Numpy教程导读-1

#The Basics

rank
demension(axis)
axis length

numpy.ndarray

ndarray.ndim
the number of axes (dimensions) of the array. In the Python world, the number of dimensions is referred to as rank.

ndarray.shape
the dimensions of the array. This is a tuple of integers indicating the size of the array in each dimension. For a matrix with n rows and m columns, shape will be (n,m). The length of the shape tuple is therefore the rank, or number of dimensions, ndim.

ndarray.size
the total number of elements of the array. This is equal to the product of the elements of shape.

ndarray.dtype
an object describing the type of the elements in the array. One can create or specify dtype’s using standard Python types. Additionally NumPy provides types of its own. numpy.int32, numpy.int16, and numpy.float64 are some examples.

ndarray.itemsize
the size in bytes of each element of the array. For example, an array of elements of type float64 has itemsize 8 (=64/8), while one of type complex32 has itemsize 4 (=32/8). It is equivalent to ndarray.dtype.itemsize.

ndarray.data
the buffer containing the actual elements of the array. Normally, we won’t need to use this attribute because we will access the elements in an array using indexing facilities.

In [1]: from numpy import *

In [2]: a = arange(15).reshape(3,5)

In [3]: a
Out[3]: 
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14]])

In [4]: a.shape
Out[4]: (3, 5)

In [5]: a.ndim
Out[5]: 2

In [6]: a.dtype.name
Out[6]: 'int32'

In [7]: a.itemsize
Out[7]: 4

In [8]: type(a)
Out[8]: numpy.ndarray

In [9]: b = array([6,7,8])

In [10]: b
Out[10]: array([6, 7, 8])

In [11]: type(b)
Out[11]: numpy.ndarray

##Array Creation

There are several ways to create arrays.
For example, you can create an array from a regular Python list or tuple using the array function. The type of the resulting array is deduced from the type of the elements in the sequences.

In [1]: from numpy import *

In [2]: a = array( [2,3,4] )

In [3]: a
Out[3]: array([2, 3, 4])

In [4]: a.dtype
Out[4]: dtype('int32')

In [5]: b = array( [1.2,3.5,4.7] )

In [6]: b
Out[6]: array([ 1.2,  3.5,  4.7])

In [7]: b.dtype
Out[7]: dtype('float64')

In [8]: b.itemsize
Out[8]: 8

In [9]: a.itemsize
Out[9]: 4

常见错误
A frequent error consists in calling array with multiple numeric arguments, rather than providing a single list of numbers as an argument.

>>> a = array(1,2,3,4)    # WRONG

>>> a = array([1,2,3,4])  # RIGHT

The type of the array can also be explicitly specified at creation time:

>>> c = array( [ [1,2], [3,4] ], dtype=complex )
>>> c
array([[ 1.+0.j,  2.+0.j],
       [ 3.+0.j,  4.+0.j]])

Often, the elements of an array are originally unknown, but its size is known. Hence, NumPy offers several functions to create arrays with initial placeholder content. These minimize the necessity of growing arrays, an expensive operation.

The function zeros creates an array full of zeros, the function ones creates an array full of ones, and the function empty creates an array whose initial content is random and depends on the state of the memory. By default, the dtype of the created array is float64.

>>> zeros( (3,4) )
array([[0.,  0.,  0.,  0.],
       [0.,  0.,  0.,  0.],
       [0.,  0.,  0.,  0.]])
>>> ones( (2,3,4), dtype=int16 )                # dtype can also be specified
array([[[ 1, 1, 1, 1],
        [ 1, 1, 1, 1],
        [ 1, 1, 1, 1]],
       [[ 1, 1, 1, 1],
        [ 1, 1, 1, 1],
        [ 1, 1, 1, 1]]], dtype=int16)
>>> empty( (2,3) )
array([[  3.73603959e-262,   6.02658058e-154,   6.55490914e-260],
       [  5.30498948e-313,   3.14673309e-307,   1.00000000e+000]])

To create sequences of numbers, NumPy provides a function analogous to range that returns arrays instead of lists

>>> arange( 10, 30, 5 )
array([10, 15, 20, 25])
>>> arange( 0, 2, 0.3 )                 # it accepts float arguments
array([ 0. ,  0.3,  0.6,  0.9,  1.2,  1.5,  1.8])

When arange is used with floating point arguments, it is generally not possible to predict the number of elements obtained, due to the finite floating point precision. For this reason, it is usually better to use the function linspace that receives as an argument the number of elements that we want, instead of the step:

精度问题
第三个参数换成需要的数的数量(number of elements)而不是步长(step)

>>> linspace( 0, 2, 9 )                 # 9 numbers from 0 to 2
array([ 0.  ,  0.25,  0.5 ,  0.75,  1.  ,  1.25,  1.5 ,  1.75,  2.  ])
>>> x = linspace( 0, 2*pi, 100 )        # useful to evaluate function at lots of points
>>> f = sin(x)

##Printing Arrays
When you print an array, NumPy displays it in a similar way to nested lists, but with the following layout:
the last axis is printed from left to right,
the second-to-last is printed from top to bottom,
the rest are also printed from top to bottom, with each slice separated from the next by an empty line.

