def add_to_cmf_dict(bar=None, cieobs='indv', K=683, M=np.eye(3)): """ Add set of cmfs to _CMF dict. Args: :bar: | None, optional | Set of CMFs. None: initializes to empty ndarray. :cieobs: | 'indv' or str, optional | Name of CMF set. :K: | 683 (lm/W), optional | Conversion factor from radiometric to photometric quantity. :M: | np.eye, optional | Matrix for lms to xyz conversion. """ if bar is None: wl3 = getwlr(_WL3) bar = np.vstack((wl3, np.empty((3, wl3.shape[0])))) _CMF['types'].append(cieobs) _CMF[cieobs] = {'bar': bar} _CMF[cieobs]['K'] = K _CMF[cieobs]['M'] = M
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_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 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 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] = 841 / 108 * 116 * XYZr[pqr[..., 1], 1] Lab[..., 1] = 500.0 * (fXYZr[..., 0] - fXYZr[..., 1]) Lab[..., 2] = 200.0 * (fXYZr[..., 1] - fXYZr[..., 2]) return Lab
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) xyz = np.empty(Yuv.shape) 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 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
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) # get L*, a*, b* and Xw, Yw, Zw: fXYZ = np.empty(lab.shape) fXYZ[..., 1] = (lab[..., 0] + 16.0) / 116.0 fXYZ[..., 0] = lab[..., 1] / 500.0 + fXYZ[..., 1] fXYZ[..., 2] = fXYZ[..., 1] - lab[..., 2] / 200.0 # apply 3rd power: xyz = (fXYZ**3.0) * xyzw # Now calculate T where T/Tn is below the knee point: pqr = fXYZ <= (24 / 116) #(24/116)**3**(1/3) xyz[pqr] = np.squeeze(xyzw[pqr] * ((fXYZ[pqr] - 16.0 / 116.0) / (841 / 108))) return xyz
def _get_distance_matrix_grouping(*X, metric='euclidean', Dscale=1): """ Get distance matrix (skbio format) and grouping indexing array from raw data""" # Create long format data array and grouping indices: ni = np.empty((len(X), ), dtype=int) for i, Xi in enumerate(X): ni[i] = Xi.shape[0] if i == 0: XY = Xi else: XY = np.vstack((XY, Xi)) grouping = [[i] * n for i, n in enumerate(ni)] grouping = list(itertools.chain(*grouping)) # Calculate pairwise distances: D = scipy.spatial.distance.pdist(XY, metric=metric) * Dscale Dsq = scipy.spatial.distance.squareform(D) # Get skbio distance matrix: Dm = skbio.stats.distance.DistanceMatrix(Dsq) return Dm, grouping
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 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) Yuvw = xyz_to_Yuv(xyzw) # convert to cie 1976 u'v' Yuv = np.empty(wuv.shape) Yuv[..., 0] = ((wuv[..., 0] + 17.0) / 25.0)**3.0 Yuv[..., 1] = Yuvw[..., 1] + wuv[..., 1] / (13.0 * wuv[..., 0]) Yuv[..., 2] = Yuvw[..., 2] + wuv[..., 2] / (13.0 * wuv[..., 0]) * ( 3.0 / 2.0) # convert to cie 1960 u, v return Yuv_to_xyz(Yuv)
def _run_monte_carlo_stats(test_stat_function, grouping, subjects, permutations, paired): """Run stat test and compute significance with Monte Carlo permutations.""" if permutations < 0: raise ValueError( "Number of permutations must be greater than or equal to zero.") stat, effect_sizes = test_stat_function(grouping, subjects, paired) p_value = np.nan if permutations > 0: perm_stats = np.empty(permutations, dtype=np.float64) for i in range(permutations): perm_grouping, perm_subjects = _permutate_grouping(grouping, subjects, paired=paired) perm_stats[i], _ = test_stat_function(perm_grouping, perm_subjects, paired) stat, effect_sizes = test_stat_function(grouping, subjects, paired) p_value = ((perm_stats >= stat).sum() + 1) / (permutations + 1) return stat, p_value, effect_sizes
