I'm trying to use Scipy leastsq to find the best fit of a "square" grid for a set of measured points coordinates in 2-D (the experimental points are approximately on a square grid).
The parameters of the grid are pitch (equal for x and y), the center position (center_x and center_y) and rotation (in degree).
I defined an error function calculating the euclidean distance for each pairs of points (experimental vs ideal grid) and taking the mean. I want to minimize this function thorugh leastsq but I get an error.
Here are the function definitions:
import numpy as np
from scipy.optimize import leastsq
def get_spot_grid(shape, pitch, center_x, center_y, rotation=0):
x_spots, y_spots = np.meshgrid(
(np.arange(shape[1]) - (shape[1]-1)/2.)*pitch,
(np.arange(shape[0]) - (shape[0]-1)/2.)*pitch)
theta = rotation/180.*np.pi
x_spots = x_spots*np.cos(theta) - y_spots*np.sin(theta) + center_x
y_spads = x_spots*np.sin(theta) + y_spots*np.cos(theta) + center_y
return x_spots, y_spots
def get_mean_distance(x1, y1, x2, y2):
return np.sqrt((x1 - x2)**2 + (y1 - y2)**2).mean()
def err_func(params, xe, ye):
pitch, center_x, center_y, rotation = params
x_grid, y_grid = get_spot_grid(xe.shape, pitch, center_x, center_y, rotation)
return get_mean_distance(x_grid, y_grid, xe, ye)
This are the experimental coordinates:
xe = np.array([ -23.31, -4.01, 15.44, 34.71, -23.39, -4.10, 15.28, 34.60, -23.75, -4.38, 15.07, 34.34, -23.91, -4.53, 14.82, 34.15]).reshape(4, 4)
ye = np.array([-16.00, -15.81, -15.72, -15.49, 3.29, 3.51, 3.90, 4.02, 22.75, 22.93, 23.18, 23.43, 42.19, 42.35, 42.69, 42.87]).reshape(4, 4)
I try to use leastsq in this way:
leastsq(err_func, x0=(19, 12, 5, 0), args=(xe, ye))
but I get the following error:
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-19-ee91cf6ce7d6> in <module>()
----> 1 leastsq(err_func, x0=(19, 12, 5, 0), args=(xe, ye))
C:\Anaconda\lib\site-packages\scipy\optimize\minpack.pyc in leastsq(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol, gtol, maxfev, epsfcn, factor, diag)
369 m = shape[0]
370 if n > m:
--> 371 raise TypeError('Improper input: N=%s must not exceed M=%s' % (n, m))
372 if epsfcn is None:
373 epsfcn = finfo(dtype).eps
TypeError: Improper input: N=4 must not exceed M=1
I can't figure out what's the problem here :(
Since the leastsq function assumes that the err_function return an array of residuals docs and it is a little difficult to write the err_function in this manner why not use another scipy's function - minimize. Then you add your metric - the error function you already have and it works. However, I think there is one more typo in get_spot_grid function (y_spots vs y_spads). The complete code:
import numpy as np
from scipy.optimize import leastsq, minimize
def get_spot_grid(shape, pitch, center_x, center_y, rotation=0):
x_spots, y_spots = np.meshgrid(
(np.arange(shape[1]) - (shape[1]-1)/2.)*pitch,
(np.arange(shape[0]) - (shape[0]-1)/2.)*pitch)
theta = rotation/180.*np.pi
x_spots = x_spots*np.cos(theta) - y_spots*np.sin(theta) + center_x
y_spots = x_spots*np.sin(theta) + y_spots*np.cos(theta) + center_y
return x_spots, y_spots
def get_mean_distance(x1, y1, x2, y2):
return np.sqrt((x1 - x2)**2 + (y1 - y2)**2).mean()
def err_func(params, xe, ye):
pitch, center_x, center_y, rotation = params
x_grid, y_grid = get_spot_grid(xe.shape, pitch, center_x, center_y, rotation)
return get_mean_distance(x_grid, y_grid, xe, ye)
xe = np.array([-23.31, -4.01, 15.44, 34.71, -23.39, -4.10, 15.28, 34.60, -23.75, -4.38, 15.07, 34.34, -23.91, -4.53, 14.82, 34.15]).reshape(4, 4)
ye = np.array([-16.00, -15.81, -15.72, -15.49, 3.29, 3.51, 3.90, 4.02, 22.75, 22.93, 23.18, 23.43, 42.19, 42.35, 42.69, 42.87]).reshape(4, 4)
# leastsq(err_func, x0=(19, 12, 5, 0), args=(xe, ye))
minimize(err_func, x0=(19, 12, 5, 0), args=(xe, ye))