用Matplotlib创建概率/频率轴网格(不规则间隔) [英] Creating Probability/Frequency Axis Grid (Irregularly Spaced) with Matplotlib
问题描述
我正在尝试创建频率曲线图，但在操纵轴以获取所需的图时遇到了麻烦.
I'm trying to create a frequency curve plot, and I'm having trouble manipulating the axis to get the plot I want.
以下是我尝试创建的所需网格/图的示例:
Here is an example of the desired grid/plot I am trying to create:
这是我使用matplotlib设法创建的内容:
Here is what I have managed to create with matplotlib:
要在此绘图中创建网格，我使用了以下代码:
To create the grid in this plot, I used the following code:
m1 = pd.np.arange(.2, 1, .1)
m2 = pd.np.arange(1, 2, .2)
m3 = pd.np.arange(2, 10, 2)
m4 = pd.np.arange(2, 20, 1)
m5 = pd.np.arange(20, 80, 2)
m6 = pd.np.arange(80, 98, 1)
xTick_minor = pd.np.concatenate((m1,m2,m3,m4, m5, m6))
xTick_major = pd.np.array([.2,.5,1,2,5,10,20,30,40,50,60,70,80,90,95,98])
m1 = range(0, 250, 50)
m2 = range(250, 500, 10)
m3 = range(500, 1000, 20)
m4 = range(1000, 5000, 100)
m5 = range(5000, 10000, 200)
m6 = range(10000, 50000, 1000)
yTick_minor = pd.np.concatenate((m1,m2,m3,m4,m5,m6))
yTick_major = pd.np.array([250, 300, 350, 400, 450, 500, 600, 700, 800, 900, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500, 5000, 6000, 7000, 8000, 9000, 10000, 15000, 20000, 25000, 30000, 35000, 40000, 45000, 50000])
axes.invert_xaxis()
axes.set_ylabel('Discharge in CFS')
axes.set_xlabel('Exceedance Probability')
axes.xaxis.set_major_formatter(FormatStrFormatter('%3.1f'))
axes.set_xticks(xTick_major)
axes.set_xticks(xTick_minor, minor=True)
axes.grid(which='major', alpha=0.7)
axes.grid(which='minor', alpha=0.4)
axes.set_yticks(yTick_major)
axes.set_yticks(yTick_minor, minor=True)
网格是正确的，但是我现在要确保在显示中，低概率范围被更多地隔开，并且对于低放电值(y轴)也是如此.本质上，我想控制刻度线之间的间距，而不是刻度线间隔本身，以使.2到.5的范围与x轴上40到50的范围相似，就像所需的网格显示.
The grid is correct, but what I now want to do is make sure the in the display, the low probability ranges get spaced out more, and the same for the low discharge values (y-axis). Essentially I want to control the spacing between ticks, not the tick interval itself, so that the range from .2 to .5 displays similarly to the range between 40 and 50 on the x-axis, as the desired grid shows.
这可以在matplotlib中完成吗?我已经阅读了有关tick_params和locator的文档，但是这些似乎都没有解决这种轴格式问题.
Can this be done in matplotlib? I have read through the documentation on tick_params and locators, but none of these seem to address this kind of axis formatting.
推荐答案
由于@Amy Teegarden使我朝着正确的方向前进，我终于提出了正确的解决方案.我以为我会在这里分享最终的解决方案，以供其他人参考！这是最终结果:
I finally came up with the correct solution, thanks to @Amy Teegarden for getting me going in the right direction. I thought I would share the final solution here for others to reference! Here is the final result:
以下是真实的概率轴刻度，使用正常的CDF及其反函数PPF(由mu和sigma表示).
Following is a true probability axis scale, using the normal CDF and its inverse, PPF, functions paramterized by mu and sigma.
import numpy as np
from matplotlib import scale as mscale
from matplotlib import transforms as mtransforms
from matplotlib.ticker import FormatStrFormatter, FixedLocator
from scipy.stats import norm
class ProbScale(mscale.ScaleBase):
"""
Scales data in range 0 to 100 using a non-standard log transform
This scale attempts to replicate "probability paper" scaling
The scale function:
A piecewise combination of exponential, linear, and logarithmic scales
The inverse scale function:
piecewise combination of exponential, linear, and logarithmic scales
Since probabilities at 0 and 100 are not represented,
there is user-defined upper and lower limit, above and below which nothing
will be plotted. This defaults to .1 and 99 for lower and upper, respectively.
