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

Question

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 de…

Accepted Answer

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))
```

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

Solution

Problem