在 Python 中使用浮点数数组作为点坐标生成 Hermite 多项式的伪范德蒙德矩阵

要生成 Hermite 多项式的伪范德蒙德矩阵，可以使用 Python Numpy 中的 hermite.hermvander2d()。该方法返回伪范德蒙德矩阵。参数 x、y 是点坐标数组，所有数组都具有相同的形状。数据类型将根据元素是否为复数转换为 float64 或 complex128。标量将转换为一维数组。参数 deg 是形式为 [x_deg, y_deg] 的最大次数列表。

步骤

首先，导入所需的库 -

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

使用 numpy.array() 方法创建所有形状相同的点坐标数组 -

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)

要生成 Hermite 多项式的伪范德蒙德矩阵，可以使用 Python Numpy 中的 hermite.hermvander2d() -

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]]

更新于: 2022-03-07

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