1,:]))
# Calculate k_neighbours closest ellipses to xy:
tree = sp.spatial.cKDTree(v_mac[:,2:4], copy_data = True)
d, inds = tree.query(xy, k = k_neighbours)
if k_neighbours > 1:
pd = 1
w = (1.0 / np.abs(d)**pd)[:,:,None] # inverse distance weigthing
if average_cik == True:
cik_long_est = np.sum(w * cik_long[inds,:], axis=1) / np.sum(w, axis=1)
else:
v_mac_est = np.sum(w * v_mac[inds,:], axis=1) / np.sum(w, axis=1) # for average xyc
else:
v_mac_est = v_mac[inds,:].copy()
# convert cik back to v:
if (average_cik == True) & (k_neighbours >1):
cik_est = np.dstack((cik_long_est[:,0:2],cik_long_est[:,2:4]))
v_mac_est = math.cik_to_v(cik_est, inverse = True)
v_mac_est[:,2:4] = xy
else:
v_mac_est = v_mac
return v_mac_est
def __eq__(self, other):
return np.abs(self - other) < self._TINY
def __pow__(self, x):
return (self * self) if x == 2 else np.abs(self)**x
def spd_normalize(data, norm_type=None, norm_f=1, wl=True, cieobs=_CIEOBS):
"""
Normalize a spectral power distribution (SPD).
Args:
:data:
| ndarray
:norm_type:
| None, optional
| - 'lambda': make lambda in norm_f equal to 1
| - 'area': area-normalization times norm_f
| - 'max': max-normalization times norm_f
| - 'ru': to :norm_f: radiometric units
| - 'pu': to :norm_f: photometric units
| - 'pusa': to :norm_f: photometric units (with Km corrected
| to standard air, cfr. CIE TN003-2015)
| - 'qu': to :norm_f: quantal energy units
:norm_f:
| 1, optional
| Normalization factor that determines the size of normalization
| for 'max' and 'area'
| or which wavelength is normalized to 1 for 'lambda' option.
:wl:
| True or False, optional
| If True, the first column of data contains wavelengths.
:cieobs:
| _CIEOBS or str, optional
| Type of cmf set to use for normalization using photometric units
| (norm_type == 'pu')
Returns:
:returns:
| ndarray with normalized data.
"""
if norm_type is not None:
if not isinstance(norm_type, list): norm_type = [norm_type]
if norm_f is not None:
if not isinstance(norm_f, list): norm_f = [norm_f]
if ('lambda' in norm_type) | ('qu' in norm_type):
wl = True # for lambda & 'qu' normalization wl MUST be first column
wlr = data[0]
if (('area' in norm_type) | ('ru' in norm_type) | ('pu' in norm_type) |
('pusa' in norm_type)) & (wl == True):
dl = getwld(data[0])
else:
dl = 1 #no wavelengths provided
offset = int(wl)
for i in range(data.shape[0] - offset):
norm_type_ = norm_type[i] if (len(norm_type) > 1) else norm_type[0]
if norm_f is not None:
norm_f_ = norm_f[i] if (len(norm_f) > 1) else norm_f[0]
else:
norm_f_ = 560.0 if (norm_type_ == 'lambda') else 1.0
if norm_type_ == 'max':
data[i + offset] = norm_f_ * data[i + offset] / np.max(
data[i + offset])
elif norm_type_ == 'area':
data[i + offset] = norm_f_ * data[i + offset] / (
np.sum(data[i + offset]) * dl)
elif norm_type_ == 'lambda':
wl_index = np.abs(wlr - norm_f_).argmin()
data[i +
offset] = data[i + offset] / data[i + offset][wl_index]
elif (norm_type_ == 'ru') | (norm_type_ == 'pu') | (
norm_type == 'pusa') | (norm_type_ == 'qu'):
rpq_power = spd_to_power(data[[0, i + offset], :],
cieobs=cieobs,
ptype=norm_type_)
data[i + offset] = (norm_f / rpq_power) * data[i + offset]
else:
data[i + offset] = data[i + offset] / norm_f_
return data
def cri_ref(ccts, wl3 = None, ref_type = _CRI_REF_TYPE, mix_range = None,
cieobs = None, norm_type = None, norm_f = None,
force_daylight_below4000K = False, n = None,
daylight_locus = None):
"""
Calculates a reference illuminant spectrum based on cct
for color rendering index calculations .
Args:
:ccts:
| list of int/floats or ndarray with ccts.
:wl3:
| None, optional
| New wavelength range for interpolation.
| Defaults to wavelengths specified by luxpy._WL3.
:ref_type:
| str or list[str], optional
| Specifies the type of reference spectrum to be calculated.
| Defaults to luxpy._CRI_REF_TYPE.
| If :ref_type: is list of strings, then for each cct in :ccts:
| a different reference illuminant can be specified.
| If :ref_type: == 'spd', then :ccts: is assumed to be an ndarray
| of reference illuminant spectra.
:mix_range:
| None or ndarray, optional
| Determines the cct range between which the reference illuminant is
| a weigthed mean of a Planckian and Daylight Phase spectrum.
| Weighthing is done as described in IES TM30:
| SPDreference = (Te-T)/(Te-Tb)*Planckian+(T-Tb)/(Te-Tb)*daylight
| with Tb and Te are resp. the starting and end CCTs of the
| mixing range and whereby the Planckian and Daylight SPDs
| have been normalized for equal luminous flux.
| If None: use the default specified for :ref_type:.
| Can be a ndarray with shape[0] > 1, in which different mixing
| ranges will be used for cct in :ccts:.
:cieobs:
| None, optional
| Required for the normalization of the Planckian and Daylight SPDs
| when calculating a 'mixed' reference illuminant.
| Required when calculating daylightphase (adjust locus parameters to cieobs)
| If None: _CIEOBS will be used.
:norm_type:
| None, optional
| - 'lambda': make lambda in norm_f equal to 1
| - 'area': area-normalization times norm_f
| - 'max': max-normalization times norm_f
| - 'ru': to :norm_f: radiometric units
| - 'pu': to :norm_f: photometric units
| - 'pusa': to :norm_f: photometric units (with Km corrected
| to standard air, cfr. CIE TN003-2015)
| - 'qu': to :norm_f: quantal energy units
:norm_f:
| 1, optional
| Normalization factor that determines the size of normalization
| for 'max' and 'area'
| or which wavelength is normalized to 1 for 'lambda' option.
:force_daylight_below4000K:
| False or True, optional
| Daylight locus approximation is not defined below 4000 K,
| but by setting this to True, the calculation can be forced to
| calculate it anyway.
:n:
| None, optional
| Refractive index (for use in calculation of blackbody radiators).
| If None: use the one stored in _BB['n']
:daylight_locus:
| None, optional
| dict with xD(T) and yD(xD) parameters to calculate daylight locus
| for specified cieobs.
| If None: use pre-calculated values.
| If 'calc': calculate them on the fly.
Returns:
:returns:
| ndarray with reference illuminant spectra.
| (:returns:[0] contains wavelengths)
Note:
Future versions will have the ability to take a dict as input
for ref_type. This way other reference illuminants can be specified
than the ones in _CRI_REF_TYPES.
"""
if ref_type == 'spd':
# ccts already contains spectrum of reference:
return spd(ccts, wl = wl3, norm_type = norm_type, norm_f = norm_f)
else:
if mix_range is not None: mix_range = np2d(mix_range)
if not (isinstance(ref_type,list) | isinstance(ref_type,dict)): ref_type = [ref_type]
for i in range(len(ccts)):
cct = ccts[i]
# get ref_type and mix_range:
if isinstance(ref_type,dict):
raise Exception("cri_ref(): dictionary ref_type: Not yet implemented")
else:
ref_type_ = ref_type[i] if (len(ref_type)>1) else ref_type[0]
if mix_range is None:
mix_range_ = _CRI_REF_TYPES[ref_type_]
else:
mix_range_ = mix_range[i] if (mix_range.shape[0]>1) else mix_range[0] #must be np2d !!!
if (mix_range_[0] == mix_range_[1]) | (ref_type_[0:2] == 'BB') | (ref_type_[0:2] == 'DL'):
if ((cct < mix_range_[0]) & (not (ref_type_[0:2] == 'DL'))) | (ref_type_[0:2] == 'BB'):
Sr = blackbody(cct, wl3, n = n)
elif ((cct >= mix_range_[0]) & (not (ref_type_[0:2] == 'BB'))) | (ref_type_[0:2] == 'DL') :
Sr = daylightphase(cct,wl3,force_daylight_below4000K = force_daylight_below4000K, cieobs = cieobs, daylight_locus = daylight_locus)
else:
SrBB = blackbody(cct, wl3, n = n)
SrDL = daylightphase(cct,wl3,verbosity = None,force_daylight_below4000K = force_daylight_below4000K, cieobs = cieobs, daylight_locus = daylight_locus)
cieobs_ = _CIEOBS if cieobs is None else cieobs
cmf = xyzbar(cieobs = cieobs_, scr = 'dict', wl_new = wl3)
wl = SrBB[0]
ld = getwld(wl)
SrBB = 100.0*SrBB[1]/np.array(np.sum(SrBB[1]*cmf[2]*ld))
SrDL = 100.0*SrDL[1]/np.array(np.sum(SrDL[1]*cmf[2]*ld))
Tb, Te = float(mix_range_[0]), float(mix_range_[1])
cBB, cDL = (Te-cct)/(Te-Tb), (cct-Tb)/(Te-Tb)
if cBB < 0.0:
cBB = 0.0
elif cBB > 1:
cBB = 1.0
if cDL < 0.0:
cDL = 0.0
elif cDL > 1:
cDL = 1.0
Sr = SrBB*cBB + SrDL*cDL
Sr[Sr==float('NaN')] = 0.0
Sr560 = Sr[np.where(np.abs(wl - 560.0) == np.min(np.abs(wl - 560.0)))[0]]
Sr = np.vstack((wl,(Sr/Sr560)))
if i == 0:
Srs = Sr[1]
else:
Srs = np.vstack((Srs,Sr[1]))
Srs = np.vstack((Sr[0],Srs))
return spd(Srs, wl = None, norm_type = norm_type, norm_f = norm_f)
def daylightphase(cct, wl3 = None, nominal_cct = False, force_daylight_below4000K = False, verbosity = None,
n = None, cieobs = None, daylight_locus = None, daylight_Mi_coeffs = None):
"""
Calculate daylight phase spectrum for correlated color temperature (cct).
