matplotlib - real - Mapa de color cíclico sin distorsiones visuales para su uso en gráficos de ángulo de fase?

matplotlib python 3

Question

Estoy buscando un buen mapa de colores circular / cíclico para representar la información del ángulo de fase (donde los valores están restringidos al rango [0, 2π] y donde 0 y 2π representan el mismo ángulo de fase).

Antecedentes: me gustaría visualizar modos normales trazando tanto la densidad espectral de potencia como la información de fase relativa de las oscilaciones en todo el sistema.

Admitiré que previamente utilicé el mapa de colores ''arco iris'' para la gráfica de potencia y el mapa de colores ''hsv'' para la gráfica de fase (vea [1]). Sin embargo, el uso del mapa de colores del arco iris es extremadamente desaconsejado debido a su falta de linealidad perceptiva y ordenación [2] [3]. Así que cambié al mapa de colores ''coolwarm'' para la trama de poder que me gusta bastante. Desafortunadamente, el mapa de colores ''hsv'' parece presentar el mismo tipo de distorsiones visuales que el mapa ''arcoiris'' (y tampoco se adapta muy bien al mapa "frío" ya que en comparación parece feo y llamativo) .

¿Alguien tiene una buena recomendación para un mapa de color circular alternativo que podría usar para los diagramas de fase?

Requisitos:

• Debe ser circular para que los valores 0 y 2π estén representados por el mismo color.

• No debería introducir distorsiones visuales; en particular, debe ser perceptualmente lineal (que el mapa de colores ''hsv'' no parece ser). No creo que el orden perceptual sea tan importante para la información de fase, pero, por supuesto, no haría ningún daño.

• Debe ser visualmente atractivo cuando se combina con el mapa de colores ''coolwarm''. Sin embargo, no estoy completamente configurado en ''coolwarm'' y estoy contento de considerar otras opciones si hay otro par de mapas de color para visualizar la información de amplitud y fase.

Puntos de bonificación si el mapa de colores está disponible (o se puede crear fácilmente) para usar en matplotlib.

¡Muchas gracias por las sugerencias!

[1] http://matplotlib.org/examples/color/colormaps_reference.html

[2] http://www.renci.org/~borland/pdfs/RainbowColorMap_VisViewpoints.pdf

[3] http://medvis.org/2012/08/21/rainbow-colormaps-what-are-they-good-for-absolutely-nothing/

Answer 1

El problema con el mapa de color hue-HUSL es que no es intuitivo leer un ángulo de él. No conozco ningún mapa de color predefinido donde esto sea posible.

Por lo tanto, sugiero que hagas tu propio mapa de colores. Aquí hay algunas posibilidades:

• Para el mapa de colores segmentado lineal , definimos algunos colores. El mapa de colores es entonces una interpolación lineal entre los colores. Esto tiene distorsiones visuales.
• Para el mapa de luminosidad-HSLUV , usamos el espacio HUSL ("HSLUV"), sin embargo, en lugar del canal de tono, usamos dos colores y el canal de luminosidad. Esto tiene distorsiones en el croma , pero tiene colores brillantes.
• El mapa de luminosidad-HPLUV , utilizamos el espacio de color HPLUV (siguiendo el comentario de @ mwaskom). Esta es la única forma de no tener realmente distorsiones visuales, pero los colores no están saturados. Así es como se ven:

Vemos que en nuestros mapas de colores personalizados, el blanco representa el 0, el azul representa el 1i, etc. En la esquina superior derecha, vemos el mapa de hue-HUSL para comparar. Allí, las asignaciones de ángulos de color son aleatorias.

Además, al trazar una función más compleja, es fácil leer la fase del resultado al usar uno de nuestros mapas de color.

