Python 基于三维数据和参数的Scipy曲线拟合

我正在用scipy拟合3d分布函数。我有一个numpy数组，它的计数在x和y-bins中，我正试图将其与一个相当复杂的三维分布函数相匹配。数据符合26个（！）参数，这些参数描述了其两个组成种群的形状

from scipy.optimize import curve_fit
import numpy as np

# 4 dimensional colville function
# definition from http://www.sfu.ca/~ssurjano/colville.html
def colville(x,x3,x4):
    x1,x2 = x[:,0],x[:,1]
    return 100*(x1**2 - x2)**2 + (x1-1)**2 + (x3-1)**2 + \
            90*(x3**2 - x4)**2 + \
            10.1*((x2 - 1)**2 + (x4 - 1)**2) + \
            19.8*(x2 - 1)*(x4 - 1)
#generate some random data slightly off

datax = np.array([[x,x] for x in range(-10,10)])
#add gaussian noise
datax+= np.random.rand(*datax.shape)
#set 2 of the 4 parameters to constants
x3 = 3.5
x4 = 4.5
#calculate the function
dataz = colville(datax, x3, x4)
#fit the function
optimalparams, covmatrix = curve_fit(colville, datax, dataz)
print 'opt:',optimalparams

我在这里学到了，当我调用leastsq时，我必须将x坐标和y坐标作为“args”传递。unutbu提供的代码与为我编写的代码一样有效，但当我尝试将其应用于我的特定案例时，出现了错误“TypeError:leastsq（）为关键字参数'args'获取了多个值”

from scipy.optimize import curve_fit
import numpy as np

# 4 dimensional colville function
# definition from http://www.sfu.ca/~ssurjano/colville.html
def colville(x,x3,x4):
    x1,x2 = x[:,0],x[:,1]
    return 100*(x1**2 - x2)**2 + (x1-1)**2 + (x3-1)**2 + \
            90*(x3**2 - x4)**2 + \
            10.1*((x2 - 1)**2 + (x4 - 1)**2) + \
            19.8*(x2 - 1)*(x4 - 1)
#generate some random data slightly off

datax = np.array([[x,x] for x in range(-10,10)])
#add gaussian noise
datax+= np.random.rand(*datax.shape)
#set 2 of the 4 parameters to constants
x3 = 3.5
x4 = 4.5
#calculate the function
dataz = colville(datax, x3, x4)
#fit the function
optimalparams, covmatrix = curve_fit(colville, datax, dataz)
print 'opt:',optimalparams

这是我的代码（很抱歉这么长）：

from scipy.optimize import curve_fit
import numpy as np

# 4 dimensional colville function
# definition from http://www.sfu.ca/~ssurjano/colville.html
def colville(x,x3,x4):
    x1,x2 = x[:,0],x[:,1]
    return 100*(x1**2 - x2)**2 + (x1-1)**2 + (x3-1)**2 + \
            90*(x3**2 - x4)**2 + \
            10.1*((x2 - 1)**2 + (x4 - 1)**2) + \
            19.8*(x2 - 1)*(x4 - 1)
#generate some random data slightly off

datax = np.array([[x,x] for x in range(-10,10)])
#add gaussian noise
datax+= np.random.rand(*datax.shape)
#set 2 of the 4 parameters to constants
x3 = 3.5
x4 = 4.5
#calculate the function
dataz = colville(datax, x3, x4)
#fit the function
optimalparams, covmatrix = curve_fit(colville, datax, dataz)
print 'opt:',optimalparams