One-dimensional arrays are then printed as rows, bidimensionals as matrices and tridimensionals as lists of matrices.

>>> a = arange(6)                         # 1d array
>>> print a
[0 1 2 3 4 5]
>>>
>>> b = arange(12).reshape(4,3)           # 2d array
>>> print b
[[ 0  1  2]
 [ 3  4  5]
 [ 6  7  8]
 [ 9 10 11]]
>>>
>>> c = arange(24).reshape(2,3,4)         # 3d array
>>> print c
[[[ 0  1  2  3]
  [ 4  5  6  7]
  [ 8  9 10 11]]

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

If an array is too large to be printed, NumPy automatically skips the central part of the array and only prints the corners:

>>> print arange(10000)
[   0    1    2 ..., 9997 9998 9999]
>>>
>>> print arange(10000).reshape(100,100)
[[   0    1    2 ...,   97   98   99]
 [ 100  101  102 ...,  197  198  199]
 [ 200  201  202 ...,  297  298  299]
 ...,
 [9700 9701 9702 ..., 9797 9798 9799]
 [9800 9801 9802 ..., 9897 9898 9899]
 [9900 9901 9902 ..., 9997 9998 9999]]

To disable this behaviour and force NumPy to print the entire array, you can change the printing options using set_printoptions.

>>> set_printoptions(threshold='nan')

##Basic Operations

elementwise 逐个元素地

>>> a = array( [20,30,40,50] )
>>> b = arange( 4 )
>>> b
array([0, 1, 2, 3])
>>> c = a-b
>>> c
array([20, 29, 38, 47])
>>> b**2
array([0, 1, 4, 9])
>>> 10*sin(a)
array([ 9.12945251, -9.88031624,  7.4511316 , -2.62374854])
>>> a<35
array([True, True, False, False], dtype=bool)

Unlike in many matrix languages, the product operator * operates elementwise in NumPy arrays. The matrix product can be performed using the dot function or creating matrix objects ( see matrix section of this tutorial ).

矩阵乘法需要使用dot(A,B)

>>> A = array( [[1,1],
...             [0,1]] )
>>> B = array( [[2,0],
...             [3,4]] )
>>> A*B                         # elementwise product
array([[2, 0],
       [0, 4]])
>>> dot(A,B)                    # matrix product
array([[5, 4],
       [3, 4]])

Some operations, such as += and *=, act in place to modify an existing array rather than create a new one.

不产生新的array的操作

注意自动的数据类型转换

b is converted to integer type

>>> a = ones((2,3), dtype=int)
>>> b = random.random((2,3))
>>> a *= 3
>>> a
array([[3, 3, 3],
       [3, 3, 3]])
>>> b += a
>>> b
array([[ 3.69092703,  3.8324276 ,  3.0114541 ],
       [ 3.18679111,  3.3039349 ,  3.37600289]])
>>> a += b                                  # b is converted to integer type
>>> a
array([[6, 6, 6],
       [6, 6, 6]])

###数据类型转换
向上转型(upcasting)

When operating with arrays of different types, the type of the resulting array corresponds to the more general or precise one (a behavior known as upcasting).

>>> a = ones(3, dtype=int32)
>>> b = linspace(0,pi,3)
>>> b.dtype.name
'float64'
>>> c = a+b
>>> c
array([ 1.        ,  2.57079633,  4.14159265])
>>> c.dtype.name
'float64'
>>> d = exp(c*1j)
>>> d
array([ 0.54030231+0.84147098j, -0.84147098+0.54030231j,
       -0.54030231-0.84147098j])
>>> d.dtype.name
'complex128'

###一元运算符
Many unary operations, such as computing the sum of all the elements in the array, are implemented as methods of the ndarray class.

