如何使用scipy查找优化函数的参数？

Question

我正在尝试复制这篇论文：Global motion estimation from coarsely sampled motion vector field and the applications

我需要找到参数m0, m1, m2....., m7 给定图像x1_1和x1_2以及方程式

Example data.

其中x'{x1_2 [1，：，]]和y'{x1_2 [0，：，]]是x1_2的值， x，y x1_1是相同风格的x1_1。

我已经参考this post中的示例来实现此实现。

有人可以帮我找到这些参数吗？

根据评论和example of leastsq function进行编辑。

下面给出了改变的程序，输出如下

import os
import sys
import numpy as np
import scipy
from scipy.optimize import leastsq


def peval (inp_mat,p):
    m0,m1,m2,m3,m4,m5,m6,m7 = p
    out_mat = np.zeros(inp_mat.shape,dtype=np.float32)
    mid = inp_mat.shape[0]/2
    for xy in range(0,inp_mat.shape[0]):
        if (xy<(inp_mat.shape[0]/2)):
            out_mat[xy] = ( (  (inp_mat[xy+mid]*m0)+(inp_mat[xy]*m1)+ m2 ) /( (inp_mat[xy+mid]*m6)+(inp_mat[xy]*m7)+1 ) )
        else:
            out_mat[xy] = ( (  (inp_mat[xy]*m3)+(inp_mat[xy-mid]*m4)+ m5 ) /( (inp_mat[xy]*m6)+(inp_mat[xy-mid]*m7)+1 ) )
    return out_mat

def residuals(p, out_mat, inp_mat):
    m0,m1,m2,m3,m4,m5,m6,m7 = p
    err=np.zeros(inp_mat.shape,dtype=np.float32)
    if (out_mat.shape == inp_mat.shape):
        for xy in range(0,inp_mat.shape[0]):
            err[xy] =  err[xy]+ (out_mat[xy] -inp_mat[xy])
        return err




f = open('/media/anilil/Data/Datasets/repo/txt_op/vid.txt','r')
x = np.loadtxt(f,dtype=np.int16,comments='#',delimiter='\t')
nof = x.shape[0]/72 # Find the number of frames
x1 = x.reshape(-1,60,40)
x1_1= x1[0,:,:].flatten()
x1_2= x1[1,:,:].flatten()

x= []
y= []

for xy in range(1,50,1):
    y.append(x1[xy,:,:].flatten())
    x.append(x1[xy-1,:,:].flatten())

x=np.array(x,dtype=np.float32)
y=np.array(y,dtype=np.float32)
length =  x1_1.shape#initail guess
p0 = np.array([1,1,1,1,1,1,1,1],dtype=np.float32)

abc=leastsq(residuals, p0,args=(y,x))
print ('Size of first matrix is '+str(x1_1.shape))
print ('Size of first matrix is '+str(x1_2.shape))

print ("Done with program")

输出

ValueError: object too deep for desired array
Traceback (most recent call last):
  File "/media/anilil/Data/charm/mv_clean/.idea/nose_reduction_mpeg.py", line 49, in <module>
    abc=leastsq(residuals, p0,args=(y,x))
  File "/usr/lib/python2.7/dist-packages/scipy/optimize/minpack.py", line 378, in leastsq
    gtol, maxfev, epsfcn, factor, diag)
minpack.error: Result from function call is not a proper array of floats.

Answer 1

查看documentation of leastsq和the example。

您需要定义目标函数，以便将所有参数作为第一个参数，然后是其他输入：

def function (M, inp_mat):
    m0, m1, m2, m3, m4, m5, m6, m7 = M
    out_mat = np.zeros(inp_mat.shape)
    ...

您的案例inp_mat中的其他参数将作为args传递给优化函数：

result = opt.leastsq(function, x0, args=(inp_mat), Dfun=None, full_output=0, col_deriv=0, ftol=1.49012e-08, xtol=1.49012e-08, gtol=0.0, maxfev=0, epsfcn=None, factor=100, diag=None)

我不知道inp_mat应该是什么。很可能它与数据有关，所以args=(x1)可能就是你想要的。

最后，您希望从优化中检索结果并使用它们执行某些操作。