파이썬 (0418) 7주차

numpy
Author

김보람

Published

April 18, 2022

import numpy as np

numpy공부 7단계

note 1: 메소드 도움말 확인하기

- 파이썬에서 함수를 적용하는 2가지 방식 - np.sum(a) - a.sum()

a=np.array([1,2,3,4,5])
a
array([1, 2, 3, 4, 5])
a.sum()
15
np.sum(a)
15

- 넘파이에서 a.sum에 대한 도움말은 보통 np.sum()에 자세히 나와있음 \(\to\) np.sum()의 도움말을 확인하고 np.sum(a)와 a.sum()이 동일함을 이용하여 a.sum()의 사용법을 미루어 유추해야함

a.sum?
np.sum?
np.sum([0.5, 1.5])
2.0

note2: hstack, vstack

- hstack, vstack를 쓰는 사람도 있다.

a=np.arange(6)
b=-a
np.vstack([a,b])
array([[ 0,  1,  2,  3,  4,  5],
       [ 0, -1, -2, -3, -4, -5]])
np.stack([a,b],axis=0)
array([[ 0,  1,  2,  3,  4,  5],
       [ 0, -1, -2, -3, -4, -5]])
np.hstack([a,b])
array([ 0,  1,  2,  3,  4,  5,  0, -1, -2, -3, -4, -5])
np.concatenate([a,b],axis=0)
array([ 0,  1,  2,  3,  4,  5,  0, -1, -2, -3, -4, -5])

note3: append

- 기능1:reshape(-1) + concat

a=np.arange(30).reshape(5,6)
b= -np.arange(8).reshape(2,2,2)
a.shape, b.shape
((5, 6), (2, 2, 2))
np.append(a,b)
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
       17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,  0, -1, -2, -3,
       -4, -5, -6, -7])
np.concatenate([a.reshape(-1), b.reshape(-1)])
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
       17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,  0, -1, -2, -3,
       -4, -5, -6, -7])

- 기능2: concat

a=np.arange(2*3*4).reshape(2,3,4)
b=-a
a.shape, b.shape, np.append(a,b, axis=0).shape   # 대괄호를 쓰지 않아도 됨
((2, 3, 4), (2, 3, 4), (4, 3, 4))
a.shape, b.shape, np.append(a,b, axis=1).shape
((2, 3, 4), (2, 3, 4), (2, 6, 4))
a.shape, b.shape, np.append(a,b, axis=2).shape
((2, 3, 4), (2, 3, 4), (2, 3, 8))

- concat과의 차이?

a=np.arange(2*3*4).reshape(2,3,4)
b=-a
c=2*a
np.concatenate([a,b,c],axis=0)
array([[[  0,   1,   2,   3],
        [  4,   5,   6,   7],
        [  8,   9,  10,  11]],

       [[ 12,  13,  14,  15],
        [ 16,  17,  18,  19],
        [ 20,  21,  22,  23]],

       [[  0,  -1,  -2,  -3],
        [ -4,  -5,  -6,  -7],
        [ -8,  -9, -10, -11]],

       [[-12, -13, -14, -15],
        [-16, -17, -18, -19],
        [-20, -21, -22, -23]],

       [[  0,   2,   4,   6],
        [  8,  10,  12,  14],
        [ 16,  18,  20,  22]],

       [[ 24,  26,  28,  30],
        [ 32,  34,  36,  38],
        [ 40,  42,  44,  46]]])

note4: revel, flatten

a=np.arange(2*3*4).reshape(2,3,4)
a
array([[[ 0,  1,  2,  3],
        [ 4,  5,  6,  7],
        [ 8,  9, 10, 11]],