>>> a = random.random((2,3))
>>> a
array([[ 0.6903007 ,  0.39168346,  0.16524769],
       [ 0.48819875,  0.77188505,  0.94792155]])
>>> a.sum()
3.4552372100521485
>>> a.min()
0.16524768654743593
>>> a.max()
0.9479215542670073

###按行按列操作

By default, these operations apply to the array as though it were a list of numbers, regardless of its shape. However, by specifying the axis parameter you can apply an operation along the specified axis of an array:

>>> b = arange(12).reshape(3,4)
>>> b
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])
>>>
>>> b.sum(axis=0)                            # sum of each column
array([12, 15, 18, 21])
>>>
>>> b.min(axis=1)                            # min of each row
array([0, 4, 8])
>>>
>>> b.cumsum(axis=1)                         # cumulative sum along each row
array([[ 0,  1,  3,  6],
       [ 4,  9, 15, 22],
       [ 8, 17, 27, 38]])

##Universal Functions
通用函数

NumPy provides familiar mathematical functions such as sin, cos, and exp. In NumPy, these are called “universal functions”(ufunc). Within NumPy, these functions operate elementwise on an array, producing an array as output.

>>> B = arange(3)
>>> B
array([0, 1, 2])
>>> exp(B)
array([ 1.        ,  2.71828183,  7.3890561 ])
>>> sqrt(B)
array([ 0.        ,  1.        ,  1.41421356])
>>> C = array([2., -1., 4.])
>>> add(B, C)
array([ 2.,  0.,  6.])

##Indexing, Slicing and Iterating

One-dimensional
One-dimensional arrays can be indexed, sliced and iterated over, much like lists and other Python sequences.

>>> a = arange(10)**3
>>> a
array([  0,   1,   8,  27,  64, 125, 216, 343, 512, 729])
>>> a[2]
8
>>> a[2:5]
array([ 8, 27, 64])
>>> a[:6:2] = -1000    # equivalent to a[0:6:2] = -1000; from start to position 6, exclusive, set every 2nd element to -1000
>>> a
array([-1000,     1, -1000,    27, -1000,   125,   216,   343,   512,   729])
>>> a[ : :-1]                                 # reversed a
array([  729,   512,   343,   216,   125, -1000,    27, -1000,     1, -1000])
>>> for i in a:
...         print i**(1/3.),
...
nan 1.0 nan 3.0 nan 5.0 6.0 7.0 8.0 9.0

Multidemensional
Multidimensional arrays can have one index per axis. These indices are given in a tuple separated by commas:

>>> def f(x,y):
...         return 10*x+y
...
>>> b = fromfunction(f,(5,4),dtype=int)
>>> b
array([[ 0,  1,  2,  3],
       [10, 11, 12, 13],
       [20, 21, 22, 23],
       [30, 31, 32, 33],
       [40, 41, 42, 43]])
>>> b[2,3]
23
>>> b[0:5, 1]                       # each row in the second column of b
array([ 1, 11, 21, 31, 41])
>>> b[ : ,1]                        # equivalent to the previous example
array([ 1, 11, 21, 31, 41])
>>> b[1:3, : ]                      # each column in the second and third row of b
array([[10, 11, 12, 13],
       [20, 21, 22, 23]])

When fewer indices are provided than the number of axes, the missing indices are considered complete slices:

>>> b[-1]                                  # the last row. Equivalent to b[-1,:]
array([40, 41, 42, 43])

The expression within brackets in b[i] is treated as an i followed by as many instances of : as needed to represent the remaining axes. NumPy also allows you to write this using dots as b[i,…].
The dots (…) represent as many colons as needed to produce a complete indexing tuple. For example, if x is a rank 5 array (i.e., it has 5 axes), then
x[1,2,…] is equivalent to x[1,2,:,:,:],
x[…,3] to x[:,:,:,:,3] and
x[4,…,5,:] to x[4,:,:,5,:].

>>> c = array( [ [[  0,  1,  2],               # a 3D array (two stacked 2D arrays)
...               [ 10, 12, 13]],
...
...              [[100,101,102],
...               [110,112,113]] ] )
>>> c.shape
(2, 2, 3)
>>> c[1,...]                                   # same as c[1,:,:] or c[1]
array([[100, 101, 102],
       [110, 112, 113]])
>>> c[...,2]                                   # same as c[:,:,2]
array([[  2,  13],
       [102, 113]])

Iterating over multidimensional arrays is done with respect to the first axis:

>>> for row in b:
...         print row
...
[0 1 2 3]
[10 11 12 13]
[20 21 22 23]
[30 31 32 33]
[40 41 42 43]

However, if one wants to perform an operation on each element in the array, one can use the flat attribute which is an iterator over all the elements of the array:

>>> for element in b.flat:
...         print element,
...
0 1 2 3 10 11 12 13 20 21 22 23 30 31 32 33 40 41 42 43