Y aquí está el código para las tramas:

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.colors as col
import seaborn as sns
import hsluv # install via pip
import scipy.special # just for the example function

##### generate custom colormaps
def make_segmented_cmap(): 
    white = ''#ffffff''
    black = ''#000000''
    red = ''#ff0000''
    blue = ''#0000ff''
    anglemap = col.LinearSegmentedColormap.from_list(
        ''anglemap'', [black, red, white, blue, black], N=256, gamma=1)
    return anglemap

def make_anglemap( N = 256, use_hpl = True ):
    h = np.ones(N) # hue
    h[:N//2] = 11.6 # red 
    h[N//2:] = 258.6 # blue
    s = 100 # saturation
    l = np.linspace(0, 100, N//2) # luminosity
    l = np.hstack( (l,l[::-1] ) )

    colorlist = np.zeros((N,3))
    for ii in range(N):
        if use_hpl:
            colorlist[ii,:] = hsluv.hpluv_to_rgb( (h[ii], s, l[ii]) )
        else:
            colorlist[ii,:] = hsluv.hsluv_to_rgb( (h[ii], s, l[ii]) )
    colorlist[colorlist > 1] = 1 # correct numeric errors
    colorlist[colorlist < 0] = 0 
    return col.ListedColormap( colorlist )

N = 256
segmented_cmap = make_segmented_cmap()
flat_huslmap = col.ListedColormap(sns.color_palette(''husl'',N))
hsluv_anglemap = make_anglemap( use_hpl = False )
hpluv_anglemap = make_anglemap( use_hpl = True )

##### generate data grid
x = np.linspace(-2,2,N)
y = np.linspace(-2,2,N)
z = np.zeros((len(y),len(x))) # make cartesian grid
for ii in range(len(y)): 
    z[ii] = np.arctan2(y[ii],x) # simple angular function
    z[ii] = np.angle(scipy.special.gamma(x+1j*y[ii])) # some complex function

##### plot with different colormaps
fig = plt.figure(1)
fig.clf()
colormapnames = [''segmented map'', ''hue-HUSL'', ''lum-HSLUV'', ''lum-HPLUV'']
colormaps = [segmented_cmap, flat_huslmap, hsluv_anglemap, hpluv_anglemap]
for ii, cm in enumerate(colormaps):
    ax = fig.add_subplot(2, 2, ii+1)
    pmesh = ax.pcolormesh(x, y, z/np.pi, 
        cmap = cm, vmin=-1, vmax=1)
    plt.axis([x.min(), x.max(), y.min(), y.max()])
    cbar = fig.colorbar(pmesh)
    cbar.ax.set_ylabel(''Phase [pi]'')
    ax.set_title( colormapnames[ii] )
plt.show()

EDITAR: Recientemente descubrí cómo hacer tales mapas de colores sin distorsiones visuales, así que extendí mi respuesta original

Answer 2

Me acabo de dar cuenta de que cmocean tiene un mapa de cmocean para este propósito.

import cmocean
import matplotlib.pyplot as plt
import numpy as np

azimuths = np.arange(0, 361, 1)
zeniths = np.arange(40, 70, 1)
values = azimuths * np.ones((30, 361))
fig, ax = plt.subplots(subplot_kw=dict(projection=''polar''))
ax.pcolormesh(azimuths*np.pi/180.0, zeniths, values, cmap=cmocean.cm.phase)
ax.set_yticks([])
plt.show()

Y el resultado es

Answer 3

Me gustan los mapas de color anteriores, pero quería arrancarles una teoría del color moderna. Puede obtener un espacio de color más uniforme perceptualmente utilizando el espacio de color CIECAM02.

El paquete colorspacious es muy bueno para convertirlo en este gran espacio de color. Usando este paquete, inicié las respuestas anteriores en un cmap personalizado propio.

from colorspacious import cspace_convert
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.colors as col
import seaborn as sns

# first draw a circle in the cylindrical JCh color space. 
# the third channel is hue in degrees. First is lightness and the second chroma
color_circle = np.ones((256,3))*60
color_circle[:,1] = np.ones((256))*45
color_circle[:,2] = np.arange(0,360,360/256)
color_circle_rgb = cspace_convert(color_circle, "JCh","sRGB1")

cm = col.ListedColormap(color_circle_rgb)