def dtlz2_(x, M): """ DTLZ2 multi-objective function | This function represents a hyper-sphere. | Using k = 10, the number of dimensions must be n = (M - 1) + k. | The Pareto optimal solutions are obtained when the last k variables of x | are equal to 0.5. Args: :x: | a n x mu ndarray with mu points and n dimensions :M: | a scalar with the number of objectives Returns: :f: | a m x mu ndarray with mu points and their m objectives computed at | the input """ k = 10 # Error check: the number of dimensions must be M-1+k n = (M-1) + k; #this is the default if x.shape[0] != n: raise Exception('Using k = 10, it is required that the number of dimensions be n = (M - 1) + k = {:1.0f} in this case.'.format(n)) xm = x[(n-k):,:].copy() #xm contains the last k variables g = ((xm - 0.5)**2).sum(axis = 0) # Computes the functions: f = np.empty((M,x.shape[1])) f[0,:] = (1 + g)*np.prod(np.cos(np.pi/2*x[:(M-1),:]), axis = 0) for ii in range(1,M-1): f[ii,:] = (1 + g) * np.prod(np.cos(np.pi/2*x[:(M-ii-1),:]), axis = 0) * np.sin(np.pi/2*x[M-ii-1,:]) f[M-1,:] = (1 + g) * np.sin(np.pi/2*x[0,:]) return f
def xyz_to_luv(xyz, xyzw=None, cieobs=_CIEOBS, **kwargs): """ Convert XYZ tristimulus values to CIE 1976 L*u*v* (CIELUV) 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: :luv: | ndarray with CIE 1976 L*u*v* (CIELUV) color coordinates """ xyz = np2d(xyz) if xyzw is None: xyzw = spd_to_xyz(_CIE_ILLUMINANTS['D65'], cieobs=cieobs) # Calculate u',v' of test and white: Yuv = xyz_to_Yuv(xyz) Yuvw = xyz_to_Yuv(todim(xyzw, xyz.shape)) # todim: make xyzw same shape as xyz #uv1976 to CIELUV luv = np.empty(xyz.shape) YdivYw = Yuv[..., 0] / Yuvw[..., 0] luv[..., 0] = 116.0 * YdivYw**(1.0 / 3.0) - 16.0 p = np.where(YdivYw <= (6.0 / 29.0)**3.0) luv[..., 0][p] = ((29.0 / 3.0)**3.0) * YdivYw[p] luv[..., 1] = 13.0 * luv[..., 0] * (Yuv[..., 1] - Yuvw[..., 1]) luv[..., 2] = 13.0 * luv[..., 0] * (Yuv[..., 2] - Yuvw[..., 2]) return luv
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 and convert to Yuv: Yuvw = todim(xyz_to_Yuv(xyzw), luv.shape, equal_shape=True) # calculate u'v' from u*,v*: Yuv = np.empty(luv.shape) Yuv[..., 1:3] = (luv[..., 1:3] / (13 * luv[..., :1])) + Yuvw[..., 1:3] Yuv[Yuv[..., 0] == 0, 1:3] = 0 Yuv[..., 0] = Yuvw[..., 0] * (((luv[..., 0] + 16.0) / 116.0)**3.0) p = np.where((Yuv[..., 0] / Yuvw[..., 0]) < ((6.0 / 29.0)**3.0)) Yuv[..., 0][p] = Yuvw[..., 0][p] * (luv[..., 0][p] / ((29.0 / 3.0)**3.0)) return Yuv_to_xyz(Yuv)