#Shape Manipulation

##Changing theshape of an array

An array has a shape given by the number of elements along each axis:

>>> a = floor(10*random.random((3,4)))
>>> a
array([[ 7.,  5.,  9.,  3.],
       [ 7.,  2.,  7.,  8.],
       [ 6.,  8.,  3.,  2.]])
>>> a.shape
(3, 4)

The shape of an array can be changed with various commands:

In [1]: from numpy import *

In [2]: a = floor(10*random.random((3,4)))

In [3]: a
Out[3]: 
array([[ 3.,  6.,  5.,  4.],
       [ 4.,  9.,  5.,  9.],
       [ 3.,  1.,  1.,  7.]])

In [4]: a.ravel()
Out[4]: array([ 3.,  6.,  5.,  4.,  4.,  9.,  5.,  9.,  3.,  1.,  1.,  7.])

In [5]: a
Out[5]: 
array([[ 3.,  6.,  5.,  4.],
       [ 4.,  9.,  5.,  9.],
       [ 3.,  1.,  1.,  7.]])

In [6]: a.shape = (6,2)

In [7]: a
Out[7]: 
array([[ 3.,  6.],
       [ 5.,  4.],
       [ 4.,  9.],
       [ 5.,  9.],
       [ 3.,  1.],
       [ 1.,  7.]])

In [8]: a.transpose()
Out[8]: 
array([[ 3.,  5.,  4.,  5.,  3.,  1.],
       [ 6.,  4.,  9.,  9.,  1.,  7.]])

In [9]: a
Out[9]: 
array([[ 3.,  6.],
       [ 5.,  4.],
       [ 4.,  9.],
       [ 5.,  9.],
       [ 3.,  1.],
       [ 1.,  7.]])

The order of the elements in the array resulting from ravel() is normally “C-style”, that is, the rightmost index “changes the fastest”, so the element after a[0,0] is a[0,1]. If the array is reshaped to some other shape, again the array is treated as “C-style”. Numpy normally creates arrays stored in this order, so ravel() will usually not need to copy its argument, but if the array was made by taking slices of another array or created with unusual options, it may need to be copied. The functions ravel() and reshape() can also be instructed, using an optional argument, to use FORTRAN-style arrays, in which the leftmost index changes the fastest.
The reshape function returns its argument with a modified shape, whereas the resize method modifies the array itself:

>>> a
array([[ 7.,  5.],
       [ 9.,  3.],
       [ 7.,  2.],
       [ 7.,  8.],
       [ 6.,  8.],
       [ 3.,  2.]])
>>> a.resize((2,6))
>>> a
array([[ 7.,  5.,  9.,  3.,  7.,  2.],
       [ 7.,  8.,  6.,  8.,  3.,  2.]])

If a dimension is given as -1 in a reshaping operation, the other dimensions are automatically calculated:

>>> a.reshape(3,-1)
array([[ 7.,  5.,  9.,  3.],
       [ 7.,  2.,  7.,  8.],
       [ 6.,  8.,  3.,  2.]])

##Stacking together different arrays

Several arrays can be stacked together along different axes:

>>> a = floor(10*random.random((2,2)))
>>> a
array([[ 1.,  1.],
       [ 5.,  8.]])
>>> b = floor(10*random.random((2,2)))
>>> b
array([[ 3.,  3.],
       [ 6.,  0.]])
>>> vstack((a,b))
array([[ 1.,  1.],
       [ 5.,  8.],
       [ 3.,  3.],
       [ 6.,  0.]])
>>> hstack((a,b))
array([[ 1.,  1.,  3.,  3.],
       [ 5.,  8.,  6.,  0.]])

The function column_stack stacks 1D arrays as columns into a 2D array. It is equivalent to vstack only for 1D arrays:

>>> column_stack((a,b))   # With 2D arrays
array([[ 1.,  1.,  3.,  3.],
       [ 5.,  8.,  6.,  0.]])
>>> a=array([4.,2.])
>>> b=array([2.,8.])
>>> a[:,newaxis]  # This allows to have a 2D columns vector
array([[ 4.],
       [ 2.]])
>>> column_stack((a[:,newaxis],b[:,newaxis]))
array([[ 4.,  2.],
       [ 2.,  8.]])
>>> vstack((a[:,newaxis],b[:,newaxis])) # The behavior of vstack is different
array([[ 4.],
       [ 2.],
       [ 2.],
       [ 8.]])

