使用pyplot中的quiver函数绘制箭头的对数长度
有没有简单的方法可以让PyPlot中的quiver函数绘制的箭头长度按对数比例缩放呢？
原因是，我在陆地和海洋上绘制风箭头，而海洋上的风速大约是陆地上的十倍。
所以，要么陆地上的箭头太小，根本看不出什么信息，要么海洋上的箭头太大，导致图表在海洋部分显得非常拥挤。
我已经尝试使用symlog函数来让数据按对数缩放，但似乎角度方面出现了一些问题。为了说明这一点，这里有一段小图的代码：
def main():
lat, lon, u, v = readmulticol2Dfile('test.txt', shape=(9,6))
# map without logarithmic scaling
plt.subplot(1,2,1)
mapproj = bm.Basemap(projection='cyl', llcrnrlon=lon.min(), urcrnrlon=lon.max(), llcrnrlat=lat.min(), urcrnrlat=lat.max())
mapproj.drawcoastlines()
mapproj.drawparallels(np.linspace(-20,20,5), labels=[1,0,0,0])
mapproj.drawmeridians(np.linspace(-80,20,5), labels=[0,0,0,1])
plt.title('linear')
plt.quiver(lon, lat, u, v, color='k', units='x')
# map with logarithmic scaling
plt.subplot(1,2,2)
mapproj = bm.Basemap(projection='cyl', llcrnrlon=lon.min(), urcrnrlon=lon.max(), llcrnrlat=lat.min(), urcrnrlat=lat.max())
mapproj.drawcoastlines()
mapproj.drawparallels(np.linspace(-20,20,5), labels=[1,0,0,0])
mapproj.drawmeridians(np.linspace(-80,20,5), labels=[0,0,0,1])
plt.quiver(lon, lat, symlog(u), symlog(v), color='k', units='x')
plt.title('logarithmic')
plt.show()
def readmulticol2Dfile(fname, header=True, delimiter='\t', shape=None):
"""reads a multicolumn txt-file and converts it to numpy arrays"""
a=np.loadtxt(fname).T
if shape is not None:
b=[np.zeros(shape=shape)]*4
for i in xrange(len(a)): b[i]=np.reshape(a[i],shape)
return b
else: return a
def symlog(x):
""" Returns the symmetric log10 value """
return np.sign(x) * np.log10(np.abs(x))
if __name__=="__main__":
main()
使用这个数据，保存在test.txt中。
# lattitude longitude u v
2.145047503739818495e+01 -8.062500000000000000e+01 -5.790064811706542969e+00 2.341136932373046875e-01
2.145047503739818495e+01 -7.312500000000000000e+01 -7.119166374206542969e+00 -1.223894119262695312e+00
2.145047503739818495e+01 -6.562500000000000000e+01 -6.140162467956542969e+00 -1.082292556762695312e+00
2.145047503739818495e+01 -5.812500000000000000e+01 -4.589381217956542969e+00 2.853832244873046875e-01
2.145047503739818495e+01 -5.062500000000000000e+01 -5.221705436706542969e+00 4.221019744873046875e-01
2.145047503739818495e+01 -4.312500000000000000e+01 -5.333521842956542969e+00 6.321525573730468750e-02
1.771996152644742750e+01 -2.812500000000000000e+01 -7.793482780456542969e+00 -3.714616775512695312e+00
1.771996152644742750e+01 -2.062500000000000000e+01 -6.195338249206542969e+00 -6.160417556762695312e+00
1.585470386969487322e+01 -7.687500000000000000e+01 -8.054713249206542969e+00 -1.638355255126953125e-01
1.585470386969487322e+01 -6.937500000000000000e+01 -7.378443717956542969e+00 -2.906990051269531250e-02
1.585470386969487322e+01 -6.187500000000000000e+01 -6.270533561706542969e+00 3.127269744873046875e-01
1.585470386969487322e+01 -5.437500000000000000e+01 -7.410181999206542969e+00 -1.028003692626953125e-01
1.212418712345576566e+01 -3.937500000000000000e+01 -8.221217155456542969e+00 -2.800065994262695312e+00