"""
# The scale class must have a member ``name`` that defines the
# string used to select the scale. For example,
# ``gca().set_yscale("mercator")`` would be used to select this
# scale.
name = 'prob_scale'
def __init__(self, axis, **kwargs):
"""
Any keyword arguments passed to ``set_xscale`` and
``set_yscale`` will be passed along to the scale's
constructor.
upper: The probability above which to crop the data.
lower: The probability below which to crop the data.
"""
mscale.ScaleBase.__init__(self)
upper = kwargs.pop("upper", 98) #Default to an upper bound of 98%
if upper <= 0 or upper >= 100:
raise ValueError("upper must be between 0 and 100.")
lower = kwargs.pop("lower", 0.2) #Default to a lower bound of .2%
if lower <= 0 or lower >= 100:
raise ValueError("lower must be between 0 and 100.")
if lower >= upper:
raise ValueError("lower must be strictly less than upper!.")
self.lower = lower
self.upper = upper
#This scale is best described by the CDF of the normal distribution
#This distribution is paramaterized by mu and sigma, these default vaules
#are provided to work generally well, but can be adjusted by the user if desired
mu = kwargs.pop("mu", 15)
sigma = kwargs.pop("sigma", 40)
self.mu = mu
self.sigma = sigma
#Need to enfore the upper and lower limits on the axes initially
axis.axes.set_xlim(lower,upper)
def get_transform(self):
"""
Override this method to return a new instance that does the
actual transformation of the data.
The ProbTransform class is defined below as a
nested class of this one.
"""
return self.ProbTransform(self.lower, self.upper, self.mu, self.sigma)
def set_default_locators_and_formatters(self, axis):
"""
Override to set up the locators and formatters to use with the
scale. This is only required if the scale requires custom
locators and formatters. Writing custom locators and
formatters: many helpful examples in ``ticker.py``.
In this case, the prob_scale uses a fixed locator from
0.1 to 99 % and a custom no formatter class
This builds both the major and minor locators, and cuts off any values
above or below the user defined thresholds: upper, lower
"""
#major_ticks = np.asarray([.2,.5,1,2,5,10,20,30,40,50,60,70,80,90,95,98])
major_ticks = np.asarray([.2,1,2,5,10,20,30,40,50,60,70,80,90,98]) #removed a couple ticks to make it look nicer
major_ticks = major_ticks[np.where( (major_ticks >= self.lower) & (major_ticks <= self.upper) )]
minor_ticks = np.concatenate( [np.arange(.2, 1, .1), np.arange(1, 2, .2), np.arange(2,20,1), np.arange(20, 80, 2), np.arange(80, 98, 1)] )
minor_ticks = minor_ticks[np.where( (minor_ticks >= self.lower) & (minor_ticks <= self.upper) )]
axis.set_major_locator(FixedLocator(major_ticks))
axis.set_minor_locator(FixedLocator(minor_ticks))
def limit_range_for_scale(self, vmin, vmax, minpos):
"""
Override to limit the bounds of the axis to the domain of the
transform. In the case of Probability, the bounds should be
limited to the user bounds that were passed in. Unlike the
autoscaling provided by the tick locators, this range limiting
will always be adhered to, whether the axis range is set
manually, determined automatically or changed through panning
and zooming.
"""
return max(self.lower, vmin), min(self.upper, vmax)
class ProbTransform(mtransforms.Transform):
# There are two value members that must be defined.
# ``input_dims`` and ``output_dims`` specify number of input
# dimensions and output dimensions to the transformation.
# These are used by the transformation framework to do some
# error checking and prevent incompatible transformations from
# being connected together. When defining transforms for a
# scale, which are, by definition, separable and have only one
# dimension, these members should always be set to 1.
input_dims = 1
output_dims = 1
is_separable = True
def __init__(self, upper, lower, mu, sigma):
mtransforms.Transform.__init__(self)
self.upper = upper
self.lower = lower
self.mu = mu
self.sigma = sigma
def transform_non_affine(self, a):
"""
This transform takes an Nx1 ``numpy`` array and returns a
transformed copy. Since the range of the Probability scale
is limited by the user-specified threshold, the input
array must be masked to contain only valid values.