Args:
:cct:
| int or float
| (for list of cct values, use cri_ref() with ref_type = 'DL')
:wl3:
| None, optional
| New wavelength range for interpolation.
| Defaults to wavelengths specified by luxpy._WL3.
:nominal_cct:
| False, optional
| If cct is nominal (e.g. when calculating D65): multiply cct first
| by 1.4388/1.4380 to account for change in 'c2' in definition of Planckian.
:cieobs:
| None or str or ndarray, optional
| CMF set to use when calculating coefficients for daylight locus and for M1, M2 weights.
| If None: use standard coefficients for CIE 1931 2° CMFs (for Si at 10 nm).
| Else: calculate coefficients following Appendix C of CIE15-2004 and Judd (1964).
:force_daylight_below4000K:
| False or True, optional
| Daylight locus approximation is not defined below 4000 K,
| but by setting this to True, the calculation can be forced to
| calculate it anyway.
:verbosity:
| None, optional
| If None: do not print warning when CCT < 4000 K.
:n:
| None, optional
| Refractive index (for use in calculation of blackbody radiators).
| If None: use the one stored in _BB['n']
:daylight_locus:
| None, optional
| dict with xD(T) and yD(xD) parameters to calculate daylight locus
| for specified cieobs.
| If None: use pre-calculated values.
| If 'calc': calculate them on the fly.
:daylight_Mi_coeffs:
| None, optional
| dict with coefficients for M1 & M2 weights for specified cieobs.
| If None: use pre-calculated values.
| If 'calc': calculate them on the fly.
Returns:
:returns:
| ndarray with daylight phase spectrum
| (:returns:[0] contains wavelengths)
References:
1. `CIE15:2018, “Colorimetry,” CIE, Vienna, Austria, 2018. <https://doi.org/10.25039/TR.015.2018>`_
2. `Judd, MacAdam, Wyszecki, Budde, Condit, Henderson, & Simonds (1964).
Spectral Distribution of Typical Daylight as a Function of Correlated Color Temperature.
J. Opt. Soc. Am., 54(8), 1031–1040.
<https://doi.org/10.1364/JOSA.54.001031>`_
"""
cct = float(cct)
if wl3 is None: wl3 = _WL3
if (cct < (4000.0)) & (force_daylight_below4000K == False):
if verbosity is not None:
print('Warning daylightphase spd not defined below 4000 K. Using blackbody radiator instead.')
return blackbody(cct,wl3, n = n)
else:
if nominal_cct: cct*=(1.4388/1.4380) # account for change in c2 in def. of Planckian
wl = getwlr(wl3)
#interpolate _S012_DAYLIGHTPHASE first to wl range:
if not np.array_equal(_S012_DAYLIGHTPHASE[0],wl):
S012_daylightphase = cie_interp(data = _S012_DAYLIGHTPHASE, wl_new = wl, kind = 'linear',negative_values_allowed = True)
else:
S012_daylightphase = _S012_DAYLIGHTPHASE
# Get coordinates of daylight locus corresponding to cct:
xD, yD = daylightlocus(cct, force_daylight_below4000K = force_daylight_below4000K, cieobs = cieobs, daylight_locus = daylight_locus)
# Get M1 & M2 component weights:
if (cieobs is None): # original M1,M2 for Si at 10 nm spacing and CIE 1931 xy
Mcoeffs = {'i':0.0241,'j':0.2562,'k':-0.7341,
'i1':-1.3515,'j1':-1.7703,'k1':5.9114,
'i2':0.0300,'j2':-31.4424,'k2':30.0717}
else:
Mcoeffs = daylight_Mi_coeffs
M1, M2, _ = _get_daylightphase_Mi_values(xD, yD, Mcoeffs = Mcoeffs, cieobs = cieobs, S012_daylightphase = S012_daylightphase)
# Calculate weigthed combination of S0, S1 & S2 components:
Sr = S012_daylightphase[1,:] + M1*S012_daylightphase[2,:] + M2*S012_daylightphase[3,:]
# Normalize to 1 at (or near) 560 nm:
Sr560 = Sr[:,np.where(np.abs(S012_daylightphase[0,:] - 560.0) == np.min(np.abs(S012_daylightphase[0,:] - 560)))[0]]
Sr /= Sr560
Sr[Sr==float('NaN')] = 0
return np.vstack((wl,Sr))
def plot_hue_bins(hbins = 16, start_hue = 0.0, scalef = 100, \
plot_axis_labels = False, bin_labels = '#', plot_edge_lines = True, \
plot_center_lines = False, plot_bin_colors = True, \
plot_10_20_circles = False,\
axtype = 'polar', ax = None, force_CVG_layout = False):
"""
Makes basis plot for Color Vector Graphic (CVG).
Args:
:hbins:
| 16 or ndarray with sorted hue bin centers (°), optional
:start_hue:
| 0.0, optional
:scalef:
| 100, optional
| Scale factor for graphic.
:plot_axis_labels:
| False, optional
| Turns axis ticks on/off (True/False).
:bin_labels:
| None or list[str] or '#', optional
| Plots labels at the bin center hues.
| - None: don't plot.
| - list[str]: list with str for each bin.
| (len(:bin_labels:) = :nhbins:)
| - '#': plots number.
:plot_edge_lines:
| True or False, optional
| Plot grey bin edge lines with '--'.
:plot_center_lines:
| False or True, optional
| Plot colored lines at 'center' of hue bin.
:plot_bin_colors:
| True, optional
| Colorize hue bins.
:plot_10_20_circles:
| False, optional
| If True and :axtype: == 'cart': Plot white circles at
| 80%, 90%, 100%, 110% and 120% of :scalef:
:axtype:
| 'polar' or 'cart', optional
| Make polar or Cartesian plot.
:ax:
| None or 'new' or 'same', optional
| - None or 'new' creates new plot
| - 'same': continue plot on same axes.
| - axes handle: plot on specified axes.
:force_CVG_layout:
| False or True, optional
| True: Force plot of basis of CVG on first encounter.
Returns:
:returns:
| gcf(), gca(), list with rgb colors for hue bins (for use in
other plotting fcns)
"""
# Setup hbincenters and hsv_hues:
if isinstance(hbins, float) | isinstance(hbins, int):
nhbins = hbins
dhbins = 360 / (nhbins) # hue bin width
hbincenters = np.arange(start_hue + dhbins / 2, 360, dhbins)
hbincenters = np.sort(hbincenters)
else:
hbincenters = hbins
idx = np.argsort(hbincenters)
if isinstance(bin_labels, list) | isinstance(bin_labels, np.ndarray):
bin_labels = bin_labels[idx]
hbincenters = hbincenters[idx]
nhbins = hbincenters.shape[0]
hbincenters = hbincenters * np.pi / 180
# Setup hbin labels:
if bin_labels is '#':
bin_labels = ['#{:1.0f}'.format(i + 1) for i in range(nhbins)]
elif isinstance(bin_labels, str):
bin_labels = [
bin_labels + '{:1.0f}'.format(i + 1) for i in range(nhbins)
]
# initializing the figure
cmap = None
if (ax is None) or (ax == 'new'):
fig = plt.figure()
newfig = True
else:
fig = plt.gcf()
newfig = False
rect = [0.1, 0.1, 0.8,
0.8] # setting the axis limits in [left, bottom, width, height]
if axtype == 'polar':
# the polar axis:
if newfig == True:
ax = fig.add_axes(rect, polar=True, frameon=False)
else:
#cartesian axis:
if newfig == True:
ax = fig.add_axes(rect)
if (newfig == True) | (force_CVG_layout == True):
# Calculate hue-bin boundaries:
r = np.vstack((np.zeros(hbincenters.shape),
1. * scalef * np.ones(hbincenters.shape)))
theta = np.vstack((np.zeros(hbincenters.shape), hbincenters))
#t = hbincenters.copy()
dU = np.roll(hbincenters.copy(), -1)
dL = np.roll(hbincenters.copy(), 1)
dtU = dU - hbincenters
dtL = hbincenters - dL
dtU[dtU < 0] = dtU[dtU < 0] + 2 * np.pi
dtL[dtL < 0] = dtL[dtL < 0] + 2 * np.pi
dL = hbincenters - dtL / 2
dU = hbincenters + dtU / 2
dt = (dU - dL)
dM = dL + dt / 2
# Setup color for plotting hue bins:
hsv_hues = hbincenters - 30 * np.pi / 180
hsv_hues = hsv_hues / hsv_hues.max()
edges = np.vstack(
(np.zeros(hbincenters.shape), dL)) # setup hue bin edges array
if axtype == 'cart':
if plot_center_lines == True:
hx = r * np.cos(theta) * 1.2
hy = r * np.sin(theta) * 1.2
if bin_labels is not None:
hxv = np.vstack((np.zeros(hbincenters.shape),
1.4 * scalef * np.cos(hbincenters)))
hyv = np.vstack((np.zeros(hbincenters.shape),
1.4 * scalef * np.sin(hbincenters)))
if plot_edge_lines == True:
#hxe = np.vstack((np.zeros(hbincenters.shape),1.2*scalef*np.cos(dL)))
#hye = np.vstack((np.zeros(hbincenters.shape),1.2*scalef*np.sin(dL)))
hxe = np.vstack(
(0.1 * scalef * np.cos(dL), 1.5 * scalef * np.cos(dL)))
hye = np.vstack(
(0.1 * scalef * np.sin(dL), 1.5 * scalef * np.sin(dL)))
# Plot hue-bins:
for i in range(nhbins):
# Create color from hue angle:
#c = np.abs(np.array(colorsys.hsv_to_rgb(hsv_hues[i], 0.75, 0.85)))
c = np.abs(np.array(colorsys.hls_to_rgb(hsv_hues[i], 0.45, 0.5)))
if i == 0:
cmap = [c]
else:
cmap.append(c)
