07-01 NumPy，NumPy配列
NumPy，NumPy配列¶
01-01. ndarray¶
# 01-01. ndarray
import numpy as np
a = np.array([1, 2, 3])
b = np.array([6, 3.3, 1])
C = np.array([[1, 5, 6], [7, 8, 9], [4, 2, 3]])
D = np.array([[2.3, 4, 7.2], [7, 9, 1], [11, 2, 9]])01-02. ndarrayの属性¶
# 01-02. ndarrayの属性
# 配列の形状
print(a.shape)
print(C.shape)
# 次元
print(b.ndim)
print(D.ndim)
# （要素の）型
print(a.dtype)
print(D.dtype)
# 配列のキャスト
e = a.astype(float)
F = D.astype(int)
print(e)
print(F)(3,)
(3, 3)
1
2
int64
float64
[1. 2. 3.]
[[ 2 4 7]
[ 7 9 1]
[11 2 9]]
01-03. 基本的な演算¶
# 01-03. 基本的な演算
# 同次元の加算・減算
print("a + b: ", a + b)
print("b - a: ", b - a)
print("C + D: \n", C + D)
print("C - F: \n", C - F)
# 異なる次元の加算・減算
print("a + C: \n", a + C)
print("D - b: \n", D - b)
# 乗算・除算
print("a*b: ", a * b)
print("C/a: \n", C / a)a + b: [7. 5.3 4. ]
b - a: [ 5. 1.3 -2. ]
C + D:
[[ 3.3 9. 13.2]
[14. 17. 10. ]
[15. 4. 12. ]]
C - F:
[[-1 1 -1]
[ 0 -1 8]
[-7 0 -6]]
a + C:
[[ 2 7 9]
[ 8 10 12]
[ 5 4 6]]
D - b:
[[-3.7 0.7 6.2]
[ 1. 5.7 0. ]
[ 5. -1.3 8. ]]
a*b: [6. 6.6 3. ]
C/a:
[[1. 2.5 2. ]
[7. 4. 3. ]
[4. 1. 1. ]]
01-04. 基本的な関数による演算¶
# 01-04. 基本的な関数による演算
# 指数
print("a**2: ", a**2)
print("np.exp(2): ", np.exp(2))
print("np.exp(a): ", np.exp(a))
# 対数
print("np.log(2): ", np.log(2))
print("np.log(C): \n", np.log(C))
# 平方根
print("np.sqrt(2): ", np.sqrt(2))
print("np.sqrt(b): ", np.sqrt(b))
# 三角関数
print("np.sin(np.pi/2): ", np.sin(np.pi / 2))
print("np.sin(D): \n", np.sin(D))
print("np.cos(e): ", np.cos(e))a**2: [1 4 9]
np.exp(2): 7.38905609893065
np.exp(a): [ 2.71828183 7.3890561 20.08553692]
np.log(2): 0.6931471805599453
np.log(C):
[[0. 1.60943791 1.79175947]
[1.94591015 2.07944154 2.19722458]
[1.38629436 0.69314718 1.09861229]]
np.sqrt(2): 1.4142135623730951
np.sqrt(b): [2.44948974 1.81659021 1. ]
np.sin(np.pi/2): 1.0
np.sin(D):
[[ 0.74570521 -0.7568025 0.79366786]
[ 0.6569866 0.41211849 0.84147098]
[-0.99999021 0.90929743 0.41211849]]
np.cos(e): [ 0.54030231 -0.41614684 -0.9899925 ]
01-05. ベクトル・行列計算¶
# 01-05. ベクトル・行列計算
# ベクトルの基本演算
print("a+b: ", a + b)
print("a-b: ", a - b)
print("3*a: ", 3 * a)
# ベクトルの内積・外積
print("a.b, np.dot(a,b): ", np.dot(a, b))
print("axb, np.cross(a,b): ", np.cross(a, b))
# 行列の基本演算
print("C+D: \n", C + D)
print("C-D: \n", C - D)
print("2*C: \n", 2 * C)
# 行列の乗算
print("C.a, np.dot(C,a): ", np.dot(C, a))
print("C.D, np.dot(C,D): \n", np.dot(C, D))
