在Python中使用4D系数数组在x、y和z的笛卡尔乘积上评估3D Chebyshev级数
要在x、y和z的笛卡尔乘积上评估3D Chebyshev级数,可以使用Python中的polynomial.chebgrid3d(x, y, z)方法。如果c的维度少于三维,那么在其形状上隐式地添加1,使其成为3D。结果的形状将为c.shape[3:] + x.shape + y.shape + z.shape。
参数x、y和z是在笛卡尔乘积x、y和z的点上评估的三维级数。如果x、y或z是列表或元组,则首先将其转换为ndarray,否则保持不变,如果它不是ndarray,则将其视为标量。参数c是按顺序排列的系数数组,使得i、j次项的系数包含在c[i,j]中。如果c的维度大于2,剩余的索引将枚举多个系数集。
步骤
首先,导入所需的库−
import numpy as np
from numpy.polynomial import chebyshev as C
创建一个4维系数数组−
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)
获取图形−
print("\nShape of our Array object...\n",c.shape)
要在x、y、z的三维Chebyshev级数上进行评估,可以使用Python的polynomial.chebgrid3d(x, y, z)方法来进行−
print("\nResult...\n",C.chebgrid3d([1,2],[1,2], [1,2], c))
示例
import numpy as np
from numpy.polynomial import chebyshev as C
# 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 3-D Chebyshev series on the Cartesian product of x, y, z, use the polynomial.chebgrid3d(x, y, z) method in Python
print("\nResult...\n",C.chebgrid3d([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...
[[[[ 552. 53976.]
[ 900. 86904.]]
[[ 972. 92844.]
[ 1566. 148176.]]]
[[[ 576. 55956.]
[ 936. 89874.]]
[[ 1008. 95814.]
[ 1620. 152631.]]]]