scipy.optimize.curve_fit报TypeError参数超数据量问题排查

你触发报错的核心原因是scipy.optimize.curve_fit的输入格式不符合要求：

• curve_fit默认要求待拟合函数返回一维数组，同时传入的目标值也必须是相同长度的一维数组
• 你当前的px_to_mm_v4返回的是(x坐标数组, y坐标数组)的二元组，curve_fit会误判你只有2个数据点（也就是报错里的M=2），远少于要优化的7个参数，因此触发参数数量不匹配的错误。

另外你代码里的2D点旋转公式存在笔误，y坐标旋转的计算式第一个三角函数项应该是math.sin，而非math.cos，如果不修正会导致拟合结果完全偏离预期。

from scipy import optimize
import numpy as np
import math

def px_to_mm_v4(coords, cf_x, cf_y, nudge_x, nudge_y, center_x, center_y, rotate_degrees):
    
    ## set lower left loc
    ll_x = center_x - (127.76/2/cf_x) ## lower left x location in pixels
    ll_y = center_y + (85.47/2/cf_y) ## lower left y location in pixels
    
    ## unpack coordinates
    x,y = coords
    
    ## rotate points around center
    rotate_radians = math.radians(rotate_degrees)
    x_rotated = center_x + math.cos(rotate_radians) * (x - center_x) - math.sin(rotate_radians) * (y - center_y)
    # 修正旋转公式的笔误，第一项改为sin
    y_rotated = center_y + math.sin(rotate_radians) * (x - center_x) + math.cos(rotate_radians) * (y - center_y)
    
    ## convert px to mm
    x_converted = (x_rotated - ll_x) * cf_x + nudge_x
    y_converted = (ll_y - y_rotated) * cf_y + nudge_y

    # 把返回值打平为一维数组，适配curve_fit要求
    return np.ravel([x_converted, y_converted])


x_px = np.array([1723,1530,1334,1135,943,747,548,2520,2322,2120,1921,1726,1530,1331,1132,937,741,545,346,349,352,355,358,358,361,361,148])
y_px = np.array([596,791,986,1176,1373,1569,1769,1973,1967,1967,1964,1962,1964,1967,1967,1967,1962,1964,1967,1769,1569,1373,1178,986,791,602,2162])

x_mm = np.array([80,70,60,50,40,30,20,120,110,100,90,80,70,60,50,40,30,20,10,10,10,10,10,10,10,10,0])
y_mm = np.array([80,70,60,50,40,30,20,10,10,10,10,10,10,10,10,10,10,10,10,20,30,40,50,60,70,80,0])
test_coords_tup = (x_px,y_px)
# 目标值也打平为一维数组，和函数返回值长度一致（27*2=54个数据点，远大于7个待优化参数）
points_to_fit = np.ravel([x_mm, y_mm])

cf_x_test = 0.05072
cf_y_test = 0.05076
nudge_x_test = -2.2
nudge_y_test = 2.1
center_x_test = 1374
center_y_test = 1290
rotate_degrees_test = 1.4

params0 = [cf_x_test,cf_y_test,nudge_x_test,nudge_y_test,center_x_test,center_y_test,rotate_degrees_test]

popt, pcov = optimize.curve_fit(px_to_mm_v4, test_coords_tup, points_to_fit, p0=params0)
# 输出优化后的参数
print("优化后参数：", popt)

内容的提问来源于stack exchange，提问作者cbcbcbc