print("D.C, np.dot(D,C): \n", np.dot(D, C))a+b: [7. 5.3 4. ]
a-b: [-5. -1.3 2. ]
3*a: [3 6 9]
a.b, np.dot(a,b): 15.6
axb, np.cross(a,b): [-7.9 17. -8.7]
C+D:
[[ 3.3 9. 13.2]
[14. 17. 10. ]
[15. 4. 12. ]]
C-D:
[[-1.3 1. -1.2]
[ 0. -1. 8. ]
[-7. 0. -6. ]]
2*C:
[[ 2 10 12]
[14 16 18]
[ 8 4 6]]
C.a, np.dot(C,a): [29 50 17]
C.D, np.dot(C,D):
[[103.3 61. 66.2]
[171.1 118. 139.4]
[ 56.2 40. 57.8]]
D.C, np.dot(D,C):
[[ 59.1 57.9 71.4]
[ 74. 109. 126. ]
[ 61. 89. 111. ]]
01-06. 線形代数向け関数¶
# 01-06. 線形代数向け関数
# 転置行列
print("C^T, C.transpose(): ", C.transpose())
print("C^T, np.transpose(C): ", np.transpose(C))
# 行列式
print("|D|, np.linalg.det(D): ", np.linalg.det(D))
# 逆行列
print("F^-1, np.linalg.inv(F): ", np.linalg.inv(F))
# 固有値・固有ベクトル
print("np.linalg.eig(C): ", np.linalg.eig(C))
print("固有値のみ, np.linalg.eigvals(C): ", np.linalg.eigvals(C))C^T, C.transpose(): [[1 7 4]
[5 8 2]
[6 9 3]]
C^T, np.transpose(C): [[1 7 4]
[5 8 2]
[6 9 3]]
|D|, np.linalg.det(D): -638.3000000000005
F^-1, np.linalg.inv(F): [[-0.12248062 0.03410853 0.09147287]
[ 0.08062016 0.09147287 -0.07286822]
[ 0.13178295 -0.0620155 0.01550388]]
np.linalg.eig(C): EigResult(eigenvalues=array([14.72735221, -3.28537742, 0.55802521]), eigenvectors=array([[ 0.43801562, 0.85468529, -0.00703173],
[ 0.84944136, -0.12913467, -0.76794748],
[ 0.29426465, -0.50282928, 0.64047421]]))
固有値のみ, np.linalg.eigvals(C): [14.72735221 -3.28537742 0.55802521]
01-07. その他の便利な関数¶
# 01-07. その他の便利な関数
# 配列の生成
Z = np.zeros([3, 4])
I = np.identity(3)
r = np.linspace(1, 2, 10)
print("Z: \n", Z)
print("I: \n", I)
print("r: ", r)
# 集約・統計
print("np.max(a)", np.max(a), a)
print("a.max()", a.max(), a)
print("np.min(C)", np.min(C), C)
print("C.min()", C.min(), C)
print("np.sum(b): ", np.sum(b), b)
print("b.sum(): ", b.sum(), b)
print("np.mean(b): ", np.mean(b))
print("b.mean(): ", b.mean(), b)
print("np.median(b): ", np.median(b))
print("np.std(D): ", np.std(D))Z:
[[0. 0. 0. 0.]
[0. 0. 0. 0.]
[0. 0. 0. 0.]]
I:
[[1. 0. 0.]
[0. 1. 0.]
[0. 0. 1.]]
r: [1. 1.11111111 1.22222222 1.33333333 1.44444444 1.55555556
1.66666667 1.77777778 1.88888889 2. ]
np.max(a) 3 [1 2 3]
a.max() 3 [1 2 3]
np.min(C) 1 [[1 5 6]
[7 8 9]
[4 2 3]]
C.min() 1 [[1 5 6]
[7 8 9]
[4 2 3]]
np.sum(b): 10.3 [6. 3.3 1. ]
b.sum(): 10.3 [6. 3.3 1. ]
np.mean(b): 3.4333333333333336
b.mean(): 3.4333333333333336 [6. 3.3 1. ]
np.median(b): 3.3
np.std(D): 3.3973846149975753