Docstrings使帖子看起来比实际更长。另外，我的问题是关于函数调用链顶部的函数。
有效的部分：
我想为指定分布制作卡方值的等高线图。我理解如何使轮廓图工作的基础知识，但我无法应用基本示例之外的技术。问题可能在于向量化我的功能。作为样本，考虑1000个点的样本高斯数据集，其平均值和分布分别为48和7。
# imports: import numpy as np, import random, from math import pi, from scipy.integrate import quad, from scipy.stats import chisquare, from scipy.optimize import minimize
dataset_gauss = [random.gauss(48, 7) for index in range(1000)]
我的函数和变量名是他们的方式，因为我的完整代码需要多个分布（高斯，对数正态）
def equation_gauss(x, a, b):
"""
This function returns the equation for the Gaussian distribution.
"""
cnorm = 1 / (b* (2*pi)**(1/2))
return cnorm * np.exp((-1) * (x - a)**2 / (2* b**2))
使用最大对数似然，我的脚本（与问题无关，因此代码未显示）返回params_gauss = [47.972906400237889, 7.0241339595841286]。
为了计算卡方，必须首先列出bin边界。然后，对于每个箱，可以将每个期望值等同于从箱的左侧到右侧的分布式的积分。每个箱的观察值是该箱内观察值的数量。人们可以通过将每个仓的预期值和观察值的平方差的商除以预期值来计算卡方。
def get_bins(distribution, num_bins=50):
"""
This function returns a specified number of equally sized bins over
the domain of the distribution.
"""
if distribution == 'gauss':
dataset = dataset_gauss
return np.linspace(min(dataset), max(dataset), num_bins)
def get_binned_expectations(distribution, args):
"""
This function returns the expectation values per bin for a dataset
given by the specified distribution.
"""
if distribution == 'gauss':
dataset = dataset_gauss
func = equation_gauss
num_obs = len(dataset)
bins = get_bins(distribution)
res = []
for idx in range(len(bins)):
if idx != len(bins)-1:
res.append(quad(func, bins[idx] , bins[idx+1], args = (args[0] , args[1]))[0] * num_obs)
return res
def get_binned_observations(distribution):
"""
This function returns the observation values per bin for a dataset
given by the specified distribution.
"""
if distribution == 'gauss':
dataset = dataset_gauss
bins = get_bins(distribution)
bin_count = []
for idx in range(len(bins)):
if idx != len(bins)-1:
summ = 0
for datum in dataset:
if datum > bins[idx] and datum <= bins[idx+1]:
summ += 1
bin_count.append(summ)
if idx == len(bins)-1:
pass
return bin_count
def get_chi_square(distribution, params):
"""
This function returns the chi square value for a specified
distribution.
EX:
distribution : 'gauss', 'lognormal'
params : [a, b] for parameters a and b
'opt' (for optimized parameters)
"""
values_observation = get_binned_observations(distribution)
if params == 'opt':
if distribution == 'gauss':
params = params_gauss
values_expectation = get_binned_expectations(distribution, params)
return chisquare(values_observation, values_expectation)
作为检查，让我们试试：
res = get_chi_square('gauss', params='opt')
print(res)
new_params = [40, 10]
new_res = get_chi_square('gauss', params=new_params)
print(new_res)
>> Power_divergenceResult(statistic=55.465132812431413, pvalue=0.21391356257718666)
>> Power_divergenceResult(statistic=14950.604250041084, pvalue=0.0)
第一个值statistic是使用相应参数获得的卡方值，而第二个值pvalue是参数拟合的概率。出于我的目的，最好只将第一个元素称为print(new_res[0])。 （概率不是很准确，因为没有规定自由度。）
为了制作轮廓图，我的理解是我需要通过dim-2数组生成网格空间。首先，我编写一个函数来返回每个参数的数字列表。这是返回x, y的函数，X, Y是meshgrid。
def get_axis_data(param, frac, size):
"""
This function returns a specified number of elements in a range
centered around the value of the inputted parameter. The extrema
of this range are specified as:
param ± param * frac
"""
update = frac * param
return np.linspace(param - update, param + update, size)
我的问题：
我知道我可以使用plt.contourf(X, Y, Z, cmap)。但是，我不知道如何格式化get_chi_square以接收meshgrid - ed参数作为输入，因为它调用scipy模块（有效地）通过列表计算卡方可优化的参数。我已经评论过我尝试过的失败的事情。
def get_grid_data(distribution, frac=1/4, size=9, func=get_chi_square, cmap='plasma'):
"""
This function returns the grid values for a contour plot of the
error metric as a function of the parameters of a specified
distribution.