##### generate data grid like in above
N=256
x = np.linspace(-2,2,N)
y = np.linspace(-2,2,N)
z = np.zeros((len(y),len(x))) # make cartesian grid
for ii in range(len(y)): 
    z[ii] = np.arctan2(y[ii],x) # simple angular function

fig = plt.figure()
ax = plt.gca()
pmesh = ax.pcolormesh(x, y, z/np.pi, 
    cmap = cm, vmin=-1, vmax=1)
plt.axis([x.min(), x.max(), y.min(), y.max()])
cbar = fig.colorbar(pmesh)
cbar.ax.set_ylabel(''Phase [pi]'')

Si no desea instalar el paquete colorspacious , puede copiar y pegar esta lista de colores y crear un mapa de color directamente:

colors = array([[0.91510904, 0.55114749, 0.67037311],
   [0.91696411, 0.55081563, 0.66264366],
   [0.91870995, 0.55055664, 0.65485881],
   [0.92034498, 0.55037149, 0.64702356],
   [0.92186763, 0.55026107, 0.63914306],
   [0.92327636, 0.55022625, 0.63122259],
   [0.9245696 , 0.55026781, 0.62326754],
   [0.92574582, 0.5503865 , 0.6152834 ],
   [0.92680349, 0.55058299, 0.6072758 ],
   [0.92774112, 0.55085789, 0.59925045],
   [0.9285572 , 0.55121174, 0.59121319],
   [0.92925027, 0.551645  , 0.58316992],
   [0.92981889, 0.55215808, 0.57512667],
   [0.93026165, 0.55275127, 0.56708953],
   [0.93057716, 0.5534248 , 0.55906469],
   [0.93076407, 0.55417883, 0.55105838],
   [0.93082107, 0.55501339, 0.54307696],
   [0.93074689, 0.55592845, 0.53512681],
   [0.9305403 , 0.55692387, 0.52721438],
   [0.93020012, 0.55799943, 0.51934621],
   [0.92972523, 0.55915477, 0.51152885],
   [0.92911454, 0.56038948, 0.50376893],
   [0.92836703, 0.56170301, 0.49607312],
   [0.92748175, 0.56309471, 0.48844813],
   [0.9264578 , 0.56456383, 0.48090073],
   [0.92529434, 0.56610951, 0.47343769],
   [0.92399062, 0.56773078, 0.46606586],
   [0.92254595, 0.56942656, 0.45879209],
   [0.92095971, 0.57119566, 0.4516233 ],
   [0.91923137, 0.5730368 , 0.44456642],
   [0.91736048, 0.57494856, 0.4376284 ],
   [0.91534665, 0.57692945, 0.43081625],
   [0.91318962, 0.57897785, 0.42413698],
   [0.91088917, 0.58109205, 0.41759765],
   [0.90844521, 0.58327024, 0.41120533],
   [0.90585771, 0.58551053, 0.40496711],
   [0.90312676, 0.5878109 , 0.3988901 ],
   [0.90025252, 0.59016928, 0.39298143],
   [0.89723527, 0.5925835 , 0.38724821],
   [0.89407538, 0.59505131, 0.38169756],
   [0.89077331, 0.59757038, 0.37633658],
   [0.88732963, 0.60013832, 0.37117234],
   [0.88374501, 0.60275266, 0.36621186],
   [0.88002022, 0.6054109 , 0.36146209],
   [0.87615612, 0.60811044, 0.35692989],
   [0.87215369, 0.61084868, 0.352622  ],
   [0.86801401, 0.61362295, 0.34854502],
   [0.86373824, 0.61643054, 0.34470535],
   [0.85932766, 0.61926872, 0.3411092 ],
   [0.85478365, 0.62213474, 0.3377625 ],
   [0.85010767, 0.6250258 , 0.33467091],
   [0.84530131, 0.62793914, 0.3318397 ],
   [0.84036623, 0.63087193, 0.32927381],
   [0.8353042 , 0.63382139, 0.32697771],
   [0.83011708, 0.63678472, 0.32495541],
   [0.82480682, 0.63975913, 0.32321038],
   [0.81937548, 0.64274185, 0.32174556],
   [0.81382519, 0.64573011, 0.32056327],
