在 Python 中生成 Chebyshev 多项式和 x、y、z 样本点的伪范德蒙矩阵
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要生成 Chebyshev 多项式和 x、y、z 样本点的伪范德蒙矩阵，请使用 Python Numpy 中的 chebyshev.chebvander()。该方法返回度 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，所有点坐标的形状都相同。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 [x_deg, y_deg, z_deg] 形式的最大度数列表。
步骤
首先，导入所需的库 −
import numpy as np from numpy.polynomial import chebyshev as C
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([1, 2]) y = np.array([3, 4]) z = np.array([5, 6])
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)
检查两个数组的维度 −
print("\nDimensions of Array1...\n",x.ndim)
print("\nDimensions of Array2...\n",y.ndim)
print("\nDimensions of Array3...\n",z.ndim)
检查两个数组的形状 −
print("\nShape of Array1...\n",x.shape)
print("\nShape of Array2...\n",y.shape)
print("\nShape of Array3...\n",z.shape)
要生成切比雪夫多项式和 x、y、z 样本点的伪范德蒙矩阵，请使用 Python 中的 chebyshev.chebvander() −
x_deg, y_deg, z_deg = 2, 3, 4
print("\n结果...\n",C.chebvander3d(x,y, z, [x_deg, y_deg, z_deg]))
示例
import numpy as np
from numpy.polynomial import chebyshev as C
# 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([1, 2])
y = np.array([3, 4])
z = np.array([5, 6])
# 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)
# 检查两个数组的维度
print("\nDimensions of Array1...\n",x.ndim)
print("\nDimensions of Array2...\n",y.ndim)
print("\nDimensions of Array3...\n",z.ndim)
# 检查两个数组的形状
print("\nShape of Array1...\n",x.shape)
print("\nShape of Array2...\n",y.shape)
print("\nShape of Array3...\n",z.shape)
# 要生成切比雪夫多项式和 x、y、z 样本点的伪范德蒙矩阵，请使用 Python Numpy 中的 chebyshev.chebvander()
# 该方法返回度 deg 和样本点 (x、y、z) 的伪范德蒙矩阵。
x_deg, y_deg, z_deg = 2, 3, 4
print("\n结果...\n",C.chebvander3d(x,y, z, [x_deg, y_deg, z_deg]))
输出
Array1... [1 2] Array2... [3 4] Array3... [5 6] Array1 datatype... int64 Array2 datatype... int64 Array3 datatype... int64 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... [[1.0000000e+00 5.0000000e+00 4.9000000e+01 4.8500000e+02 4.8010000e+03 3.0000000e+00 1.5000000e+01 1.4700000e+02 1.4550000e+03 1.4403000e+04 1.7000000e+01 8.5000000e+01 8.3300000e+02 8.2450000e+03 8.1617000e+04 9.9000000e+01 4.9500000e+02 4.8510000e+03 4.8015000e+04 4.7529900e+05 1.0000000e+00 5.0000000e+00 4.9000000e+01 4.8500000e+02 4.8010000e+03 3.0000000e+00 1.5000000e+01 1.4700000e+02 1.4550000e+03 1.4403000e+04 1.7000000e+01 8.5000000e+01 8.3300000e+02 8.2450000e+03 8.1617000e+04 9.9000000e+01 4.9500000e+02 4.8510000e+03 4.8015000e+04 4.7529900e+05 1.0000000e+00 5.0000000e+00 4.9000000e+01 4.8500000e+02 4.8010000e+03 3.0000000e+00 1.5000000e+01 1.4700000e+02 1.4550000e+03 1.4403000e+04 1.7000000e+01 8.5000000e+01 8.3300000e+02 8.2450000e+03 8.1617000e+04 9.9000000e+01 4.9500000e+02 4.8510000e+03 4.8015000e+04 4.7529900e+05] [1.0000000e+00 6.0000000e+00 7.1000000e+01 8.4600000e+02 1.0081000e+04 4.0000000e+00 2.4000000e+01 2.8400000e+02 3.3840000e+03 4.0324000e+04 3.1000000e+01 1.8600000e+02 2.2010000e+03 2.6226000e+04 3.1251100e+05 2.4400000e+02 1.4640000e+03 1.7324000e+04 2.0642400e+05 2.4597640e+06 2.0000000e+00 1.2000000e+01 1.4200000e+02 1.6920000e+03 2.0162000e+04 8.0000000e+00 4.8000000e+01 5.6800000e+02 6.7680000e+03 8.0648000e+04 6.2000000e+01 3.7200000e+02 4.4020000e+03 5.2452000e+04 6.2502200e+05 4.8800000e+02 2.9280000e+03 3.4648000e+04 4.1284800e+05 4.9195280e+06 7.0000000e+00 4.2000000e+01 4.9700000e+02 5.9220000e+03 7.0567000e+04 2.8000000e+01 1.6800000e+02 1.9880000e+03 2.3688000e+04 2.8226800e+05 2.1700000e+02 1.3020000e+03 1.5407000e+04 1.8358200e+05 2.1875770e+06 1.7080000e+03 1.0248000e+04 1.2126800e+05 1.4449680e+06 1.7218348e+07]]