       [[12, 13, 14, 15],
        [16, 17, 18, 19],
        [20, 21, 22, 23]]])
a.reshape(-1) #디멘전 1차원으로
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
       17, 18, 19, 20, 21, 22, 23])
a.ravel()
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
       17, 18, 19, 20, 21, 22, 23])
a.flatten()
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
       17, 18, 19, 20, 21, 22, 23])

note 5: 기타 통계함수들

- 평균, 중앙값, 표준편차, 분산

a=np.random.normal(loc=0, scale=2, size=(100,))
a
array([-2.01759369e+00,  1.70831942e+00, -7.66284153e-01,  2.15177363e+00,
        1.93917905e+00, -2.74073590e-01, -2.04642372e+00, -1.98463689e+00,
        1.83815582e+00,  4.49207271e+00, -5.40520993e-03,  1.45933943e+00,
       -1.88730370e+00,  2.53422937e+00, -1.43846951e+00, -2.69938884e-01,
       -2.68912083e+00,  6.01230062e-01,  1.21155692e+00, -1.78259314e+00,
        3.08941967e-01,  1.22338707e+00, -1.03232597e+00, -1.79667669e+00,
        2.19458228e+00,  5.75514508e-01, -3.02570319e+00, -1.21868604e+00,
       -9.60932070e-01,  1.11771254e+00, -5.34063250e-01, -2.68962004e+00,
       -4.62864312e+00,  4.64113175e+00, -1.05051461e+00, -6.14152261e-01,
       -1.56320062e+00,  1.18863285e-01,  1.71819177e+00,  5.04434396e-01,
       -1.59021839e+00, -8.40274272e-01, -1.92903415e+00, -3.31025301e+00,
       -5.44121948e+00,  1.71770231e+00,  1.78729433e+00,  1.04315736e+00,
       -1.44847729e+00,  3.41070754e+00,  2.81655462e+00,  2.88886247e-01,
        2.61248115e+00, -5.28811327e-01, -2.47391400e+00, -6.04240520e-02,
       -2.86388739e+00,  2.50495252e+00,  5.34019240e+00,  8.27782165e-01,
       -2.19088172e+00, -7.82626427e-01, -1.12548033e+00, -2.09109091e+00,
       -2.06466297e+00, -5.36374068e-01, -3.65861892e+00, -1.42345921e+00,
       -6.67080354e-01, -2.57114581e+00, -2.37356246e-01, -1.01485014e-02,
       -3.65219208e+00,  1.30174327e+00,  9.43287089e-01, -5.41965726e-01,
        1.89596089e+00, -3.26373304e+00, -1.66761926e+00, -1.14963754e+00,
        4.34701574e-01, -4.87043020e-01, -5.10792557e-01, -9.05609502e-01,
        3.51588424e-01, -9.72910253e-01, -1.11823422e+00, -8.02920775e-01,
       -1.51091269e+00,  4.97543437e-01, -8.98957916e-03,  1.47902427e+00,
       -8.44007525e-01, -5.03900902e-01,  1.26720080e+00, -5.25199252e+00,
       -3.15857694e+00,  2.43006841e+00, -6.43759610e-01,  1.16296529e+00])
np.mean(a)
-0.34664187661644286
np.median(a)
-0.5352186588272133
np.std(a)
2.0168674618593685
np.var(a)
4.0677543587070515

- corr matrix, cov matrix

np.random.seed(43052)
x=np.random.randn(10000)
y=np.random.randn(10000)*2
z=np.random.randn(10000)*0.5
np.corrcoef([x,y,z]).round(2)
array([[ 1.  , -0.01,  0.01],
       [-0.01,  1.  ,  0.  ],
       [ 0.01,  0.  ,  1.  ]])
np.cov([x,y,z]).round(2)
array([[ 0.99, -0.02,  0.  ],
       [-0.02,  4.06,  0.  ],
       [ 0.  ,  0.  ,  0.25]])

note 6 : dtype

- np.array는 항상 dtype이 있다.

a=np.array([1,2,3])
a
array([1, 2, 3])
a.dtype
dtype('int32')
a=np.array([1.0,2.0,3.0])
a
array([1., 2., 3.])
a.dtype
dtype('float64')
a=1
type(a)
int
a=1.0
type(a)
float

- 같은 int라도 int16, int32, int64으로 나누어진다.

a= np.array([1,2,3], dtype=np.int64)
a
array([1, 2, 3], dtype=int64)
a= np.array([1,2,3], dtype=np.int32)
a
array([1, 2, 3])
a.dtype
dtype('int32')

- float도 float16, float32, float64가 있다.

a=np.array([1,2,3],dtype=np.float64) #64는 기본이라 표시가 안된당. 
a
array([1., 2., 3.])
a=np.array([1,2,3],dtype=np.float32)
a
array([1., 2., 3.], dtype=float32)