def cie2006cmfsEx(age = 32,fieldsize = 10, wl = None,\ var_od_lens = 0, var_od_macula = 0, \ var_od_L = 0, var_od_M = 0, var_od_S = 0,\ var_shft_L = 0, var_shft_M = 0, var_shft_S = 0,\ out = 'LMS', allow_negative_values = False): """ Generate Individual Observer CMFs (cone fundamentals) based on CIE2006 cone fundamentals and published literature on observer variability in color matching and in physiological parameters. Args: :age: | 32 or float or int, optional | Observer age :fieldsize: | 10, optional | Field size of stimulus in degrees (between 2° and 10°). :wl: | None, optional | Interpolation/extraplation of :LMS: output to specified wavelengths. | None: output original _WL = np.array([390,780,5]) :var_od_lens: | 0, optional | Std Dev. in peak optical density [%] of lens. :var_od_macula: | 0, optional | Std Dev. in peak optical density [%] of macula. :var_od_L: | 0, optional | Std Dev. in peak optical density [%] of L-cone. :var_od_M: | 0, optional | Std Dev. in peak optical density [%] of M-cone. :var_od_S: | 0, optional | Std Dev. in peak optical density [%] of S-cone. :var_shft_L: | 0, optional | Std Dev. in peak wavelength shift [nm] of L-cone. :var_shft_L: | 0, optional | Std Dev. in peak wavelength shift [nm] of M-cone. :var_shft_S: | 0, optional | Std Dev. in peak wavelength shift [nm] of S-cone. :out: | 'LMS' or , optional | Determines output. :allow_negative_values: | False, optional | Cone fundamentals or color matching functions should not have negative values. | If False: X[X<0] = 0. Returns: :returns: | - 'LMS' : ndarray with individual observer area-normalized | cone fundamentals. Wavelength have been added. | [- 'trans_lens': ndarray with lens transmission | (no wavelengths added, no interpolation) | - 'trans_macula': ndarray with macula transmission | (no wavelengths added, no interpolation) | - 'sens_photopig' : ndarray with photopigment sens. | (no wavelengths added, no interpolation)] References: 1. `Asano Y, Fairchild MD, and Blondé L (2016). Individual Colorimetric Observer Model. PLoS One 11, 1–19. <http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0145671>`_ 2. `Asano Y, Fairchild MD, Blondé L, and Morvan P (2016). Color matching experiment for highlighting interobserver variability. Color Res. Appl. 41, 530–539. <https://onlinelibrary.wiley.com/doi/abs/10.1002/col.21975>`_ 3. `CIE, and CIE (2006). Fundamental Chromaticity Diagram with Physiological Axes - Part I (Vienna: CIE). <http://www.cie.co.at/publications/fundamental-chromaticity-diagram-physiological-axes-part-1>`_ 4. `Asano's Individual Colorimetric Observer Model <https://www.rit.edu/cos/colorscience/re_AsanoObserverFunctions.php>`_ """ fs = fieldsize rmd = _INDVCMF_DATA['rmd'].copy() LMSa = _INDVCMF_DATA['LMSa'].copy() docul = _INDVCMF_DATA['docul'].copy() # field size corrected macular density: pkOd_Macula = 0.485 * np.exp(-fs / 6.132) * ( 1 + var_od_macula / 100) # varied peak optical density of macula corrected_rmd = rmd * pkOd_Macula # age corrected lens/ocular media density: if (age <= 60): correct_lomd = docul[:1] * (1 + 0.02 * (age - 32)) + docul[1:2] else: correct_lomd = docul[:1] * (1.56 + 0.0667 * (age - 60)) + docul[1:2] correct_lomd = correct_lomd * (1 + var_od_lens / 100 ) # varied overall optical density of lens # Peak Wavelength Shift: wl_shifted = np.empty(LMSa.shape) wl_shifted[0] = _WL + var_shft_L wl_shifted[1] = _WL + var_shft_M wl_shifted[2] = _WL + var_shft_S LMSa_shft = np.empty(LMSa.shape) kind = 