在Python中生成Legendre多项式和点的伪范德蒙矩阵

要生成Legendre多项式的伪范德蒙矩阵，可以使用Python Numpy中的legendre.legvander2d()方法。该方法返回伪范德蒙矩阵。返回矩阵的形状为x.shape + (deg + 1,)，其中最后一个索引是相应Legendre多项式的次数。dtype将与转换后的x相同。

参数x、y是具有相同形状的点坐标数组。元素的dtype将根据是否存在复数来转换为float64或complex128。标量将转换为1-D数组。参数deg是形式为[x_deg, y_deg]的最大次数列表。

步骤

首先，导入所需库：

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([1, 2])
y = np.array([3, 4])

展示数组 –

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 Numpy中的legendre.legvander2d()方法生成勒让德多项式的伪范德蒙德矩阵-

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([1, 2])
y = np.array([3, 4])

# 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...
   [1 2]

Array2...
   [3 4]

Array1 datatype...
int64

Array2 datatype...
int64

Dimensions of Array1...
1

Dimensions of Array2...
1

Shape of Array1...
(2,)

Shape of Array2...
(2,)

Result...
   [[ 1. 3. 13. 63. 1. 3. 13. 63. 1. 3.
     13. 63. ]
   [ 1. 4. 23.5 154. 2. 8. 47. 308. 5.5 22.
    129.25 847. ]]