- 데이터타입은 아래와 같은 방법으로 변환시킬 수 있다.

a = np.array([1,2,3],dtype=np.int32)
a
array([1, 2, 3])
a=a.astype(dtype=np.int64)
a.dtype
dtype('int64')

- 문자열의 경우

a= np.array(['a','b','c'])
a
array(['a', 'b', 'c'], dtype='<U1')
a= np.array(['ab','b','c'])
a
array(['ab', 'b', 'c'], dtype='<U2')
a= np.array(['absfd','b','c'])
a
array(['absfd', 'b', 'c'], dtype='<U5')

- 문자열+숫자혼합 => 문자열로 통일

a=np.array(['a',1])
a
array(['a', '1'], dtype='<U11')
a=np.array(['a',1423])
a
array(['a', '1423'], dtype='<U11')
a=np.array(['a',1.0])
a
array(['a', '1.0'], dtype='<U32')

- 숫자를 문자열로 전환:

a=np.array([1,2,3])
a
array([1, 2, 3])
a.astype(np.str_)

# 문자열 타입으로 바뀌는
array(['1', '2', '3'], dtype='<U11')

note 7: 브로드캐스팅과 시간측정

(예비학습)

import time
t1=time.time()
t2=time.time()
t2-t1
14.808058738708496

예비학습끝

(예제) x=[0,1,2,3,4]인 벡터가 있다고 하자. (i,j)의 원소는 (x[i]-x[j])**2를 의미하는 \(5\times5\) 매트릭스를 구하라..

(풀이)

x=np.array(range(5))
x
array([0, 1, 2, 3, 4])
dist= np.zeros([5,5])
dist
array([[0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0.]])
for i in range(5):
    for j in range(5):
        dist[i,j] = (x[i]-x[j])**2
dist
array([[ 0.,  1.,  4.,  9., 16.],
       [ 1.,  0.,  1.,  4.,  9.],
       [ 4.,  1.,  0.,  1.,  4.],
       [ 9.,  4.,  1.,  0.,  1.],
       [16.,  9.,  4.,  1.,  0.]])

(풀이2)

x1=x.reshape(5,1).astype(dtype=np.float64)
x2=x.reshape(1,5).astype(dtype=np.float64)
x1
array([[0.],
       [1.],
       [2.],
       [3.],
       [4.]])
x2
array([[0., 1., 2., 3., 4.]])
x1-x2
array([[ 0., -1., -2., -3., -4.],
       [ 1.,  0., -1., -2., -3.],
       [ 2.,  1.,  0., -1., -2.],
       [ 3.,  2.,  1.,  0., -1.],
       [ 4.,  3.,  2.,  1.,  0.]])
  • (i,j)th element = x[i] - x[j]
(x1-x2)**2
array([[ 0,  1,  4,  9, 16],
       [ 1,  0,  1,  4,  9],
       [ 4,  1,  0,  1,  4],
       [ 9,  4,  1,  0,  1],
       [16,  9,  4,  1,  0]], dtype=int32)
y=x=np.array(range(10000))
dist= np.zeros([10000,10000])
dist
array([[0., 0., 0., ..., 0., 0., 0.],
       [0., 0., 0., ..., 0., 0., 0.],
       [0., 0., 0., ..., 0., 0., 0.],
       ...,
       [0., 0., 0., ..., 0., 0., 0.],
       [0., 0., 0., ..., 0., 0., 0.],
       [0., 0., 0., ..., 0., 0., 0.]])
t1=time.time()
for i in range(10000):
    for j in range(10000):
        dist[i,j] = (y[i]-y[j])**2
t2=time.time()
t2-t1
66.71002793312073
y1=y.reshape(10000,1).astype(np.float64)
y2=y.reshape(1,10000).astype(np.float64)
t1=time.time()
dist2=(y1-y2)**2
t2=time.time()
t2-t1
0.426450252532959
dist[:5,:5], dist2[:5,:5]
(array([[ 0.,  1.,  4.,  9., 16.],
        [ 1.,  0.,  1.,  4.,  9.],
        [ 4.,  1.,  0.,  1.,  4.],
        [ 9.,  4.,  1.,  0.,  1.],
        [16.,  9.,  4.,  1.,  0.]]),
 array([[ 0.,  1.,  4.,  9., 16.],
        [ 1.,  0.,  1.,  4.,  9.],
        [ 4.,  1.,  0.,  1.,  4.],
        [ 9.,  4.,  1.,  0.,  1.],
        [16.,  9.,  4.,  1.,  0.]]))
(dist-dist2).sum()
0.0

