例題6-8 利用LU分解求行列式的值

例題6-8 利用LU分解求行列式的值

# Python Program to Perform LU Decomposition of any Matrix

def lu(a,l,u,n):
    for  i in range(0 , n):
        for  j in range(0 , n):
            if (j < i):
                l[j][i] = 0;
            else:
                l[j][i] = a[j][i];
                for k in range (0 , i):
                    l[j][i] = l[j][i] - l[j][k] * u[k][i];

        for  j in range(0 , n):
            if (j < i):
                u[i][j] = 0;
            elif (j == i):
                u[i][j] = 1
            else:
                u[i][j] = a[i][j] / l[i][i];
                for k in range  (0 ,  i):
                    u[i][j] = u[i][j] - ((l[i][k] * u[k][j]) / l[i][i]);

#+++++++++++++++++++++++++++++++++++++++++
n=3
print("\nEnter size of 2d array(Square matrix) : ",n)
a=  [ [0.0 for i in range(n+1)]  for j in range(n+1) ]       #[n][n+1],
l=  [ [0.0 for i in range(n+1)]  for j in range(n+1) ]       #[n][n+1],
u=  [ [0.0 for i in range(n+1)]  for j in range(n+1) ]       #[n][n+1],
x= [0.0 for i in range(n+1)]; 

print("\nEnter the elements of the augmented-matrix row-wise:\n")
'''
a=[[2.0 ,  1.0 , -3.0 , 0.0],
      [-1.0 , 3.0 , 2.0,  0.0],
      [3.0 ,  1.0 ,  -3.0 , 0.0]]
'''
a=[[4.0 ,  -2.0 ,  1.0 ],
      [3.0 ,  0.0 ,  -5.0],
      [1.0 ,  -3.0 ,  -4.0]]

for i in range(0 ,n):
    for j in range(0,n):
        print( "a[",i,"][",j,"]=",round(a[i][j],4),'\t',end='')
    print("")


lu(a, l, u, n);
print("\nL Decomposition\n\n")
for i in range(0 ,n):
    for j in range(0,n):
        print( "L[",i,"][",j,"]=",round(l[i][j],4),'\t',end='')
    print("")

print("\nU Decomposition\n\n")
for i in range(0 ,n):
    for j in range(0,n):
        print( "U[",i,"][",j,"]=",round(u[i][j],4),'\t',end='')
    print("")

det=1.0
for i in range(0 ,n):
    det=det *l[i][i]

print( "\ndet A=",round(det,4) )

輸出畫面
============= RESTART: F:/2018-09勤益科大數值分析/數值分析/PYTHON/EX6-7-1.py =============

Enter size of 2d array(Square matrix) :  3

Enter the elements of the augmented-matrix row-wise:

a[ 0 ][ 0 ]= 2.0 a[ 0 ][ 1 ]= 1.0 a[ 0 ][ 2 ]= -3.0
a[ 1 ][ 0 ]= -1.0 a[ 1 ][ 1 ]= 3.0 a[ 1 ][ 2 ]= 2.0
a[ 2 ][ 0 ]= 3.0 a[ 2 ][ 1 ]= 1.0 a[ 2 ][ 2 ]= -3.0

L Decomposition


L[ 0 ][ 0 ]= 2.0 L[ 0 ][ 1 ]= 0 L[ 0 ][ 2 ]= 0
L[ 1 ][ 0 ]= -1.0 L[ 1 ][ 1 ]= 3.5 L[ 1 ][ 2 ]= 0
L[ 2 ][ 0 ]= 3.0 L[ 2 ][ 1 ]= -0.5 L[ 2 ][ 2 ]= 1.5714

U Decomposition


U[ 0 ][ 0 ]= 1 U[ 0 ][ 1 ]= 0.5 U[ 0 ][ 2 ]= -1.5
U[ 1 ][ 0 ]= 0 U[ 1 ][ 1 ]= 1 U[ 1 ][ 2 ]= 0.1429
U[ 2 ][ 0 ]= 0 U[ 2 ][ 1 ]= 0 U[ 2 ][ 2 ]= 1
det A= 11.0
>>> 
============= RESTART: F:/2018-09勤益科大數值分析/數值分析/PYTHON/EX6-7-1.py =============

Enter size of 2d array(Square matrix) :  3

Enter the elements of the augmented-matrix row-wise:

a[ 0 ][ 0 ]= 4.0 a[ 0 ][ 1 ]= -2.0 a[ 0 ][ 2 ]= 1.0
a[ 1 ][ 0 ]= 3.0 a[ 1 ][ 1 ]= 0.0 a[ 1 ][ 2 ]= -5.0
a[ 2 ][ 0 ]= 1.0 a[ 2 ][ 1 ]= -3.0 a[ 2 ][ 2 ]= -4.0

L Decomposition


L[ 0 ][ 0 ]= 4.0 L[ 0 ][ 1 ]= 0 L[ 0 ][ 2 ]= 0
L[ 1 ][ 0 ]= 3.0 L[ 1 ][ 1 ]= 1.5 L[ 1 ][ 2 ]= 0
L[ 2 ][ 0 ]= 1.0 L[ 2 ][ 1 ]= -2.5 L[ 2 ][ 2 ]= -13.8333

U Decomposition


U[ 0 ][ 0 ]= 1 U[ 0 ][ 1 ]= -0.5 U[ 0 ][ 2 ]= 0.25
U[ 1 ][ 0 ]= 0 U[ 1 ][ 1 ]= 1 U[ 1 ][ 2 ]= -3.8333
U[ 2 ][ 0 ]= 0 U[ 2 ][ 1 ]= 0 U[ 2 ][ 2 ]= 1

det A= -83.0
>>>