在Python中生成拉盖尔多项式和x、y浮点数数组的伪Vandermonde矩阵

要生成拉盖尔多项式的伪Vandermonde矩阵，使用Python的Numpy库中的laguerre.lagvander2d()方法。该方法返回伪Vandermonde矩阵。返回矩阵的形状为x.shape + (deg + 1,)，其中最后一个索引是对应的拉盖尔多项式的次数。dtype将与转换后的x相同。

参数x、y返回一个点的数组。dtype根据元素是否复数而转换为float64或complex128。如果x是标量，则将其转换为1-D数组。参数deg是形如[x_deg, y_deg]的最大度的列表。

步骤

首先，导入所需的库−

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

使用numpy.array()方法创建具有相同形状的点坐标数组 –

x = np.array([0.1, 1.4])
y = np.array([1.7, 2.8])

显示数组 –

print("Array1...\n",x)
print("\nArray2...\n",y)

显示数据类型 –

print("\nArray1 datatype...\n",x.dtype)
print("\nArray2 datatype...\n",y.dtype)

检查两个数组的维度 –

print("\nDimensions of Array1...\n",x.ndim)
print("\nDimensions of Array2...\n",y.ndim)

检查两个数组的形状 –

print("\nShape of Array1...\n",x.shape)
print("\nShape of Array2...\n",y.shape)

使用Python的Numpy中的laguerre.lagvander2d()函数生成Laguerre多项式的伪Vandermonde矩阵−

x_deg, y_deg = 2, 3
print("\nResult...\n",L.lagvander2d(x,y, [x_deg, y_deg]))

示例

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

# Create arrays of point coordinates, all of the same shape using the numpy.array() method
x = np.array([0.1, 1.4])
y = np.array([1.7, 2.8])

# Display the arrays
print("Array1...\n",x)
print("\nArray2...\n",y)

# Display the datatype
print("\nArray1 datatype...\n",x.dtype)
print("\nArray2 datatype...\n",y.dtype)

# Check the Dimensions of both the arrays
print("\nDimensions of Array1...\n",x.ndim)
print("\nDimensions of Array2...\n",y.ndim)

# Check the Shape of both the arrays
print("\nShape of Array1...\n",x.shape)
print("\nShape of Array2...\n",y.shape)

# To generate a pseudo Vandermonde matrix of the Laguerre polynomial, use the laguerre.lagvander2d() in Python Numpy

x_deg, y_deg = 2, 3
print("\nResult...\n",L.lagvander2d(x,y, [x_deg, y_deg]))

输出

Array1...
   [0.1 1.4]

Array2...
   [1.7 2.8]

Array1 datatype...
float64

Array2 datatype...
float64

Dimensions of Array1...
1

Dimensions of Array2...
1

Shape of Array1...
(2,)

Shape of Array2...
(2,)

Result...
   [[ 1.     -0.7    -0.955 -0.58383333  0.9      -0.63
     -0.8595 -0.52545 0.805 -0.5635     -0.768775 -0.46998583]
   [ 1.    -1.8        -0.68 0.70133333 -0.4       0.72
     0.272 -0.28053333 -0.82 1.476       0.5576   -0.57509333]]