exp(A), A is a matrix

Programe is:
#
# Calculate A**n, A is a matrix,  n is an integer
#                 A has maximum 15 rows and 15 columns
#
AA =  [[1,2,3,4],
      [2,3,4,5],
      [3,4,5,6],
      [4,5,6,7]]
AAA = [[2,2],
      [2,2]]
BB =  [[1,1,1,1],
      [1,1,1,1],
      [1,1,1,1],
      [2,2,2,2]]
NN_row = 4
NN_column = 4
def product_AB(A, B, N_row, N_column):
    C =  [[1,1,1,1],
      [1,1,1,1],
      [1,1,1,1],
      [2,2,2,2]]
   # C = [[0]*N_row]*N_column
    for i in range(N_row):
        for j in range(N_column):
            C[i][j]=0
            for k in range(N_column):
                C[i][j] += A[i][k]*B[k][j]
    return C
CC = product_AB(AA, BB, NN_row, NN_column)
print(CC)
def power_matrixAn(A,N_row, n):
    An = [[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
          [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
          [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
          [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
          [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
          [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
          [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
          [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
          [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
          [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
          [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
          [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
          [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
          [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
          [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]]
    for i in range(N_row):
        for j in range(N_row):
            if i == j:
                An[i][j]=1
            else:
                An[i][j]=0
    for i in range(n):
        An = product_AB(An, A, N_row, N_row)
    # print("delta")
    return An
def print_matrix(An,N_row,N_column):
    for i in range(N_row):
        for j in range (N_column):
            print(An[i][j], end = " ")
        print(' ')
N = 0
NN_row=2
CC2 = power_matrixAn(AAA,NN_row, N)
print("Power matrix A** ", N)
print_matrix(CC2,NN_row, NN_row)
N = 1
NN_row=2
print("Power matrix A** ", N)
CC2 = power_matrixAn(AAA,NN_row, N)
print_matrix(CC2,NN_row, NN_row)
N = 2
NN_row=2
print("Power matrix A** ", N)
CC2 = power_matrixAn(AAA,NN_row, N)
print_matrix(CC2,NN_row, NN_row)
N = 3
NN_row=2
print("Power matrix A** ", N)
CC2 = power_matrixAn(AAA,NN_row, N)
print_matrix(CC2,NN_row, NN_row)
#
#  exp(A) = E/0! + A/1! + A**2/2! + A**3/3! + ...+ A**n/n!
#
def divide_const(AA, N_row, N_column, const):
                 AX = [[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]]
                 for i in range(N_row):
                    for j in range (N_column):
                        AX[i][j] = float(AA[i][j])/float(const)
                 return AX
CONST = 4
BX = divide_const(CC2, NN_row, NN_row, CONST)
print("Matrix divided by ", CONST)
print_matrix(BX,NN_row, NN_row)
def factorial_n(n):
    facto = 1
    for i in range(1,n+1):
        facto *= i
    return facto
def add_mat(A,B,m,n):
    ADD = [[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]]
    for i in range(m):
        for j in range(n):
            ADD[i][j] = A[i][j] + B[i][j]
    return ADD
        
    
R = 5
T = factorial_n(R)
print( R, "! is ", T)
def exp_matrix(A, N_row, N_term): # calculate exp(A), A is matrix
                     AX = [[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
                      [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]]
                     for i in range(1,N_term):
                         POW_X = power_matrixAn(A,N_row, i)
                         FACT_i = factorial_n(i)
                         DIV_X = divide_const(POW_X, N_row,N_row,FACT_i)
                         AX = AX + DIV_X 
                         AX = add_mat(AX, DIV_X,NN_row, NN_row)
                     return AX
NN_term = 50
NN_row = 2
DDD = [[2,2],
      [2,2]]
EXP_A = exp_matrix(DDD, NN_row, NN_term)
print("Matrix exp(A) wich", NN_term, " terms in sum is:  ")
print_matrix(EXP_A,NN_row, NN_row)

Results are:
================ RESTART: /Users/ionivan/Documents/EXP_Matrix.py ===============
[[14, 14, 14, 14], [19, 19, 19, 19], [24, 24, 24, 24], [29, 29, 29, 29]]
Power matrix A**  0
1 0  
0 1  
Power matrix A**  1
2 2  
2 2  
Power matrix A**  2
8 8  
8 8  
Power matrix A**  3
32 32  
32 32  
Matrix divided by  4
8.0 8.0  
8.0 8.0  
5 ! is  120
Matrix exp(A) wich 50  terms in sum is:  
27.799075016572132 26.799075016572132  
26.799075016572132 27.799075016572132  

(March 30, 2022)
            
            
        

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