使用Python在给定复杂点数组的情况下生成Vandermonde矩阵

要生成给定阶数的Vandermonde矩阵，可以使用Python Numpy中的polynomial.polyvander()方法。该方法返回Vandermonde矩阵。返回矩阵的shape为x.shape + (deg + 1,)，其中最后一个索引是x的幂。dtype与转换后的x相同。

参数a是点数组。可能根据元素是否复杂将其dtype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是结果矩阵的阶数。

步骤

首先，导入所需的库−

import numpy as np
from numpy.polynomial.polynomial import polyvander

创建一个数组 −

x = np.array([-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j])

显示数组 –

print("Our Array...\n",x)

检查尺寸 –

print("\nDimensions of our Array...\n",x.ndim)

获取数据类型

print("\nDatatype of our Array object...\n",x.dtype)

获取形状−

print("\nShape of our Array object...\n",x.shape)

要生成给定阶数的范德蒙矩阵，在Python的Numpy中使用polynomial.polyvander()函数进行操作 –

print("\nResult...\n",polyvander(x, 2))

示例

import numpy as np
from numpy.polynomial.polynomial import polyvander

# Create an array
x = np.array([-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j])

# Display the array
print("Our Array...\n",x)

# Check the Dimensions
print("\nDimensions of our Array...\n",x.ndim)

# Get the Datatype
print("\nDatatype of our Array object...\n",x.dtype)

# Get the Shape
print("\nShape of our Array object...\n",x.shape)

# To generate a Vandermonde matrix of given degree, use the polynomial.polyvander() in Python Numpy
print("\nResult...\n",polyvander(x, 2))

输出

Our Array...
[-2.+2.j -1.+2.j 0.+2.j 1.+2.j 2.+2.j]

Dimensions of our Array...
1

Datatype of our Array object...
complex128

Shape of our Array object...
(5,)

Result...
[[ 1.+0.j -2.+2.j 0.-8.j]
[ 1.+0.j -1.+2.j -3.-4.j]
[ 1.+0.j 0.+2.j -4.+0.j]
[ 1.+0.j 1.+2.j -3.+4.j]
[ 1.+0.j 2.+2.j 0.+8.j]]