1.212418712345576566e+01 -3.187500000000000000e+01 -7.579127311706542969e+00 -3.560319900512695312e+00
1.212418712345576566e+01 -2.437500000000000000e+01 -5.761256217956542969e+00 -5.112565994262695312e+00
1.025892816800637597e+01 -8.062500000000000000e+01 -4.789576530456542969e+00 -4.363542556762695312e+00
1.025892816800637597e+01 -7.312500000000000000e+01 -1.818385124206542969e+00 -1.677995681762695312e+00
1.025892816800637597e+01 -6.562500000000000000e+01 -3.078639030456542969e+00 -1.554460525512695312e+00
6.528409401479990493e+00 -5.062500000000000000e+01 -7.822779655456542969e+00 -1.683855056762695312e+00
6.528409401479990493e+00 -4.312500000000000000e+01 -8.200709342956542969e+00 -2.835222244262695312e+00
6.528409401479990493e+00 -3.562500000000000000e+01 -7.456568717956542969e+00 -2.850358963012695312e+00
6.528409401479990493e+00 -2.812500000000000000e+01 -5.878443717956542969e+00 -2.700944900512695312e+00
6.528409401479990493e+00 -2.062500000000000000e+01 -2.720240592956542969e+00 -1.258562088012695312e+00
4.663149706177883935e+00 -7.687500000000000000e+01 1.257298469543457031e+00 -1.143815994262695312e+00
9.326299678379910141e-01 -6.187500000000000000e+01 -6.386976242065429688e-01 -2.507495880126953125e-01
9.326299678379910141e-01 -5.437500000000000000e+01 -2.149439811706542969e+00 -1.390886306762695312e+00
9.326299678379910141e-01 -4.687500000000000000e+01 -5.939478874206542969e+00 -1.460222244262695312e+00
9.326299678379910141e-01 -3.937500000000000000e+01 -6.882838249206542969e+00 -5.959644317626953125e-01
9.326299678379910141e-01 -3.187500000000000000e+01 -6.343287467956542969e+00 -1.565113067626953125e-01
9.326299678379910141e-01 -2.437500000000000000e+01 -5.749537467956542969e+00 3.444652557373046875e-01
-4.663149706177883935e+00 -7.312500000000000000e+01 -7.033824920654296875e-02 -3.654956817626953125e-01
-4.663149706177883935e+00 -6.562500000000000000e+01 -5.674085617065429688e-01 -3.176441192626953125e-01
-4.663149706177883935e+00 -5.812500000000000000e+01 -1.063014030456542969e+00 -1.213550567626953125e-01
-4.663149706177883935e+00 -5.062500000000000000e+01 -1.417994499206542969e+00 -2.028980255126953125e-01
-4.663149706177883935e+00 -4.312500000000000000e+01 -1.486842155456542969e+00 -8.557300567626953125e-01
-4.663149706177883935e+00 -3.562500000000000000e+01 -5.729517936706542969e+00 1.451887130737304688e+00
-8.393668907692383385e+00 -2.062500000000000000e+01 -6.579615592956542969e+00 2.450422286987304688e+00
-1.025892816800637597e+01 -7.687500000000000000e+01 4.018297195434570312e-01 -1.755542755126953125e-01
-1.025892816800637597e+01 -6.937500000000000000e+01 2.187242507934570312e-01 -5.783863067626953125e-01
-1.025892816800637597e+01 -6.187500000000000000e+01 -3.462171554565429688e-01 -8.737964630126953125e-01
-1.025892816800637597e+01 -5.437500000000000000e+01 -4.731702804565429688e-01 -3.200855255126953125e-01
