使用Python在给定的阶数和复杂数组点坐标中生成一个伪范德蒙矩阵

要生成给定阶数的伪范德蒙矩阵，请使用Python NumPy中的polynomial.polyvander2()方法。该方法返回阶数为deg和样本点(x, y)的伪范德蒙矩阵。参数x和y是点坐标的数组，所有的形状相同。dtype将根据元素是否为复数来转换为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]的最大度的列表。

步骤

首先，导入所需的库−

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

使用numpy.array()方法创建相同形状的点坐标数组 –

x = np.array([-2.+2.j, -1.+2.j])
y = np.array([1.+2.j, 2.+2.j])

显示数组 –

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)

检查两个数组的尺寸 –

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)

使用 Python Numpy 中的 polynomial.polyvander2() 函数，可以生成给定阶数的伪范德蒙德矩阵 –

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([-2.+2.j, -1.+2.j])
y = np.array([1.+2.j, 2.+2.j])

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

输出

Array1...
   [-2.+2.j -1.+2.j]

Array2...
   [1.+2.j 2.+2.j]

Array1 datatype...
complex128

Array2 datatype...
complex128

Dimensions of Array1...
1

Dimensions of Array2...
1

Shape of Array1...
(2,)

Shape of Array2...
(2,)

Result...
   [[ 1. +0.j 1. +2.j -3. +4.j -11. -2.j -2. +2.j -6. -2.j -2.-14.j 26.-18.j 0. -8.j 16. -8.j 32.+24.j                -16.+88.j]
   [ 1. +0.j 2. +2.j 0. +8.j -16.+16.j -1. +2.j -6. +2.j -16. -8.j -16.-48.j -3. -4.j 2.-14.j 32.-24.j                112.+16.j]]