在 Python 中生成给定度数和 x、y、z 点的伪范德蒙矩阵
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要生成给定度数和样本点 (x、y、z) 的范德蒙矩阵，请使用 Python Numpy 中的 polynomial.polyvander3d()。该方法返回度数 deg 和样本点 (x、y、z) 的伪范德蒙矩阵。参数 x、y、z 是点坐标的数组，所有数组的形状相同。dtype 将转换为 float64 或 complex128，具体取决于是否有任何元素是复数。标量将转换为一维数组。参数 deg 是形式为 [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() 方法创建点坐标数组，所有数组的形状相同 −
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)
检查维度 −
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)
要生成给定度数和样本点 (x, y, z) 的范德蒙矩阵，请使用 Python Numpy 中的 polynomial.polyvander3d() −
x_deg, y_deg, z_deg = 2, 3, 4
print("\n结果...\n",polyvander3d(x,y, z, [x_deg, y_deg, z_deg]))
示例
import numpy as np
from numpy.polynomial.polynomial import polyvander3d
# 使用 numpy.array() 方法创建点坐标数组，所有数组的形状相同
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)
# 检查维度
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)
# 要生成给定度数和样本点 (x, y, z) 的范德蒙矩阵，请使用 Python Numpy 中的 polynomial.polyvander3d()
x_deg, y_deg, z_deg = 2, 3, 4
print("\n结果...\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,) 结果... [[ 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]]
