在Python中生成给定次数的伪范德蒙矩阵

要生成给定次数的伪范德蒙矩阵，可以使用Python Numpy中的polynomial.polyvander2()方法。该方法返回给定次数deg和样本点(x, y)的伪范德蒙矩阵。参数x和y是具有相同形状的点坐标数组。数据类型将根据元素是否有复数而被转换为float64或complex128。标量将被转换为1-D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.polynomial import polyvander2d

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])

展示数组 –

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)

要生成给定次数的伪Vandermonde矩阵，请在Python Numpy中使用polynomial.polyvander2()函数：

x_deg, y_deg = 2, 3
print("\nResult...\n",polyvander2d(x,y, [x_deg, y_deg]))

示例

import numpy as np
from numpy.polynomial.polynomial import polyvander2d

# 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])

# 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 given degree, use the polynomial.polyvander2() in Python Numpy
# The method returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y).
x_deg, y_deg = 2, 3
print("\nResult...\n",polyvander2d(x,y, [x_deg, y_deg]))

输出

Array1...
   [1 2]

Array2...
   [3 4]

Array1 datatype...
int64

Array2 datatype...
int64

Dimensions of Array1...
1

Dimensions of Array2...
1

Shape of Array1...
(2,)

Shape of Array2...
(2,)

Result...
   [[ 1. 3. 9. 27. 1. 3. 9. 27. 1. 3. 9. 27.]
   [ 1. 4. 16. 64. 2. 8. 32. 128. 4. 16. 64. 256.]]