python - 为什么 numpy.polyfit 大幅下降？

Question

我正在尝试使用 np.polyfit适合一个相当简单的数据集，但它有相当大的差距:

还有代码:

import numpy as np
import matplotlib as plt

fit = np.polyfit(xvals, yvals, 1)
f = np.poly1d(fit)
plt.scatter(xvals, yvals, color="blue", label="input")
plt.scatter(xvals, f(yvals), color="red", label="fit")
plt.legend()

我做错了什么？我怎样才能提高契合度？

原始数据:

xvals = array([  0,   1,   2,   3,   4,   5,   7,   8,   9,  10,  11,  12,  14,
                15,  16,  17,  18,  20,  21,  22,  23,  24,  25,  27,  28,  29,
                30,  31,  32,  34,  35,  36,  37,  38,  40,  41,  42,  43,  44,
                45,  47,  48,  49,  50,  51,  52,  54,  55,  56,  57,  58,  60,
                61,  62,  63,  64,  65,  67,  68,  69,  70,  71,  72,  74,  75,
                76,  77,  78,  80,  81,  82,  83,  84,  85,  87,  88,  89,  90,
                91,  92,  94,  95,  96,  97,  98, 100])
yvals = array([  0,   3,   5,   8,  10,  12,  15,  17,  19,  21,  23,  25,  27,
                28,  30,  32,  33,  35,  36,  37,  39,  40,  41,  43,  44,  45,
                46,  47,  48,  49,  50,  51,  52,  53,  54,  54,  55,  56,  57,
                58,  58,  59,  60,  61,  61,  62,  63,  63,  64,  65,  66,  66,
                67,  67,  68,  69,  70,  70,  71,  72,  73,  73,  74,  75,  76,
                77,  77,  78,  79,  80,  81,  82,  83,  84,  85,  86,  87,  89,
                90,  91,  92,  94,  95,  97,  98, 100])

Answer 1

您需要 f(xvals) 而不是 f(yvals)。但是当然你可以用高阶多项式更好地处理这些数据。例如，

import numpy as np
import matplotlib.pyplot as plt

xvals = np.array([  0,   1,   2,   3,   4,   5,   7,   8,   9,  10,  11,  12,  14,
                15,  16,  17,  18,  20,  21,  22,  23,  24,  25,  27,  28,  29,
                30,  31,  32,  34,  35,  36,  37,  38,  40,  41,  42,  43,  44,
                45,  47,  48,  49,  50,  51,  52,  54,  55,  56,  57,  58,  60,
                61,  62,  63,  64,  65,  67,  68,  69,  70,  71,  72,  74,  75,
                76,  77,  78,  80,  81,  82,  83,  84,  85,  87,  88,  89,  90,
                91,  92,  94,  95,  96,  97,  98, 100])
yvals = np.array([  0,   3,   5,   8,  10,  12,  15,  17,  19,  21,  23,  25,  27,
                28,  30,  32,  33,  35,  36,  37,  39,  40,  41,  43,  44,  45,
                46,  47,  48,  49,  50,  51,  52,  53,  54,  54,  55,  56,  57,
                58,  58,  59,  60,  61,  61,  62,  63,  63,  64,  65,  66,  66,
                67,  67,  68,  69,  70,  70,  71,  72,  73,  73,  74,  75,  76,
                77,  77,  78,  79,  80,  81,  82,  83,  84,  85,  86,  87,  89,
                90,  91,  92,  94,  95,  97,  98, 100])

fit = np.polyfit(xvals, yvals, 3)
f = np.poly1d(fit)
#print f
fig, ax = plt.subplots(1,1,figsize=(6,4),dpi=400)
ax.scatter(xvals, yvals, color="blue", label="input")
ax.scatter(xvals, f(xvals), color="red", label="fit")
ax.legend()
plt.show()