python一维插值scipy.interpolate.interp1d

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SciPy的interpolate模块提供了许多对数据进行插值运算的函数，范围涵盖简单的一维插值到复杂多维插值求解。当样本数据变化归因于一个独立的变量时，就使用一维插值；反之样本数据归因于多个独立变量时，使用多维插值。

class scipy.interpolate.interp1d(x, y, kind=’linear’, axis=-1, copy=True, bounds_error=None, fill_value=nan, assume_sorted=False)[source]

Interpolate a 1-D function.

x and y are arrays of values used to approximate some function f: y = f(x). This class returns a function whose call method uses interpolation to find the value of new points.x和y是用来逼近函数f: y = f(x)的值的数组。该类返回一个函数，该函数的调用方法使用插值表达式来查找新点的值。

Note that calling interp1d with NaNs present in input values results in undefined behaviour.注意，使用在输入值中出现的NaNs调用interp1d会导致未定义的行为。

Parameters

x(N,) array_like

A 1-D array of real values.实值的一维数组。

y(…,N,…) array_like

A N-D array of real values. The length of y along the interpolation axis must be equal to the length of x.实值的N-D数组。沿插补轴的y的长度必须等于x的长度。

kind str or int, optional

Specifies the kind of interpolation as a string (‘linear’, ‘nearest’, ‘zero’, ‘slinear’, ‘quadratic’, ‘cubic’, ‘previous’, ‘next’, where ‘zero’, ‘slinear’, ‘quadratic’ and ‘cubic’ refer to a spline interpolation of zeroth, first, second or third order; ‘previous’ and ‘next’ simply return the previous or next value of the point) or as an integer specifying the order of the spline interpolator to use. Default is ‘linear’.指定插值类型为一个字符串(‘ linear ‘， ‘ nearest ‘， ‘ zero ‘， ‘ slinear ‘， ‘ second ‘， ‘ cubic ‘， ‘ previous ‘， ‘ next ‘，其中’ zero ‘， ‘ slinear ‘， ‘ second ‘ and ‘ cubic ‘指的是插值为零、一阶、二阶或三阶的样条曲线;’ previous ‘和’ next ‘简单地返回该点的上一个或下一个值)，或者作为一个整数指定样条插值器使用的顺序。默认设置是“线性”。

axis int, optional

Specifies the axis of y along which to interpolate. Interpolation defaults to the last axis of y.指定要沿其插入的y轴。插值默认是y的最后一个轴。

copy bool, optional

If True, the class makes internal copies of x and y. If False, references to x and y are used. The default is to copy.如果为真，则该类将创建x和y的内部副本。如果为假，则使用对x和y的引用。默认是复制。

bounds_error bool, optional

If True, a ValueError is raised any time interpolation is attempted on a value outside of the range of x (where extrapolation is necessary). If False, out of bounds values are assigned fill_value. By default, an error is raised unless fill_value="extrapolate".如果为真，则在试图对x范围之外的值进行插值时(需要外推的地方)会产生ValueError。如果为假，则为越界值分配fill_value。默认情况下，除非fill_value=”extrapolate”，否则将引发一个错误。

fill_value array-like or (array-like, array_like) or “extrapolate”, optional

• if a ndarray (or float), this value will be used to fill in for requested points outside of the data range. If not provided, then the default is NaN. The array-like must broadcast properly to the dimensions of the non-interpolation axes.如果是ndarray(或float)，则此值将用于填充数据范围之外的请求点。如果没有提供，那么缺省值是NaN。类数组必须正确地传播到非插值轴的维度。
• If a two-element tuple, then the first element is used as a fill value for x_new < x[0] and the second element is used forx_new > x[-1]. Anything that is not a 2-element tuple (e.g., list or ndarray, regardless of shape) is taken to be a single array-like argument meant to be used for both bounds asbelow, above = fill_value, fill_value.如果是双元素元组，则第一个元素用作x_new < x[0]的填充值，第二个元素用作forx_new > x[-1]。任何非2元素元组(例如list或ndarray，无论其形状如何)的内容都被视为一个类似数组的参数，用于下面、上面的两个边界= fill_value、fill_value。 New in version 0.17.0.
• If “extrapolate”, then points outside the data range will be extrapolated.如果“外推”，则外推数据范围之外的点。 New in version 0.17.0.

assume_sorted bool, optional

If False, values of x can be in any order and they are sorted first. If True, x has to be an array of monotonically increasing values.如果为假，则x的值可以是任意顺序的，并且可以先排序。如果为真，则x必须是一个值单调递增的数组。

>>> import numpy as np
>>> import matplotlib.pyplot as pl
>>> from scipy.interpolate import interp1d
>>> 
>>> x=np.linspace(0,10,11)
>>> y=np.sin(x)
>>> x
array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.])
>>> y
array([ 0.        ,  0.84147098,  0.90929743,  0.14112001, -0.7568025 ,
       -0.95892427, -0.2794155 ,  0.6569866 ,  0.98935825,  0.41211849,
       -0.54402111])
>>> pl.plot(x,y,"o")
[<matplotlib.lines.Line2D object at 0x000000000AE3BF48>]
>>> pl.show()

python一维插值scipy.interpolate.interp1d

>>> x_new = np.linspace(0, 10, 101)
>>> x_new
array([ 0. ,  0.1,  0.2,  0.3,  0.4,  0.5,  0.6,  0.7,  0.8,  0.9,  1. ,
        1.1,  1.2,  1.3,  1.4,  1.5,  1.6,  1.7,  1.8,  1.9,  2. ,  2.1,
        2.2,  2.3,  2.4,  2.5,  2.6,  2.7,  2.8,  2.9,  3. ,  3.1,  3.2,
        3.3,  3.4,  3.5,  3.6,  3.7,  3.8,  3.9,  4. ,  4.1,  4.2,  4.3,
        4.4,  4.5,  4.6,  4.7,  4.8,  4.9,  5. ,  5.1,  5.2,  5.3,  5.4,
        5.5,  5.6,  5.7,  5.8,  5.9,  6. ,  6.1,  6.2,  6.3,  6.4,  6.5,
        6.6,  6.7,  6.8,  6.9,  7. ,  7.1,  7.2,  7.3,  7.4,  7.5,  7.6,
        7.7,  7.8,  7.9,  8. ,  8.1,  8.2,  8.3,  8.4,  8.5,  8.6,  8.7,
        8.8,  8.9,  9. ,  9.1,  9.2,  9.3,  9.4,  9.5,  9.6,  9.7,  9.8,
        9.9, 10. ])
>>> 
>>> kind_lst = ['nearest', 'zero', 'slinear', 'cubic', 'previous',  'next']
>>> for k in kind_lst:
	f = interp1d(x,y,kind=k)
	y_new = f(x_new)
	pl.plot(x_new, y_new, label=k)

	
[<matplotlib.lines.Line2D object at 0x000000000F74CE08>]
[<matplotlib.lines.Line2D object at 0x000000000F6FF948>]
[<matplotlib.lines.Line2D object at 0x000000000DC41908>]
[<matplotlib.lines.Line2D object at 0x000000000F757FC8>]
[<matplotlib.lines.Line2D object at 0x000000000F6FF808>]
[<matplotlib.lines.Line2D object at 0x000000000F6F3908>]
>>> 
>>> pl.legend(loc="lower right")
<matplotlib.legend.Legend object at 0x000000000DEC9C08>
>>> pl.show()
>>> 

python一维插值scipy.interpolate.interp1d

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