if axtype == 'polar':
if plot_edge_lines == True:
ax.plot(edges[:, i],
r[:, i] * 1.,
color='grey',
marker='None',
linestyle='--',
linewidth=1,
markersize=2)
if plot_center_lines == True:
if np.mod(i, 2) == 1:
ax.plot(theta[:, i],
r[:, i],
color=c,
marker=None,
linestyle='--',
linewidth=1)
else:
ax.plot(theta[:, i],
r[:, i],
color=c,
marker=None,
linestyle='--',
linewidth=1,
markersize=10)
if plot_bin_colors == True:
bar = ax.bar(dM[i],
r[1, i],
width=dt[i],
color=c,
alpha=0.25)
if bin_labels is not None:
ax.text(hbincenters[i],
1.3 * scalef,
bin_labels[i],
fontsize=10,
horizontalalignment='center',
verticalalignment='center',
color=np.array([1, 1, 1]) * 0.45)
if plot_axis_labels == False:
ax.set_xticklabels([])
ax.set_yticklabels([])
else:
axis_ = 1. * np.array(
[-scalef * 1.5, scalef * 1.5, -scalef * 1.5, scalef * 1.5])
if plot_edge_lines == True:
ax.plot(hxe[:, i],
hye[:, i],
color='grey',
marker='None',
linestyle='--',
linewidth=1,
markersize=2)
if plot_center_lines == True:
if np.mod(i, 2) == 1:
ax.plot(hx[:, i],
hy[:, i],
color=c,
marker=None,
linestyle='--',
linewidth=1)
else:
ax.plot(hx[:, i],
hy[:, i],
color=c,
marker=None,
linestyle='--',
linewidth=1,
markersize=10)
if bin_labels is not None:
ax.text(hxv[1, i],
hyv[1, i],
bin_labels[i],
fontsize=10,
horizontalalignment='center',
verticalalignment='center',
color=np.array([1, 1, 1]) * 0.45)
ax.axis(axis_)
if plot_axis_labels == False:
ax.set_xticklabels([])
ax.set_yticklabels([])
else:
ax.set_xlabel("a'")
ax.set_ylabel("b'")
ax.plot(0, 0, color='grey', marker='+', linestyle=None, markersize=6)
if (axtype != 'polar') & (plot_10_20_circles == True):
r = np.array([
0.8, 0.9, 1.1, 1.2
]) * scalef # plot circles at 80, 90, 100, 110, 120 % of scale f
plotcircle(radii=r,
angles=np.arange(0, 365, 5),
color='w',
linestyle='-',
axh=ax,
linewidth=0.5)
plotcircle(radii=[scalef],
angles=np.arange(0, 365, 5),
color='k',
linestyle='-',
axh=ax,
linewidth=1)
ax.text(0,
-0.75 * scalef,
'-20%',
fontsize=8,
horizontalalignment='center',
verticalalignment='center',
color='w')
ax.text(0,
-1.25 * scalef,
'+20%',
fontsize=8,
horizontalalignment='center',
verticalalignment='center',
color='w')
if (axtype != 'polar') & (plot_bin_colors == True) & (_CVG_BG
is not None):
ax.imshow(_CVG_BG, origin='upper', extent=axis_)
return fig, ax, cmap
def run(data,
xyzw=_DEFAULT_WHITE_POINT,
Yw=None,
outin='J,aM,bM',
conditions=None,
forward=True,
yellowbluepurplecorrect=False,
mcat='cat02'):
"""
Run CIECAM02 color appearance model in forward or backward modes.
Args:
:data:
| ndarray with relative sample xyz values (forward mode) or J'a'b' coordinates (inverse mode)
:xyzw:
| ndarray with relative white point tristimulus values
:Yw:
| None, optional
| Luminance factor of white point.
| If None: xyz (in data) and xyzw are entered as relative tristimulus values
| (normalized to Yw = 100).
| If not None: input tristimulus are absolute and Yw is used to
| rescale the absolute values to relative ones
| (relative to a reference perfect white diffuser
| with Ywr = 100).
| Yw can be < 100 for e.g. paper as white point. If Yw is None, it
| is assumed that the relative Y-tristimulus value in xyzw
| represents the luminance factor Yw.
:conditions:
| None, optional
| Dictionary with viewing condition parameters for:
| La, Yb, D and surround.
| surround can contain:
| - str (options: 'avg','dim','dark') or
| - dict with keys c, Nc, F.
| None results in:
| {'La':100, 'Yb':20, 'D':1, 'surround':'avg'}
:forward:
| True, optional
| If True: run in CAM in forward mode, else: inverse mode.
:outin:
| 'J,aM,bM', optional
| String with requested output (e.g. "J,aM,bM,M,h") [Forward mode]
| - attributes: 'J': lightness,'Q': brightness,
| 'M': colorfulness,'C': chroma, 's': saturation,
| 'h': hue angle, 'H': hue quadrature/composition,
| String with inputs in data [inverse mode].
| Input must have data.shape[-1]==3 and last dim of data must have
| the following structure for inverse mode:
| * data[...,0] = J or Q,
| * data[...,1:] = (aM,bM) or (aC,bC) or (aS,bS) or (M,h) or (C, h), ...
:yellowbluepurplecorrect:
| False, optional
| If False: don't correct for yellow-blue and purple problems in ciecam02.
| If 'brill-suss':
| for yellow-blue problem, see:
| - Brill [Color Res Appl, 2006; 31, 142-145] and
| - Brill and Süsstrunk [Color Res Appl, 2008; 33, 424-426]
| If 'jiang-luo':
| for yellow-blue problem + purple line problem, see:
| - Jiang, Jun et al. [Color Res Appl 2015: 40(5), 491-503]
:mcat:
| 'cat02', optional
| Specifies CAT sensor space.
| - options:
| - None defaults to 'cat02'
| (others e.g. 'cat02-bs', 'cat02-jiang',
| all trying to correct gamut problems of original cat02 matrix)
| - str: see see luxpy.cat._MCATS.keys() for options
| (details on type, ?luxpy.cat)
| - ndarray: matrix with sensor primaries
Returns:
:camout:
| ndarray with color appearance correlates (forward mode)
| or
| XYZ tristimulus values (inverse mode)
References:
1. `N. Moroney, M. D. Fairchild, R. W. G. Hunt, C. Li, M. R. Luo, and T. Newman, (2002),
"The CIECAM02 color appearance model,”
IS&T/SID Tenth Color Imaging Conference. p. 23, 2002.
<http://rit-mcsl.org/fairchild/PDFs/PRO19.pdf>`_
"""
outin = outin.split(',') if isinstance(outin, str) else outin
#--------------------------------------------
# Get condition parameters:
if conditions is None:
conditions = _DEFAULT_CONDITIONS
D, Dtype, La, Yb, surround = (conditions[x]
for x in sorted(conditions.keys()))
surround_parameters = _SURROUND_PARAMETERS
if isinstance(surround, str):
surround = surround_parameters[conditions['surround']]
F, FLL, Nc, c = [surround[x] for x in sorted(surround.keys())]
#--------------------------------------------
# Define sensor space and cat matrices:
# Hunt-Pointer-Estevez sensors (cone fundamentals)
mhpe = cat._MCATS['hpe']
# chromatic adaptation sensors:
if (mcat is None) | (mcat == 'cat02'):
mcat = cat._MCATS['cat02']
if yellowbluepurplecorrect == 'brill-suss':
mcat = cat._MCATS[
'cat02-bs'] # for yellow-blue problem, Brill [Color Res Appl 2006;31:142-145] and Brill and Süsstrunk [Color Res Appl 2008;33:424-426]
elif yellowbluepurplecorrect == 'jiang-luo':
mcat = cat._MCATS[
'cat02-jiang-luo'] # for yellow-blue problem + purple line problem
elif isinstance(mcat, str):
mcat = cat._MCATS[mcat]
#--------------------------------------------
# pre-calculate some matrices:
invmcat = np.linalg.inv(mcat)
mhpe_x_invmcat = np.dot(mhpe, invmcat)
if not forward: mcat_x_invmhpe = np.dot(mcat, np.linalg.inv(mhpe))
#--------------------------------------------
# Set Yw:
if Yw is not None:
Yw = (Yw * np.ones_like(xyzw2[..., 1:2]).T)
else:
Yw = xyzw[..., 1:2].T
#--------------------------------------------
# calculate condition dependent parameters:
k = 1.0 / (5.0 * La + 1.0)
FL = 0.2 * (k**4.0) * (5.0 * La) + 0.1 * ((1.0 - k**4.0)**2.0) * (
(5.0 * La)**(1.0 / 3.0)) # luminance adaptation factor
n = Yb / Yw
Nbb = 0.725 * (1 / n)**0.2
Ncb = Nbb
z = 1.48 + FLL * n**0.5
yw = xyzw[..., 1:2].T # original Y in xyzw (pre-transposed)
#--------------------------------------------
# Calculate degree of chromatic adaptation:
if D is None:
D = F * (1.0 - (1.0 / 3.6) * np.exp((-La - 42.0) / 92.0))
#===================================================================
# WHITE POINT transformations (common to forward and inverse modes):
#--------------------------------------------
# Normalize white point (keep transpose for next step):
xyzw = Yw * xyzw.T / yw
#--------------------------------------------
# transform from xyzw to cat sensor space:
rgbw = math.dot23(mcat, xyzw)
#--------------------------------------------
# apply von Kries cat:
rgbwc = (
(D * Yw / rgbw) + (1 - D)
) * rgbw # factor 100 from ciecam02 is replaced with Yw[i] in ciecam16, but see 'note' in Fairchild's "Color Appearance Models" (p291 ni 3ed.)
