pandas 两个数据点之间的线性插值
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linear interpolation between two data points
提问by Al_Iskander
I have two data points xand y:
我有两个数据点x和y：
x = 5 (value corresponding to 95%)
y = 17 (value corresponding to 102.5%)
No I would like to calculate the value for xiwhich should correspond to 100%.
不，我想计算xi应对应于 100% 的值。
x = 5 (value corresponding to 95%)
xi = ?? (value corresponding to 100%)
y = 17 (value corresponding to 102.5%)
How should I do this using python?
我应该如何使用 python 做到这一点？
回答by MaxU
is that what you want?
那是你要的吗？
In [145]: s = pd.Series([5, np.nan, 17], index=[95, 100, 102.5])
In [146]: s
Out[146]:
95.0 5.0
100.0 NaN
102.5 17.0
dtype: float64
In [147]: s.interpolate(method='index')
Out[147]:
95.0 5.0
100.0 13.0
102.5 17.0
dtype: float64
回答by Tim
We can easily plot this on a graph without Python:
我们可以在没有 Python 的情况下轻松地将其绘制在图形上：
This shows us what the answer should be (13).
这向我们展示了答案应该是什么（13）。
But how do we calculate this? First, we find the gradient with this:
但是我们如何计算呢？首先，我们找到梯度：
The numbers substituted into the equation give this:
代入方程的数字给出了这个：
So we know for 0.625 we increase the Y value by, we increase the X value by 1.
所以我们知道对于 0.625，我们将 Y 值增加了，我们将 X 值增加了 1。
We've been given that Y is 100. We know that 102.5 relates to 17. 100 - 102.5 = -2.5. -2.5 / 0.625 = -4and then 17 + -4 = 13.
我们已经知道 Y 是 100。我们知道 102.5 与 17 相关100 - 102.5 = -2.5。-2.5 / 0.625 = -4然后17 + -4 = 13。
This also works with the other numbers: 100 - 95 = 5, 5 / 0.625 = 8, 5 + 8 = 13.
这也适用于其他数字：100 - 95 = 5, 5 / 0.625 = 8, 5 + 8 = 13。
We can also go backwards using the reciprocal of the gradient (1 / m).
我们也可以使用梯度的倒数 ( 1 / m)倒退。
We've been given that X is 13. We know that 102.5 relates to 17. 13 - 17 = -4. -4 / 0.625 = -2.5and then 102.5 + -2.5 = 100.
我们已经知道 X 是 13。我们知道 102.5 与 17 相关13 - 17 = -4。-4 / 0.625 = -2.5然后102.5 + -2.5 = 100。
How do we do this in python?
我们如何在python中做到这一点？
def findXPoint(xa,xb,ya,yb,yc):
m = (xa - xb) / (ya - yb)
xc = (yc - yb) * m + xb
return
And to find a Y point given the X point:
并在给定 X 点的情况下找到 Y 点：
def findYPoint(xa,xb,ya,yb,xc):
m = (ya - yb) / (xa - xb)
yc = (xc - xb) * m + yb
return yc
This function will also extrapolate from the data points.
此函数还将根据数据点进行推断。
回答by Vlad Bezden
You can use numpy.interpfunction to interpolate a value
您可以使用numpy.interp函数来插入一个值
import numpy as np
import matplotlib.pyplot as plt
x = [95, 102.5]
y = [5, 17]
x_new = 100
y_new = np.interp(x_new, x, y)
print(y_new)
# 13.0
plt.plot(x, y, "og-", x_new, y_new, "or");