这是我的数据，只是箱子少了一些：

[[  1.00000000e+01   1.10000000e+01   2.10000000e+01   1.90000000e+01
1.70000000e+01   2.10000000e+01   2.40000000e+01   1.90000000e+01
2.80000000e+01   1.90000000e+01]
[  1.40000000e+01   4.50000000e+01   6.00000000e+01   6.80000000e+01
1.34000000e+02   1.97000000e+02   2.23000000e+02   2.90000000e+02
3.23000000e+02   3.03000000e+02]
[  3.00000000e+01   1.17000000e+02   3.78000000e+02   9.74000000e+02
1.71900000e+03   2.27700000e+03   2.39000000e+03   2.25500000e+03
1.85600000e+03   1.31000000e+03]
[  1.52000000e+02   9.32000000e+02   2.89000000e+03   5.23800000e+03
6.66200000e+03   6.19100000e+03   4.54900000e+03   3.14600000e+03
2.09000000e+03   1.33800000e+03]
[  5.39000000e+02   2.58100000e+03   6.51300000e+03   8.89900000e+03
8.52900000e+03   6.22900000e+03   3.55000000e+03   2.14300000e+03
1.19000000e+03   6.92000000e+02]
[  1.49600000e+03   4.49200000e+03   8.77200000e+03   1.07610000e+04
9.76700000e+03   7.04900000e+03   4.23200000e+03   2.47200000e+03
1.41500000e+03   7.02000000e+02]
[  2.31800000e+03   7.01500000e+03   1.28870000e+04   1.50840000e+04
1.35590000e+04   8.55600000e+03   4.15600000e+03   1.77100000e+03
6.57000000e+02   2.55000000e+02]
[  1.57500000e+03   3.79300000e+03   5.20900000e+03   4.77800000e+03
3.26600000e+03   1.44700000e+03   5.31000000e+02   1.85000000e+02
9.30000000e+01   4.90000000e+01]
[  7.01000000e+02   1.21600000e+03   1.17600000e+03   7.93000000e+02
4.79000000e+02   2.02000000e+02   8.80000000e+01   3.90000000e+01
2.30000000e+01   1.90000000e+01]
[  2.93000000e+02   3.93000000e+02   2.90000000e+02   1.97000000e+02
1.18000000e+02   6.40000000e+01   4.10000000e+01   1.20000000e+01
1.10000000e+01   4.00000000e+00]]

from scipy.optimize import curve_fit
import numpy as np

# 4 dimensional colville function
# definition from http://www.sfu.ca/~ssurjano/colville.html
def colville(x,x3,x4):
    x1,x2 = x[:,0],x[:,1]
    return 100*(x1**2 - x2)**2 + (x1-1)**2 + (x3-1)**2 + \
            90*(x3**2 - x4)**2 + \
            10.1*((x2 - 1)**2 + (x4 - 1)**2) + \
            19.8*(x2 - 1)*(x4 - 1)
#generate some random data slightly off

datax = np.array([[x,x] for x in range(-10,10)])
#add gaussian noise
datax+= np.random.rand(*datax.shape)
#set 2 of the 4 parameters to constants
x3 = 3.5
x4 = 4.5
#calculate the function
dataz = colville(datax, x3, x4)
#fit the function
optimalparams, covmatrix = curve_fit(colville, datax, dataz)
print 'opt:',optimalparams

---

非常感谢

那么

leastsq

所做的就是尝试：

from scipy.optimize import curve_fit
import numpy as np

# 4 dimensional colville function
# definition from http://www.sfu.ca/~ssurjano/colville.html
def colville(x,x3,x4):
    x1,x2 = x[:,0],x[:,1]
    return 100*(x1**2 - x2)**2 + (x1-1)**2 + (x3-1)**2 + \
            90*(x3**2 - x4)**2 + \
            10.1*((x2 - 1)**2 + (x4 - 1)**2) + \
            19.8*(x2 - 1)*(x4 - 1)
#generate some random data slightly off

datax = np.array([[x,x] for x in range(-10,10)])
#add gaussian noise
datax+= np.random.rand(*datax.shape)
#set 2 of the 4 parameters to constants
x3 = 3.5
x4 = 4.5
#calculate the function
dataz = colville(datax, x3, x4)
#fit the function
optimalparams, covmatrix = curve_fit(colville, datax, dataz)
print 'opt:',optimalparams

“最小化一组方程的平方和” -

from scipy.optimize import curve_fit
import numpy as np

# 4 dimensional colville function
# definition from http://www.sfu.ca/~ssurjano/colville.html
def colville(x,x3,x4):
    x1,x2 = x[:,0],x[:,1]
    return 100*(x1**2 - x2)**2 + (x1-1)**2 + (x3-1)**2 + \
            90*(x3**2 - x4)**2 + \
            10.1*((x2 - 1)**2 + (x4 - 1)**2) + \
            19.8*(x2 - 1)*(x4 - 1)
#generate some random data slightly off

datax = np.array([[x,x] for x in range(-10,10)])
#add gaussian noise
datax+= np.random.rand(*datax.shape)
#set 2 of the 4 parameters to constants
x3 = 3.5
x4 = 4.5
#calculate the function
dataz = colville(datax, x3, x4)
#fit the function
optimalparams, covmatrix = curve_fit(colville, datax, dataz)
print 'opt:',optimalparams

