python - 如何在 Matplotlib 中制作四向对数图？

Question

四向对数图是振动控制和地震防护中非常常用的图形。我对如何在 Matplotlib 中绘制此图而不是在 Inkscape 中添加轴非常感兴趣。此处为四向对数图示例。

快速而肮脏的 Python 代码可以生成图形的主要部分，但我无法将两个轴添加到图形上。 http://matplotlib.org/examples/axes_grid/demo_curvelinear_grid.html提供了添加轴的示例，但我无法使其正常工作。有没有人有类似的向 Matplotlib 图形添加轴的经验？

from pylab import *
from  mpl_toolkits.axisartist.grid_helper_curvelinear import GridHelperCurveLinear
from mpl_toolkits.axisartist import Subplot
beta=logspace(-1,1,500)
Rd={}
for zeta in [0.01,0.1,0.2,0.7,1]:
    Rd[zeta]=beta/sqrt((1-beta*beta)**2+(2*beta*zeta)**2)
    loglog(beta,Rd[zeta])
ylim([0.1,10])
xlim([0.1,10])
grid('on',which='minor')

更新:谢谢大家!我用Inkscape修改了上图。我觉得结果刚刚好。但是，我仍在寻找在 Matplotlib 中绘制此图的方法。

Answer 1

这是部分解决方案。我仍在研究如何在自然 loglog() 图中完成所有这些操作，而不是缩放数据。 (要完成此示例，您必须定义自定义刻度标签，以便它们显示 10**x 而不是 x。)

%matplotlib inline                   # I am doing this in an IPython notebook.
from matplotlib import pyplot as plt
import numpy as np
from numpy import log10

# Generate the data
beta = np.logspace(-1, 1, 500)[:, None]
zeta = np.array([0.01,0.1,0.2,0.7,1])[None, :]
Rd = beta/np.sqrt((1 - beta*beta)**2 + (2*beta*zeta)**2)

def draw(beta=beta, Rd=Rd):
    plt.plot(log10(beta), log10(Rd))
    plt.ylim([log10(0.1), log10(10)])
    plt.xlim([log10(0.1), log10(10)])
    plt.grid('on',which='minor')
    ax = plt.gca()
    ax.set_aspect(1)

from mpl_toolkits.axisartist import GridHelperCurveLinear
from matplotlib.transforms import Affine2D
from mpl_toolkits.axisartist import SubplotHost
from mpl_toolkits.axisartist import Subplot

#tr = Affine2D().rotate(-np.pi/2)
#inv_tr = Affine2D().rotate(np.pi/2)

class Transform(object):
    """Provides transforms to go to and from rotated grid.

    Parameters
    ----------
    ilim : (xmin, xmax, ymin, ymax)
       The limits of the displayed axes (in physical units)
    olim : (xmin, xmax, ymin, ymax)
       The limits of the rotated axes (in physical units)
    """
    def __init__(self, ilim, olim):
        # Convert each to a 3x3 matrix and compute the transform
        # [x1, y1, 1] = A*[x0, y0, 1]
        x0, x1, y0, y1 = np.log10(ilim)
        I = np.array([[x0, x0, x1],
                      [y0, y1, y1],
                      [ 1,  1,  1]])

        x0, x1, y0, y1 = np.log10(olim)
        x_mid = (x0 + x1)/2
        y_mid = (y0 + y1)/2
        O = np.array([[   x0, x_mid, x1],
                      [y_mid,    y1, y_mid],
                      [    1,     1,     1]])
        self.A = np.dot(O, np.linalg.inv(I))
        self.Ainv = np.linalg.inv(self.A)

    def tr(self, x, y):
        """From "curved" (rotated) coords to rectlinear coords"""
        x, y = map(np.asarray, (x, y))
        return np.dot(self.A, np.asarray([x, y, 1]))[:2]

    def inv_tr(self, x, y):
        """From rectlinear coords to "curved" (rotated) coords"""
        x, y = map(np.asarray, (x, y))
        return np.dot(self.Ainv, np.asarray([x, y, 1]))[:2]

ilim = (0.1, 10)
olim = (0.01, 100)
tr = Transform(ilim + ilim, olim + olim)

grid_helper = GridHelperCurveLinear((tr.tr, tr.inv_tr))

fig = plt.gcf()
ax0 = Subplot(fig, 1, 1, 1)
ax1 = Subplot(fig, 1, 1, 1, grid_helper=grid_helper, frameon=False)
ax1.set_xlim(*np.log10(olim))
ax1.set_ylim(*np.log10(olim))
ax1.axis["left"] = ax1.new_floating_axis(0, 0.)
ax1.axis["bottom"] = ax1.new_floating_axis(1, 0.0)
fig.add_subplot(ax0)
fig.add_subplot(ax1)
ax0.grid('on', which='both')
ax1.grid('on', which='both')

plt.plot(log10(beta), log10(Rd))
plt.ylim(np.log10(ilim))
plt.xlim(np.log10(ilim))