#--------------------------------------------
# convert from cat02 sensor space to cone sensors (hpe):
rgbwp = math.dot23(mhpe_x_invmcat, rgbwc).T
#--------------------------------------------
# apply Naka_rushton repsonse compression to white:
NK = lambda x, forward: naka_rushton(x,
scaling=400,
n=0.42,
sig=27.13**(1 / 0.42),
noise=0.1,
forward=forward)
pw = np.where(rgbwp < 0)
# if requested apply yellow-blue correction:
if (yellowbluepurplecorrect == 'brill-suss'
): # Brill & Susstrunck approach, for purple line problem
rgbwp[pw] = 0.0
rgbwpa = NK(FL * rgbwp / 100.0, True)
rgbwpa[pw] = 0.1 - (NK(FL * np.abs(rgbwp[pw]) / 100.0, True) - 0.1)
#--------------------------------------------
# Calculate achromatic signal of white:
Aw = (2.0 * rgbwpa[..., 0] + rgbwpa[..., 1] +
(1.0 / 20.0) * rgbwpa[..., 2] - 0.305) * Nbb
# massage shape of data for broadcasting:
original_ndim = data.ndim
if data.ndim == 2: data = data[:, None]
#===================================================================
# STIMULUS transformations
if forward:
#--------------------------------------------
# Normalize xyz (keep transpose for matrix multiplication in next step):
xyz = (Yw / yw)[..., None] * data.T
#--------------------------------------------
# transform from xyz to cat sensor space:
rgb = math.dot23(mcat, xyz)
#--------------------------------------------
# apply von Kries cat:
rgbc = (
(D * Yw / rgbw)[..., None] + (1 - D)
) * rgb # factor 100 from ciecam02 is replaced with Yw[i] in ciecam16, but see 'note' in Fairchild's "Color Appearance Models" (p291 ni 3ed.)
#--------------------------------------------
# convert from cat02 sensor space to cone sensors (hpe):
rgbp = math.dot23(mhpe_x_invmcat, rgbc).T
#--------------------------------------------
# apply Naka_rushton repsonse compression:
p = np.where(rgbp < 0)
if (yellowbluepurplecorrect == 'brill-suss'
): # Brill & Susstrunck approach, for purple line problem
rgbp[p] = 0.0
rgbpa = NK(FL * rgbp / 100.0, forward)
rgbpa[p] = 0.1 - (NK(FL * np.abs(rgbp[p]) / 100.0, forward) - 0.1)
#--------------------------------------------
# Calculate achromatic signal:
A = (2.0 * rgbpa[..., 0] + rgbpa[..., 1] +
(1.0 / 20.0) * rgbpa[..., 2] - 0.305) * Nbb
#--------------------------------------------
# calculate initial opponent channels:
a = rgbpa[..., 0] - 12.0 * rgbpa[..., 1] / 11.0 + rgbpa[..., 2] / 11.0
b = (1.0 / 9.0) * (rgbpa[..., 0] + rgbpa[..., 1] - 2.0 * rgbpa[..., 2])
#--------------------------------------------
# calculate hue h and eccentricity factor, et:
h = hue_angle(a, b, htype='deg')
et = (1.0 / 4.0) * (np.cos(h * np.pi / 180 + 2.0) + 3.8)
#--------------------------------------------
# calculate Hue quadrature (if requested in 'out'):
if 'H' in outin:
H = hue_quadrature(h, unique_hue_data=_UNIQUE_HUE_DATA)
else:
H = None
#--------------------------------------------
# calculate lightness, J:
J = 100.0 * (A / Aw)**(c * z)
#--------------------------------------------
# calculate brightness, Q:
Q = (4.0 / c) * ((J / 100.0)**0.5) * (Aw + 4.0) * (FL**0.25)
#--------------------------------------------
# calculate chroma, C:
t = ((50000.0 / 13.0) * Nc * Ncb * et *
((a**2.0 + b**2.0)**0.5)) / (rgbpa[..., 0] + rgbpa[..., 1] +
(21.0 / 20.0 * rgbpa[..., 2]))
C = (t**0.9) * ((J / 100.0)**0.5) * (1.64 - 0.29**n)**0.73
#--------------------------------------------
# calculate colorfulness, M:
M = C * FL**0.25
#--------------------------------------------
# calculate saturation, s:
s = 100.0 * (M / Q)**0.5
S = s # make extra variable, jsut in case 'S' is called
#--------------------------------------------
# calculate cartesian coordinates:
if ('aS' in outin):
aS = s * np.cos(h * np.pi / 180.0)
bS = s * np.sin(h * np.pi / 180.0)
if ('aC' in outin):
aC = C * np.cos(h * np.pi / 180.0)
bC = C * np.sin(h * np.pi / 180.0)
if ('aM' in outin):
aM = M * np.cos(h * np.pi / 180.0)
bM = M * np.sin(h * np.pi / 180.0)
#--------------------------------------------
if outin != ['J', 'aM', 'bM']:
camout = eval('ajoin((' + ','.join(outin) + '))')
else:
camout = ajoin((J, aM, bM))
if (camout.shape[1] == 1) & (original_ndim < 3):
camout = camout[:, 0, :]
return camout
elif forward == False:
#--------------------------------------------
# Get Lightness J from data:
if ('J' in outin[0]):
J = data[..., 0].copy()
elif ('Q' in outin[0]):
Q = data[..., 0].copy()
J = 100.0 * (Q / ((Aw + 4.0) * (FL**0.25) * (4.0 / c)))**2.0
else:
raise Exception(
'No lightness or brightness values in data. Inverse CAM-transform not possible!'
)
#--------------------------------------------
if 'a' in outin[1]:
# calculate hue h:
h = hue_angle(data[..., 1], data[..., 2], htype='deg')
#--------------------------------------------
# calculate Colorfulness M or Chroma C or Saturation s from a,b:
MCs = (data[..., 1]**2.0 + data[..., 2]**2.0)**0.5
else:
h = data[..., 2]
MCs = data[..., 1]
if ('S' in outin[1]):
Q = (4.0 / c) * ((J / 100.0)**0.5) * (Aw + 4.0) * (FL**0.25)
M = Q * (MCs / 100.0)**2.0
C = M / (FL**0.25)
if ('M' in outin[1]): # convert M to C:
C = MCs / (FL**0.25)
if ('C' in outin[1]):
C = MCs
#--------------------------------------------
# calculate t from J, C:
t = (C / ((J / 100.0)**(1.0 / 2.0) * (1.64 - 0.29**n)**0.73))**(1.0 /
0.9)
#--------------------------------------------
# calculate eccentricity factor, et:
et = (np.cos(h * np.pi / 180.0 + 2.0) + 3.8) / 4.0
#--------------------------------------------
# calculate achromatic signal, A:
A = Aw * (J / 100.0)**(1.0 / (c * z))
#--------------------------------------------
# calculate temporary cart. co. at, bt and p1,p2,p3,p4,p5:
at = np.cos(h * np.pi / 180.0)
bt = np.sin(h * np.pi / 180.0)
p1 = (50000.0 / 13.0) * Nc * Ncb * et / t
p2 = A / Nbb + 0.305
p3 = 21.0 / 20.0
p4 = p1 / bt
p5 = p1 / at
#--------------------------------------------
#q = np.where(np.abs(bt) < np.abs(at))[0]
q = (np.abs(bt) < np.abs(at))
b = p2 * (2.0 + p3) * (460.0 / 1403.0) / (p4 + (2.0 + p3) *
(220.0 / 1403.0) *
(at / bt) -
(27.0 / 1403.0) + p3 *
(6300.0 / 1403.0))
a = b * (at / bt)
a[q] = p2[q] * (2.0 + p3) * (460.0 / 1403.0) / (p5[q] + (2.0 + p3) *
(220.0 / 1403.0) -
((27.0 / 1403.0) - p3 *
(6300.0 / 1403.0)) *
(bt[q] / at[q]))
b[q] = a[q] * (bt[q] / at[q])
#--------------------------------------------
# calculate post-adaptation values
rpa = (460.0 * p2 + 451.0 * a + 288.0 * b) / 1403.0
gpa = (460.0 * p2 - 891.0 * a - 261.0 * b) / 1403.0
bpa = (460.0 * p2 - 220.0 * a - 6300.0 * b) / 1403.0
#--------------------------------------------
# join values:
rgbpa = ajoin((rpa, gpa, bpa))
#--------------------------------------------
# decompress signals:
rgbp = (100.0 / FL) * NK(rgbpa, forward)
# apply yellow-blue correction:
if (yellowbluepurplecorrect == 'brill-suss'
): # Brill & Susstrunck approach, for purple line problem
p = np.where(rgbp < 0.0)
rgbp[p] = 0.0
#--------------------------------------------
# convert from to cone sensors (hpe) cat02 sensor space:
rgbc = math.dot23(mcat_x_invmhpe, rgbp.T)
#--------------------------------------------
# apply inverse von Kries cat:
rgb = rgbc / ((D * Yw / rgbw)[..., None] + (1.0 - D))
#--------------------------------------------
# transform from cat sensor space to xyz:
xyz = math.dot23(invmcat, rgb)
#--------------------------------------------
# unnormalize xyz:
xyz = ((yw / Yw)[..., None] * xyz).T
return xyz
def _get_hue_map(hbins = 16, start_hue = 0.0,
hbinnrs = None, xyzri = None, xyzrw = None, cri_type = None):
"""
Generate color map for hue bins.
Args:
:hbins:
| 16 or ndarray with sorted hue bin centers (°), optional
:start_hue:
| 0.0, optional
:hbinnrs:
| None, optional
| ndarray with hue bin number of each sample.
| If hbinnrs, xyzri, xyzrw and cri_type are all not-None:
| use these to calculate color map, otherwise just use number of
| hue bins :hbins: and :start_hue:
:xyzri:
| None, optional
| relative xyz tristimulus values of samples under ref. illuminant.
| see :hbinnrs: for more info when this is used.
:xyzrw:
| None, optional
| relative xyz tristimulus values of ref. illuminant white point.
| see :hbinnrs: for more info when this is used.
:cri_type:
| None, optional
| Specifies dict with default cri model parameters
| (needed to get correct :cieobs:)
| see :hbinnrs: for more info when this is used.
Returns:
:cmap:
| list with rgb values (one for each hue bin) for plotting.
