Để tạo pseudo Vandermonde matrix của Legendre polynomial với điểm mẫu x, y, z, dùng phương thức legendre.legvander3d() trong Python NumPy. Trả về pseudo-Vandermonde matrix của degrees deg và sample points (x, y, z).
Tham số x, y, z là mảng tọa độ điểm, tất cả cùng shape. Dtypes chuyển thành float64 hoặc complex128 tùy element có complex hay không. Scalar chuyển thành 1-D arrays. Tham số deg là list max degrees dạng [x_deg, y_deg, z_deg].
Các bước
Đầu tiên, import thư viện cần thiết:
import numpy as np from numpy.polynomial import legendre as L
Tạo mảng tọa độ điểm, cùng shape dùng numpy.array():
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])
Hiển thị mảng:
print("Array1...\n", x)
print("\nArray2...\n", y)
print("\nArray3...\n", z)
Hiển thị datatype:
print("\nArray1 datatype...\n", x.dtype)
print("\nArray2 datatype...\n", y.dtype)
print("\nArray3 datatype...\n", z.dtype)
Kiểm tra Dimensions:
print("\nDimensions of Array1...\n", x.ndim)
print("\nDimensions of Array2...\n", y.ndim)
print("\nDimensions of Array3...\n", z.ndim)
Kiểm tra Shape:
print("\nShape of Array1...\n", x.shape)
print("\nShape of Array2...\n", y.shape)
print("\nShape of Array3...\n", z.shape)
Tạo pseudo Vandermonde matrix Legendre polynomial với x, y, z sample points, dùng legendre.legvander3d():
x_deg, y_deg, z_deg = 2, 3, 4
print("\nResult...\n", L.legvander3d(x, y, z, [x_deg, y_deg, z_deg]))
Ví dụ
import numpy as np
from numpy.polynomial import legendre as L
# 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 of both the arrays
print("\nDimensions of Array1...\n", x.ndim)
print("\nDimensions of Array2...\n", y.ndim)
print("\nDimensions of Array3...\n", z.ndim)
# Check the Shape of both the arrays
print("\nShape of Array1...\n", x.shape)
print("\nShape of Array2...\n", y.shape)
print("\nShape of Array3...\n", z.shape)
# To generate a pseudo Vandermonde matrix of the Legendre polynomial with x, y, z sample points, use the legendre.legvander3d() method in Python Numpy
x_deg, y_deg, z_deg = 2, 3, 4
print("\nResult...\n", L.legvander3d(x, y, z, [x_deg, y_deg, z_deg]))
Kết quả
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... [[ 1.00000000e+00 +0.0000000e+00j 2.00000000e+00 +2.0000000e+00j -5.00000000e-01 +1.2000000e+01j -4.30000000e+01 +3.7000000e+01j -2.79625000e+02 -3.0000000e+01j 0.00000000e+00 +2.0000000e+00j -4.00000000e+00 +4.0000000e+00j -2.40000000e+01 -1.0000000e+00j -7.40000000e+01 -8.6000000e+01j 6.00000000e+01 -5.5925000e+02j -6.50000000e+00 +0.0000000e+00j -1.30000000e+01 -1.3000000e+01j 3.25000000e+00 -7.8000000e+01j 2.79500000e+02 -2.4050000e+02j 1.81756250e+03 +1.9500000e+02j 0.00000000e+00 -2.3000000e+01j 4.60000000e+01 -4.6000000e+01j 2.76000000e+02 +1.1500000e+01j 8.51000000e+02 +9.8900000e+02j -6.90000000e+02 +6.4313750e+03j -2.00000000e+00 +2.0000000e+00j -8.00000000e+00 +0.0000000e+00j -2.30000000e+01 -2.5000000e+01j 1.20000000e+01 -1.6000000e+02j 6.19250000e+02 -4.9925000e+02j -4.00000000e+00 -4.0000000e+00j 