20191203-python解多元一次方程

2023-05-16

https://blog.csdn.net/qq_24395387/article/details/103370434
python 解 多元一次方程

间歇性学习狂躁症 2019-12-03 16:43:20  3806  收藏 7
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1. 待解方程式
已知ai,bi,ci,求解x,y,z。

a1*x + b1*y+c1*z = 1
a2*x + b2*y+c2*z = 2
a3*x + b3*y+c3*z = 3
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2. 需要的模块与方法

numpy
np.linalg.solve(m, n)
3. 输入格式
其中 np.linalg.solve(m, n)的m,n输入格式为:

 m = np.array([[a1, b1, c1], [a2, b2. c2], [a3, b3, c3]])
 n = np.array([1, 2, 3]) #可替换为式子右边的常数
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4. 结果

solution = np.linalg.solve(m, n) #solution format: np.array([x, y, z])
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完整伪代码如下:

import numpy as np
"""
a1*x + b1*y+c1*z = 1
a2*x + b2*y+c2*z = 2
a3*x + b3*y+c3*z = 3
"""
 m = np.array([[a1, b1, c1], [a2, b2. c2], [a3, b3, c3]])
 n = np.array([0, 0, 0]) #可替换为式子右边的常数
 solution = np.linalg.solve(m, n) #solution format: np.array([x, y, z])
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注意: np.linalg.solve前提是m矩阵可逆。
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版权声明:本文为CSDN博主「间歇性学习狂躁症」的原创文章,遵循CC 4.0 BY-SA版权协议,转载请附上原文出处链接及本声明。
原文链接:https://blog.csdn.net/qq_24395387/article/details/103370434