   [0.80815818, 0.6487212 , 0.31966522],
   [0.80237677, 0.65171241, 0.31905244],
   [0.79648336, 0.65470106, 0.31872531],
   [0.79048044, 0.65768455, 0.31868352],
   [0.78437059, 0.66066026, 0.31892606],
   [0.77815645, 0.66362567, 0.31945124],
   [0.77184076, 0.66657827, 0.32025669],
   [0.76542634, 0.66951562, 0.3213394 ],
   [0.75891609, 0.67243534, 0.32269572],
   [0.75231298, 0.67533509, 0.32432138],
   [0.74562004, 0.6782126 , 0.32621159],
   [0.73884042, 0.68106567, 0.32836102],
   [0.73197731, 0.68389214, 0.33076388],
   [0.72503398, 0.68668995, 0.33341395],
   [0.7180138 , 0.68945708, 0.33630465],
   [0.71092018, 0.69219158, 0.33942908],
   [0.70375663, 0.69489159, 0.34278007],
   [0.69652673, 0.69755529, 0.34635023],
   [0.68923414, 0.70018097, 0.35013201],
   [0.6818826 , 0.70276695, 0.35411772],
   [0.67447591, 0.70531165, 0.3582996 ],
   [0.667018  , 0.70781354, 0.36266984],
   [0.65951284, 0.71027119, 0.36722061],
   [0.65196451, 0.71268322, 0.37194411],
   [0.64437719, 0.71504832, 0.37683259],
   [0.63675512, 0.71736525, 0.38187838],
   [0.62910269, 0.71963286, 0.38707389],
   [0.62142435, 0.72185004, 0.39241165],
   [0.61372469, 0.72401576, 0.39788432],
   [0.60600841, 0.72612907, 0.40348469],
   [0.59828032, 0.72818906, 0.40920573],
   [0.59054536, 0.73019489, 0.41504052],
   [0.58280863, 0.73214581, 0.42098233],
   [0.57507535, 0.7340411 , 0.42702461],
   [0.5673509 , 0.7358801 , 0.43316094],
   [0.55964082, 0.73766224, 0.43938511],
   [0.55195081, 0.73938697, 0.44569104],
   [0.54428677, 0.74105381, 0.45207286],
   [0.53665478, 0.74266235, 0.45852483],
   [0.52906111, 0.74421221, 0.4650414 ],
   [0.52151225, 0.74570306, 0.47161718],
   [0.5140149 , 0.74713464, 0.47824691],
   [0.506576  , 0.74850672, 0.48492552],
   [0.49920271, 0.74981912, 0.49164808],
   [0.49190247, 0.75107171, 0.4984098 ],
   [0.48468293, 0.75226438, 0.50520604],
   [0.47755205, 0.7533971 , 0.51203229],
   [0.47051802, 0.75446984, 0.5188842 ],
   [0.46358932, 0.75548263, 0.52575752],
   [0.45677469, 0.75643553, 0.53264815],
   [0.45008317, 0.75732863, 0.5395521 ],
   [0.44352403, 0.75816207, 0.54646551],
   [0.43710682, 0.758936  , 0.55338462],
   [0.43084133, 0.7596506 , 0.56030581],
   [0.42473758, 0.76030611, 0.56722555],
   [0.41880579, 0.76090275, 0.5741404 ],
   [0.41305637, 0.76144081, 0.58104704],
   [0.40749984, 0.76192057, 0.58794226],
   [0.40214685, 0.76234235, 0.59482292],
   [0.39700806, 0.7627065 , 0.60168598],
   [0.39209414, 0.76301337, 0.6085285 ],
   [0.38741566, 0.76326334, 0.6153476 ],
   [0.38298304, 0.76345681, 0.62214052],
   [0.37880647, 0.7635942 , 0.62890454],
   [0.37489579, 0.76367593, 0.63563704],
   [0.37126045, 0.76370246, 0.64233547],
   [0.36790936, 0.76367425, 0.64899736],
   [0.36485083, 0.76359176, 0.6556203 ],
   [0.36209245, 0.76345549, 0.66220193],
   [0.359641  , 0.76326594, 0.66873999],
   [0.35750235, 0.76302361, 0.67523226],
   [0.35568141, 0.76272903, 0.68167659],
   [0.35418202, 0.76238272, 0.68807086],
