numpy创建单位矩阵和对角矩阵的实例


Posted in Python onNovember 29, 2019

在学习linear regression时经常处理的数据一般多是矩阵或者n维向量的数据形式,所以必须对矩阵有一定的认识基础。

numpy中创建单位矩阵借助identity()函数。更为准确的说,此函数创建的是一个n*n的单位数组,返回值的dtype=array数据形式。其中接受的参数有两个,第一个是n值大小,第二个为数据类型,一般为浮点型。单位数组的概念与单位矩阵相同,主对角线元素为1,其他元素均为零,等同于单位1。而要想得到单位矩阵,只要用mat()函数将数组转换为矩阵即可。

>>> import numpy as np
>>> help(np.identity)
     
Help on function identity in module numpy:

identity(n, dtype=None)
  Return the identity array.
  
  The identity array is a square array with ones on
  the main diagonal.
  
  Parameters
  ----------
  n : int
    Number of rows (and columns) in `n` x `n` output.
  dtype : data-type, optional
    Data-type of the output. Defaults to ``float``.
  
  Returns
  -------
  out : ndarray
    `n` x `n` array with its main diagonal set to one,
    and all other elements 0.
  
  Examples
  --------
  >>> np.identity(3)
  array([[ 1., 0., 0.],
      [ 0., 1., 0.],
      [ 0., 0., 1.]])
>>> np.identity(5)
     
array([[1., 0., 0., 0., 0.],
    [0., 1., 0., 0., 0.],
    [0., 0., 1., 0., 0.],
    [0., 0., 0., 1., 0.],
    [0., 0., 0., 0., 1.]])
>>> A = np.mat(np.identity(5))
     
>>> A
     
matrix([[1., 0., 0., 0., 0.],
    [0., 1., 0., 0., 0.],
    [0., 0., 1., 0., 0.],
    [0., 0., 0., 1., 0.],
    [0., 0., 0., 0., 1.]])

矩阵的运算中还经常使用对角阵,numpy中的对角阵用eye()函数来创建。eye()函数接受五个参数,返回一个单位数组。第一个和第二个参数N,M分别对应表示创建数组的行数和列数,当然当你只设定一个值时,就默认了N=M。第三个参数k是对角线指数,跟diagonal中的offset参数是一样的,默认值为0,就是主对角线的方向,上三角方向为正,下三角方向为负,可以取-n到+m的范围。第四个参数是dtype,用于指定元素的数据类型,第五个参数是order,用于排序,有‘C'和‘F'两个参数,默认值为‘C',为行排序,‘F'为列排序。返回值为一个单位数组。

>>> help(np.eye)
    
Help on function eye in module numpy:

eye(N, M=None, k=0, dtype=<class 'float'>, order='C')
  Return a 2-D array with ones on the diagonal and zeros elsewhere.
  
  Parameters
  ----------
  N : int
   Number of rows in the output.
  M : int, optional
   Number of columns in the output. If None, defaults to `N`.
  k : int, optional
   Index of the diagonal: 0 (the default) refers to the main diagonal,
   a positive value refers to an upper diagonal, and a negative value
   to a lower diagonal.
  dtype : data-type, optional
   Data-type of the returned array.
  order : {'C', 'F'}, optional
    Whether the output should be stored in row-major (C-style) or
    column-major (Fortran-style) order in memory.
  
    .. versionadded:: 1.14.0
  
  Returns
  -------
  I : ndarray of shape (N,M)
   An array where all elements are equal to zero, except for the `k`-th
   diagonal, whose values are equal to one.
  
  See Also
  --------
  identity : (almost) equivalent function
  diag : diagonal 2-D array from a 1-D array specified by the user.
  
  Examples
  --------
  >>> np.eye(2, dtype=int)
  array([[1, 0],
      [0, 1]])
  >>> np.eye(3, k=1)
  array([[ 0., 1., 0.],
      [ 0., 0., 1.],
      [ 0., 0., 0.]])

numpy中的diagonal()方法可以对n*n的数组和方阵取对角线上的元素,diagonal()接受三个参数。第一个offset参数是主对角线的方向,默认值为0是主对角线,上三角方向为正,下三角方向为负,可以取-n到+n的范围。第二个参数和第三个参数是在数组大于2维时指定一个2维数组时使用,默认值axis1=0,axis2=1。

>>> help(A.diagonal)
     
Help on built-in function diagonal:

diagonal(...) method of numpy.matrix instance
  a.diagonal(offset=0, axis1=0, axis2=1)
  
  Return specified diagonals. In NumPy 1.9 the returned array is a
  read-only view instead of a copy as in previous NumPy versions. In
  a future version the read-only restriction will be removed.
  
