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#!/usr/bin/env python
# coding: utf-8
# # Numpy tutorial
# ## 참고 사이트
# [Python Tutorial](https://docs.python.org/3/tutorial/)
# [Numpy Tutorial](https://docs.scipy.org/doc/numpy/user/quickstart.html)
# [Numpy Reference](https://docs.scipy.org/doc/numpy/reference/index.html#reference)
# [Numpy 참고사이트](http://taewan.kim/post/numpy_cheat_sheet/#2-배열-생성)
# ---
# ## 1. The Basics
# ### 1.1 An example
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import numpy as np
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a = np.arange(15).reshape(3, 5)
a
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a.shape
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a.ndim
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a.dtype.name
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a.itemsize # size(byte) of item
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a.size
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type(a)
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b = np.array([6, 7, 8])
b
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type(b)
# ### 1.2 Array Creation
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a = np.array([2,3,4])
a
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a.dtype
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b = np.array([1.2, 3.5, 5.1])
b.dtype
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a = np.array(1,2,3,4) # WRONG
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a = np.array([1,2,3,4]) # RIGHT
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b = np.array([(1.5,2,3), (4,5,6)])
b
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c = np.array( [ [1,2], [3,4] ], dtype=complex )
c
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np.zeros( (3,4) )
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np.ones( (2,3,4), dtype=np.int16 )
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np.empty( (2,3) )
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np.arange( 10, 30, 5 )
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np.arange( 0, 2, 0.3 ) # it accepts float arguments
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from numpy import pi
np.linspace( 0, 2, 9 ) # 9 numbers from 0 to 2
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x = np.linspace( 0, 2*pi, 100 ) # useful to evaluate function at lots of points
f = np.sin(x)
f
# ### 1.3 Printing Arrays
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a = np.arange(6) # 1d array
print(a)
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b = np.arange(12).reshape(4,3) # 2d array
print(b)
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c = np.arange(24).reshape(2,3,4) # 3d array
print(c)
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print(np.arange(10000))
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print(np.arange(10000).reshape(100,100))
# ### 1.4 Basic Operations
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a = np.array( [20,30,40,50] )
a
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b = np.arange( 4 )
b
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c = a-b
c
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b**2
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10 * np.sin(a)
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a < 35
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A = np.array( [[1,1],
[0,1]] )
B = np.array( [[2,0],
[3,4]] )
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A * B # elementwise product
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A @ B # matrix product
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A.dot(B) # another matrix product
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a = np.ones((2,3), dtype=int)
b = np.random.random((2,3))
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a *= 3
a
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b += a
b
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a += b # b is not automatically converted to integer type
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a = np.ones(3, dtype=np.int32)
b = np.linspace(0,pi,3)
b.dtype.name
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c = a+b
c
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c.dtype.name
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d = np.exp(c*1j)
d
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d.dtype.name
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a = np.random.random((2,3))
a
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a.sum()
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a.min()
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a.max()
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b = np.arange(12).reshape(3,4)
b
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b.sum(axis=0) # sum of each column
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b.min(axis=1) # min of each row
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b.cumsum(axis=1) # cumulative sum along each row
# ### 1.5 Universal Functions
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B = np.arange(3)
B
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np.exp(B)
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np.sqrt(B)
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C = np.array([2., -1., 4.])
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np.add(B, C)
# ### 1.6 Indexing, Slicing and Iterating
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a = np.arange(10)**3
a
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a[2]
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a[2:5]
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a[:6:2] = -1000
a
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a[ : :-1] # reversed a
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for i in a:
print(i**(1/3.))
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def f(x,y):
return 10*x+y
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b = np.fromfunction(f,(5,4),dtype=int)
b
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b[2,3]
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b[0:5, 1] # each row in the second column of b
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b[ : ,1] # equivalent to the previous example
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b[1:3, : ] # each column in the second and third row of b
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b[-1] # the last row. Equivalent to b[-1,:]
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c = np.array( [[[ 0, 1, 2], # a 3D array (two stacked 2D arrays)
[ 10, 12, 13]],
[[100,101,102],
[110,112,113]]])
c.shape
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c[1,...] # same as c[1,:,:] or c[1]
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c[...,2] # same as c[:,:,2]
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for row in b:
print(row)
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for element in b.flat:
print(element)
# ---
# ## 2. Shape Manipulation
# ### 2.1 Changing the shape of an array
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a = np.floor(10*np.random.random((3,4)))
a
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a.shape
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a.ravel() # returns the array, flattened
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a.reshape(6,2) # returns the array with a modified shape
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a.T # returns the array, transposed
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a.T.shape
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a.shape
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# The reshape function returns its argument with a modified shape,
# whereas the ndarray.resize method modifies the array itself
a
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a.resize((2,6))
a
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a.reshape(3,-1)
# ### 2.2 Stacking together different arrays
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a = np.floor(10*np.random.random((2,2)))
a
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b = np.floor(10*np.random.random((2,2)))
b
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np.vstack((a,b))
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np.hstack((a,b))
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from numpy import newaxis
np.column_stack((a,b)) # with 2D arrays
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a = np.array([4.,2.])