   [0.3530069 , 0.76198523, 0.69441305],
   [0.35215761, 0.7615371 , 0.70070115],
   [0.35163454, 0.76103888, 0.70693324],
   [0.35143685, 0.76049114, 0.71310742],
   [0.35156253, 0.75989444, 0.71922184],
   [0.35200839, 0.75924936, 0.72527472],
   [0.3527701 , 0.75855647, 0.73126429],
   [0.3538423 , 0.75781637, 0.73718884],
   [0.3552186 , 0.75702964, 0.7430467 ],
   [0.35689171, 0.75619688, 0.74883624],
   [0.35885353, 0.75531868, 0.75455584],
   [0.36109522, 0.75439565, 0.76020396],
   [0.36360734, 0.75342839, 0.76577905],
   [0.36637995, 0.75241752, 0.77127961],
   [0.3694027 , 0.75136364, 0.77670417],
   [0.37266493, 0.75026738, 0.7820513 ],
   [0.37615579, 0.74912934, 0.78731957],
   [0.37986429, 0.74795017, 0.79250759],
   [0.38377944, 0.74673047, 0.797614  ],
   [0.38789026, 0.74547088, 0.80263746],
   [0.3921859 , 0.74417203, 0.80757663],
   [0.39665568, 0.74283455, 0.81243022],
   [0.40128912, 0.74145908, 0.81719695],
   [0.406076  , 0.74004626, 0.82187554],
   [0.41100641, 0.73859673, 0.82646476],
   [0.41607073, 0.73711114, 0.83096336],
   [0.4212597 , 0.73559013, 0.83537014],
   [0.42656439, 0.73403435, 0.83968388],
   [0.43197625, 0.73244447, 0.8439034 ],
   [0.43748708, 0.73082114, 0.84802751],
   [0.44308905, 0.72916502, 0.85205505],
   [0.44877471, 0.72747678, 0.85598486],
   [0.45453694, 0.72575709, 0.85981579],
   [0.46036897, 0.72400662, 0.8635467 ],
   [0.4662644 , 0.72222606, 0.86717646],
   [0.47221713, 0.72041608, 0.87070395],
   [0.47822138, 0.71857738, 0.87412804],
   [0.4842717 , 0.71671065, 0.87744763],
   [0.4903629 , 0.71481659, 0.88066162],
   [0.49649009, 0.71289591, 0.8837689 ],
   [0.50264864, 0.71094931, 0.88676838],
   [0.50883417, 0.70897752, 0.88965898],
   [0.51504253, 0.70698127, 0.89243961],
   [0.52126981, 0.70496128, 0.8951092 ],
   [0.52751231, 0.70291829, 0.89766666],
   [0.53376652, 0.70085306, 0.90011093],
   [0.54002912, 0.69876633, 0.90244095],
   [0.54629699, 0.69665888, 0.90465565],
   [0.55256715, 0.69453147, 0.90675397],
   [0.55883679, 0.69238489, 0.90873487],
   [0.56510323, 0.69021993, 0.9105973 ],
   [0.57136396, 0.68803739, 0.91234022],
   [0.57761655, 0.68583808, 0.91396258],
   [0.58385872, 0.68362282, 0.91546336],
   [0.59008831, 0.68139246, 0.91684154],
   [0.59630323, 0.67914782, 0.9180961 ],
   [0.60250152, 0.67688977, 0.91922603],
   [0.60868128, 0.67461918, 0.92023033],
   [0.61484071, 0.67233692, 0.921108  ],
   [0.62097809, 0.67004388, 0.92185807],
   [0.62709176, 0.66774097, 0.92247957],
   [0.63318012, 0.66542911, 0.92297153],
   [0.63924166, 0.66310923, 0.92333301],
   [0.64527488, 0.66078227, 0.92356308],
   [0.65127837, 0.65844919, 0.92366082],
   [0.65725076, 0.65611096, 0.92362532],
   [0.66319071, 0.65376857, 0.92345572],
   [0.66909691, 0.65142302, 0.92315115],
   [0.67496813, 0.64907533, 0.92271076],
   [0.68080311, 0.64672651, 0.92213374],
   [0.68660068, 0.64437763, 0.92141929],
   [0.69235965, 0.64202973, 0.92056665],
   [0.69807888, 0.6396839 , 0.91957507],