The function rowstack, on the other hand, stacks 1D arrays as rows into a 2D array.
For arrays of with more than two dimensions, hstack stacks along their second axes, vstack stacks along their first axes, and concatenate allows for an optional arguments giving the number of the axis along which the concatenation should happen.
Note
In complex cases, r[] and c_[] are useful for creating arrays by stacking numbers along one axis. They allow the use of range literals (“:”) :

>>> r_[1:4,0,4]
array([1, 2, 3, 0, 4])

##Splitting one array into several smaller ones

Using hsplit, you can split an array along its horizontal axis, either by specifying the number of equally shaped arrays to return, or by specifying the columns after which the division should occur:

>>> a = floor(10*random.random((2,12)))
>>> a
array([[ 8.,  8.,  3.,  9.,  0.,  4.,  3.,  0.,  0.,  6.,  4.,  4.],
       [ 0.,  3.,  2.,  9.,  6.,  0.,  4.,  5.,  7.,  5.,  1.,  4.]])
>>> hsplit(a,3)   # Split a into 3
[array([[ 8.,  8.,  3.,  9.],
       [ 0.,  3.,  2.,  9.]]), array([[ 0.,  4.,  3.,  0.],
       [ 6.,  0.,  4.,  5.]]), array([[ 0.,  6.,  4.,  4.],
       [ 7.,  5.,  1.,  4.]])]
>>> hsplit(a,(3,4))   # Split a after the third and the fourth column
[array([[ 8.,  8.,  3.],
       [ 0.,  3.,  2.]]), array([[ 9.],
       [ 9.]]), array([[ 0.,  4.,  3.,  0.,  0.,  6.,  4.,  4.],
       [ 6.,  0.,  4.,  5.,  7.,  5.,  1.,  4.]])]

#Copies and Views

When operating and manipulating arrays, their data is sometimes copied into a new array and sometimes not. This is often a source of confusion for beginners. There are three cases:

##No Copy at All

Simple assignments make no copy of array objects or of their data.

>>> a = arange(12)
>>> b = a            # no new object is created
>>> b is a           # a and b are two names for the same ndarray object
True
>>> b.shape = 3,4    # changes the shape of a
>>> a.shape
(3, 4)

##View or Shallow Copy

Different array objects can share the same data. The view method creates a new array object that looks at the same data.

视图的形状改变不影响原始数据的形状
视图内容的改变与原始数据同步

>>> c = a.view()
>>> c is a
False
>>> c.base is a                        # c is a view of the data owned by a
True
>>> c.flags.owndata
False
>>>
>>> c.shape = 2,6                      # a's shape doesn't change
>>> a.shape
(3, 4)
>>> c[0,4] = 1234                      # a's data changes
>>> a
array([[   0,    1,    2,    3],
       [1234,    5,    6,    7],
       [   8,    9,   10,   11]])

所有的对array的slice其实返回的都是视图
Slicing an array returns a view of it:

>>> s = a[ : , 1:3]     # spaces added for clarity; could also be written "s = a[:,1:3]"
>>> s[:] = 10           # s[:] is a view of s. Note the difference between s=10 and s[:]=10
>>> a
array([[   0,   10,   10,    3],
       [1234,   10,   10,    7],
       [   8,   10,   10,   11]])

##Deep Copy

The copy method makes a complete copy of the array and its data.

>>> d = a.copy()                          # a new array object with new data is created
>>> d is a
False
>>> d.base is a                           # d doesn't share anything with a
False
>>> d[0,0] = 9999
>>> a
array([[   0,   10,   10,    3],
       [1234,   10,   10,    7],
       [   8,   10,   10,   11]])

##Functions and Methods Overview

Here is a list of NumPy functions and methods names ordered in some categories. The names link to the Numpy Example List so that you can see the functions in action.

Array Creation
arange, array, copy, empty, empty_like, eye, fromfile, fromfunction, identity, linspace, logspace, mgrid, ogrid, ones, ones_like, r , zeros, zeros_like
Conversions
astype, atleast 1d, atleast 2d, atleast 3d, mat
Manipulations
array split, column stack, concatenate, diagonal, dsplit, dstack, hsplit, hstack, item, newaxis, ravel, repeat, reshape, resize, squeeze, swapaxes, take, transpose, vsplit, vstack
Questions
all, any, nonzero, where
Ordering
argmax, argmin, argsort, max, min, ptp, searchsorted, sort
Operations
choose, compress, cumprod, cumsum, inner, fill, imag, prod, put, putmask, real, sum
Basic Statistics
cov, mean, std, var
Basic Linear Algebra
cross, dot, outer, svd, vdot

#参考资料
[1] Tentative NumPy Tutorial