在Python中生成给定阶数和x、y、z为复杂数组的伪范德蒙矩阵

要生成给定阶数和样本点(x, y, z)的范德蒙矩阵，请使用Python Numpy中的polynomial.polyvander3d()方法。该方法返回给定阶数和样本点(x, y, z)的伪范德蒙矩阵。参数x、y、z是具有相同形状的点坐标数组。元素的类型将根据是否有复数来转换为float64或complex128。标量将被转换为1D数组。参数deg是形如[x_deg, y_deg, z_deg]的最大度数列表。

步骤

首先，导入所需的库−

import numpy as np
from numpy.polynomial.polynomial import polyvander3d

使用numpy.array()方法创建具有相同形状的点坐标数组-

x = np.array([-2.+2.j, -1.+2.j])
y = np.array([0.+2.j, 1.+2.j])
z = np.array([2.+2.j, 3. + 3.j])

显示数组 –

print("Array1...\n",x)
print("\nArray2...\n",y)
print("\nArray3...\n",z)

显示数据类型−

print("\nArray1 datatype...\n",x.dtype)
print("\nArray2 datatype...\n",y.dtype)
print("\nArray3 datatype...\n",z.dtype)

检查尺寸 –

print("\nDimensions of Array1...\n",x.ndim)
print("\nDimensions of Array2...\n",y.ndim)
print("\nDimensions of Array3...\n",z.ndim)

检查形状 –

print("\nShape of Array1...\n",x.shape)
print("\nShape of Array2...\n",y.shape)
print("\nShape of Array3...\n",z.shape)

要生成给定程度和样本点（x，y，z）的Vandermonde矩阵，请使用Python Numpy中的polynomial.polyvander3d()。

x_deg, y_deg, z_deg = 2, 3, 4
print("\nResult...\n",polyvander3d(x,y, z, [x_deg, y_deg, z_deg]))

示例

import numpy as np
from numpy.polynomial.polynomial import polyvander3d

# 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([0.+2.j, 1.+2.j])
z = np.array([2.+2.j, 3. + 3.j])

# Display the arrays
print("Array1...\n",x)
print("\nArray2...\n",y)
print("\nArray3...\n",z)

# Display the datatype
print("\nArray1 datatype...\n",x.dtype)
print("\nArray2 datatype...\n",y.dtype)
print("\nArray3 datatype...\n",z.dtype)

# Check the Dimensions
print("\nDimensions of Array1...\n",x.ndim)
print("\nDimensions of Array2...\n",y.ndim)
print("\nDimensions of Array3...\n",z.ndim)

# Check the Shape
print("\nShape of Array1...\n",x.shape)
print("\nShape of Array2...\n",y.shape)
print("\nShape of Array3...\n",z.shape)

# To generate a Vandermonde matrix of given degree and sample points (x, y, z)., use the polynomial.polyvander3d() in Python Numpy
x_deg, y_deg, z_deg = 2, 3, 4
print("\nResult...\n",polyvander3d(x,y, z, [x_deg, y_deg, z_deg]))

输出

Array1...
[-2.+2.j -1.+2.j]

Array2...
[0.+2.j 1.+2.j]

Array3...
[2.+2.j 3.+3.j]

Array1 datatype...
complex128

Array2 datatype...
complex128

Array3 datatype...
complex128

Dimensions of Array1...
1

Dimensions of Array2...
1

Dimensions of Array3...
1

Shape of Array1...
(2,)

Shape of Array2...
(2,)

Shape of Array3...
(2,)

