在Python中使用给定的点坐标生成给定阶数的伪范德蒙德矩阵

要生成给定阶数的伪范德蒙德矩阵，可以使用Python Numpy中的polynomial.polyvander2()方法。此方法返回阶数为deg和样本点(x, y)的伪范德蒙德矩阵。

参数x和y是点坐标的数组，形状都相同。数据类型将根据元素是否为复数而转换为float64或complex128。标量将被转换为1-D数组。参数deg是形如[x_deg, y_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.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([0.1, 1.4])
y = np.array([1.7, 2.8])

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)

使用polynomial.polyvander2()函数可以生成给定次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([0.1, 1.4])
y = np.array([1.7, 2.8])

# 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...
   [0.1 1.4]

Array2...
   [1.7 2.8]

Array1 datatype...
float64

Array2 datatype...
float64

Dimensions of Array1...
1

Dimensions of Array2...
1

Shape of Array1...
(2,)

Shape of Array2...
(2,)

Result...
   [[1.000000e+00 1.700000e+00 2.890000e+00 4.913000e+00 1.000000e-01
      1.700000e-01 2.890000e-01 4.913000e-01 1.000000e-02 1.700000e-02
      2.890000e-02 4.913000e-02]
   [1.000000e+00 2.800000e+00 7.840000e+00 2.195200e+01 1.400000e+00
      3.920000e+00 1.097600e+01 3.073280e+01 1.960000e+00 5.488000e+00
      1.536640e+01 4.302592e+01]]