在Python中使用复数数组的拉盖尔多项式生成Vandermonde矩阵

在Python中使用复数数组的拉盖尔多项式生成Vandermonde矩阵

要生成拉盖尔多项式的伪Vandermonde矩阵，可以使用Python Numpy中的laguerre.lagvander()方法。该方法返回伪Vandermonde矩阵。返回矩阵的形状是 x.shape + (deg + 1,), 其中最后一个索引是对应拉盖尔多项式的度。数据类型将与转换后的x相同。

参数x返回一个点数组。数据类型根据元素是否为复数进行转换为float64或complex128。如果x是标量，则转换为1-D数组。参数deg是结果矩阵的度。

步骤

首先，导入所需的库-

import numpy as np
from numpy.polynomial import laguerre as L

创建一个数组 −

x = np.array([-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j])

显示数组 –

print("Our Array...\n",c)

检查尺寸−

print("\nDimensions of our Array...\n",c.ndim)

获取数据类型 –

print("\nDatatype of our Array object...\n",c.dtype)

获取形状

print("\nShape of our Array object...\n",c.shape)

要生成拉盖尔多项式的伪Vandermonde矩阵，在Python Numpy中使用laguerre.lagvander()函数。

print("\nResult...\n",L.lagvander(x, 2))

示例

import numpy as np
from numpy.polynomial import laguerre as L

# Create an array
x = np.array([-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j])

# Display the array
print("Our Array...\n",x)

# Check the Dimensions
print("\nDimensions of our Array...\n",x.ndim)

# Get the Datatype
print("\nDatatype of our Array object...\n",x.dtype)

# Get the Shape
print("\nShape of our Array object...\n",x.shape)

# To generate a pseudo Vandermonde matrix of the Laguerre polynomial, use the laguerre.lagvander() in Python Numpy
# The method returns the pseudo-Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1,), where The last index is the degree of the corresponding Laguerre polynomial. The dtype will be the same as the converted x.
print("\nResult...\n",L.lagvander(x, 2))

输出

Our Array...
   [-2.+2.j -1.+2.j 0.+2.j 1.+2.j 2.+2.j]

Dimensions of our Array...
1

Datatype of our Array object...
complex128

Shape of our Array object...
(5,)

Result...
   [[ 1. +0.j 3. -2.j 5. -8.j]
   [ 1. +0.j 2. -2.j 1.5-6.j]
   [ 1. +0.j 1. -2.j -1. -4.j]
   [ 1. +0.j 0. -2.j -2.5-2.j]
   [ 1. +0.j -1. -2.j -3. +0.j]]