在Python中使用4D系数数组计算三维Hermite级数在点(x,y,z)处的值

要计算在点(x, y, z)处的三维Hermite级数的值，可以使用Python的Numpy库中的hermite.hermval3d()方法。该方法返回由x、y和z的对应值组成的点上多维多项式的值。第一个参数是x、y和z。在点(x, y, z)处计算三维级数时，x、y和z必须具有相同的形状。如果x、y或z中的任何一个是列表或元组，则首先将其转换为ndarray，否则将保持不变，如果它不是ndarray，则将其视为标量。

第二个参数C是一个系数数组，其顺序排列，使得多重度为i、j、k的项的系数包含在c[i,j,k]中。如果c的维度大于3，则其余的索引将枚举多组系数。

步骤

首先，导入所需的库 –

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

创建一个系数的4维数组 −

c = np.arange(48).reshape(2,2,6,2)

显示数组 –

print("Our Array...\n",c)

检查尺寸 −

print("\nDimensions of our Array...\n",c.ndim)

获取数据类型 –

print("\nDatatype of our Array object...\n",c.dtype)

获得形状 −

print("\nShape of our Array object...\n",c.shape)

要在点(x, y, z)处评估3D Hermite series，请使用Python Numpy中的hermite.hermval3d()方法。

print("\nResult...\n",H.hermval3d([1,2],[1,2],[1,2],c))

示例

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

# Create a 4d array of coefficients
c = np.arange(48).reshape(2,2,6,2)

# Display the array
print("Our Array...\n",c)

# Check the Dimensions
print("\nDimensions of our Array...\n",c.ndim)

# Get the Datatype
print("\nDatatype of our Array object...\n",c.dtype)

# Get the Shape
print("\nShape of our Array object...\n",c.shape)

# To evaluate a 3D Hermite series at points (x, y, z), use the hermite.hermval3d() method in Python Numpy
# The method returns the values of the multidimensional polynomial on points formed with triples of corresponding values from x, y, and z.

print("\nResult...\n",H.hermval3d([1,2],[1,2],[1,2],c))

输出

Our Array...
   [[[[ 0 1]
    [ 2 3]
    [ 4 5]
    [ 6 7]
    [ 8 9]
    [10 11]]

   [[12 13]
    [14 15]
    [16 17]
    [18 19]
    [20 21]
    [22 23]]]


    [[[24 25]
    [26 27]
    [28 29]
    [30 31]
    [32 33]
    [34 35]]

   [[36 37]
    [38 39]
    [40 41]
    [42 43]
    [44 45]
    [46 47]]]]

Dimensions of our Array...
4

Datatype of our Array object...
int64

Shape of our Array object...
(2, 2, 6, 2)

Result...
   [[ -8100. 104480.]
   [ -8343. 107455.]]