   [0.70375724, 0.63734122, 0.91844386],
   [0.70939361, 0.63500279, 0.91717232],
   [0.7149869 , 0.63266974, 0.91575983],
   [0.72053602, 0.63034321, 0.91420578],
   [0.72603991, 0.62802433, 0.9125096 ],
   [0.7314975 , 0.62571429, 0.91067077],
   [0.73690773, 0.62341425, 0.9086888 ],
   [0.74226956, 0.62112542, 0.90656328],
   [0.74758193, 0.61884899, 0.90429382],
   [0.75284381, 0.6165862 , 0.90188009],
   [0.75805413, 0.61433829, 0.89932181],
   [0.76321187, 0.6121065 , 0.89661877],
   [0.76831596, 0.6098921 , 0.89377082],
   [0.77336536, 0.60769637, 0.89077786],
   [0.77835901, 0.6055206 , 0.88763988],
   [0.78329583, 0.6033661 , 0.88435693],
   [0.78817477, 0.60123418, 0.88092913],
   [0.79299473, 0.59912616, 0.87735668],
   [0.79775462, 0.59704339, 0.87363986],
   [0.80245335, 0.59498722, 0.86977904],
   [0.8070898 , 0.592959  , 0.86577468],
   [0.81166284, 0.5909601 , 0.86162732],
   [0.81617134, 0.5889919 , 0.8573376 ],
   [0.82061414, 0.58705579, 0.85290625],
   [0.82499007, 0.58515315, 0.84833413],
   [0.82929796, 0.58328538, 0.84362217],
   [0.83353661, 0.58145389, 0.83877142],
   [0.8377048 , 0.57966009, 0.83378306],
   [0.8418013 , 0.57790538, 0.82865836],
   [0.84582486, 0.57619119, 0.82339871],
   [0.84977422, 0.57451892, 0.81800565],
   [0.85364809, 0.57289   , 0.8124808 ],
   [0.85744519, 0.57130585, 0.80682595],
   [0.86116418, 0.56976788, 0.80104298],
   [0.86480373, 0.56827749, 0.79513394],
   [0.86836249, 0.56683612, 0.789101  ],
   [0.87183909, 0.56544515, 0.78294645],
   [0.87523214, 0.56410599, 0.77667274],
   [0.87854024, 0.56282002, 0.77028247],
   [0.88176195, 0.56158863, 0.76377835],
   [0.88489584, 0.56041319, 0.75716326],
   [0.88794045, 0.55929505, 0.75044023],
   [0.89089432, 0.55823556, 0.74361241],
   [0.89375596, 0.55723605, 0.73668312],
   [0.89652387, 0.55629781, 0.72965583],
   [0.89919653, 0.55542215, 0.72253414],
   [0.90177242, 0.55461033, 0.71532181],
   [0.90425   , 0.55386358, 0.70802274],
   [0.90662774, 0.55318313, 0.70064098],
   [0.90890408, 0.55257016, 0.69318073],
   [0.91107745, 0.55202582, 0.68564633],
   [0.91314629, 0.55155124, 0.67804225]])

cmap = col.ListedColormap(colors)

Answer 4

Podría probar el sistema "husl" , que es similar a hls / hsv pero con mejores propiedades visuales. Está disponible en seaborn y como un paquete independiente .

Aquí hay un ejemplo simple:

import numpy as np
from numpy import sin, cos, pi
import matplotlib.pyplot as plt
import seaborn as sns

n = 314
theta = np.linspace(0, 2 * pi, n)

x = cos(theta)
y = sin(theta)

f = plt.figure(figsize=(10, 5))
with sns.color_palette("husl", n):
    ax = f.add_subplot(121)
    ax.plot([np.zeros_like(x), x], [np.zeros_like(y), y], lw=3)
    ax.set_axis_off()
    ax.set_title("HUSL space")

with sns.color_palette("hls", n):
    ax = f.add_subplot(122)
    ax.plot([np.zeros_like(x), x], [np.zeros_like(y), y], lw=3)
    ax.set_axis_off()
    ax.set_title("HLS space")

f.tight_layout()