在Python中使用浮点数组点坐标生成Hermite_e多项式的伪Vandermonde矩阵

要生成Hermite多项式的伪Vandermonde矩阵，请使用Python Numpy中的hermite_e.hermevander2d()方法。该方法返回伪Vandermonde矩阵。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，数据类型将转换为float64或complex128。标量将被转换为1-D数组。参数deg是最大度数的列表，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 hermite as H

创建具有相同形状的点坐标数组，使用numpy.array()方法-。

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)

使用Python Numpy中的hermite_e.hermevander2d()函数生成Hermite多项式的伪Vandermonde矩阵：

x_deg, y_deg = 2, 3
print("\nResult...\n",H.hermevander2d(x,y, [x_deg, y_deg]))

示例

import numpy as np
from numpy.polynomial import hermite_e as H

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

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

# To generate a pseudo Vandermonde matrix of the Hermite polynomial, use the hermite_e.hermevander2d() in Python Numpy

x_deg, y_deg = 2, 3
print("\nResult...\n",H.hermevander2d(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...
  [[ 1.000000e+00 1.700000e+00  1.890000e+00 -1.870000e-01  1.000000e-01
     1.700000e-01 1.890000e-01 -1.870000e-02 -9.900000e-01 -1.683000e+00
    -1.871100e+00 1.851300e-01]
  [ 1.000000e+00 2.800000e+00 6.840000e+00 1.355200e+01 1.400000e+00
    3.920000e+00 9.576000e+00 1.897280e+01 9.600000e-01 2.688000e+00
    6.566400e+00 1.300992e+01]]