极客笔记使用Python生成Laguerre多项式和x、y、z样本点的伪Vandermonde矩阵
要生成Laguerre多项式和x、y、z样本点的伪Vandermonde矩阵，请使用Python中的Numpy库中的laguerre.lagvander3d()方法。参数x、y、z返回一个点数组。数据类型根据元素是否为复数进行转换，转换为float64或complex128。如果x是标量，则将其转换为1-D数组。参数deg是形如[x_deg, y_deg, z_deg]的最大阶数的列表。
步骤
首先，导入所需的库 –
import numpy as np
from numpy.polynomial import laguerre as L
使用numpy.array()方法创建具有相同形状的点坐标数组：
x = np.array([1, 2])
y = np.array([3, 4])
z = np.array([5, 6])
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)
要使用Python中的laguerre.lagvander3d()函数生成带有x、y、z样本点的Laguerre多项式的伪Vandermonde矩阵， 请使用以下HTML格式−
x_deg, y_deg, z_deg = 2, 3, 4
print("\nResult...\n",L.lagvander3d(x,y,z, [x_deg, y_deg, z_deg]))
示例
import numpy as np
from numpy.polynomial import laguerre as L
# Create arrays of point coordinates, all of the same shape using the numpy.array() method
x = np.array([1, 2])
y = np.array([3, 4])
z = np.array([5, 6])
# Display the arrays
print("Array1...\n",x)
print("\nArray2...\n",y)
print("\nArray3...\n",z)
# Display the datatype
print("\nArray1 datatype...\n",x.dtype)
print("\nArray2 datatype...\n",y.dtype)
print("\nArray3 datatype...\n",z.dtype)
# Check the Dimensions of both the arrays
print("\nDimensions of Array1...\n",x.ndim)
print("\nDimensions of Array2...\n",y.ndim)
print("\nDimensions of Array3...\n",z.ndim)
# Check the Shape of both the arrays
print("\nShape of Array1...\n",x.shape)
print("\nShape of Array2...\n",y.shape)
print("\nShape of Array3...\n",z.shape)
# To generate a pseudo Vandermonde matrix of the Laguerre polynomial with x, y, z sample points, use the laguerre.lagvander3d() in Python Numpy
x_deg, y_deg, z_deg = 2, 3, 4
print("\nResult...\n",L.lagvander3d(x,y,z, [x_deg, y_deg, z_deg]))
输出
Array1...
[1 2]
Array2...
[3 4]
Array3...
[5 6]
Array1 datatype...
int64
Array2 datatype...
int64
Array3 datatype...
int64
Dimensions of Array1...
1
Dimensions of Array2...
1
Dimensions of Array3...
1
Shape of Array1...
(2,)
Shape of Array2...
(2,)
Shape of Array3...
(2,)
Result...
[[ 1. -4. 3.5 2.66666667 -1.29166667
-2. 8. -7. -5.33333333 2.58333333
-0.5 2. -1.75 -1.33333333 0.64583333
1. -4. 3.5 2.66666667 -1.29166667
0. -0. 0. 0. -0.
-0. 0. -0. -0. 0.
-0. 0. -0. -0. 0.
0. - 0. 0. 0. -0.
-0.5 2. -1.75 -1.33333333 0.64583333
1. -4. 3.5 2.66666667 -1.29166667
0.25 -1. 0.875 0.66666667 -0.32291667
-0.5 2. -1.75 -1.33333333 0.64583333]
[ 1. -5. 7. 1. -5.
-3. 15. -21. -3. 15.
1. -5. 7. 1. -5.
2.33333333 -11.66666667 16.33333333 2.33333333 -11.66666667
-1. 5. -7. -1. 5.
3. -15. 21. 3. -15.
-1. 5. -7. -1. 5.
-2.33333333 11.66666667 -16.33333333 -2.33333333 11.66666667
-1. 5. -7. -1. 5.
3. -15. 21. 3. -15.
-1. 5. -7. -1. 5.
-2.33333333 11.66666667 -16.33333333 -2.33333333 11.66666667]]