"""
# Setup hbincenters and hsv_hues:
if isinstance(hbins,float) | isinstance(hbins,int):
nhbins = hbins
dhbins = 360/(nhbins) # hue bin width
hbincenters = np.arange(start_hue + dhbins/2, 360, dhbins)
hbincenters = np.sort(hbincenters)
else:
hbincenters = hbins
idx = np.argsort(hbincenters)
hbincenters = hbincenters[idx]
nhbins = hbincenters.shape[0]
cmap = []
if (hbinnrs is not None) & (xyzri is not None) & (xyzrw is not None) & (cri_type is not None):
xyzw = spd_to_xyz(_CIE_D65, relative = True, cieobs = cri_type['cieobs']['xyz'])
xyzri = cat.apply(xyzri[:,0,:],xyzw1 = xyzrw, xyzw2 = xyzw)
# Create color from xyz average:
for i in range(nhbins):
xyzrhi = xyzri[hbinnrs[:,0] == i,:].mean(axis=0,keepdims=True)
rgbrhi = xyz_to_srgb(xyzrhi)/255
cmap.append(rgbrhi)
else:
# Create color from hue angle:
# Setup color for plotting hue bins:
hbincenters = hbincenters*np.pi/180
hsv_hues = hbincenters - 30*np.pi/180
hsv_hues = hsv_hues/hsv_hues.max()
for i in range(nhbins):
#c = np.abs(np.array(colorsys.hsv_to_rgb(hsv_hues[i], 0.75, 0.85)))
c = np.abs(np.array(colorsys.hls_to_rgb(hsv_hues[i], 0.45, 0.5)))
cmap.append(c)
return cmap
def apply_poly_model_at_hue_x(poly_model, pmodel, dCHoverC_res, \
hx = None, Cxr = 40, sig = _VF_SIG):
"""
Applies base color shift model at (hue,chroma) coordinates
Args:
:poly_model:
| function handle to model
:pmodel:
| ndarray with model parameters.
:dCHoverC_res:
| ndarray with residuals between 'dCoverC,dH' of samples
| and 'dCoverC,dH' predicted by the model.
| Note: dCoverC = (Ct - Cr)/Cr and dH = ht - hr
| (predicted from model, see notes luxpy.cri.get_poly_model())
:hx:
| None or ndarray, optional
| None defaults to np.arange(np.pi/10.0,2*np.pi,2*np.pi/10.0)
:Cxr:
| 40, optional
:sig:
| _VF_SIG or float, optional
| Determines smooth transition between hue-bin-boundaries (no hard
| cutoff at hue bin boundary).
Returns:
:returns:
| ndarrays with dCoverC_x, dCoverC_x_sig, dH_x, dH_x_sig
| Note '_sig' denotes the uncertainty:
| e.g. dH_x_sig is the uncertainty of dH at input (hue/chroma).
"""
if hx is None:
dh = 2 * np.pi / 10.0
hx = np.arange(
dh / 2, 2 * np.pi, dh
) #hue angles at which to apply model, i.e. calculate 'average' measures
# A calculate reference coordinates:
axr = Cxr * np.cos(hx)
bxr = Cxr * np.sin(hx)
# B apply model at reference coordinates to obtain test coordinates:
axt, bxt, Cxt, hxt, axr, bxr, Cxr, hxr = apply_poly_model_at_x(
poly_model, pmodel, axr, bxr)
# C Calculate dC/C, dH for test and ref at fixed hues:
dCoverC_x = (Cxt - Cxr) / (np.hstack((Cxr + Cxt)).max())
dH_x = (180 / np.pi) * (hxt - hxr)
# dCoverC_x = np.round(dCoverC_x,decimals = 2)
# dH_x = np.round(dH_x,decimals = 0)
# D calculate 'average' noise measures using sig-value:
href = dCHoverC_res[:, 0:1]
dCoverC_res = dCHoverC_res[:, 1:2]
dHoverC_res = dCHoverC_res[:, 2:3]
dHsigi = np.exp((np.dstack(
(np.abs(hx - href), np.abs((hx - href - 2 * np.pi)),
np.abs(hx - href - 2 * np.pi))).min(axis=2)**2) / (-2) / sig)
dH_x_sig = (180 / np.pi) * (np.sqrt(
(dHsigi * (dHoverC_res**2)).sum(axis=0, keepdims=True) /
dHsigi.sum(axis=0, keepdims=True)))
#dH_x_sig_avg = np.sqrt(np.sum(dH_x_sig**2,axis=1)/hx.shape[0])
dCoverC_x_sig = (np.sqrt(
(dHsigi * (dCoverC_res**2)).sum(axis=0, keepdims=True) /
dHsigi.sum(axis=0, keepdims=True)))
#dCoverC_x_sig_avg = np.sqrt(np.sum(dCoverC_x_sig**2,axis=1)/hx.shape[0])
return dCoverC_x, dCoverC_x_sig, dH_x, dH_x_sig
def plot_tm30_Rhshj(spd, cri_type = 'ies-tm30', axh = None,
xlabel = True, y_offset = 0,
font_size = _TM30_FONT_SIZE, **kwargs):
"""
Plot Local Hue Shift values (Rhshj) (one for each hue-bin).
Args:
:spd:
| ndarray or dict
| If ndarray: single spectral power distribution.
| If dict: dictionary with pre-computed parameters (using _tm30_process_spd()).
| required keys:
| 'Rf','Rg','cct','duv','Sr','cri_type','xyzri','xyzrw',
| 'hbinnrs','Rfi','Rfhi','Rcshi','Rhshi',
| 'jabt_binned','jabr_binned',
| 'nhbins','start_hue','normalize_gamut','normalized_chroma_ref'
| see cri.spd_to_cri() for more info on parameters.
:cri_type:
| _CRI_TYPE_DEFAULT or str or dict, optional
| -'str: specifies dict with default cri model parameters
| (for supported types, see luxpy.cri._CRI_DEFAULTS['cri_types'])
| - dict: user defined model parameters
| (see e.g. luxpy.cri._CRI_DEFAULTS['cierf']
| for required structure)
| Note that any non-None input arguments (in kwargs)
| to the function will override default values in cri_type dict.
:axh:
| None, optional
| If None: create new figure with single axes, else plot on specified axes.
:xlabel:
| True, optional
| If False: don't add label and numbers to x-axis
| (useful when plotting plotting all 'Local Rfhi, Rcshi, Rshhi'
| values in 3x1 subplots with 'shared x-axis': saves vertical space)
:y_offset:
| 0, optional
| text-offset from top of bars in barplot.
:font_size:
| _TM30_FONT_SIZE, optional
| Font size of text, axis labels and axis values.
:kwargs:
| Additional optional keyword arguments,
| the same as in cri.spd_to_cri()
Returns:
:axh:
| handle to figure axes.
:data:
| dictionary with required parameters for plotting functions.
"""
data = _tm30_process_spd(spd, cri_type = 'ies-tm30',**kwargs)
Rhshi = data['Rhshi']
# Get color map based on sample colors:
cmap = _get_hue_map(hbins = data['nhbins'], start_hue = data['start_hue'],
hbinnrs = data['hbinnrs'],
xyzri = data['xyzri'],
xyzrw = data['xyzrw'],
cri_type = data['cri_type'])
# Plot local hue shift, Rhshi:
hbins = range(data['nhbins'])
if axh is None:
fig, axh = plt.subplots(nrows = 1, ncols = 1)
for j in hbins:
axh.bar(hbins[j],Rhshi[j,0], color = cmap[j], width = 1,edgecolor = 'k', alpha = 1)
ypos = ((np.abs(Rhshi[j,0]) + 0.05 + y_offset))*np.sign(Rhshi[j,0])
axh.text(hbins[j],ypos, '{:1.2f}'.format(Rhshi[j,0]) ,fontsize = font_size,horizontalalignment='center',verticalalignment='center',color = np.array([1,1,1])*0.3, rotation = 90)
xticks = np.array(hbins)
axh.set_xticks(xticks)
if xlabel == True:
xtickslabels = ['{:1.0f}'.format(ii+1) for ii in hbins]
axh.set_xlabel('Hue-Angle Bin (j)', fontsize = font_size)
else:
xtickslabels = [''.format(ii+1) for ii in hbins]
axh.set_xticklabels(xtickslabels, fontsize = font_size)
axh.set_xlim([-0.5,data['nhbins']-0.5])
axh.set_ylabel(r'Local Hue Shift $(R_{hs,hj})$', fontsize = 9)
axh.set_ylim([min([-0.5,Rhshi.min()]),max([0.5,Rhshi.max()])])
return axh, data
import copy
from luxpy import (math, spd_to_xyz, xyz_to_cct, getwld, getwlr, _CMF,
blackbody, daylightphase, _CRI_RFL, _CRI_REF_TYPES,
_CRI_REF_TYPE, _CIEOBS, xyzbar, cie_interp)
from luxpy.utils import np, plt
from luxpy.color.cri.utils.DE_scalers import log_scale
from luxpy.color.cri.utils.helpers import _get_hue_bin_data
__all__ = ['_cri_ref', '_xyz_to_jab_cam02ucs',
'spd_to_tm30'] # new or redefined
_DL = 1
_WL3 = [360, 830, _DL]
_WL = getwlr(_WL3)
_POS_WL560 = np.where(np.abs(_WL - 560.0) == np.min(np.abs(_WL - 560.0)))[0]
_TM30_SAMPLE_SET = _CRI_RFL['ies-tm30-18']['99']['{:1.0f}nm'.format(_DL)]
def _cri_ref_i(cct,
wl3=_WL,
ref_type='iestm30',
mix_range=[4000, 5000],
cieobs='1931_2',
force_daylight_below4000K=False,
n=None,
daylight_locus=None):
"""
Calculates a reference illuminant spectrum based on cct
for color rendering index calculations.
"""
def apply(data, n_step = 2, catmode = None, cattype = 'vonkries', xyzw1 = None, xyzw2 = None, xyzw0 = None,\
D = None, mcat = [_MCAT_DEFAULT], normxyz0 = None, outtype = 'xyz', La = None, F = None, Dtype = None):
"""
Calculate corresponding colors by applying a von Kries chromatic adaptation
transform (CAT), i.e. independent rescaling of 'sensor sensitivity' to data
to adapt from current adaptation conditions (1) to the new conditions (2).
Args:
:data:
| ndarray of tristimulus values (can be NxMx3)
:n_step:
| 2, optional
| Number of step in CAT (1: 1-step, 2: 2-step)
:catmode:
| None, optional
| - None: use :n_step: to set mode: 1 = '1>2', 2:'1>0>2'
| -'1>0>2': Two-step CAT
| from illuminant 1 to baseline illuminant 0 to illuminant 2.
| -'1>2': One-step CAT
| from illuminant 1 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.
:cattype:
| 'vonkries' (others: 'rlab', see Farchild 1990), optional
:xyzw1:
| None, depending on :catmode: optional (can be Mx3)
:xyzw2:
| None, depending on :catmode: optional (can be Mx3)
:xyzw0:
| None, depending on :catmode: optional (can be Mx3)
:D:
| None, optional
| Degrees of adaptation. Defaults to [1.0, 1.0].
