在Python中生成带有浮点数组点坐标的Hermite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.hermvander2d()函数。该方法返回伪Vandermonde矩阵。 参数x和y是一个具有相同形状的点坐标数组。dtypes将根据元素是否为复数而转换为float64或complex128。标量将被转换为1-D数组。参数deg是形式为[x_deg, y_deg]的最大度列表。

步骤

首先，导入所需的库−

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

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])

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)

要生成一个赫米特多项式的伪范德蒙德矩阵，请使用Python Numpy中的hermite.hermvander2d()函数-

x_deg, y_deg = 2, 3
print("\nResult...\n",H.hermvander2d(x,y, [x_deg, y_deg]))

示例

import numpy as np
from numpy.polynomial import hermite 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 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 Hermite polynomial, use the hermite.hermvander2d() in Python Numpy
x_deg, y_deg = 2, 3

print("\nResult...\n",H.hermvander2d(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  3.4000000e+00  9.5600000e+00  1.8904000e+01
      2.0000000e-01  6.8000000e-01  1.9120000e+00  3.7808000e+00
     -1.9600000e+00 -6.6640000e+00 -1.8737600e+01 -3.7051840e+01]
   [  1.0000000e+00   5.6000000e+00  2.9360000e+01 1.4201600e+02
      2.8000000e+00   1.5680000e+01  8.2208000e+01 3.9764480e+02
      5.8400000e+00   3.2704000e+01  1.7146240e+02 8.2937344e+02]]