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rootroot@rootroot-System-Product-Name:~$ ifconfig
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rootroot@rootroot-System-Product-Name:~$ python
Python 2.7.18 (default, Mar  8 2021, 13:02:45) 
[GCC 9.3.0] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> exit()
rootroot@rootroot-System-Product-Name:~$ 
rootroot@rootroot-System-Product-Name:~$ 
rootroot@rootroot-System-Product-Name:~$ python3
Python 3.8.10 (default, Sep 28 2021, 16:10:42) 
[GCC 9.3.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> exit9)
  File "<stdin>", line 1
    exit9)
         ^
SyntaxError: unmatched ')'
>>> 
>>> 
>>> exit()
rootroot@rootroot-System-Product-Name:~$ 
rootroot@rootroot-System-Product-Name:~$ 
rootroot@rootroot-System-Product-Name:~$ 
rootroot@rootroot-System-Product-Name:~$ python3
Python 3.8.10 (default, Sep 28 2021, 16:10:42) 
[GCC 9.3.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import numpy as np
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ModuleNotFoundError: No module named 'numpy'
>>> exit()
rootroot@rootroot-System-Product-Name:~$ 
rootroot@rootroot-System-Product-Name:~$ 
rootroot@rootroot-System-Product-Name:~$ python3 -m pip install numpy
/usr/bin/python3: No module named pip
rootroot@rootroot-System-Product-Name:~$ sudo apt-get install pip
[sudo] password for rootroot: 
Reading package lists... Done
Building dependency tree       
Reading state information... Done
Note, selecting 'python3-pip' instead of 'pip'
The following additional packages will be installed:
  libexpat1-dev libpython3-dev libpython3.8-dev python-pip-whl python3-dev python3-wheel python3.8-dev zlib1g-dev
The following NEW packages will be installed:
  libexpat1-dev libpython3-dev libpython3.8-dev python-pip-whl python3-dev python3-pip python3-wheel python3.8-dev zlib1g-dev
0 upgraded, 9 newly installed, 0 to remove and 88 not upgraded.
Need to get 6,797 kB of archives.
After this operation, 25.5 MB of additional disk space will be used.
Do you want to continue? [Y/n] y
Get:1 http://cn.archive.ubuntu.com/ubuntu focal/main amd64 libexpat1-dev amd64 2.2.9-1build1 [116 kB]
Get:2 http://cn.archive.ubuntu.com/ubuntu focal-updates/main amd64 libpython3.8-dev amd64 3.8.10-0ubuntu1~20.04.1 [3,948 kB]
Get:3 http://cn.archive.ubuntu.com/ubuntu focal/main amd64 libpython3-dev amd64 3.8.2-0ubuntu2 [7,236 B]
Get:4 http://cn.archive.ubuntu.com/ubuntu focal-updates/universe amd64 python-pip-whl all 20.0.2-5ubuntu1.6 [1,805 kB]
Get:5 http://cn.archive.ubuntu.com/ubuntu focal-updates/main amd64 zlib1g-dev amd64 1:1.2.11.dfsg-2ubuntu1.2 [155 kB]
Get:6 http://cn.archive.ubuntu.com/ubuntu focal-updates/main amd64 python3.8-dev amd64 3.8.10-0ubuntu1~20.04.1 [510 kB]
Get:7 http://cn.archive.ubuntu.com/ubuntu focal/main amd64 python3-dev amd64 3.8.2-0ubuntu2 [1,212 B]
Get:8 http://cn.archive.ubuntu.com/ubuntu focal/universe amd64 python3-wheel all 0.34.2-1 [23.8 kB]
Get:9 http://cn.archive.ubuntu.com/ubuntu focal-updates/universe amd64 python3-pip all 20.0.2-5ubuntu1.6 [231 kB]
Fetched 6,797 kB in 3s (2,340 kB/s)  
Selecting previously unselected package libexpat1-dev:amd64.
(Reading database ... 202310 files and directories currently installed.)
Preparing to unpack .../0-libexpat1-dev_2.2.9-1build1_amd64.deb ...
Unpacking libexpat1-dev:amd64 (2.2.9-1build1) ...
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Preparing to unpack .../3-python-pip-whl_20.0.2-5ubuntu1.6_all.deb ...
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Preparing to unpack .../7-python3-wheel_0.34.2-1_all.deb ...
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Selecting previously unselected package python3-pip.
Preparing to unpack .../8-python3-pip_20.0.2-5ubuntu1.6_all.deb ...
Unpacking python3-pip (20.0.2-5ubuntu1.6) ...
Setting up python3-wheel (0.34.2-1) ...
Setting up libexpat1-dev:amd64 (2.2.9-1build1) ...
Setting up libpython3.8-dev:amd64 (3.8.10-0ubuntu1~20.04.1) ...
Setting up zlib1g-dev:amd64 (1:1.2.11.dfsg-2ubuntu1.2) ...
Setting up python-pip-whl (20.0.2-5ubuntu1.6) ...
Setting up libpython3-dev:amd64 (3.8.2-0ubuntu2) ...
Setting up python3-pip (20.0.2-5ubuntu1.6) ...
Setting up python3.8-dev (3.8.10-0ubuntu1~20.04.1) ...
Setting up python3-dev (3.8.2-0ubuntu2) ...
Processing triggers for man-db (2.9.1-1) ...
rootroot@rootroot-System-Product-Name:~$ 
rootroot@rootroot-System-Product-Name:~$ 
rootroot@rootroot-System-Product-Name:~$ 
rootroot@rootroot-System-Product-Name:~$ python3 -m pip install numpy
Collecting numpy
  Downloading numpy-1.21.4-cp38-cp38-manylinux_2_12_x86_64.manylinux2010_x86_64.whl (15.7 MB)
     |████████████████████████████████| 15.7 MB 124 kB/s 
Installing collected packages: numpy
  WARNING: The scripts f2py, f2py3 and f2py3.8 are installed in '/home/rootroot/.local/bin' which is not on PATH.
  Consider adding this directory to PATH or, if you prefer to suppress this warning, use --no-warn-script-location.
Successfully installed numpy-1.21.4
rootroot@rootroot-System-Product-Name:~$ 
rootroot@rootroot-System-Product-Name:~$ 
rootroot@rootroot-System-Product-Name:~$ python3
Python 3.8.10 (default, Sep 28 2021, 16:10:42) 
[GCC 9.3.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import numpy as np
>>> m = np.array([[a1, b1, c1], [a2, b2. c2], [a3, b3, c3]])
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
NameError: name 'a1' is not defined
>>> m = np.array([[0.8, 0.1, 0.2], [0.15, 0.9. 0.15], [0.2, 0.1, 0.95]])
  File "<stdin>", line 1
    m = np.array([[0.8, 0.1, 0.2], [0.15, 0.9. 0.15], [0.2, 0.1, 0.95]])
                                               ^
SyntaxError: invalid syntax
>>> m = np.array([[0.8, 0.1, 0.2], [0.15, 0.9, 0.15], [0.2, 0.1, 0.95]])
>>> n = np.array([0, 0, 0])
>>> n
array([0, 0, 0])
>>> n = np.array([1, 2, 3])
>>> solution = np.linalg.solve(m, n)
>>> solution
array([0.31063321, 1.68458781, 2.91517324])
>>> 
 

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