:La:
| None, optional
| Adapting luminances.
| If None: xyz values are absolute or relative.
| If not None: xyz are relative.
:F:
| None, optional
| Surround parameter(s) for CAT02/CAT16 calculations
| (:Dtype: == 'cat02' or 'cat16')
| Defaults to [1.0, 1.0].
:Dtype:
| None, optional
| Type of degree of adaptation function from literature
| See luxpy.cat.get_degree_of_adaptation()
:mcat:
| [_MCAT_DEFAULT], optional
| List[str] or List[ndarray] of sensor space matrices for each
| condition pair. If len(:mcat:) == 1, the same matrix is used.
:normxyz0:
| None, optional
| Set of xyz tristimulus values to normalize the sensor space matrix to.
:outtype:
| 'xyz' or 'lms', optional
| - 'xyz': return corresponding tristimulus values
| - 'lms': return corresponding sensor space excitation values
| (e.g. for further calculations)
Returns:
:returns:
| ndarray with corresponding colors
Reference:
1. `Smet, K. A. G., & Ma, S. (2020).
Some concerns regarding the CAT16 chromatic adaptation transform.
Color Research & Application, 45(1), 172–177.
<https://doi.org/10.1002/col.22457>`_
"""
if (xyzw1 is None) & (xyzw2 is None):
return data # do nothing
else:
# Set catmode:
if catmode is None:
if n_step == 2:
catmode = '1>0>2'
elif n_step == 1:
catmode = '1>2'
else:
raise Exception(
'cat.apply(n_step = {:1.0f}, catmode = None): Unknown requested n-step CAT mode !'
.format(n_step))
# Make data 2d:
data = np2d(data)
data_original_shape = data.shape
if data.ndim < 3:
target_shape = np.hstack((1, data.shape))
data = data * np.ones(target_shape)
else:
target_shape = data.shape
target_shape = data.shape
# initialize xyzw0:
if (xyzw0 is None): # set to iLL.E
xyzw0 = np2d([100.0, 100.0, 100.0])
xyzw0 = np.ones(target_shape) * xyzw0
La0 = xyzw0[..., 1, None]
# Determine cat-type (1-step or 2-step) + make input same shape as data for block calculations:
expansion_axis = np.abs(1 * (len(data_original_shape) == 2) - 1)
if ((xyzw1 is not None) & (xyzw2 is not None)):
xyzw1 = xyzw1 * np.ones(target_shape)
xyzw2 = xyzw2 * np.ones(target_shape)
default_La12 = [xyzw1[..., 1, None], xyzw2[..., 1, None]]
elif (xyzw2 is None) & (xyzw1
is not None): # apply one-step CAT: 1-->0
catmode = '1>0' #override catmode input
xyzw1 = xyzw1 * np.ones(target_shape)
default_La12 = [xyzw1[..., 1, None], La0]
elif (xyzw1 is None) & (xyzw2 is not None):
raise Exception(
"von_kries(): cat transformation '0>2' not supported, use '1>0' !"
)
# Get or set La (La == None: xyz are absolute or relative, La != None: xyz are relative):
target_shape_1 = tuple(np.hstack((target_shape[:-1], 1)))
La1, La2 = parse_x1x2_parameters(La,
target_shape=target_shape_1,
catmode=catmode,
expand_2d_to_3d=expansion_axis,
default=default_La12)
# Set degrees of adaptation, D10, D20: (note D20 is degree of adaptation for 2-->0!!)
D10, D20 = parse_x1x2_parameters(D,
target_shape=target_shape_1,
catmode=catmode,
expand_2d_to_3d=expansion_axis)
# Set F surround in case of Dtype == 'cat02':
F1, F2 = parse_x1x2_parameters(F,
target_shape=target_shape_1,
catmode=catmode,
expand_2d_to_3d=expansion_axis)
# Make xyz relative to go to relative xyz0:
if La is None:
data = 100 * data / La1
xyzw1 = 100 * xyzw1 / La1
xyzw0 = 100 * xyzw0 / La0
if (catmode == '1>0>2') | (catmode == '1>2'):
xyzw2 = 100 * xyzw2 / La2
# transform data (xyz) to sensor space (lms) and perform cat:
xyzc = np.zeros(data.shape)
xyzc.fill(np.nan)
mcat = np.array(mcat)
if (mcat.shape[0] != data.shape[1]) & (mcat.shape[0] == 1):
mcat = np.repeat(mcat, data.shape[1], axis=0)
elif (mcat.shape[0] != data.shape[1]) & (mcat.shape[0] > 1):
raise Exception(
'von_kries(): mcat.shape[0] > 1 and does not match data.shape[0]!'
)
for i in range(xyzc.shape[1]):
# get cat sensor matrix:
if mcat[i].dtype == np.float64:
mcati = mcat[i]
else:
mcati = _MCATS[mcat[i]]
# normalize sensor matrix:
if normxyz0 is not None:
mcati = math.normalize_3x3_matrix(mcati, xyz0=normxyz0)
# convert from xyz to lms:
lms = np.dot(mcati, data[:, i].T).T
lmsw0 = np.dot(mcati, xyzw0[:, i].T).T
if (catmode == '1>0>2') | (catmode == '1>0'):
lmsw1 = np.dot(mcati, xyzw1[:, i].T).T
Dpar1 = dict(D=D10[:, i],
F=F1[:, i],
La=La1[:, i],
La0=La0[:, i],
order='1>0')
D10[:, i] = get_degree_of_adaptation(
Dtype=Dtype,
**Dpar1) #get degree of adaptation depending on Dtype
lmsw2 = None # in case of '1>0'
if (catmode == '1>0>2'):
lmsw2 = np.dot(mcati, xyzw2[:, i].T).T
Dpar2 = dict(D=D20[:, i],
F=F2[:, i],
La=La2[:, i],
La0=La0[:, i],
order='0>2')
D20[:, i] = get_degree_of_adaptation(
Dtype=Dtype,
**Dpar2) #get degree of adaptation depending on Dtype
if (catmode == '1>2'):
lmsw1 = np.dot(mcati, xyzw1[:, i].T).T
lmsw2 = np.dot(mcati, xyzw2[:, i].T).T
Dpar12 = dict(D=D10[:, i],
F=F1[:, i],
La=La1[:, i],
La2=La2[:, i],
order='1>2')
D10[:, i] = get_degree_of_adaptation(
Dtype=Dtype,
**Dpar12) #get degree of adaptation depending on Dtype
# Determine transfer function Dt:
Dt = get_transfer_function(cattype=cattype,
catmode=catmode,
lmsw1=lmsw1,
lmsw2=lmsw2,
lmsw0=lmsw0,
D10=D10[:, i],
D20=D20[:, i],
La1=La1[:, i],
La2=La2[:, i])
# Perform cat:
lms = np.dot(np.diagflat(Dt[0]), lms.T).T
# Make xyz, lms 'absolute' again:
if (catmode == '1>0>2'):
lms = (La2[:, i] / La1[:, i]) * lms
elif (catmode == '1>0'):
lms = (La0[:, i] / La1[:, i]) * lms
elif (catmode == '1>2'):
lms = (La2[:, i] / La1[:, i]) * lms
# transform back from sensor space to xyz (or not):
if outtype == 'xyz':
xyzci = np.dot(np.linalg.inv(mcati), lms.T).T
xyzci[np.where(xyzci < 0)] = _EPS
xyzc[:, i] = xyzci
else:
xyzc[:, i] = lms
# return data to original shape:
if len(data_original_shape) == 2:
xyzc = xyzc[0]
return xyzc
def _polyarea(x, y):
return 0.5 * np.abs(
np.dot(x, np.roll(y, 1, axis=0)) - np.dot(y, np.roll(x, 1, axis=0)))
def Ydlep_to_xyz(Ydlep,
cieobs=_CIEOBS,
xyzw=_COLORTF_DEFAULT_WHITE_POINT,
flip_axes=False,
SL_max_lambda=None,
**kwargs):
"""
Convert Y, dominant (complementary) wavelength and excitation purity to XYZ
tristimulus values.
Args:
:Ydlep:
| ndarray with Y, dominant (complementary) wavelength
and excitation purity
:xyzw:
| None or narray with tristimulus values of a single (!) native white point, optional
| None defaults to xyz of CIE D65 using the :cieobs: observer.
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when calculating spectrum locus coordinates.
:flip_axes:
| False, optional
| If True: flip axis 0 and axis 1 in Ydelep to increase speed of loop in function.
| (single xyzw with is not flipped!)