matplotlib

import matplotlib.pyplot as plt

plt.plot

- 기본그림

plt.plot([1,2,3],[3,4,5],'.')

plt.plot(np.array([1,2,3]),np.array([3,4,5]),'.')

- 예제들

t=np.linspace(-6,6,100)
t
array([-6.        , -5.87878788, -5.75757576, -5.63636364, -5.51515152,
       -5.39393939, -5.27272727, -5.15151515, -5.03030303, -4.90909091,
       -4.78787879, -4.66666667, -4.54545455, -4.42424242, -4.3030303 ,
       -4.18181818, -4.06060606, -3.93939394, -3.81818182, -3.6969697 ,
       -3.57575758, -3.45454545, -3.33333333, -3.21212121, -3.09090909,
       -2.96969697, -2.84848485, -2.72727273, -2.60606061, -2.48484848,
       -2.36363636, -2.24242424, -2.12121212, -2.        , -1.87878788,
       -1.75757576, -1.63636364, -1.51515152, -1.39393939, -1.27272727,
       -1.15151515, -1.03030303, -0.90909091, -0.78787879, -0.66666667,
       -0.54545455, -0.42424242, -0.3030303 , -0.18181818, -0.06060606,
        0.06060606,  0.18181818,  0.3030303 ,  0.42424242,  0.54545455,
        0.66666667,  0.78787879,  0.90909091,  1.03030303,  1.15151515,
        1.27272727,  1.39393939,  1.51515152,  1.63636364,  1.75757576,
        1.87878788,  2.        ,  2.12121212,  2.24242424,  2.36363636,
        2.48484848,  2.60606061,  2.72727273,  2.84848485,  2.96969697,
        3.09090909,  3.21212121,  3.33333333,  3.45454545,  3.57575758,
        3.6969697 ,  3.81818182,  3.93939394,  4.06060606,  4.18181818,
        4.3030303 ,  4.42424242,  4.54545455,  4.66666667,  4.78787879,
        4.90909091,  5.03030303,  5.15151515,  5.27272727,  5.39393939,
        5.51515152,  5.63636364,  5.75757576,  5.87878788,  6.        ])
x=np.sin(t)
y=np.cos(t)
plt.plot(t,x)

plt.plot(t,y)

plt.plot(t,x)
plt.plot(t,y)

plt.plot(t,x)
plt.plot(t,y,'.')

plt.plot(t,x)
plt.plot(t,y,'--')

plt.hist

X=np.random.randn(1000)
plt.hist(X)
(array([  3.,  14.,  66., 157., 232., 245., 155.,  92.,  28.,   8.]),
 array([-3.29472542, -2.65210581, -2.0094862 , -1.36686658, -0.72424697,
        -0.08162736,  0.56099226,  1.20361187,  1.84623148,  2.4888511 ,
         3.13147071]),
 <BarContainer object of 10 artists>)

Y=np.random.rand(1000)
plt.hist(Y)
(array([ 98., 127., 107.,  87.,  83.,  86.,  85., 118., 110.,  99.]),
 array([0.00162071, 0.10140453, 0.20118836, 0.30097218, 0.40075601,
        0.50053983, 0.60032366, 0.70010748, 0.79989131, 0.89967513,
        0.99945896]),
 <BarContainer object of 10 artists>)

plt.hist(X)
plt.hist(Y)
(array([ 98., 127., 107.,  87.,  83.,  86.,  85., 118., 110.,  99.]),
 array([0.00162071, 0.10140453, 0.20118836, 0.30097218, 0.40075601,
        0.50053983, 0.60032366, 0.70010748, 0.79989131, 0.89967513,
        0.99945896]),
 <BarContainer object of 10 artists>)