正如它所说的，它是最小化一组函数，因此实际上没有以最简单的方式接受任何x或y数据输入，如果你看参数，那么你可以随心所欲地做，然后传递一个剩余函数，使用

curve\u fit

曲线拟合（它为您提供了这样的功能：）并创建必要的方程式要简单得多

from scipy.optimize import curve_fit
import numpy as np

# 4 dimensional colville function
# definition from http://www.sfu.ca/~ssurjano/colville.html
def colville(x,x3,x4):
    x1,x2 = x[:,0],x[:,1]
    return 100*(x1**2 - x2)**2 + (x1-1)**2 + (x3-1)**2 + \
            90*(x3**2 - x4)**2 + \
            10.1*((x2 - 1)**2 + (x4 - 1)**2) + \
            19.8*(x2 - 1)*(x4 - 1)
#generate some random data slightly off

datax = np.array([[x,x] for x in range(-10,10)])
#add gaussian noise
datax+= np.random.rand(*datax.shape)
#set 2 of the 4 parameters to constants
x3 = 3.5
x4 = 4.5
#calculate the function
dataz = colville(datax, x3, x4)
#fit the function
optimalparams, covmatrix = curve_fit(colville, datax, dataz)
print 'opt:',optimalparams

对于拟合，您应该使用：如果您对他们使用的通用残差没有异议，那么实际上就是您传递给自己的函数

res=leastsq（func，p0，args=args，full_output=1，**kw）

，如果您查看

from scipy.optimize import curve_fit
import numpy as np

# 4 dimensional colville function
# definition from http://www.sfu.ca/~ssurjano/colville.html
def colville(x,x3,x4):
    x1,x2 = x[:,0],x[:,1]
    return 100*(x1**2 - x2)**2 + (x1-1)**2 + (x3-1)**2 + \
            90*(x3**2 - x4)**2 + \
            10.1*((x2 - 1)**2 + (x4 - 1)**2) + \
            19.8*(x2 - 1)*(x4 - 1)
#generate some random data slightly off

datax = np.array([[x,x] for x in range(-10,10)])
#add gaussian noise
datax+= np.random.rand(*datax.shape)
#set 2 of the 4 parameters to constants
x3 = 3.5
x4 = 4.5
#calculate the function
dataz = colville(datax, x3, x4)
#fit the function
optimalparams, covmatrix = curve_fit(colville, datax, dataz)
print 'opt:',optimalparams

e、 g.如果我在2d中拟合rosenbrock函数并猜测y参数：

from scipy.optimize import curve_fit
from itertools import imap
import numpy as np
# use only an even number of arguments
def rosen2d(x,a):
    return (1-x)**2 + 100*(a - (x**2))**2
#generate some random data slightly off

datax = np.array([.01*x for x in range(-10,10)])
datay = 2.3
dataz = np.array(map(lambda x: rosen2d(x,datay), datax))
optimalparams, covmatrix = curve_fit(rosen2d, datax, dataz)
print 'opt:',optimalparams

from scipy.optimize import curve_fit
import numpy as np

# 4 dimensional colville function
# definition from http://www.sfu.ca/~ssurjano/colville.html
def colville(x,x3,x4):
    x1,x2 = x[:,0],x[:,1]
    return 100*(x1**2 - x2)**2 + (x1-1)**2 + (x3-1)**2 + \
            90*(x3**2 - x4)**2 + \
            10.1*((x2 - 1)**2 + (x4 - 1)**2) + \
            19.8*(x2 - 1)*(x4 - 1)
#generate some random data slightly off

datax = np.array([[x,x] for x in range(-10,10)])
#add gaussian noise
datax+= np.random.rand(*datax.shape)
#set 2 of the 4 parameters to constants
x3 = 3.5
x4 = 4.5
#calculate the function
dataz = colville(datax, x3, x4)
#fit the function
optimalparams, covmatrix = curve_fit(colville, datax, dataz)
print 'opt:',optimalparams

在4d中拟合colville函数：

from scipy.optimize import curve_fit
import numpy as np

# 4 dimensional colville function
# definition from http://www.sfu.ca/~ssurjano/colville.html
def colville(x,x3,x4):
    x1,x2 = x[:,0],x[:,1]
    return 100*(x1**2 - x2)**2 + (x1-1)**2 + (x3-1)**2 + \
            90*(x3**2 - x4)**2 + \
            10.1*((x2 - 1)**2 + (x4 - 1)**2) + \
            19.8*(x2 - 1)*(x4 - 1)
#generate some random data slightly off

datax = np.array([[x,x] for x in range(-10,10)])
#add gaussian noise
datax+= np.random.rand(*datax.shape)
#set 2 of the 4 parameters to constants
x3 = 3.5
x4 = 4.5
#calculate the function
dataz = colville(datax, x3, x4)
#fit the function
optimalparams, covmatrix = curve_fit(colville, datax, dataz)
print 'opt:',optimalparams