:SL_max_lambda:
| None or float, optional
| Maximum wavelength of spectrum locus before it turns back on itelf in the high wavelength range (~700 nm)
Returns:
:xyz:
| ndarray with tristimulus values
"""
Ydlep3 = np3d(Ydlep).copy().astype(np.float)
# flip axis so that longest dim is on first axis (save time in looping):
if (Ydlep3.shape[0] < Ydlep3.shape[1]) & (flip_axes == True):
axes12flipped = True
Ydlep3 = Ydlep3.transpose((1, 0, 2))
else:
axes12flipped = False
# convert xyzw to Yxyw:
Yxyw = xyz_to_Yxy(xyzw)
Yxywo = Yxyw.copy()
# get spectrum locus Y,x,y and wavelengths:
SL = _CMF[cieobs]['bar']
SL = SL[:, SL[1:].sum(axis=0) >
0] # avoid div by zero in xyz-to-Yxy conversion
wlsl = SL[0, None].T
Yxysl = xyz_to_Yxy(SL[1:4].T)[:, None]
# Get maximum wavelength of spectrum locus (before it turns back on itself)
if SL_max_lambda is None:
pmaxlambda = Yxysl[..., 1].argmax() # lambda with largest x value
dwl = np.diff(
Yxysl[:, 0,
1]) # spectrumlocus in that range should have increasing x
dwl[wlsl[:-1, 0] < 600] = 10000
pmaxlambda = np.where(
dwl <= 0)[0][0] # Take first element with zero or <zero slope
else:
pmaxlambda = np.abs(wlsl - SL_max_lambda).argmin()
Yxysl = Yxysl[:(pmaxlambda + 1), :]
wlsl = wlsl[:(pmaxlambda + 1), :1]
# center on xyzw:
Yxysl = Yxysl - Yxyw
Yxyw = Yxyw - Yxyw
#split:
Y, dom, pur = asplit(Ydlep3)
Yw, xw, yw = asplit(Yxyw)
Ywo, xwo, ywo = asplit(Yxywo)
Ysl, xsl, ysl = asplit(Yxysl)
# loop over longest dim:
x = np.empty(Y.shape)
y = np.empty(Y.shape)
for i in range(Ydlep3.shape[1]):
# find closest wl's to dom:
#wlslb,wlib = meshblock(wlsl,np.abs(dom[i,:])) #abs because dom<0--> complemtary wl
wlib, wlslb = np.meshgrid(np.abs(dom[:, i]), wlsl)
dwl = wlslb - wlib
q1 = np.abs(dwl).argmin(axis=0) # index of closest wl
sign_q1 = np.sign(dwl[q1])
dwl[np.sign(dwl) ==
sign_q1] = 1000000 # set all dwl on the same side as q1 to a very large value
q2 = np.abs(dwl).argmin(
axis=0) # index of second closest (enclosing) wl
# calculate x,y of dom:
x_dom_wl = xsl[q1, 0] + (xsl[q2, 0] - xsl[q1, 0]) * (
np.abs(dom[:, i]) - wlsl[q1, 0]) / (wlsl[q2, 0] - wlsl[q1, 0]
) # calculate x of dom. wl
y_dom_wl = ysl[q1, 0] + (ysl[q2, 0] - ysl[q1, 0]) * (
np.abs(dom[:, i]) - wlsl[q1, 0]) / (wlsl[q2, 0] - wlsl[q1, 0]
) # calculate y of dom. wl
# calculate x,y of test:
d_wl = (x_dom_wl**2.0 +
y_dom_wl**2.0)**0.5 # distance from white point to dom
d = pur[:, i] * d_wl
hdom = math.positive_arctan(x_dom_wl, y_dom_wl, htype='deg')
x[:, i] = d * np.cos(hdom * np.pi / 180.0)
y[:, i] = d * np.sin(hdom * np.pi / 180.0)
# complementary:
pc = np.where(dom[:, i] < 0.0)
hdom[pc] = hdom[pc] - np.sign(dom[:, i][pc] -
180.0) * 180.0 # get positive hue angle
# calculate intersection of line through white point and test point and purple line:
xy = np.vstack((x_dom_wl, y_dom_wl)).T
xyw = np.vstack((xw, yw)).T
xypl1 = np.vstack((xsl[0, None], ysl[0, None])).T
xypl2 = np.vstack((xsl[-1, None], ysl[-1, None])).T
da = (xy - xyw)
db = (xypl2 - xypl1)
dp = (xyw - xypl1)
T = np.array([[0.0, -1.0], [1.0, 0.0]])
dap = np.dot(da, T)
denom = np.sum(dap * db, axis=1, keepdims=True)
num = np.sum(dap * dp, axis=1, keepdims=True)
xy_linecross = (num / denom) * db + xypl1
d_linecross = np.atleast_2d(
(xy_linecross[:, 0]**2.0 + xy_linecross[:, 1]**2.0)**0.5).T[:, 0]
x[:, i][pc] = pur[:, i][pc] * d_linecross[pc] * np.cos(
hdom[pc] * np.pi / 180)
y[:, i][pc] = pur[:, i][pc] * d_linecross[pc] * np.sin(
hdom[pc] * np.pi / 180)
Yxy = np.dstack((Ydlep3[:, :, 0], x + xwo, y + ywo))
if axes12flipped == True:
Yxy = Yxy.transpose((1, 0, 2))
else:
Yxy = Yxy.transpose((0, 1, 2))
return Yxy_to_xyz(Yxy).reshape(Ydlep.shape)
def ipt_to_xyz(ipt, cieobs=_CIEOBS, xyzw=None, M=None, **kwargs):
"""
Convert XYZ tristimulus values to IPT color coordinates.
| I: Lightness axis, P, red-green axis, T: yellow-blue axis.
Args:
:ipt:
| ndarray with IPT 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 for rescaling Mxyz2lms
| (only when not None).
:M: | None, optional
| None defaults to xyz to lms conversion matrix determined by:cieobs:
Returns:
:xyz:
| ndarray with tristimulus values
Note:
:xyz: is assumed to be under D65 viewing conditions! If necessary perform chromatic adaptation !
Reference:
1. `Ebner F, and Fairchild MD (1998).
Development and testing of a color space (IPT) with improved hue uniformity.
In IS&T 6th Color Imaging Conference, (Scottsdale, Arizona, USA), pp. 8–13.
<http://www.ingentaconnect.com/content/ist/cic/1998/00001998/00000001/art00003?crawler=true>`_
"""
ipt = np2d(ipt)
# get M to convert xyz to lms and apply normalization to matrix or input your own:
if M is None:
M = _IPT_M['xyz2lms'][cieobs].copy(
) # matrix conversions from xyz to lms
if xyzw is None:
xyzw = spd_to_xyz(_CIE_ILLUMINANTS['D65'], cieobs=cieobs,
out=1) / 100.0
else:
xyzw = xyzw / 100.0
M = math.normalize_3x3_matrix(M, xyzw)
# convert from ipt to lms':
if len(ipt.shape) == 3:
lmsp = np.einsum('ij,klj->kli', np.linalg.inv(_IPT_M['lms2ipt']), ipt)
else:
lmsp = np.einsum('ij,lj->li', np.linalg.inv(_IPT_M['lms2ipt']), ipt)
# reverse response compression: lms' to lms
lms = lmsp**(1.0 / 0.43)
p = np.where(lmsp < 0.0)
lms[p] = -np.abs(lmsp[p])**(1.0 / 0.43)
# convert from lms to xyz:
if np.ndim(M) == 2:
if len(ipt.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)
else:
if len(
ipt.shape
) == 3: # second dim of lms must match dim of 1st of M and 1st dim of xyzw
xyz = np.concatenate([
np.einsum('ij,klj->kli', np.linalg.inv(M[i]),
lms[:, i:i + 1, :]) for i in range(M.shape[0])
],
axis=1)
else: # first dim of lms must match dim of 1st of M and 1st dim of xyzw
xyz = np.concatenate([
np.einsum('ij,lj->li', np.linalg.inv(M[i]), lms[i:i + 1, :])
for i in range(M.shape[0])
],
axis=0)
#xyz = np.dot(np.linalg.inv(M),lms.T).T
xyz = xyz * 100.0
xyz[np.where(xyz < 0.0)] = 0.0
return xyz
def xyz_to_Ydlep_(xyz,
cieobs=_CIEOBS,
xyzw=_COLORTF_DEFAULT_WHITE_POINT,
flip_axes=False,
**kwargs):
"""
Convert XYZ tristimulus values to Y, dominant (complementary) wavelength
and excitation purity.
Args:
:xyz:
| ndarray with tristimulus values
:xyzw:
| None or ndarray with tristimulus values of a single (!) native white point, optional
| None defaults to xyz of CIE D65 using the :cieobs: observer.
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when calculating spectrum locus coordinates.
:flip_axes:
| False, optional
| If True: flip axis 0 and axis 1 in Ydelep to increase speed of loop in function.
| (single xyzw with is not flipped!)
