Pythonでエルミート多項式とx、y、z複素数の点の配列の疑似ファンデルモンド行列を生成します

エルミート多項式とx、y、zサンプルポイントの疑似ファンデルモンド行列を生成するには、Python Numpyでhermite.hermvander3d（）を使用します。このメソッドは、疑似ファンデルモンド行列を返します。パラメータx、y、zは、すべて同じ形状の点座標の配列です。 dtypeは、要素のいずれかが複雑であるかどうかに応じて、float64またはcomplex128のいずれかに変換されます。スカラーは1-D配列に変換されます。パラメータdegは、[x_deg、y_deg、z_deg]の形式の最大度のリストです。

ステップ

まず、必要なライブラリをインポートします-

numpy as np
from numpy.polynomial import hermite as H

numpy.array（）メソッドを使用して、すべて同じ形状の点座標の配列を作成します-

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])

配列を表示する-

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

データ型を表示する-

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

両方のアレイの寸法を確認してください-

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

両方のアレイの形状を確認してください-

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

エルミート多項式とx、y、zサンプルポイントの疑似ファンデルモンド行列を生成するには、hermite.hermvander3d（）-

x_deg, y_deg, z_deg = 2, 3, 4
print("\nResult...\n",H.hermvander3d(x,y,z, [x_deg, y_deg, z_deg]))

例

import numpy as np
from numpy.polynomial import hermite as H

# 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 Hermite polynomial and x, y, z sample points, use the hermite.hermvander3d() in Python Numpy
x_deg, y_deg, z_deg = 2, 3, 4
print("\nResult...\n",H.hermvander3d(x,y,z, [x_deg, y_deg, z_deg]))

出力

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...
[[ 1.000000e+00+0.000000e+00j 4.000000e+00+4.000000e+00j
-2.000000e+00+3.200000e+01j -1.520000e+02+1.040000e+02j
-1.012000e+03-3.840000e+02j 0.000000e+00+4.000000e+00j
-1.600000e+01+1.600000e+01j -1.280000e+02-8.000000e+00j
-4.160000e+02-6.080000e+02j 1.536000e+03-4.048000e+03j
-1.800000e+01+0.000000e+00j -7.200000e+01-7.200000e+01j
3.600000e+01-5.760000e+02j 2.736000e+03-1.872000e+03j
1.821600e+04+6.912000e+03j 0.000000e+00-8.800000e+01j
3.520000e+02-3.520000e+02j 2.816000e+03+1.760000e+02j
9.152000e+03+1.337600e+04j -3.379200e+04+8.905600e+04j
-4.000000e+00+4.000000e+00j -3.200000e+01+0.000000e+00j
-1.200000e+02-1.360000e+02j 1.920000e+02-1.024000e+03j
5.584000e+03-2.512000e+03j -1.600000e+01-1.600000e+01j
0.000000e+00-1.280000e+02j 5.440000e+02-4.800000e+02j
4.096000e+03+7.680000e+02j 1.004800e+04+2.233600e+04j
7.200000e+01-7.200000e+01j 5.760000e+02+0.000000e+00j
2.160000e+03+2.448000e+03j -3.456000e+03+1.843200e+04j
-1.005120e+05+4.521600e+04j 3.520000e+02+3.520000e+02j
0.000000e+00+2.816000e+03j -1.196800e+04+1.056000e+04j
-9.011200e+04-1.689600e+04j -2.210560e+05-4.913920e+05j
-2.000000e+00-3.200000e+01j 1.200000e+02-1.360000e+02j
1.028000e+03+0.000000e+00j 3.632000e+03+4.656000e+03j
-1.026400e+04+3.315200e+04j 1.280000e+02-8.000000e+00j
5.440000e+02+4.800000e+02j 0.000000e+00+4.112000e+03j
-1.862400e+04+1.452800e+04j -1.326080e+05-4.105600e+04j
3.600000e+01+5.760000e+02j -2.160000e+03+2.448000e+03j
-1.850400e+04+0.000000e+00j -6.537600e+04-8.380800e+04j
1.847520e+05-5.967360e+05j -2.816000e+03+1.760000e+02j
-1.196800e+04-1.056000e+04j 0.000000e+00-9.046400e+04j
4.097280e+05-3.196160e+05j 2.917376e+06+9.032320e+05j]
[ 1.000000e+00+0.000000e+00j 6.000000e+00+6.000000e+00j
-2.000000e+00+7.200000e+01j -4.680000e+02+3.960000e+02j
-5.172000e+03-8.640000e+02j 2.000000e+00+4.000000e+00j
-1.200000e+01+3.600000e+01j -2.920000e+02+1.360000e+02j
-2.520000e+03-1.080000e+03j -6.888000e+03-2.241600e+04j
-1.400000e+01+1.600000e+01j -1.800000e+02+1.200000e+01j
-1.124000e+03-1.040000e+03j 2.160000e+02-1.303200e+04j
8.623200e+04-7.065600e+04j -1.000000e+02-4.000000e+01j
-3.600000e+02-8.400000e+02j 3.080000e+03-7.120000e+03j
6.264000e+04-2.088000e+04j 4.826400e+05+2.932800e+05j
-2.000000e+00+4.000000e+00j -3.600000e+01+1.200000e+01j
-2.840000e+02-1.520000e+02j -6.480000e+02-2.664000e+03j
1.380000e+04-1.896000e+04j -2.000000e+01+0.000000e+00j
-1.200000e+02-1.200000e+02j 4.000000e+01-1.440000e+03j
9.360000e+03-7.920000e+03j 1.034400e+05+1.728000e+04j
-3.600000e+01-8.800000e+01j 3.120000e+02-7.440000e+02j
6.408000e+03-2.416000e+03j 5.169600e+04+2.692800e+04j
1.101600e+05+4.862400e+05j 3.600000e+02-3.200000e+02j
4.080000e+03+2.400000e+02j 2.232000e+04+2.656000e+04j
-4.176000e+04+2.923200e+05j -2.138400e+06+1.344000e+06j
-1.400000e+01-1.600000e+01j 1.200000e+01-1.800000e+02j
1.180000e+03-9.760000e+02j 1.288800e+04+1.944000e+03j
5.858400e+04+9.484800e+04j 3.600000e+01-8.800000e+01j
7.440000e+02-3.120000e+02j 6.264000e+03+2.768000e+03j
1.800000e+04+5.544000e+04j -2.622240e+05+4.240320e+05j
4.520000e+02+0.000000e+00j 2.712000e+03+2.712000e+03j
-9.040000e+02+3.254400e+04j -2.115360e+05+1.789920e+05j
-2.337744e+06-3.905280e+05j 7.600000e+02+2.160000e+03j
-8.400000e+03+1.752000e+04j -1.570400e+05+5.040000e+04j
-1.211040e+06-7.099200e+05j -2.064480e+06-1.182816e+07j]]