  Refer to :func:`numpy.diagonal` for full documentation.
  
  See Also
  --------
  numpy.diagonal : equivalent function
>>> help(np.diagonal)
     
Help on function diagonal in module numpy:

diagonal(a, offset=0, axis1=0, axis2=1)
  Return specified diagonals.
  
  If `a` is 2-D, returns the diagonal of `a` with the given offset,
  i.e., the collection of elements of the form ``a[i, i+offset]``. If
  `a` has more than two dimensions, then the axes specified by `axis1`
  and `axis2` are used to determine the 2-D sub-array whose diagonal is
  returned. The shape of the resulting array can be determined by
  removing `axis1` and `axis2` and appending an index to the right equal
  to the size of the resulting diagonals.
  
  In versions of NumPy prior to 1.7, this function always returned a new,
  independent array containing a copy of the values in the diagonal.
  
  In NumPy 1.7 and 1.8, it continues to return a copy of the diagonal,
  but depending on this fact is deprecated. Writing to the resulting
  array continues to work as it used to, but a FutureWarning is issued.
  
  Starting in NumPy 1.9 it returns a read-only view on the original array.
  Attempting to write to the resulting array will produce an error.
  
  In some future release, it will return a read/write view and writing to
  the returned array will alter your original array. The returned array
  will have the same type as the input array.
  
  If you don't write to the array returned by this function, then you can
  just ignore all of the above.
  
  If you depend on the current behavior, then we suggest copying the
  returned array explicitly, i.e., use ``np.diagonal(a).copy()`` instead
  of just ``np.diagonal(a)``. This will work with both past and future
  versions of NumPy.
  
  Parameters
  ----------
  a : array_like
    Array from which the diagonals are taken.
  offset : int, optional
    Offset of the diagonal from the main diagonal. Can be positive or
    negative. Defaults to main diagonal (0).
  axis1 : int, optional
    Axis to be used as the first axis of the 2-D sub-arrays from which
    the diagonals should be taken. Defaults to first axis (0).
  axis2 : int, optional
    Axis to be used as the second axis of the 2-D sub-arrays from
    which the diagonals should be taken. Defaults to second axis (1).
  
  Returns
  -------
  array_of_diagonals : ndarray
    If `a` is 2-D, then a 1-D array containing the diagonal and of the
    same type as `a` is returned unless `a` is a `matrix`, in which case
    a 1-D array rather than a (2-D) `matrix` is returned in order to
    maintain backward compatibility.
    
    If ``a.ndim > 2``, then the dimensions specified by `axis1` and `axis2`
    are removed, and a new axis inserted at the end corresponding to the
    diagonal.
  
  Raises
  ------
  ValueError
    If the dimension of `a` is less than 2.
  
  See Also
  --------
  diag : MATLAB work-a-like for 1-D and 2-D arrays.
  diagflat : Create diagonal arrays.
  trace : Sum along diagonals.
  
  Examples
  --------
  >>> a = np.arange(4).reshape(2,2)
  >>> a
  array([[0, 1],
      [2, 3]])
  >>> a.diagonal()
  array([0, 3])
  >>> a.diagonal(1)
  array([1])
  
  A 3-D example:
  
  >>> a = np.arange(8).reshape(2,2,2); a
  array([[[0, 1],
      [2, 3]],
      [[4, 5],
      [6, 7]]])
  >>> a.diagonal(0, # Main diagonals of two arrays created by skipping
  ...      0, # across the outer(left)-most axis last and
  ...      1) # the "middle" (row) axis first.
  array([[0, 6],
      [1, 7]])
  
  The sub-arrays whose main diagonals we just obtained; note that each
  corresponds to fixing the right-most (column) axis, and that the
  diagonals are "packed" in rows.
  
