尝试拟合高斯分布：错误 scipy/optimize/minpack.py"，第 765 行，在 curve_fit raise ValueError("`sigma` has incorrect shape.")

Question

我有一个众所周知的问题，但目前无法解决。这是关于 curve_fit 函数：我得到错误：

Error scipy/optimize/minpack.py", line 765, in curve_fit raise ValueError("`sigma` has incorrect shape.")

这是代码，不要对循环 for 小心，它只是我想要 5 个不同的直方图:

for i in range(5):
  mean_o[i] = np.mean(y3[:,i])
  sigma_o[i] = np.std(y3[:,i])

## Histograms
# Number of bins
Nbins=100
binwidth = np.zeros(5)

# Fitting curves
def gaussian(x, a, mean, sigma):
  return a * np.exp(-((x - mean)**2 / (2 * sigma**2)))

for i in range(5):

  binwidth[i] = (max(y3[:,i]) - min(y3[:,i]))/Nbins
  bins_plot = np.arange(min(y3[:,i]), max(y3[:,i]) + binwidth[i], binwidth[i])
  plt.title('Distribution of O observable for redshift bin = '+str(z_ph_fid[i]))
  plt.hist(y3[:,i], bins=bins_plot, label='bin '+str(z_ph_fid[i]))
  plt.legend(loc='upper right')
  # Fitting and plot
  range_fit = np.linspace(min(y3[:,i]), max(y3[:,i]), len(y3[:,i]))
  popt, pcov = curve_fit(gaussian, range_fit, y3[:,i], mean_o[i], sigma_o[i])
  plt.plot(range_fit, gaussian(range_fit, *popt))
  # Save figure
  plt.savefig('chi2_gaussian_bin_'+str(i+1)+'.png')
  plt.close()

第一个直方图 i=0 看起来像：

我想在直方图上绘制红色高斯拟合。

如果有人可以帮我解决这个错误...

Answer 1

OP 有两个问题。

第一个问题是代码试图使随机样本符合正态分布。这是错误的。不过，可以拟合直方图的输出。这显示在下面的代码中。更好的方法是使用 scipy.stats.norm.fit() 来拟合随机样本。这也显示了。

第二个问题是sigma-shape。这里 curve_fit 实际上是期待 y-data 上的错误，这自然需要 y-data 的形状。应该做的是：为拟合提供起始值。这也显示在下面。

代码如下：

import matplotlib.pyplot as plt
import numpy as np

from scipy.stats import norm
from scipy.optimize import curve_fit

mean_o = list()
sigma_o = list()
y3 = list()

### generate some data
for i in range( 5 ):
    y3.append( norm.rvs( size=150000 ) )
y3 = np.transpose( y3 )

for i in range(5):
    mean_o.append( np.mean( y3[ :, i ] ) )
    sigma_o.append(  np.std( y3[ :, i ] ) )

## Histograms
# Number of bins
Nbins=100
binwidth = np.zeros(5)

# Fitting curves
def gaussian( x, a , mean, sigma ):
  return a * np.exp( -( ( x - mean )**2 / (2 * sigma**2 ) ) )

fig = plt.figure()
ax = { i : fig.add_subplot( 2, 3, i+1) for i in range( 5 ) }


for i in range(5):
    ymin = min(y3[:,i])
    ymax = max(y3[:,i])
    binwidth[i] = ( ymax - ymin) / Nbins
    bins_plot = np.arange( ymin, ymax + binwidth[i], binwidth[i])
    histdata = ax[i].hist(
        y3[:,i],
        bins=bins_plot,
        label='bin '+str(i)
    )

    range_fit = np.linspace( ymin, ymax, 250)
    # Fitting and plot version 1
    popt, pcov = curve_fit(
        gaussian,
        0.5 * ( histdata[1][:-1] + histdata[1][1:] ),
        histdata[0],
        p0=( max(histdata[0]), mean_o[i], sigma_o[i] ) )
    ax[i].plot(range_fit, gaussian( range_fit, *popt ) )
    ax[i].axvline( x=mean_o[i], ls=':', c='r' )

    # Fitting and plot version 2
    params = norm.fit( y3[ ::, i ], loc=mean_o[i], scale=sigma_o[i] )
    nth = gaussian(
        range_fit,
        len( y3[::, i]) * binwidth[i] / np.sqrt( 2 * np.pi ),
        *params
    )
    ax[i].plot(range_fit, nth, ls="--" )
plt.tight_layout()
plt.show()

尝试拟合高斯分布：错误 scipy/optimize/minpack.py"，第 765 行，在 curve_fit raise ValueError("`sigma` has incorrect shape.")

Attempt of fit a Gaussian distribution : Error scipy/optimize/minpack.py", line 765, in curve_fit raise ValueError("`sigma` has incorrect shape.")

python

gaussian

curve-fitting

scipy

standard-deviation