在Python中生成Legendre多项式和x，y复数点的伪Vandermonde矩阵

要生成Legendre多项式的伪Vandermonde矩阵，请使用Python Numpy中的legendre.legvander2d()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Legendre多项式的阶数。dtype将与转换后的x相同。

参数x，y是一个具有相同形状的点坐标数组。根据元素是否为复数，将其转换为float64或complex128。标量将转换为1维数组。参数deg是形式为[x_deg，y_deg]的最大阶数列表。

步骤

首先，导入所需的库−

import numpy as np
from numpy.polynomial import legendre 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([-2.+2.j, -1.+2.j])
y = np.array([1.+2.j, 2.+2.j])

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)

生成Legendre多项式的伪Vandermonde矩阵，使用Python Numpy中的legendre.legvander2d()方法−

x_deg, y_deg = 2, 3
print("\nResult...\n",L.legvander2d(x,y, [x_deg, y_deg]))

示例

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

# Create arrays of point coordinates, all of the same shape using the numpy.array() method
x = np.array([-2.+2.j, -1.+2.j])
y = np.array([1.+2.j, 2.+2.j])

# 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 Legendre polynomial, use the legendre.legvander2d() method in Python Numpy

x_deg, y_deg = 2, 3
print("\nResult...\n",L.legvander2d(x,y, [x_deg, y_deg]))

输出

Array1...
   [-2.+2.j -1.+2.j]

Array2...
   [1.+2.j 2.+2.j]

Array1 datatype...
complex128

Array2 datatype...
complex128

Dimensions of Array1...
1

Dimensions of Array2...
1

Shape of Array1...
(2,)

Shape of Array2...
(2,)

Result...
    [[ 1.  +0.j  1. +2.j  -5.   +6.j -29.  -8.j  -2.  +2.j  -6.   -2.j
      -2. -22.j 74. -42.j -0.5 -12.j  23.5 -13.j 74.5 +57.j -81.5 +352.j]
    [ 1.  +0.j   2.   +2.j  -0.5 +12.j -43. +37.j  -1. +2.j  -6.  +2.j
    -23.5 -13.j -31. -123.j -5.  -6.j   2.  -22.j 74.5 -57.j 437. +73.j]]