python - Scipy leastsq: fitting a square grid to experimental points in 2D -

i'm trying use scipy leastsq find best fit of "square" grid set of measured points coordinates in 2-d (the experimental points approximately on square grid).

the parameters of grid pitch (equal x , y), center position (center_x , center_y) , rotation (in degree).

i defined error function calculating euclidean distance each pairs of points (experimental vs ideal grid) , taking mean. want minimize function thorugh leastsq error.

here function definitions:

import numpy np 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 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 use leastsq in way:

leastsq(err_func, x0=(19, 12, 5, 0), args=(xe, ye)) 

but 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 none:     373         epsfcn = finfo(dtype).eps  typeerror: improper input: n=4 must not exceed m=1 

i can't figure out what's problem here :(

since leastsq function assumes err_function return array of residuals docs , little difficult write err_function in manner why not use scipy's function - minimize. add metric - error function have , works. however, think there 1 more typo in get_spot_grid function (y_spots vs y_spads). complete code:

import numpy np 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))