'cubic' LMSa_shft[0] = sp.interpolate.interp1d(wl_shifted[0], LMSa[0], kind=kind, bounds_error=False, fill_value="extrapolate")(_WL) LMSa_shft[1] = sp.interpolate.interp1d(wl_shifted[1], LMSa[1], kind=kind, bounds_error=False, fill_value="extrapolate")(_WL) LMSa_shft[2] = sp.interpolate.interp1d(wl_shifted[2], LMSa[2], kind=kind, bounds_error=False, fill_value="extrapolate")(_WL) # LMSa[2,np.where(_WL >= _WL_CRIT)] = 0 #np.nan # Not defined above 620nm # LMSa_shft[2,np.where(_WL >= _WL_CRIT)] = 0 ssw = np.hstack( (0, np.sign(np.diff(LMSa_shft[2, :])) )) #detect poor interpolation (sign switch due to instability) LMSa_shft[2, np.where((ssw >= 0) & (_WL > 560))] = np.nan # corrected LMS (no age correction): pkOd_L = (0.38 + 0.54 * np.exp(-fs / 1.333)) * ( 1 + var_od_L / 100) # varied peak optical density of L-cone pkOd_M = (0.38 + 0.54 * np.exp(-fs / 1.333)) * ( 1 + var_od_M / 100) # varied peak optical density of M-cone pkOd_S = (0.30 + 0.45 * np.exp(-fs / 1.333)) * ( 1 + var_od_S / 100) # varied peak optical density of S-cone alpha_lms = 0. * LMSa_shft alpha_lms[0] = 1 - 10**(-pkOd_L * (10**LMSa_shft[0])) alpha_lms[1] = 1 - 10**(-pkOd_M * (10**LMSa_shft[1])) alpha_lms[2] = 1 - 10**(-pkOd_S * (10**LMSa_shft[2])) # this fix is required because the above math fails for alpha_lms[2,:]==0 alpha_lms[2, np.where(_WL >= _WL_CRIT)] = 0 # Corrected to Corneal Incidence: lms_barq = alpha_lms * (10**(-corrected_rmd - correct_lomd)) * np.ones( alpha_lms.shape) # Corrected to Energy Terms: lms_bar = lms_barq * _WL # Set NaN values to zero: lms_bar[np.isnan(lms_bar)] = 0 # normalized: LMS = 100 * lms_bar / np.nansum(lms_bar, axis=1, keepdims=True) # Output extra: trans_lens = 10**(-correct_lomd) trans_macula = 10**(-corrected_rmd) sens_photopig = alpha_lms * _WL # Add wavelengths: LMS = np.vstack((_WL, LMS)) if ('xyz' in out.lower().split(',')): LMS = lmsb_to_xyzb(LMS, fieldsize, out='xyz', allow_negative_values=allow_negative_values) out = out.replace('xyz', 'LMS').replace('XYZ', 'LMS') if ('lms' in out.lower().split(',')): out = out.replace('lms', 'LMS') # Interpolate/extrapolate: if wl is None: interpolation = None else: interpolation = 'cubic' LMS = spd(LMS, wl=wl, interpolation=interpolation, norm_type='area') if (out == 'LMS'): return LMS elif (out == 'LMS,trans_lens,trans_macula,sens_photopig'): return LMS, trans_lens, trans_macula, sens_photopig elif (out == 'LMS,trans_lens,trans_macula,sens_photopig,LMSa'): return LMS, trans_lens, trans_macula, sens_photopig, LMSa else: return eval(out)
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 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 spd_to_ies_tm30_metrics(SPD, cri_type = None, \ hbins = 16, start_hue = 0.0,\ scalef = 100, \ vf_model_type = _VF_MODEL_TYPE, \ vf_pcolorshift = _VF_PCOLORSHIFT,\ scale_vf_chroma_to_sample_chroma = False): """ Calculates IES TM30 metrics from spectral data. Args: :data: | numpy.ndarray with spectral data :cri_type: | None, optional | If None: defaults to cri_type = 'iesrf'. | Not none values of :hbins:, :start_hue: and :scalef: overwrite | input in cri_type['rg_pars'] :hbins: | None or numpy.ndarray with sorted hue bin centers (°), optional :start_hue: | None, optional :scalef: | None, optional | Scale factor for reference circle. :vf_pcolorshift: | _VF_PCOLORSHIFT or user