Result...
[[ 1.000e+00+0.000e+00j 2.000e+00+2.000e+00j 0.000e+00+8.000e+00j
  -1.600e+01+1.600e+01j -6.400e+01+0.000e+00j 0.000e+00+2.000e+00j
  -4.000e+00+4.000e+00j -1.600e+01+0.000e+00j -3.200e+01-3.200e+01j
  -0.000e+00-1.280e+02j -4.000e+00+0.000e+00j -8.000e+00-8.000e+00j
  -0.000e+00-3.200e+01j 6.400e+01-6.400e+01j 2.560e+02-0.000e+00j
   0.000e+00-8.000e+00j 1.600e+01-1.600e+01j 6.400e+01+0.000e+00j
   1.280e+02+1.280e+02j 0.000e+00+5.120e+02j -2.000e+00+2.000e+00j
  -8.000e+00+0.000e+00j -1.600e+01-1.600e+01j 0.000e+00-6.400e+01j
   1.280e+02-1.280e+02j -4.000e+00-4.000e+00j 0.000e+00-1.600e+01j
   3.200e+01-3.200e+01j 1.280e+02+0.000e+00j 2.560e+02+2.560e+02j
   8.000e+00-8.000e+00j 3.200e+01+0.000e+00j 6.400e+01+6.400e+01j
   0.000e+00+2.560e+02j -5.120e+02+5.120e+02j 1.600e+01+1.600e+01j
   0.000e+00+6.400e+01j -1.280e+02+1.280e+02j -5.120e+02+0.000e+00j
  -1.024e+03-1.024e+03j 0.000e+00-8.000e+00j 1.600e+01-1.600e+01j
   6.400e+01+0.000e+00j 1.280e+02+1.280e+02j 0.000e+00+5.120e+02j
   1.600e+01+0.000e+00j 3.200e+01+3.200e+01j 0.000e+00+1.280e+02j
  -2.560e+02+2.560e+02j -1.024e+03+0.000e+00j 0.000e+00+3.200e+01j
  -6.400e+01+6.400e+01j -2.560e+02+0.000e+00j -5.120e+02-5.120e+02j
  -0.000e+00-2.048e+03j -6.400e+01+0.000e+00j -1.280e+02-1.280e+02j
  -0.000e+00-5.120e+02j 1.024e+03-1.024e+03j 4.096e+03-0.000e+00j]
 [ 1.000e+00+0.000e+00j 3.000e+00+3.000e+00j 0.000e+00+1.800e+01j
  -5.400e+01+5.400e+01j -3.240e+02+0.000e+00j 1.000e+00+2.000e+00j
  -3.000e+00+9.000e+00j -3.600e+01+1.800e+01j -1.620e+02-5.400e+01j
  -3.240e+02-6.480e+02j -3.000e+00+4.000e+00j -2.100e+01+3.000e+00j
  -7.200e+01-5.400e+01j -5.400e+01-3.780e+02j 9.720e+02-1.296e+03j
  -1.100e+01-2.000e+00j -2.700e+01-3.900e+01j 3.600e+01-1.980e+02j
   7.020e+02-4.860e+02j 3.564e+03+6.480e+02j -1.000e+00+2.000e+00j
  -9.000e+00+3.000e+00j -3.600e+01-1.800e+01j -5.400e+01-1.620e+02j
   3.240e+02-6.480e+02j -5.000e+00+0.000e+00j -1.500e+01-1.500e+01j
  -0.000e+00-9.000e+01j 2.700e+02-2.700e+02j 1.620e+03-0.000e+00j
  -5.000e+00-1.000e+01j 1.500e+01-4.500e+01j 1.800e+02-9.000e+01j
   8.100e+02+2.700e+02j 1.620e+03+3.240e+03j 1.500e+01-2.000e+01j
   1.050e+02-1.500e+01j 3.600e+02+2.700e+02j 2.700e+02+1.890e+03j
  -4.860e+03+6.480e+03j -3.000e+00-4.000e+00j 3.000e+00-2.100e+01j
   7.200e+01-5.400e+01j 3.780e+02+5.400e+01j 9.720e+02+1.296e+03j
   5.000e+00-1.000e+01j 4.500e+01-1.500e+01j 1.800e+02+9.000e+01j
   2.700e+02+8.100e+02j -1.620e+03+3.240e+03j 2.500e+01+0.000e+00j
   7.500e+01+7.500e+01j 0.000e+00+4.500e+02j -1.350e+03+1.350e+03j
  -8.100e+03+0.000e+00j 2.500e+01+5.000e+01j -7.500e+01+2.250e+02j
  -9.000e+02+4.500e+02j -4.050e+03-1.350e+03j -8.100e+03-1.620e+04j]]