Returns:
:Ydlep:
| ndarray with Y, dominant (complementary) wavelength
| and excitation purity
"""
xyz3 = np3d(xyz).copy().astype(np.float)
# flip axis so that shortest dim is on axis0 (save time in looping):
if (xyz3.shape[0] < xyz3.shape[1]) & (flip_axes == True):
axes12flipped = True
xyz3 = xyz3.transpose((1, 0, 2))
else:
axes12flipped = False
# convert xyz to Yxy:
Yxy = xyz_to_Yxy(xyz3)
Yxyw = xyz_to_Yxy(xyzw)
# get spectrum locus Y,x,y and wavelengths:
SL = _CMF[cieobs]['bar']
SL = SL[:, SL[1:].sum(axis=0) >
0] # avoid div by zero in xyz-to-Yxy conversion
wlsl = SL[0]
Yxysl = xyz_to_Yxy(SL[1:4].T)[:, None]
pmaxlambda = Yxysl[..., 1].argmax()
maxlambda = wlsl[pmaxlambda]
maxlambda = 700
print(np.where(wlsl == maxlambda))
pmaxlambda = np.where(wlsl == maxlambda)[0][0]
Yxysl = Yxysl[:(pmaxlambda + 1), :]
wlsl = wlsl[:(pmaxlambda + 1)]
# center on xyzw:
Yxy = Yxy - Yxyw
Yxysl = Yxysl - Yxyw
Yxyw = Yxyw - Yxyw
#split:
Y, x, y = asplit(Yxy)
Yw, xw, yw = asplit(Yxyw)
Ysl, xsl, ysl = asplit(Yxysl)
# calculate hue:
h = math.positive_arctan(x, y, htype='deg')
print(h)
print('rh', h[0, 0] - h[0, 1])
print(wlsl[0], wlsl[-1])
hsl = math.positive_arctan(xsl, ysl, htype='deg')
hsl_max = hsl[0] # max hue angle at min wavelength
hsl_min = hsl[-1] # min hue angle at max wavelength
if hsl_min < hsl_max: hsl_min += 360
dominantwavelength = np.empty(Y.shape)
purity = np.empty(Y.shape)
print('xyz:', xyz)
for i in range(xyz3.shape[1]):
print('\ni:', i, h[:, i], hsl_max, hsl_min)
print(h)
# find index of complementary wavelengths/hues:
pc = np.where(
(h[:, i] > hsl_max) & (h[:, i] < hsl_min)
) # hue's requiring complementary wavelength (purple line)
print('pc', (h[:, i] > hsl_max) & (h[:, i] < hsl_min))
h[:, i][pc] = h[:, i][pc] - np.sign(
h[:, i][pc] - 180.0
) * 180.0 # add/subtract 180° to get positive complementary wavelength
# find 2 closest hues in sl:
#hslb,hib = meshblock(hsl,h[:,i:i+1])
hib, hslb = np.meshgrid(h[:, i:i + 1], hsl)
dh = np.abs(hslb - hib)
q1 = dh.argmin(axis=0) # index of closest hue
dh[q1] = 1000000.0
q2 = dh.argmin(axis=0) # index of second closest hue
print('q1q2', q2, q1)
print('wls:', h[:, i], wlsl[q1], wlsl[q2])
print('hsls:', hsl[q2, 0], hsl[q1, 0])
print('d', (wlsl[q2] - wlsl[q1]), (hsl[q2, 0] - hsl[q1, 0]),
(wlsl[q2] - wlsl[q1]) / (hsl[q2, 0] - hsl[q1, 0]))
print('(h[:,i] - hsl[q1,0])', (h[:, i] - hsl[q1, 0]))
print('div', np.divide((wlsl[q2] - wlsl[q1]),
(hsl[q2, 0] - hsl[q1, 0])))
print(
'mult(...)',
np.multiply((h[:, i] - hsl[q1, 0]),
np.divide((wlsl[q2] - wlsl[q1]),
(hsl[q2, 0] - hsl[q1, 0]))))
dominantwavelength[:, i] = wlsl[q1] + np.multiply(
(h[:, i] - hsl[q1, 0]),
np.divide((wlsl[q2] - wlsl[q1]), (hsl[q2, 0] - hsl[q1, 0]))
) # calculate wl corresponding to h: y = y1 + (x-x1)*(y2-y1)/(x2-x1)
print('dom', dominantwavelength[:, i])
dominantwavelength[(dominantwavelength[:,
i] > max(wlsl[q1], wlsl[q2])),
i] = max(wlsl[q1], wlsl[q2])
dominantwavelength[(dominantwavelength[:,
i] < min(wlsl[q1], wlsl[q2])),
i] = min(wlsl[q1], wlsl[q2])
dominantwavelength[:, i][pc] = -dominantwavelength[:, i][
pc] #complementary wavelengths are specified by '-' sign
# calculate excitation purity:
x_dom_wl = xsl[q1, 0] + (xsl[q2, 0] - xsl[q1, 0]) * (h[:, i] - hsl[
q1, 0]) / (hsl[q2, 0] - hsl[q1, 0]) # calculate x of dom. wl
y_dom_wl = ysl[q1, 0] + (ysl[q2, 0] - ysl[q1, 0]) * (h[:, i] - hsl[
q1, 0]) / (hsl[q2, 0] - hsl[q1, 0]) # calculate y of dom. wl
d_wl = (x_dom_wl**2.0 +
y_dom_wl**2.0)**0.5 # distance from white point to sl
d = (x[:, i]**2.0 +
y[:, i]**2.0)**0.5 # distance from white point to test point
purity[:, i] = d / d_wl
# correct for those test points that have a complementary wavelength
# calculate intersection of line through white point and test point and purple line:
xy = np.vstack((x[:, i], y[:, i])).T
xyw = np.hstack((xw, yw))
xypl1 = np.hstack((xsl[0, None], ysl[0, None]))
xypl2 = np.hstack((xsl[-1, None], ysl[-1, None]))
da = (xy - xyw)
db = (xypl2 - xypl1)
dp = (xyw - xypl1)
T = np.array([[0.0, -1.0], [1.0, 0.0]])
dap = np.dot(da, T)
denom = np.sum(dap * db, axis=1, keepdims=True)
num = np.sum(dap * dp, axis=1, keepdims=True)
xy_linecross = (num / denom) * db + xypl1
d_linecross = np.atleast_2d(
(xy_linecross[:, 0]**2.0 + xy_linecross[:, 1]**2.0)**0.5).T #[0]
purity[:, i][pc] = d[pc] / d_linecross[pc][:, 0]
Ydlep = np.dstack((xyz3[:, :, 1], dominantwavelength, purity))
if axes12flipped == True:
Ydlep = Ydlep.transpose((1, 0, 2))
else:
Ydlep = Ydlep.transpose((0, 1, 2))
return Ydlep.reshape(xyz.shape)
def get_pixel_coordinates(jab,
jab_ranges=None,
jab_deltas=None,
limit_grid_radius=0):
"""
Get pixel coordinates corresponding to array of jab color coordinates.
Args:
:jab:
| ndarray of color coordinates
:jab_ranges:
| None or ndarray, optional
| Specifies the pixelization of color space.
| (ndarray.shape = (3,3), with first axis: J,a,b, and second
axis: min, max, delta)
:jab_deltas:
| float or ndarray, optional
| Specifies the sampling range.
| A float uses jab_deltas as the maximum Euclidean distance to select
| samples around each pixel center. A ndarray of 3 deltas, uses
| a city block sampling around each pixel center.
:limit_grid_radius:
| 0, optional
| A value of zeros keeps grid as specified by axr,bxr.
| A value > 0 only keeps (a,b) coordinates within :limit_grid_radius:
Returns:
:returns:
| gridp, idxp, jabp, samplenrs, samplesIDs
| - :gridp: ndarray with coordinates of all pixel centers.
| - :idxp: list[int] with pixel index for each non-empty pixel
| - :jabp: ndarray with center color coordinates of non-empty pixels
| - :samplenrs: list[list[int]] with sample numbers belong to each
| non-empty pixel
| - :sampleIDs: summarizing list,
| with column order: 'idxp, jabp, samplenrs'
"""
if jab_deltas is None:
jab_deltas = np.array([_VF_DELTAR, _VF_DELTAR, _VF_DELTAR])
if jab_ranges is None:
jab_ranges = np.vstack(
([0, 100, jab_deltas[0]
], [-_VF_MAXR, _VF_MAXR + jab_deltas[1], jab_deltas[1]],
[-_VF_MAXR, _VF_MAXR + jab_deltas[2], jab_deltas[2]]))
# Get pixel grid:
gridp = generate_grid(jab_ranges=jab_ranges,
limit_grid_radius=limit_grid_radius)
# determine pixel coordinates of each sample in jab:
samplesIDs = []
for idx in range(gridp.shape[0]):
# get pixel coordinates:
jp = gridp[idx, 0]
ap = gridp[idx, 1]
bp = gridp[idx, 2]
#Cp = np.sqrt(ap**2+bp**2)
if type(jab_deltas) == np.ndarray:
sampleID = np.where(
((np.abs(jab[..., 0] - jp) <= jab_deltas[0] / 2) &
(np.abs(jab[..., 1] - ap) <= jab_deltas[1] / 2) &
(np.abs(jab[..., 2] - bp) <= jab_deltas[2] / 2)))
else:
sampleID = np.where(
(np.sqrt((jab[..., 0] - jp)**2 + (jab[..., 1] - ap)**2 +
(jab[..., 2] - bp)**2) <= jab_deltas / 2))
if (sampleID[0].shape[0] > 0):
samplesIDs.append(
np.hstack((idx, np.array([jp, ap, bp]), sampleID[0])))
idxp = [np.int(samplesIDs[i][0]) for i in range(len(samplesIDs))]
jabp = np.vstack([samplesIDs[i][1:4] for i in range(len(samplesIDs))])
samplenrs = [
np.array(samplesIDs[i][4:], dtype=int).tolist()
for i in range(len(samplesIDs))
]
return gridp, idxp, jabp, samplenrs, samplesIDs
def _compute_f_stat(sample_size, num_groups, tri_idxs, distances, group_sizes,
s_T, grouping, subjects, paired):
"""Compute PERMANOVA Pseudo-F."""
s_WG, s_WS, s_WG_V = _compute_s_W_S(sample_size, num_groups, tri_idxs,
distances, group_sizes, grouping,
subjects, paired)
# for pseudo-F1:
s_BG = s_T - s_WG # = s_Effect
dfBG = (num_groups - 1)
if (paired == True):
s_BS = s_T - s_WS
s_Error = s_WS - s_BG
dfErr = (num_groups - 1) * (len(np.unique(subjects)) - 1)
if np.isclose(s_Error, 0, atol=1e-9):
s_Error = np.abs(s_Error)
if (s_Error < 0):
print('WARNING: s_Error = {:1.4f} < 0!'.format(s_Error))
print(
' s_BG = {:1.4f}, s_WG = {:1.4f}, s_BS = {:1.4f}, s_WS = {:1.4f}.'
.format(s_BG, s_WG, s_BS, s_WS))
print(
' Setting s_Error to s_WGB (s_S -> 0) (cfr. paired = False)!'
)
s_Error = s_WG
s_BS = np.nan
dfErr = (sample_size - num_groups)
else:
s_Error = s_WG # for pseudo-F1
s_Error2 = s_WG_V # for pseudo-F2
s_BS = np.nan
dfErr = (sample_size - num_groups)
# test statistic, pseudo-F1:
stat_ = (s_BG / dfBG) / (s_Error / dfErr)
if paired == True:
# test statistic, pseudo-F2 (equals pseudo-F1 for equal sample sizes!):
stat = stat_
else:
# test statistic, pseudo-F2:
stat = (s_BG) / (s_Error2)
# effect sizes:
p_eta2 = s_BG / (s_BG + s_Error)
omega2 = (s_BG - dfBG * (s_Error / dfErr)) / (s_T - (s_Error / dfErr))
R2 = 1.0 - 1 / (1 + stat * (dfBG / dfErr))
#print('t:',sample_size, num_groups, (sample_size - num_groups - 1))
R2adj = 1.0 - ((1 - R2) * (sample_size - 1) /
(sample_size - num_groups - 1))
effect_sizes = {
'p_eta2': p_eta2,
'omega2': omega2,
'R2': R2,
'R2adj': R2adj
}
# print('s_BG = {:1.2f}, s_WG = {:1.2f}, s_BS = {:1.2f}, s_WS = {:1.2f}, s_Err = {:1.2f} -- > s_T = {:1.2f}(Sum={:1.2f}:{:1.2f}).'.format(s_BG, s_WG, s_BS, s_WS, s_Error, s_T, s_BG + s_WG, s_BS + s_WS))
if s_Error < 0:
print('WARNING: s_Error = {:1.4f} <= 0!'.format(s_Error))
print(
' s_BG = {:1.4f}, s_WG = {:1.4f}, s_BS = {:1.4f}, s_WS = {:1.4f}.'
.format(s_BG, s_WG, s_BS, s_WS))
print(' Setting F to NaN.')
stat = np.nan
return stat, effect_sizes