  >>> a[:,:,0] # main diagonal is [0 6]
  array([[0, 2],
      [4, 6]])
  >>> a[:,:,1] # main diagonal is [1 7]
  array([[1, 3],
      [5, 7]])
>>> A = np.random.randint(low=5, high=30, size=(5, 5))
     
>>> A
     
array([[25, 15, 26, 6, 22],
    [27, 14, 22, 16, 21],
    [22, 17, 10, 14, 25],
    [11, 9, 27, 20, 6],
    [24, 19, 19, 26, 14]])
>>> A.diagonal()
     
array([25, 14, 10, 20, 14])
>>> A.diagonal(offset=1)
     
array([15, 22, 14, 6])
>>> A.diagonal(offset=-2)
     
array([22, 9, 19])

以上这篇numpy创建单位矩阵和对角矩阵的实例就是小编分享给大家的全部内容了,希望能给大家一个参考,也希望大家多多支持三水点靠木。

Python 相关文章推荐
centos系统升级python 2.7.3
Jul 03 Python
python采集博客中上传的QQ截图文件
Jul 18 Python
Python通过解析网页实现看报程序的方法
Aug 04 Python
用Python解析XML的几种常见方法的介绍
Apr 09 Python
Python的math模块中的常用数学函数整理
Feb 04 Python
python去除文件中空格、Tab及回车的方法
Apr 12 Python
python解决Fedora解压zip时中文乱码的方法
Sep 18 Python
python实现教务管理系统
Mar 12 Python
解决Pycharm中import时无法识别自己写的程序方法
May 18 Python
python实现大文件分割与合并
Jul 22 Python
Python实现数值积分方式
Nov 20 Python
Python爬虫UA伪装爬取的实例讲解
Feb 19 Python
python中从for循环延申到推导式的具体使用
Nov 29 #Python
python 实现矩阵按对角线打印
Nov 29 #Python
python之列表推导式的用法
Nov 29 #Python
python 实现方阵的对角线遍历示例
Nov 29 #Python
python 实现一个反向单位矩阵示例
Nov 29 #Python
python 实现矩阵填充0的例子
Nov 29 #Python
python循环嵌套的多种使用方法解析
Nov 29 #Python
You might like
discuz免激活同步登入代码修改方法(discuz同步登录)
2013/12/24 PHP
PHP记录搜索引擎蜘蛛访问网站足迹的方法
2015/04/15 PHP
yii2实现根据时间搜索的方法
2016/05/25 PHP
详解如何实现Laravel的服务容器的方法示例
2019/04/15 PHP
不用写JS也能使用EXTJS视频演示
2008/12/29 Javascript
深入理解JavaScript系列(4) 立即调用的函数表达式
2012/01/15 Javascript
jQuery动画效果animate和scrollTop结合使用实例
2014/04/02 Javascript
详解JavaScript中常用的函数类型
2015/11/18 Javascript
JS如何设置iOS中微信浏览器的title
2016/11/22 Javascript
js实现表单提交后不重新刷新当前页面
2016/11/30 Javascript
HTML页面定时跳转方法解析(2种任选)
2016/12/22 Javascript
BootStrap Fileinput的使用教程
2016/12/30 Javascript
JavaScript数据结构之二叉树的查找算法示例
2017/04/13 Javascript
js使用i18n实现页面国际化的方法
2017/05/09 Javascript
Vue学习笔记进阶篇之函数化组件解析
2017/07/21 Javascript
js中apply与call简单用法详解
2017/11/06 Javascript
vue 循环加载数据并获取第一条记录的方法
2018/09/26 Javascript
jQuery实现高级检索功能
2019/05/28 jQuery
微信小程序中的video视频实现 自定义播放按钮、封面图、视频封面上文案
2020/01/02 Javascript
Python写入CSV文件的方法
2015/07/08 Python
Python网络爬虫项目:内容提取器的定义
2016/10/25 Python
python爬虫 使用真实浏览器打开网页的两种方法总结
2018/04/21 Python
解决Mac安装scrapy失败的问题
2018/06/13 Python
Python监控服务器实用工具psutil使用解析
2019/12/19 Python
Python图像处理库PIL的ImageEnhance模块使用介绍
2020/02/26 Python
Window系统下Python如何安装OpenCV库
2020/03/05 Python
python 爬取腾讯视频评论的实现步骤
2021/02/18 Python
西班牙手机之家:Phone House
2018/10/18 全球购物
数据库笔试题
2013/05/09 面试题
经典的班主任推荐信
2013/10/28 职场文书
路政管理专业推荐信
2013/11/11 职场文书
小学班级特色活动方案
2014/08/31 职场文书
2019职场实习报告该怎么写?
2019/07/01 职场文书
制定企业培训计划的五大要点!
2019/07/10 职场文书
详解MySQL多版本并发控制机制(MVCC)源码
2021/06/23 MySQL
Go Grpc Gateway兼容HTTP协议文档自动生成网关
2022/06/16 Golang