在 Python 中生成 Hermite_e 多项式的伪范德蒙矩阵和 x、y、z 点的复数数组
pythonnumpyserver side programmingprogramming更新于 2024/7/14 23:40:17
要生成 Hermite_e 多项式的伪范德蒙矩阵和 x、y、z 样本点，请使用 Python Numpy 中的 hermite_e.hermevander3d()。该方法返回伪范德蒙矩阵。参数 x、y、z 是点坐标的数组，所有数组的形状都相同。dtype 将转换为 float64 或 complex128，具体取决于是否有任何元素是复数。标量将转换为一维数组。参数 deg 是 [x_deg, y_deg, z_deg] 形式的最大度数列表。
步骤
首先，导入所需的库 −
import numpy as np from numpy.polynomial import hermite_e as H
使用 numpy.array() 方法 − 创建点坐标数组，所有数组的形状相同
x = np.array([-2.+2.j, -1.+2.j]) y = np.array([0.+2.j, 1.+2.j]) z = np.array([2.+2.j, 3. + 3.j])
显示数组−
print("Array1...\n",x)
print("\nArray2...\n",y)
print("\nArray3...\n",z)
显示数据类型 −
print("\nArray1 datatype...\n",x.dtype)
print("\nArray2 datatype...\n",y.dtype)
print("\nArray3 datatype...\n",z.dtype)
检查两个数组的维度 −
print("\nDimensions of Array1...\n",x.ndim)
print("\nDimensions of Array2...\n",y.ndim)
print("\nDimensions of Array3...\n",z.ndim)
检查两个数组的形状 −
print("\nShape of Array1...\n",x.shape)
print("\nShape of Array2...\n",y.shape)
print("\nShape of Array3...\n",z.shape)
要生成 Hermite_e 多项式和 x、y、z 样本点的伪 Vandermonde 矩阵，请使用 hermite_e.hermevander3d() 方法 −
x_deg, y_deg, z_deg = 2, 3, 4
print("\n结果...\n",H.hermevander3d(x,y,z, [x_deg, y_deg, z_deg]))
示例
import numpy as np
from numpy.polynomial import hermite_e as H
# 使用 numpy.array() 方法创建点坐标数组，所有数组的形状相同
x = np.array([-2.+2.j, -1.+2.j])
y = np.array([0.+2.j, 1.+2.j])
z = np.array([2.+2.j, 3. + 3.j])
# 显示数组
print("Array1...\n",x)
print("\nArray2...\n",y)
print("\nArray3...\n",z)
# 显示数据类型
print("\nArray1 datatype...\n",x.dtype)
print("\nArray2 datatype...\n",y.dtype)
print("\nArray3 datatype...\n",z.dtype)
# 检查两个数组的维度
print("\nDimensions of Array1...\n",x.ndim)
print("\nDimensions of Array2...\n",y.ndim)
print("\nDimensions of Array3...\n",z.ndim)
# 检查两个数组的形状
print("\nShape of Array1...\n",x.shape)
print("\nShape of Array2...\n",y.shape)
print("\nShape of Array3...\n",z.shape)
# 要生成 Hermite_e 多项式和 x、y、z 样本点的伪 Vandermonde 矩阵，请使用 Python Numpy 中的 hermite_e.hermevander3d()
x_deg, y_deg, z_deg = 2, 3, 4
print("\n结果...\n",H.hermevander3d(x,y,z, [x_deg, y_deg, z_deg]))
输出
Array1...
[-2.+2.j -1.+2.j]
Array2...
[0.+2.j 1.+2.j]
Array3...
[2.+2.j 3.+3.j]
Array1 datatype...
complex128
Array2 datatype...
complex128
Array3 datatype...
complex128
Dimensions of Array1...
1
Dimensions of Array2...
1
Dimensions of Array3...
1
Shape of Array1...
(2,)
Shape of Array2...
(2,)
Shape of Array3...
(2,)
结果...
