SAMPLES.txt

Here some help and samples about the Py_Matrix Module.
======================================================

------------
| SAMPLES: |
------------
0) Import the module:
---------------------
    >>> import Py_Matrix as py_m
    
1) Create a Matrix from a dataset:
----------------------------------
    >>> A = py_m.Matrix([1,2,3,4], 2, 2)
    
2) Print a Matrix:
------------------
    >>> print(A) #A previously declared
    Output:
    0| 1     2     
    1| 3     4     
       --    --
       0     1

3) Print an element of the matrix, knowing row and column:
----------------------------------------------------------
    WARNING: the first row is number 0, same as first column. It does not starts with 1
    >>> print(A.elem(1,0) #A previously declared
    Output: 3

4) Add two Matrix (Matrix + Matrix):
------------------------------------
    WARNING: Matrix must have same rows and columns
    >>> A = py_m.Matrix([1,2,3,4], 2, 2)
    >>> B = py_m.Matrix([4,3,2,1], 2, 2)
    >>> print(A+B)
    Output:
    0| 5     5     
    1| 5     5     
       --    --
       0     1

5) Matrix * Matrix:
-------------------
    WARNING: Matrix multiplication is not commutative
    >>>print(A*B) #A and B previously declared
    Output:
    0| 8     5     
    1| 20    13    
       --    --    
       0     1 
    
6) Matrix * number:
-------------------
    WARNING: 2*A is not implemented.
    >>> print(A*2) #A and B previously declared
    Output:
    0| 2     4     
    1| 6     8     
       --    --    
       0     1   

7) Transpose of a Matrix:
-------------------------
    >>> print(A.t()) #A previously declared
    Output:
    0| 1     3     
    1| 2     4     
       --    --    
       0     1 

8) Elementary operation 3:
--------------------------
    >>> A.elementary_op3(0,1,-3)
    Then:
    0| 1           2     
    1| 3+(1)*(-3)  4+(2)*(-3)
       --          --    
       0           1
    Output:
    0| 1     2     
    1| 0     -2    
       --    --    
       0     1

9) Submatrix of a matrix:
-------------------------
    >>> print(A.sub(0,0)) #A previously declared
    Output:
    0| 4       
       --   
       0

10) Determinant of a matrix (2 ways):
-------------------------------------
    1)
    >>> print(A.det)
    #return a number

    2)
    >>> print(det_nxn(A))

    Better to use 1) instead of 2)

11) Cofactor of a Matrix:
-------------------------
    #deleting the element in (0,0)
    >>> print(A.cofactor(0,0)) #A previously declared
    Output: 4

12) Inverse Matrix:
-------------------
    >>> print(A.inverse()) #A previously declared
    Output:
    0| -2.000 1.000 
    1| 1.500 -0.500 
       --    --    
       0     1  
    
13) Cramer Rule on Linear System:
---------------------------------
    >>> B = Matrix([4,3],2,1)
    >>> print(cramer_rule(A,B)) #A previously declared
    Output:
    0| -5.000 
    1| 4.500 
       --    
       0
14) Matrix Infromations:
------------------------
    >>> A.info() #A previously declared

15) Matrix Iteration:
---------------------
    >>> for i in A: #A previously declared as Matrix([1,2,3,4],2,2)
            print(i)
    Output:
    1
    2
    3
    4

16) Lenght:
-----------
    >>> print(len(A)) #A previously declared as Matrix([1,2,3,4],2,2)
    Output:
    4

17) Find Pivot:
---------------
    >>> print(A) #A previously declared as Matrix([1,2,0,4],2,2)
    Output:
    0| 1     2     
    1| 0     4    
       --    --    
       0     1
    >>> print(A.find_pivot(1)) 
    Output:
    4

18) Pivot List:
---------------
    >>> A = py_m.Matrix([1,2,3,4], 2, 2)
    >>> print(A.pivot_list())
    Output:
    [(0, 0, 1), (0, 1, 3)]

19) Sort a Matrix:
------------------
    >>> A = py_m.Matrix([0,1,3,4], 2, 2)
    >>> print(A.sort())
    Output:
    0| 3     4     
    1| 0     1     
       --    --    
       0     1
       
20) Gaussian Elimination:
-------------------------
    >>> A = py_m.Matrix([0,1,3,4], 2, 2)
    >>> print(A.gaussian_elimination())
    Output:
    0| 5     1     3     
    1| 0.000 2.600 -3.200 
    2| 0.000 0.000 -7.077 
       --    --    --    
       0     1     2   
       
21) Characteristic Polynomial:
------------------------------
    >>> A = py_m.Matrix([0,1,3,4], 2, 2)
    >>> print(A.characteristic_polynomial())
    Output:
    '(((0+-x)*(4+-x)) + (-1)*((3+0)*(1+0)))'

22) Rotate a Matrix counterclockwise:
-------------------------------------
    >>> A = py_m.Matrix([0,1,3,4], 2, 2)
    >>> print(A.rotate())
    Output:
    0| 1     4
    1| 0     3
       --    --
       0     1