a
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b = np.array([3.,8.])
b
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np.column_stack((a,b)) # returns a 2D array
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np.hstack((a,b)) # the result is different
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a[:,newaxis] # this allows to have a 2D columns vector
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np.column_stack((a[:,newaxis],b[:,newaxis]))
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np.hstack((a[:,newaxis],b[:,newaxis])) # the result is the same
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# In complex cases, r_ and c_ are useful for creating arrays by stacking numbers along one axis.
# They allow the use of range literals (“:”)
np.r_[1:4,0,4]
# ### 2.3 Splitting one array into several smaller ones
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a = np.floor(10*np.random.random((2,12)))
a
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np.hsplit(a,3) # Split a into 3
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np.hsplit(a,(3,4)) # Split a after the third and the fourth column
# ---
# ## 3. Copies and Views
# ### 3.1 No Copy at All
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a = np.arange(12)
a
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b = a # no new object is created
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b is a # a and b are two names for the same ndarray object
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b.shape = 3,4 # changes the shape of a
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a.shape
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def f(x):
print(id(x))
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id(a) # id is a unique identifier of an object
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f(a)
# ### 3.2 View or Shallow Copy
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c = a.view()
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c is a
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c.base is a # c is a view of the data owned by a
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c.flags.owndata
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c.shape = 2,6 # a's shape doesn't change
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a.shape
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c[0,4] = 1234 # a's data changes
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a
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s = a[ : , 1:3] # spaces added for clarity; could also be written "s = a[:,1:3]"
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s[:] = 10 # s[:] is a view of s. Note the difference between s=10 and s[:]=10
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a
# ### 3.3 Deep Copy
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d = a.copy() # a new array object with new data is created
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d is a
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d.base is a # d doesn't share anything with a
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d[0,0] = 9999
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a
# ---
# ## 4. Fancy indexing and index tricks
# ### 4.1 Indexing with Arrays of Indices
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a = np.arange(12)**2 # the first 12 square numbers
a
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i = np.array( [ 1,1,3,8,5 ] ) # an array of indices
i
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a[i] # the elements of a at the positions i
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j = np.array( [ [ 3, 4], [ 9, 7 ] ] ) # a bidimensional array of indices
j
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a[j]
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palette = np.array( [ [0,0,0], # black
[255,0,0], # red
[0,255,0], # green
[0,0,255], # blue
[255,255,255] ] ) # white
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image = np.array( [ [ 0, 1, 2, 0 ], # each value corresponds to a color in the palette
[ 0, 3, 4, 0 ] ] )
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palette[image] # the (2,4,3) color image
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a = np.arange(12).reshape(3,4)
a
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i = np.array( [ [0,1], # indices for the first dim of a
[1,2] ] )
j = np.array( [ [2,1], # indices for the second dim
[3,3] ] )
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a[i,j] # i and j must have equal shape
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a[i,2]
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a[:,j] # i.e., a[ : , j]
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l = [i,j]
l
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a[l] # equivalent to a[i,j]
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s = np.array( [i,j] )
s
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a[s] # not what we want
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a[tuple(s)] # same as a[i,j]
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time = np.linspace(20, 145, 5) # time scale
time
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data = np.sin(np.arange(20)).reshape(5,4) # 4 time-dependent series
data
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ind = data.argmax(axis=0) # index of the maxima for each series
ind
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time_max = time[ind] # times corresponding to the maxima
time_max
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data_max = data[ind, range(data.shape[1])] # => data[ind[0],0], data[ind[1],1]...