-1.025892816800637597e+01 -4.687500000000000000e+01 -8.545179367065429688e-01 -4.890308380126953125e-01
-1.398944571235667311e+01 -3.187500000000000000e+01 -7.993678092956542969e+00 1.462230682373046875e-01
-1.398944571235667311e+01 -2.437500000000000000e+01 -8.063502311706542969e+00 1.512434005737304688e+00
-1.585470386969487322e+01 -8.062500000000000000e+01 -2.528346061706542969e+00 3.198469161987304688e+00
-1.585470386969487322e+01 -7.312500000000000000e+01 2.924547195434570312e-01 1.297590255737304688e+00
-1.585470386969487322e+01 -6.562500000000000000e+01 -3.598890304565429688e-01 -1.232194900512695312e+00
-1.585470386969487322e+01 -5.812500000000000000e+01 4.196643829345703125e-02 -1.524187088012695312e+00
-1.958521860882233057e+01 -4.312500000000000000e+01 -1.116724967956542969e+00 -3.195972442626953125e-01
-1.958521860882233057e+01 -3.562500000000000000e+01 -5.567896842956542969e+00 -3.761003494262695312e+00
-1.958521860882233057e+01 -2.812500000000000000e+01 -7.378443717956542969e+00 -1.043718338012695312e+00
-1.958521860882233057e+01 -2.062500000000000000e+01 -8.015162467956542969e+00 7.102775573730468750e-02
-2.145047503739818495e+01 -7.687500000000000000e+01 2.352025032043457031e+00 2.376691818237304688e+00
-2.145047503739818495e+01 -6.937500000000000000e+01 2.939915657043457031e+00 1.054914474487304688e+00
但不幸的是，结果看起来有点奇怪。长度确实是按对数缩放的，但在某些区域，角度的表现却很奇怪。
非常感谢你的帮助！=)
PS：我没有足够的声望来添加图像或第二个链接，所以我把它上传到了ftp服务器，那里会在两周后自动删除。你只需将上面的数据链接中的'.txt'替换为'.png'就可以访问图像。
2 个回答
1
我在遇到这个问题时，采用了和Greg类似的方法，但你注意到他对向量的调整有个问题，就是没有保持箭头的方向。要做到这一点，你需要在代码中按相同的比例调整U和V，具体如下：
def transform(u, v):
arrow_lengths = np.sqrt(u*u + v*v)
len_adjust_factor = np.log10(arrow_lengths + 1) / arrow_lengths
return u*len_adjust_factor, v*len_adjust_factor
U2, V2 = transform(U, V)
这个调整只是改变了箭头的长度，使得新的长度是旧长度的以10为底的对数。
注意：我使用log10(x+1)而不是log10(x)，这样做是为了确保函数的输出不会因为输入的变化而改变符号，并且函数从(0,0)这个点开始。
1
根据我的理解，你可以在传入箭头之前先调整它们的长度。这里有个例子：
import matplotlib.pyplot as plt
import numpy as np
def symlog(x):
""" Returns the symmetric log10 value """
return np.sign(x) * np.log10(np.abs(x))
fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(10,5))
# Generate fake data
N = 50
X,Y = np.meshgrid(np.linspace(0, 1, N), np.linspace(0, 1, N))
U = np.random.normal(0, 0.2, size=(50, 50))
V = np.random.normal(0, 0.2, size=(50, 50))
# Set RHS data to be larger than LHS
U[:, N/2:] *= 1000
V[:, N/2:] *= 1000
angles=np.arctan2(V,U)*180.0/np.pi # calculate angles manually
#Without scaling
HEAD_LENGTH = 4
Q = ax1.quiver( X[::3, ::3], Y[::3, ::3], U[::3, ::3], V[::3, ::3],
color='k', units='x', headaxislength=HEAD_LENGTH)
#With scaling
Q = ax2.quiver( X[::3, ::3], Y[::3, ::3], symlog(U[::3, ::3]), symlog(V[::3, ::3]),
color='k', units='x', headaxislength=HEAD_LENGTH, angles=angles)
plt.show()
左边是原始数据，右边则是我用 symlog() 调整过箭头长度的结果。这个方法可以在保持数值符号的情况下，调整数值的大小，否则你在处理负数时会出现错误。