defined dict, optional | The polynomial models of degree 5 and 6 can be fully specified or | summarized by the model parameters themselved OR by calculating the | dCoverC and dH at resp. 5 and 6 hues. :VF_pcolorshift: specifies | these hues and chroma level. :scale_vf_chroma_to_sample_chroma: | False, optional | Scale chroma of reference and test vf fields such that average of | binned reference chroma equals that of the binned sample chroma | before calculating hue bin metrics. Returns: :data: | dict with color rendering data: | - 'SPD' : ndarray test SPDs | - 'bjabt': ndarray with binned jab data under test SPDs | - 'bjabr': ndarray with binned jab data under reference SPDs | - 'jabti': ndarray with individual jab data under test SPDs (scaled such that bjabr are on a circle) | - 'jabri': ndarray with individual jab data under reference SPDs (scaled such that bjabr are on a circle) | - 'hbinnr': ndarray with the hue bin number the samples belong to. | - 'cct' : ndarray with CCT of test SPD | - 'duv' : ndarray with distance to blackbody locus of test SPD | - 'Rf' : ndarray with general color fidelity indices | - 'Rg' : ndarray with gamut area indices | - 'Rfi' : ndarray with specific color fidelity indices | - 'Rfhi' : ndarray with local (hue binned) fidelity indices | - 'Rcshi': ndarray with local chroma shifts indices | - 'Rhshi': ndarray with local hue shifts indices | - 'Rt' : ndarray with general metameric uncertainty index Rt | - 'Rti' : ndarray with specific metameric uncertainty indices Rti | - 'Rfhi_vf' : ndarray with local (hue binned) fidelity indices | obtained from VF model predictions at color space | pixel coordinates | - 'Rcshi_vf': ndarray with local chroma shifts indices | (same as above) | - 'Rhshi_vf': ndarray with local hue shifts indices | (same as above) """ if cri_type is None: cri_type = 'iesrf' #Calculate color rendering measures for SPDs in data: out = 'Rf,Rg,cct,duv,Rfi,jabt,jabr,Rfhi,Rcshi,Rhshi,cri_type' if isinstance(cri_type, str): # get dict cri_type = copy.deepcopy(_CRI_DEFAULTS[cri_type]) if hbins is not None: cri_type['rg_pars']['nhbins'] = hbins if start_hue is not None: cri_type['rg_pars']['start_hue'] = start_hue if scalef is not None: cri_type['rg_pars']['normalized_chroma_ref'] = scalef Rf, Rg, cct, duv, Rfi, jabt, jabr, Rfhi, Rcshi, Rhshi, cri_type = spd_to_cri( SPD, cri_type=cri_type, out=out) rg_pars = cri_type['rg_pars'] #Calculate Metameric uncertainty and base color shifts: dataVF = VF_colorshift_model(SPD, cri_type=cri_type, model_type=vf_model_type, cspace=cri_type['cspace'], sampleset=eval(cri_type['sampleset']), pool=False, pcolorshift=vf_pcolorshift, vfcolor=0) Rf_ = np.array([dataVF[i]['metrics']['Rf'] for i in range(len(dataVF))]).T Rt = np.array([dataVF[i]['metrics']['Rt'] for i in range(len(dataVF))]).T Rti = np.array([dataVF[i]['metrics']['Rti'] for i in range(len(dataVF))][0]) # Get normalized and sliced sample data for plotting: rg_pars = cri_type['rg_pars'] nhbins, normalize_gamut, normalized_chroma_ref, start_hue = [ rg_pars[x] for x in sorted(rg_pars.keys()) ] normalized_chroma_ref = scalef # np.sqrt((jabr[...,1]**2 + jabr[...,2]**2)).mean(axis = 0).mean() if