[[ 1.0000e+00 +0.000e+00j 2.0000e+00 +2.000e+00j -1.0000e+00 +8.000e+00j
-2.2000e+01 +1.000e+01j -6.1000e+01-4.800e+01j 0.0000e+00 +2.000e+00j
-4.0000e+00 +4.000e+00j -1.6000e+01-2.000e+00j -2.0000e+01 -4.400e+01j
9.6000e+01 -1.220e+02j -5.0000e+00+0.000e+00j -1.0000e+01 -1.000e+01j
5.0000e+00 -4.000e+01j 1.1000e+02 -5.000e+01j 3.0500e+02 +2.400e+02j
0.0000e+00 -1.400e+01j 2.8000e+01 -2.800e+01j 1.1200e+02 +1.400e+01j
1.4000e+02 +3.080e+02j -6.7200e+02 +8.540e+02j -2.0000e+00 +2.000e+00j
-8.0000e+00 +0.000e+00j -1.4000e+01 -1.800e+01j 2.4000e+01 -6.400e+01j
2.1800e+02 -2.600e+01j -4.0000e+00 -4.000e+00j 0.0000e+00 -1.600e+01j
3.6000e+01 -2.800e+01j 1.2800e+02 +4.800e+01j 5.2000e+01 +4.360e+02j
1.0000e+01 -1.000e+01j 4.0000e+01 +0.000e+00j 7.0000e+01 +9.000e+01j
-1.2000e+02 +3.200e+02j -1.0900e+03 +1.300e+02j 2.8000e+01 +2.800e+01j
0.0000e+00 +1.120e+02j -2.5200e+02 +1.960e+02j -8.9600e+02 -3.360e+02j
-3.6400e+02 -3.052e+03j -1.0000e+00 -8.000e+00j 1.4000e+01 -1.800e+01j
6.5000e+01 +0.000e+00j 1.0200e+02 +1.660e+02j -3.2300e+02 +5.360e+02j
1.6000e+01 -2.000e+00j 3.6000e+01 +2.800e+01j 0.0000e+00 +1.300e+02j
-3.3200e+02 +2.040e+02j -1.0720e+03 -6.460e+02j 5.0000e+00 +4.000e+01j
-7.0000e+01 +9.000e+01j -3.2500e+02 +0.000e+00j -5.1000e+02 -8.300e+02j
1.6150e+03 -2.680e+03j -1.1200e+02 +1.400e+01j -2.5200e+02 -1.960e+02j
0.0000e+00 -9.100e+02j 2.3240e+03 -1.428e+03j 7.5040e+03 +4.522e+03j]
[ 1.0000e+00 +0.000e+00j 3.0000e+00 +3.000e+00j -1.0000e+00 +1.800e+01j
-6.3000e+01 +4.500e+01j -3.2100e+02 -1.080e+02j 1.0000e+00 +2.000e+00j
-3.0000e+00 +9.000e+00j -3.7000e+01 +1.600e+01j -1.5300e+02 -8.100e+01j
-1.0500e+02 -7.500e+02j -4.0000e+00 +4.000e+00j -2.4000e+01 +0.000e+00j
-6.8000e+01 -7.600e+01j 7.2000e+01 -4.320e+02j 1.7160e+03 -8.520e+02j
-1.4000e+01 -8.000e+00j -1.8000e+01 -6.600e+01j 1.5800e+02 -2.440e+02j
1.2420e+03 -1.260e+02j 3.6300e+03 +4.080e+03j -1.0000e+00 +2.000e+00j
-9.0000e+00 +3.000e+00j -3.5000e+01 -2.000e+01j -2.7000e+01 -1.710e+02j
5.3700e+02 -5.340e+02j -5.0000e+00 +0.000e+00j -1.5000e+01 -1.500e+01j
5.0000e+00 -9.000e+01j 3.1500e+02 -2.250e+02j 1.6050e+03 +5.400e+02j
-4.0000e+00 -1.200e+01j 2.4000e+01 -4.800e+01j 2.2000e+02 -6.000e+01j
7.9200e+02 +5.760e+02j -1.2000e+01 +4.284e+03j 3.0000e+01 -2.000e+01j
1.5000e+02 +3.000e+01j 3.3000e+02 +5.600e+02j -9.9000e+02 +2.610e+03j
-1.1790e+04 +3.180e+03j -4.0000e+00 -4.000e+00j 0.0000e+00 -2.400e+01j
7.6000e+01 -6.800e+01j 4.3200e+02 +7.200e+01j 8.5200e+02 +1.716e+03j
4.0000e+00 -1.200e+01j 4.8000e+01 -2.400e+01j 2.1200e+02 +8.400e+01j
2.8800e+02 +9.360e+02j -2.5800e+03 +3.420e+03j 3.2000e+01 +0.000e+00j
9.6000e+01 +9.600e+01j -3.2000e+01 +5.760e+02j -2.0160e+03 +1.440e+03j
-1.0272e+04 -3.456e+03j 2.4000e+01 +8.800e+01j -1.9200e+02 +3.360e+02j
-1.6080e+03 +3.440e+02j -5.4720e+03 -4.464e+03j 1.8000e+03 -3.084e+04j]]
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