data_max
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np.all(data_max == data.max(axis=0))
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a = np.arange(5)
a
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a[[1,3,4]] = 0
a
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a = np.arange(5)
a
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a[[0,0,2]]=[1,2,3]
a
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a = np.arange(5)
a
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a[[0,0,2]]+=1
a
# ### 4.2 Indexing with Boolean Arrays
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a = np.arange(12).reshape(3,4)
a
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b = a > 4
b # b is a boolean with a's shape
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a[b] # 1d array with the selected elements
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a[b] = 0 # All elements of 'a' higher than 4 become 0
a
# [망델브로 집합](https://ko.wikipedia.org/wiki/망델브로_집합)
# In[ ]:
import numpy as np
import matplotlib.pyplot as plt
get_ipython().run_line_magic('matplotlib', 'inline')
def mandelbrot( h,w, maxit=20 ):
"""Returns an image of the Mandelbrot fractal of size (h,w)."""
y,x = np.ogrid[ -1.4:1.4:h*1j, -2:0.8:w*1j ]
c = x+y*1j
z = c
divtime = maxit + np.zeros(z.shape, dtype=int)
for i in range(maxit):
z = z**2 + c
diverge = z*np.conj(z) > 2**2 # who is diverging
div_now = diverge & (divtime==maxit) # who is diverging now
divtime[div_now] = i # note when
z[diverge] = 2 # avoid diverging too much
return divtime
plt.imshow(mandelbrot(400,400))
plt.show()
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a = np.arange(12).reshape(3,4)
a
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b1 = np.array([False,True,True]) # first dim selection
b2 = np.array([True,False,True,False]) # second dim selection
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a[b1,:] # selecting rows
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a[b1] # same thing
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a[:,b2] # selecting columns
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a[b1,b2] # a weird thing to do
# ### 4.3 The ix_() function
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a = np.array([2,3,4,5])
b = np.array([8,5,4])
c = np.array([5,4,6,8,3])
# In[ ]:
ax,bx,cx = np.ix_(a,b,c)
# In[ ]:
ax
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bx
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cx
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ax.shape, bx.shape, cx.shape
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result = ax+bx*cx
result
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result[3,2,4]
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a[3]+b[2]*c[4]
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def ufunc_reduce(ufct, *vectors):
vs = np.ix_(*vectors)
r = ufct.identity
for v in vs:
r = ufct(r,v)
return r
# In[ ]:
ufunc_reduce(np.add,a,b,c)
# ---
# ## 5. Linear Algebra
# [<참고>선형대수 함수](https://rfriend.tistory.com/380)
# ### 5.1 Simple Array Operations
# In[ ]:
import numpy as np
a = np.array([[1.0, 2.0], [3.0, 4.0]])
print(a)
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a.transpose()
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np.linalg.inv(a)
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u = np.eye(2) # unit 2x2 matrix; "eye" represents "I"
u
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j = np.array([[0.0, -1.0], [1.0, 0.0]])
j
# In[ ]:
j @ j # matrix product
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np.trace(u) # trace
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y = np.array([[5.], [7.]])
y
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np.linalg.solve(a, y)
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np.linalg.eig(j)
# ---
# ## 6. Tricks and Tips
# ### 6.1 Automatic Reshaping
# In[ ]:
a = np.arange(30)
a
# In[ ]:
a.shape = 2,-1,3 # -1 means "whatever is needed"
a.shape
# In[ ]:
a
# ### 6.2 Vector Stacking
# In[ ]:
x = np.arange(0,10,2) # x=([0,2,4,6,8])
x
# In[ ]:
y = np.arange(5) # y=([0,1,2,3,4])
y
# In[ ]:
m = np.vstack([x,y]) # m=([[0,2,4,6,8],
m
# In[ ]:
xy = np.hstack([x,y]) # xy =([0,2,4,6,8,0,1,2,3,4])
xy
# ### 6.3 Histograms
# In[ ]:
import numpy as np
import matplotlib.pyplot as plt
get_ipython().run_line_magic('matplotlib', 'inline')
# Build a vector of 10000 normal deviates with variance 0.5^2 and mean 2
mu, sigma = 2, 0.5
v = np.random.normal(mu,sigma,10000)
# Plot a normalized histogram with 50 bins
plt.hist(v, bins=50, density=1) # matplotlib version (plot)
plt.show()
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# Compute the histogram with numpy and then plot it
(n, bins) = np.histogram(v, bins=50, density=True) # NumPy version (no plot)
plt.plot(.5*(bins[1:]+bins[:-1]), n)
plt.show()
# ---
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# end of file
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