在 Python 中生成给定度数的伪范德蒙矩阵,并使用复数数组作为点坐标


要生成给定度数的伪范德蒙矩阵,请在 Python Numpy 中使用 polynomial.polyvander2()。此方法返回度数为 deg 和采样点 (x, y) 的伪范德蒙矩阵。参数 x 和 y 是点坐标数组,形状相同。数据类型将转换为 float64 或 complex128,具体取决于元素是否为复数。标量将转换为一维数组。参数 deg 是最大度数列表,格式为 [x_deg, y_deg]。

步骤

首先,导入所需的库 -

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

使用 numpy.array() 方法创建形状相同的点坐标数组 -

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)

要生成给定度数的伪范德蒙矩阵,请在 Python Numpy 中使用 polynomial.polyvander2() -

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]]

更新于: 2022-03-01

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