EX:
func: 'chi square', 'maximum log-likelihood' (error metric)
"""
if distribution == 'gauss':
opt_params = params_gauss
a_vals = get_axis_data(opt_params[0], frac, size)
b_vals = get_axis_data(opt_params[1], frac, size)
X, Y = np.meshgrid(a_vals, b_vals)
# func = np.vectorize(func)
# Z = func(distribution, [X, Y])[0]
return X, Y#, Z
X, Y = get_grid_data('gauss')
print("X")
print(X)
print("")
print("Y")
print(Y)
运行以上命令：
X
[[ 35.9796798 38.97798645 41.9762931 44.97459975 47.9729064
50.97121305 53.9695197 56.96782635 59.966133 ]
[ 35.9796798 38.97798645 41.9762931 44.97459975 47.9729064
50.97121305 53.9695197 56.96782635 59.966133 ]
[ 35.9796798 38.97798645 41.9762931 44.97459975 47.9729064
50.97121305 53.9695197 56.96782635 59.966133 ]
[ 35.9796798 38.97798645 41.9762931 44.97459975 47.9729064
50.97121305 53.9695197 56.96782635 59.966133 ]
[ 35.9796798 38.97798645 41.9762931 44.97459975 47.9729064
50.97121305 53.9695197 56.96782635 59.966133 ]
[ 35.9796798 38.97798645 41.9762931 44.97459975 47.9729064
50.97121305 53.9695197 56.96782635 59.966133 ]
[ 35.9796798 38.97798645 41.9762931 44.97459975 47.9729064
50.97121305 53.9695197 56.96782635 59.966133 ]
[ 35.9796798 38.97798645 41.9762931 44.97459975 47.9729064
50.97121305 53.9695197 56.96782635 59.966133 ]
[ 35.9796798 38.97798645 41.9762931 44.97459975 47.9729064
50.97121305 53.9695197 56.96782635 59.966133 ]]
Y
[[ 5.26810047 5.26810047 5.26810047 5.26810047 5.26810047 5.26810047
5.26810047 5.26810047 5.26810047]
[ 5.70710884 5.70710884 5.70710884 5.70710884 5.70710884 5.70710884
5.70710884 5.70710884 5.70710884]
[ 6.14611721 6.14611721 6.14611721 6.14611721 6.14611721 6.14611721
6.14611721 6.14611721 6.14611721]
[ 6.58512559 6.58512559 6.58512559 6.58512559 6.58512559 6.58512559
6.58512559 6.58512559 6.58512559]
[ 7.02413396 7.02413396 7.02413396 7.02413396 7.02413396 7.02413396
7.02413396 7.02413396 7.02413396]
[ 7.46314233 7.46314233 7.46314233 7.46314233 7.46314233 7.46314233
7.46314233 7.46314233 7.46314233]
[ 7.9021507 7.9021507 7.9021507 7.9021507 7.9021507 7.9021507
7.9021507 7.9021507 7.9021507 ]
[ 8.34115908 8.34115908 8.34115908 8.34115908 8.34115908 8.34115908
8.34115908 8.34115908 8.34115908]
[ 8.78016745 8.78016745 8.78016745 8.78016745 8.78016745 8.78016745
8.78016745 8.78016745 8.78016745]]
我想以与上面代码中Z或X相同的格式打印Y。如何以这种方式获得卡方函数值？
修改
如果我将函数get_grid_data更改为get_grid_params并重新定义get_grid_data，如下所示，我可以生成81个卡方值。我认为这是向前迈出的一步，但我不确定等高线图所需的res（又名Z）中数组元素的顺序。
def get_grid_params(distribution, frac, size):
"""
This function returns the grid values for a contour plot of the
error metric as a function of the parameters of a specified
distribution.
EX:
func: 'chi square', 'maximum log-likelihood' (error metric)
"""
if distribution == 'gauss':
opt_params = params_gauss
a_vals = get_axis_data(opt_params[0], frac, size)
b_vals = get_axis_data(opt_params[1], frac, size)
X, Y = np.meshgrid(a_vals, b_vals)
# func = np.vectorize(func)
# Z = func(distribution, [X, Y])
return X, Y
def get_grid_data(distribution, frac=1/4, size=9, func=get_chi_square):
"""
"""
X, Y = get_grid_params(distribution, frac, size)
res = []
for idx in range(len(X)):
for jdx in range(len(Y)):
res.append(func(distribution, [X[idx][jdx], Y[idx][jdx]])[0])
print(res)
get_grid_data('gauss')
打印
# 81 elements ==> 9x9 grid
[4208765217.1232886, 79756867.433148235, 2102012.2187297232, 77845.812346977109, 4299.2223157168837, 2529.7286507333743, 20486.858965000847, 257923.37090704756, 4854102.2912357552, 93281349.868633255, 3214630.1060019895, 149308.23999474355, 9526.0996064385563, 892.28204593366377, 1078.7222202890009, 6755.3095776326609, 53291.09528539874, 588864.18413363863, 4691132.998034155, 266721.46912966535, 20459.717521392733, 2093.3255539124393, 279.78284725132187, 577.3737260040574, 3111.9705345888774, 17462.38755758019, 125880.4188491786, 450519.22715869371, 40667.241172187212, 5020.7992346344054, 744.8798302729781, 116.9962855442742, 364.63898596547921, 1791.3456214870084, 7916.7426067634342, 40972.313769493878, 76104.092836489493, 10798.249475713539, 2013.1185415524558, 381.52353083113587, 66.126519584745949, 264.93942984225561, 1200.5798834763946, 4482.867919608283, 18107.837200860213, 21572.225934943446, 4551.094178016996, 1136.7099239043926, 253.51850353558262, 54.455759914884304, 218.13425049819415, 897.03841272531849, 2952.9334085022683, 9936.4277408736034, 9337.1516297669732, 2622.2698023608255, 789.26686546629082, 202.78664001629076, 60.365012999827258, 199.40257099587109, 726.84333101567586, 2159.6632005396755, 6339.5377293121628, 5372.7483380962221, 1815.8139713332946, 620.16531689499118, 184.61780691354744, 75.563465535153725, 196.96163816097214, 626.64757117448494, 1701.8233311097256, 4494.3117008380068, 3664.4699687203392, 1400.0096023072927, 527.65588603959168, 182.94718825996048, 96.20249715692033, 204.59025315045054, 566.75361531867895, 1416.8609878368447, 3434.8994517014899]
# reshape as 9x9 shows the order of params is wrong.
