numpy中的norm()函數求範數範例

2023-02-05 14:01:48

numpy norm()函數求範數

函數：

norm(x, ord = None, axis = None, keepdims = False)

ord表示求什麼型別的範數

舉例說明

import numpy as np

x = [1,2,3,4]
x1 = np.linalg.norm(x=x, ord=1)
x2 = np.linalg.norm(x=x, ord=2)
x3 = np.linalg.norm(x=x, ord=np.inf)
print(x1)
print(x2)
print(x3)

執行結果：

axis=0表示對矩陣的每一列求範數，axis=1表示對矩陣的每一行求範數， keeptdims=True表示結果保留二維特性，keepdims=False表示結果不保留二維特性

import numpy as np

x = np.array([[0, 1, 2],
              [3, 4, 5]])
x1 = np.linalg.norm(x=x, ord=1, axis=0, keepdims=True)
x2 = np.linalg.norm(x=x, ord=1, axis=1, keepdims=True)
x3 = np.linalg.norm(x=x, ord=1, axis=0, keepdims=False)
x4 = np.linalg.norm(x=x, ord=1, axis=1, keepdims=False)

print(x1)
print(x2)
print(x3)
print(x4)

執行結果：

numpy求解範數(numpy.linalg.norm)以及各階範數詳解

numpy.linalg.norm

語法

numpy.linalg.norm(x,ord=None,axis=None,keepdims=False)

Parameters

x: array_like

Input array. If axis is None, x must be 1-D or 2-D, unless ord is None. If both axis and ord are None, the 2-norm of x.ravel will be returned.

X是輸入的array, array的情況必須是以下三種情況之一:

axis未指定，ord指定。此時x必須是一維或二維陣列
axis指定，x任意
axis未指定，ord未指定，此時x任意，返回值為x被展平後的一維向量x.ravel的二範數。

ord：{non-zero int, inf, -inf, ‘fro’, ‘nuc’}, optional

Order of the norm (see table under Notes). inf means numpy’s inf object. The default is None.

範數的階數，可以不指定。預設為None。inf代表無窮大，-inf為無窮小。

可選的階數見下圖：

axis:{None, int, 2-tuple of ints},optional

If axis is an integer, it specifies the axis of x along which to compute the vector norms. If axis is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed. If axis is None then either a vector norm (when x is 1-D) or a matrix norm (when x is 2-D) is returned. The default is None.

如果axis是整數，指定了一個維度，在該維度上按照向量進行範數計算。如果是一個二元整陣列，指定了兩個維度，在指定的這兩個維度上可以構成矩陣。

對這些矩陣進行計算。如果沒有指定axis,那麼對於一維輸入返回其向量形式的範數計算值，對於二維輸入返回其矩陣形式的範數。預設值為None

keepdims: bool, optional

If this is set to True, the axes which are normed over are left in the result as dimensions with size one. With this option the result will broadcast correctly against the original x.

如果keepdims=True，被指定計算範數的維度將在返回結果中保留，其size為1。計算結果會在該維度上進行broadcast