scale_vf_chroma_to_sample_chroma == True: normalize_gamut = False bjabt, bjabr = gamut_slicer( jabt, jabr, out='jabt,jabr', nhbins=nhbins, start_hue=start_hue, normalize_gamut=normalize_gamut, normalized_chroma_ref=normalized_chroma_ref, close_gamut=True) Cr_s = (np.sqrt(bjabr[:-1, ..., 1]**2 + bjabr[:-1, ..., 2]**2)).mean( axis=0) # for rescaling vector field average reference chroma normalize_gamut = True #(for plotting) bjabt, bjabr, binnrs, jabti, jabri = gamut_slicer( jabt, jabr, out='jabt,jabr,binnr,jabti,jabri', nhbins=nhbins, start_hue=start_hue, normalize_gamut=normalize_gamut, normalized_chroma_ref=normalized_chroma_ref, close_gamut=True) Rfhi_vf = np.empty(Rfhi.shape) Rcshi_vf = np.empty(Rcshi.shape) Rhshi_vf = np.empty(Rhshi.shape) for i in range(cct.shape[0]): # Get normalized and sliced VF data for hue specific metrics: vfjabt = np.hstack( (np.ones(dataVF[i]['fielddata']['vectorfield']['axt'].shape), dataVF[i]['fielddata']['vectorfield']['axt'], dataVF[i]['fielddata']['vectorfield']['bxt'])) vfjabr = np.hstack( (np.ones(dataVF[i]['fielddata']['vectorfield']['axr'].shape), dataVF[i]['fielddata']['vectorfield']['axr'], dataVF[i]['fielddata']['vectorfield']['bxr'])) nhbins, normalize_gamut, normalized_chroma_ref, start_hue = [ rg_pars[x] for x in sorted(rg_pars.keys()) ] vfbjabt, vfbjabr, vfbDEi = gamut_slicer( vfjabt, vfjabr, out='jabt,jabr,DEi', nhbins=nhbins, start_hue=start_hue, normalize_gamut=normalize_gamut, normalized_chroma_ref=normalized_chroma_ref, close_gamut=False) if scale_vf_chroma_to_sample_chroma == True: #rescale vfbjabt and vfbjabr to same chroma level as bjabr. Cr_vfb = np.sqrt(vfbjabr[..., 1]**2 + vfbjabr[..., 2]**2) Cr_vf = np.sqrt(vfjabr[..., 1]**2 + vfjabr[..., 2]**2) hr_vf = np.arctan2(vfjabr[..., 2], vfjabr[..., 1]) Ct_vf = np.sqrt(vfjabt[..., 1]**2 + vfjabt[..., 2]**2) ht_vf = np.arctan2(vfjabt[..., 2], vfjabt[..., 1]) fC = Cr_s.mean() / Cr_vfb.mean() vfjabr[..., 1] = fC * Cr_vf * np.cos(hr_vf) vfjabr[..., 2] = fC * Cr_vf * np.sin(hr_vf) vfjabt[..., 1] = fC * Ct_vf * np.cos(ht_vf) vfjabt[..., 2] = fC * Ct_vf * np.sin(ht_vf) vfbjabt, vfbjabr, vfbDEi = gamut_slicer( vfjabt, vfjabr, out='jabt,jabr,DEi', nhbins=nhbins, start_hue=start_hue, normalize_gamut=normalize_gamut, normalized_chroma_ref=normalized_chroma_ref, close_gamut=False) scale_factor = cri_type['scale']['cfactor'] scale_fcn = cri_type['scale']['fcn'] vfRfhi, vfRcshi, vfRhshi = jab_to_rhi( jabt=vfbjabt, jabr=vfbjabr, DEi=vfbDEi, cri_type=cri_type, scale_factor=scale_factor, scale_fcn=scale_fcn, use_bin_avg_DEi=True ) # [:-1,...] removes last row from jab as this was added to close the gamut. Rfhi_vf[:, i:i + 1] = vfRfhi Rhshi_vf[:, i:i + 1] = vfRhshi Rcshi_vf[:, i:i + 1] = vfRcshi # Create dict with CRI info: data = {'SPD' : SPD, 'cct' : cct, 'duv' : duv, 'bjabt' : bjabt, 'bjabr' : bjabr,\ 'jabti':jabti, 'jabri':jabri, 'hbinnr':binnrs,\ 'Rf' : Rf, 'Rg' : Rg, 'Rfi': Rfi, 'Rfhi' : Rfhi, 'Rcshi' : Rcshi, 'Rhshi' : Rhshi, \ 'Rt' : Rt, 'Rti' : Rti, 'Rfhi_vf' : Rfhi_vf, 'Rfcshi_vf' : Rcshi_vf, 'Rfhshi_vf' : Rhshi_vf, \ 'dataVF' : dataVF,'cri_type' : cri_type, # 'jabt_':jabt_,'jabr_':jabr_ } return data
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)