``matplotlib`` will handle masked arrays and remove the
out-of-range data from the plot. Importantly, the
``transform`` method *must* return an array that is the
same shape as the input array, since these values need to
remain synchronized with values in the other dimension.
"""
masked = np.ma.masked_where( (a < self.upper) & (a > self.lower) , a)
#Get the CDF of the normal distribution located at mu and scaled by sigma
#Multiply these by 100 to put it into a percent scale
cdf = norm.cdf(masked, self.mu, self.sigma)*100
return cdf
def inverted(self):
"""
Override this method so matplotlib knows how to get the
inverse transform for this transform.
"""
return ProbScale.InvertedProbTransform(self.lower, self.upper, self.mu, self.sigma)
class InvertedProbTransform(mtransforms.Transform):
input_dims = 1
output_dims = 1
is_separable = True
def __init__(self, lower, upper, mu, sigma):
mtransforms.Transform.__init__(self)
self.lower = lower
self.upper = upper
self.mu = mu
self.sigma = sigma
def transform_non_affine(self, a):
#Need to get the PPF value for a, which is in a percent scale [0,100], so move back to probability range [0,1]
inverse = norm.ppf(a/100, self.mu, self.sigma)
return inverse
def inverted(self):
return ProbScale.ProbTransform(self.lower, self.upper)
# Now that the Scale class has been defined, it must be registered so
# that ``matplotlib`` can find it.
mscale.register_scale(ProbScale)
此外，为了获得所需的y轴结果，我发现对数刻度确实可以通过一些额外的调整来使用，以获得合理的图形.这是用于强制对数刻度具有适当的小刻度的代码:
Also, to get the desired y-axis results, I discovered that the log-scale could indeed be used with a few extra tweaks to get a reasonable graph. This is the code used to force the log scale to have appropriate minor ticks:
axes.set_yscale('log', basey=10, subsy=[2,3,4,5,6,7,8,9])
然后，您可以使用定位器和格式化程序修改标签:
Then you can modify the labeling with the locator and formatter:
#Adjust the yaxis labels and format
axes.yaxis.set_minor_locator(FixedLocator([200, 500, 1500, 2500, 3500, 4500, 5000, 6000, 7000, 8000, 9000, 15000, 20000, 25000, 30000, 35000, 40000, 45000, 50000]))
axes.yaxis.set_minor_formatter(FormatStrFormatter('%d'))
axes.yaxis.set_major_formatter(FormatStrFormatter('%d'))
因此完整的轴maninputlation看起来像这样:
So the complete axes maninputlation looks like this:
axes.set_ylabel('Discharge in CFS')
axes.set_xlabel('Exceedance Probability')
plt.setp(plt.xticks()[1], rotation=45)
#Adjust the scales of the x and y axis
axes.set_yscale('log', basey=10, subsy=[2,3,4,5,6,7,8,9])
axes.set_xscale('prob_scale', upper=98, lower=.2)
#Adjust the yaxis labels and format
axes.yaxis.set_minor_locator(FixedLocator([200, 500, 1500, 2500, 3500, 4500, 5000, 6000, 7000, 8000, 9000, 15000, 20000, 25000, 30000, 35000, 40000, 45000, 50000]))
axes.yaxis.set_minor_formatter(FormatStrFormatter('%d'))
axes.yaxis.set_major_formatter(FormatStrFormatter('%d'))
#Finally set the y-limit of the plot to be reasonable
axes.set_ylim((0, 2*pp['Q'].max()))
#Invert the x-axis
axes.invert_xaxis()
#Turn on major and minor grid lines
axes.grid(which='both', alpha=.9)
这提供了半对数标度概率纸图！有了不错的特性，在这些轴上绘制的任何东西都以直线表示，表明它来自正态分布！
This provides a semi-log scale probability paper plot! With the nice property that anything plotted on these axes that plots in a straight line indicates that it comes from a normal distribution!
这篇关于用Matplotlib创建概率/频率轴网格(不规则间隔)的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！
