在Python中生成Legendre多项式和x、y浮点数组的伪Vandermonde矩阵

要生成Legendre多项式的伪Vandermonde矩阵，可以使用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相应Legendre多项式的阶数。dtype将与转换后的x相同。

参数x、y是具有相同形状的坐标点数组。dtype将根据元素是否为复数而转换为float64或complex128。标量将转换为1-D数组。参数deg是最大阶数的列表，形式为[x_deg, y_deg]。

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([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)

检查两个数组的尺寸-

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)

要生成勒让德多项式的伪范德蒙矩阵，可以使用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([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 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...
   [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...
   [[ 1.0000000e+00  1.7000000e+00  3.8350000e+00  9.7325000e+00
      1.0000000e-01  1.7000000e-01  3.8350000e-01  9.7325000e-01
     -4.8500000e-01 -8.2450000e-01 -1.8599750e+00 -4.7202625e+00]
   [ 1.0000000e+00 2.8000000e+00 1.1260000e+01 5.0680000e+01
     1.4000000e+00 3.9200000e+00 1.5764000e+01 7.0952000e+01
     2.4400000e+00 6.8320000e+00 2.7474400e+01 1.2365920e+02]]