例題6-5 將A矩陣 分解成 L 與 U矩陣

例題6-5 將A矩陣 分解成 L 與 U矩陣

# Program to Perform LU Decomposition of any Matrix
def LUdecomposition( 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("Enter the order of square matrix: ",n)
a =[ [-1.0 ,   1.0 ,   2.0],
         [3.0 ,  -1.0 ,   1.0],
         [-1.0 ,   3.0 ,   4.0]]
l=  [ [0.0 for i in range(n+1)]  for j in range(n+1) ]       #[n][n],
u=  [ [0.0 for i in range(n+1)]  for j in range(n+1) ]       #[n][n],

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

print("\nL Decomposition is as follows...")
print("\n[L]: \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 is as follows...")
print("\n[U]: \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("")

======== RESTART: F:/2018-09勤益科大數值分析/數值分析/PYTHON/EX6-5-3.py ===========
Enter the order of square matrix:  3
a[ 0 ][ 0 ]= -1.0 a[ 0 ][ 1 ]= 1.0 a[ 0 ][ 2 ]= 2.0
a[ 1 ][ 0 ]= 3.0 a[ 1 ][ 1 ]= -1.0 a[ 1 ][ 2 ]= 1.0
a[ 2 ][ 0 ]= -1.0 a[ 2 ][ 1 ]= 3.0 a[ 2 ][ 2 ]= 4.0

L Decomposition is as follows...

[L]: 

L[ 0 ][ 0 ]= -1.0 L[ 0 ][ 1 ]= 0 L[ 0 ][ 2 ]= 0
L[ 1 ][ 0 ]= 3.0 L[ 1 ][ 1 ]= 2.0 L[ 1 ][ 2 ]= 0
L[ 2 ][ 0 ]= -1.0 L[ 2 ][ 1 ]= 2.0 L[ 2 ][ 2 ]= -5.0

U Decomposition is as follows...

[U]: 

U[ 0 ][ 0 ]= 1 U[ 0 ][ 1 ]= -1.0 U[ 0 ][ 2 ]= -2.0
U[ 1 ][ 0 ]= 0 U[ 1 ][ 1 ]= 1 U[ 1 ][ 2 ]= 3.5
U[ 2 ][ 0 ]= 0 U[ 2 ][ 1 ]= 0 U[ 2 ][ 2 ]= 1
>>>