0.00000000e+00 -1.6000000e+01j 5.00000000e+01 -4.6000000e+01j 3.20000000e+02 +2.4000000e+01j 9.98500000e+02 +1.2385000e+03j 1.30000000e+01 -1.3000000e+01j 5.20000000e+01 +0.0000000e+00j 1.49500000e+02 +1.6250000e+02j -7.80000000e+01 +1.0400000e+03j -4.02512500e+03 +3.2451250e+03j 4.60000000e+01 +4.6000000e+01j 0.00000000e+00 +1.8400000e+02j -5.75000000e+02 +5.2900000e+02j -3.68000000e+03 -2.7600000e+02j -1.14827500e+04 -1.4242750e+04j -5.00000000e-01 -1.2000000e+01j 2.30000000e+01 -2.5000000e+01j 1.44250000e+02 +0.0000000e+00j 4.65500000e+02 +4.9750000e+02j -2.20187500e+02 +3.3705000e+03j 2.40000000e+01 -1.0000000e+00j 5.00000000e+01 +4.6000000e+01j 0.00000000e+00 +2.8850000e+02j -9.95000000e+02 +9.3100000e+02j -6.74100000e+03 -4.4037500e+02j 3.25000000e+00 +7.8000000e+01j -1.49500000e+02 +1.6250000e+02j -9.37625000e+02 +0.0000000e+00j -3.02575000e+03 -3.2337500e+03j 1.43121875e+03 -2.1908250e+04j -2.76000000e+02 +1.1500000e+01j -5.75000000e+02 -5.2900000e+02j 0.00000000e+00 -3.3177500e+03j 1.14425000e+04 -1.0706500e+04j 7.75215000e+04 +5.0643125e+03j] [ 1.00000000e+00 +0.0000000e+00j 3.00000000e+00 +3.0000000e+00j -5.00000000e-01 +2.7000000e+01j -1.39500000e+02 +1.3050000e+02j -1.41712500e+03 -6.7500000e+01j 1.00000000e+00 +2.0000000e+00j -3.00000000e+00 +9.0000000e+00j -5.45000000e+01 +2.6000000e+01j -4.00500000e+02 -1.4850000e+02j -1.28212500e+03 -2.9017500e+03j -5.00000000e+00 +6.0000000e+00j -3.30000000e+01 +3.0000000e+00j -1.59500000e+02 -1.3800000e+02j -8.55000000e+01 -1.4895000e+03j 7.49062500e+03 -8.1652500e+03j -2.90000000e+01 -8.0000000e+00j -6.30000000e+01 -1.1100000e+02j 2.30500000e+02 -7.7900000e+02j 5.08950000e+03 -2.6685000e+03j 4.05566250e+04 +1.3294500e+04j -1.00000000e+00 +2.0000000e+00j -9.00000000e+00 +3.0000000e+00j -5.35000000e+01 -2.8000000e+01j -1.21500000e+02 -4.0950000e+02j 1.55212500e+03 -2.7667500e+03j -5.00000000e+00 +0.0000000e+00j -1.50000000e+01 -1.5000000e+01j 2.50000000e+00 -1.3500000e+02j 6.97500000e+02 -6.5250000e+02j 7.08562500e+03 +3.3750000e+02j -7.00000000e+00 -1.6000000e+01j 2.70000000e+01 -6.9000000e+01j 4.35500000e+02 -1.8100000e+02j 3.06450000e+03 +1.3185000e+03j 8.83987500e+03 +2.3146500e+04j 4.50000000e+01 -5.0000000e+01j 2.85000000e+02 -1.5000000e+01j 1.32750000e+03 +1.2400000e+03j 2.47500000e+02 +1.2847500e+04j -6.71456250e+04 +6.7818750e+04j -5.00000000e+00 -6.0000000e+00j 3.00000000e+00 -3.3000000e+01j 1.64500000e+02 -1.3200000e+02j 1.48050000e+03 +1.8450000e+02j 6.68062500e+03 +8.8402500e+03j 7.00000000e+00 -1.6000000e+01j 6.90000000e+01 -2.7000000e+01j 4.28500000e+02 +1.9700000e+02j 1.11150000e+03 +3.1455000e+03j -1.09998750e+04 +2.2201500e+04j 6.10000000e+01 +0.0000000e+00j 1.83000000e+02 +1.8300000e+02j -3.05000000e+01 +1.6470000e+03j -8.50950000e+03 +7.9605000e+03j -8.64446250e+04 -4.1175000e+03j 9.70000000e+01 +2.1400000e+02j -3.51000000e+02 +9.3300000e+02j -5.82650000e+03 +2.5120000e+03j -4.14585000e+04 -1.7194500e+04j -1.23016125e+05 -3.0981225e+05j]]