使用自定义残差函数：

from scipy.optimize import curve_fit
import numpy as np

# 4 dimensional colville function
# definition from http://www.sfu.ca/~ssurjano/colville.html
def colville(x,x3,x4):
    x1,x2 = x[:,0],x[:,1]
    return 100*(x1**2 - x2)**2 + (x1-1)**2 + (x3-1)**2 + \
            90*(x3**2 - x4)**2 + \
            10.1*((x2 - 1)**2 + (x4 - 1)**2) + \
            19.8*(x2 - 1)*(x4 - 1)
#generate some random data slightly off

datax = np.array([[x,x] for x in range(-10,10)])
#add gaussian noise
datax+= np.random.rand(*datax.shape)
#set 2 of the 4 parameters to constants
x3 = 3.5
x4 = 4.5
#calculate the function
dataz = colville(datax, x3, x4)
#fit the function
optimalparams, covmatrix = curve_fit(colville, datax, dataz)
print 'opt:',optimalparams

from scipy.optimize import leastsq
import numpy as np

# 4 dimensional colville function
# definition from http://www.sfu.ca/~ssurjano/colville.html
def colville(x,x3,x4):
    x1,x2 = x[:,0],x[:,1]
    return 100*(x1**2 - x2)**2 + (x1-1)**2 + (x3-1)**2 + \
            90*(x3**2 - x4)**2 + \
            10.1*((x2 - 1)**2 + (x4 - 1)**2) + \
            19.8*(x2 - 1)*(x4 - 1)
#generate some random data slightly off


datax = np.array([[x,x] for x in range(-10,10)])
#add gaussian noise
datax+= np.random.rand(*datax.shape)
#set 2 of the 4 parameters to constants
x3 = 3.5
x4 = 4.5

def residual(p, x, y):
    return y - colville(x,*p)
#calculate the function
dataz = colville(datax, x3, x4)
#guess some initial parameter values
p0 = [0,0]
#calculate a minimization of the residual
optimalparams = leastsq(residual, p0, args=(datax, dataz))[0]
print 'opt:',optimalparams

---

编辑：您同时使用了位置和关键字arg作为

args

：如果查看，您将看到它使用位置3，但也可以用作关键字参数。您同时使用了这两个选项，这意味着函数与预期的一样混乱。

您介意为数据添加标签吗？e、 上面一节中的自变量和因变量。添加了一些注释来解释x和yno。我的意思是，您的代码目前甚至不可运行，并且您没有标记它以使其易于运行。最好的代码片段是可以复制的短代码片段。我了解leastsq的功能，我之所以使用它，是因为我可以定义一个自定义的残差（最终，我将合并参数约束）。所以，我的第二段代码中的数据是因变量，我试图用一个从x&y到H的函数来拟合它。给出了一个使用这种技术的例子。据我所知，“参数”作为拟合的一部分传递给“残差”，而“参数”只是用作拟合的输入。我的问题是我收到了上面的类型错误。@EiyrioüHi，我如何才能获得您的邮件id或联系人？我在寻找最佳拟合曲面函数方面遇到了很大的困难。如果你能帮我一点忙，我将不胜感激。谢谢，我道歉，我没有说出来-试着问一个带着scipy标签的问题好吗？

from scipy.optimize import curve_fit
import numpy as np

# 4 dimensional colville function
# definition from http://www.sfu.ca/~ssurjano/colville.html
def colville(x,x3,x4):
    x1,x2 = x[:,0],x[:,1]
    return 100*(x1**2 - x2)**2 + (x1-1)**2 + (x3-1)**2 + \
            90*(x3**2 - x4)**2 + \
            10.1*((x2 - 1)**2 + (x4 - 1)**2) + \
            19.8*(x2 - 1)*(x4 - 1)
#generate some random data slightly off

datax = np.array([[x,x] for x in range(-10,10)])
#add gaussian noise
datax+= np.random.rand(*datax.shape)
#set 2 of the 4 parameters to constants
x3 = 3.5
x4 = 4.5
#calculate the function
dataz = colville(datax, x3, x4)
#fit the function
optimalparams, covmatrix = curve_fit(colville, datax, dataz)
print 'opt:',optimalparams