numpy notes

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[TOC]
The fundamental package for scientific computing with Python.

Introduction

  1. Best tutorial: Quickstart tutorial

  2. Since pythoner usually do import numpy as np, in most scenes ‘np’ measn ‘numpy’

  3. Note: an 1d array in numpy acts like a row vector in linear algebra, but most lienar algebra textbook are written in column form!
    In text book: matrix x column vector = column vector
    In numpy: row vector x matrix.T = row vector

  4. string type numpy array automatically encode the string to bytes!

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    new_a = a.astype('U') # get string instead of bytes

  5. 帮助：np.info
    例如np.info(np.random)

broadcasting

Broadcasting is one of most error-prone concept in numpy.

When operating on two arrays, NumPy compares their shapes element-wise. It starts with the trailing dimensions, and works its way forward. Two dimensions are compatible when:

  1. they are equal, or
  2. one of them is 1

  1. reshape can turn off the broadcast

  2. an telling example

    A (4d array): 8 x 1 x 6 x 1
    B (3d array): 7 x 1 x 5
    Result (4d array): 8 x 7 x 6 x 5

    So for a single dimension, the broadcast means numpy will expand (6 x 1) to (6 x 5)， and then do element-wise operation.

ndarray学习

numpy中的ndarray方法和属性

  • ndarray.mean(axis=None, dtype=None, out=None)：返回指定轴的数组元素均值

  • ndarray.var(axis=None, dtype=None, out=None, ddof=0)：返回数组的方差，沿指定的轴。

  • ndarray.std(axis=None, dtype=None, out=None, ddof=0)：沿给定的轴返回数则的标准差
    注意std默认是除以N而不是N-1的，如果要除以N-1，将ddof设为1；另外，pandas中std是除以N-1的。

  • ndarray.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)：返回沿对角线的数组元素之和

  • ndarray.diagonal(offset=0, axis1=0, axis2=1)：返回对角线的所有元素。

  • 最大/小值

    • ndarray.argmin(axis=None, out=None):返回指定轴最小元素的索引。
    • darray.min(axis=None, out=None)：返回指定轴的最小值

  • flat/flatten

    • ndarray.flat 和 ndarray.T 一样不是函数调用
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       >>> x = X.flat
       >>> x
    <numpy.flatiter object at 0x9e82278>
                                # 不直接返回一维数组
                                # 但可直接索引
    • flatten()是函数调用，可以指定平坦化的参数。
      ndarray.flatten(order='C')
      可选参数，order：
      （1）’C’：C-style，行序优先
      （2）’F’：Fortran-style，列序优先
      （3）’A’：保持
      （4）默认为’C’

  • ndarray.transpose(*axes) :返回矩阵的转置矩阵

  • ndarray.take(indices, axis=None, out=None, mode=’raise’):获得数组的指定索引的数据，如：

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       >>> a.take([1,3],axis=1) #提取1，3列的数据
    array([[ 1,  3],
    [ 5,  7],
    [ 9, 11]])

  • numpy.argmax(a, axis=None, out=None) 非常有用
    Returns the indices of the maximum values along an axis. doc

构造矩阵

  • arange()/linspace()
  • numpy.zeros，numpy.ones，numpy.eye, numpy.empty((2,3)), numpy.full((2,2),7) 
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       >>> print np.zeros((3,4))
    [[ 0.  0.  0.  0.]
     [ 0.  0.  0.  0.]
     [ 0.  0.  0.  0.]]
       >>> print np.ones((3,4))
    [[ 1.  1.  1.  1.]
     [ 1.  1.  1.  1.]
     [ 1.  1.  1.  1.]]
       >>> print np.eye(3)
    [[ 1.  0.  0.]
     [ 0.  1.  0.]
     [ 0.  0.  1.]]

矩阵indexing

  1. automatic reshaping

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       >>> a = np.arange(30)
       >>> a.shape = 2,-1,3  # -1 means "whatever is needed"
       >>> a.shape
    (2, 5, 3)

  2. Indexing with Arrays of Indices

  • Suppose a and idx is a np.array, then a[i].shape == idx.shape
  • Supose a, idx_i and idx_j is a np.array, if idx_i.shape == idx_j.shape, then a[i,j].shape == idx_i.shape, idx_i is the first axis index of array a, idx_j is the second axis index of array a. 
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    list_ij=[i,j]
    a[list_ij] == a[i,j] # this statement is true
  1. Indexing with Boolean Arrays
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       >>> a = np.arange(12).reshape(3,4)
       >>> b = a > 4
       >>> b                                          # b is a boolean with a's shape
    array([[False, False, False, False],
           [False,  True,  True,  True],
           [ True,  True,  True,  True]], dtype=bool)
       >>> a[b]                                       # 1d array with the selected elements
    array([ 5,  6,  7,  8,  9, 10, 11])
       >>> a[b]=0
       >>> a
    array([[0, 1, 2, 3],
           [4, 0, 0, 0],
           [0, 0, 0, 0]])

Note that a[b] is a 1d array! But a[b]=0 is a 2d array! This is because if you don’t assign a value to the ‘False’ element, there is no value for that element.

数据添加与拷贝

  • c=a.copy深拷贝

  • vstack和hstack函数：
    vstack、hstack是深拷贝

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       >>> a = np.ones((2,2))
       >>> b = np.eye(2)
       >>> print np.vstack((a,b))
    [[ 1.  1.]
     [ 1.  1.]
     [ 1.  0.]
     [ 0.  1.]]

  • row_stack(matrix,a_row) 向二维矩阵尾部添加一行

numpy.linalg

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   >>> import numpy.linalg as nplg
   >>> a = np.array([[1,0],[2,3]])
   >>> print nplg.eig(a)
(array([ 3.,  1.]), array([[ 0.        ,  0.70710678],
       [ 1.        , -0.70710678]]))

comparison

  • a == b #逐个元素比较
  • a < 2
  • np.array_equal(a,b)

arithmetic operation

  • +, -, *, / #element-wise
  • np.dot(a,b) # matrix multiply

I/O

  • np.save(‘myarray’,a)
  • np.savez(‘myarray.npz’,a,b)
  • np.save(‘myarray.npy’,a)
  • np.loadtxt/savetxt/genfromtxt

Other

  • np.newaxis
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a=np.array([1,2,3,4,5])
b=a[np.newaxis,:]
print(a.shape,b.shape)
(5,) (1, 5)
a=np.array([1,2,3,4,5])
b=a[:,np.newaxis]
print(a.shape,b.shape)
(5,) (5, 1)
谢谢~