例題 6-1 利用高斯消去法 求 n x n 線性代數的解

'''
例題 6-1 利用高斯消去法 求 n x n 線性代數的解

/* ex6-1.c based on Gaussian Elimination method
 * for solving the n x n linear algebra system
 * a11 x1+a12 x2+...+a1n xn=b1
 * a21 x1+a22 x2+...+a2n xn=b2
 * .       .         .       .
 * .       .         .       .
 * an1 x1+an2 x2+...+ann xn=bn
 * Input number of unknowns and equations n
 * with coefficent a11,a12,...,ann and b1,b2,
 * ...bn. Output solution x1,x2,x3,...,xn.
 */
'''
def myGauss(m):
    #eliminate columns
    for col in range(len(m[0])):
        for row in range(col+1, len(m)):
            r = [(rowValue * (-(m[row][col] / m[col][col]))) for rowValue in m[col]]
            m[row] = [sum(pair) for pair in zip(m[row], r)]
    #now backsolve by substitution
    ans = []
    m.reverse() #makes it easier to backsolve
    for sol in range(len(m)):
            if sol == 0:
                ans.append(m[sol][-1] / m[sol][-2])
            else:
                inner = 0
                #substitute in all known coefficients
                for x in range(sol):
                    inner += (ans[x]*m[sol][-2-x])
                #the equation is now reduced to ax + b = c form
                #solve with (c - b) / a
                ans.append((m[sol][-1]-inner)/m[sol][-sol-2])
    ans.reverse()
    return ans

#=======================
a1=[[-3.0,2.0,-6.0,6.0],
       [5.0,7.0,-5.0,6.0],
       [1.0,4.0,-2.0,8.0]]
a= myGauss(a1)
n=3
for i in range(0 ,n):
    for j in range(0,n+1):
        print( "a[",i,"][",j,"]=",round(a1[i][j],4),'\t',end='')
    print("")
print("x1=",round(a[0],4), '\t',"x2=",round(a[1],4), '\t',"x3=",round(a[2],4) )
print()
#=======================
a1=[[-1.0 , 1.0 , 2.0 , 2.0],
        [3.0 , -1.0 , 1.0 , 6.0],
        [-1.0 , 3.0 , 4.0 , 4.0]]
a= myGauss(a1)
n=3
for i in range(0 ,n):
    for j in range(0,n+1):
        print( "a[",i,"][",j,"]=",round(a1[i][j],4),'\t',end='')
    print("")

print("x1=",round(a[0],4), '\t',"x2=",round(a[1],4), '\t',"x3=",round(a[2],4) )
print()
#=======================
a1=[[2.0 , -1.5 , 3.0 , 1.0] ,
        [-1.0 ,  0.0 , 2.0 , 3.0] ,
        [ 4.0  ,-4.5 , 5.0 , 1.0] ]
n=3
a= myGauss(a1 )
for i in range(0 ,n):
    for j in range(0,n+1):
        print( "a[",i,"][",j,"]=",round(a1[i][j],4),'\t',end='')
    print("")

print("x1=",round(a[0],4), '\t',"x2=",round(a[1],4), '\t',"x3=",round(a[2],4) )
print()
#=======================
a1=[[4.01 , 1.23 ,  1.43 , -0.73 ,  5.94],
        [1.23 , 7.41  , 2.41 ,  3.02 , 14.07],
        [1.43 , 2.41 ,  5.79 , -1.11 ,  8.52],
        [-0.73 ,  3.02 , -1.11 ,   6.41 ,  7.59]]
n=4
a= myGauss(a1)
for i in range(0 ,n):
    for j in range(0,n+1):
        print( "a[",i,"][",j,"]=",round(a1[i][j],4),'\t',end='')
    print("")
print("x1=",round(a[0],4), '\t',"x2=",round(a[1],4), '\t',"x3=",round(a[2],4), '\t',"x4=",round(a[3],4) )
#=======================


======== RESTART: F:\2018-09勤益科大數值分析\數值分析\PYTHON\EX6-1-1.py ===========
a[ 0 ][ 0 ]= 0.0 a[ 0 ][ 1 ]= 0.0 a[ 0 ][ 2 ]= 2.7742 a[ 0 ][ 3 ]= 2.7742
a[ 1 ][ 0 ]= 0.0 a[ 1 ][ 1 ]= 10.3333 a[ 1 ][ 2 ]= -15.0 a[ 1 ][ 3 ]= 16.0
a[ 2 ][ 0 ]= -3.0 a[ 2 ][ 1 ]= 2.0 a[ 2 ][ 2 ]= -6.0 a[ 2 ][ 3 ]= 6.0
x1= -2.0 x2= 3.0 x3= 1.0

a[ 0 ][ 0 ]= 0.0 a[ 0 ][ 1 ]= 0.0 a[ 0 ][ 2 ]= -5.0 a[ 0 ][ 3 ]= -10.0
a[ 1 ][ 0 ]= 0.0 a[ 1 ][ 1 ]= 2.0 a[ 1 ][ 2 ]= 7.0 a[ 1 ][ 3 ]= 12.0
a[ 2 ][ 0 ]= -1.0 a[ 2 ][ 1 ]= 1.0 a[ 2 ][ 2 ]= 2.0 a[ 2 ][ 3 ]= 2.0
x1= 1.0 x2= -1.0 x3= 2.0

a[ 0 ][ 0 ]= 0.0 a[ 0 ][ 1 ]= 0.0 a[ 0 ][ 2 ]= -8.0 a[ 0 ][ 3 ]= -8.0
a[ 1 ][ 0 ]= 0.0 a[ 1 ][ 1 ]= -0.75 a[ 1 ][ 2 ]= 3.5 a[ 1 ][ 3 ]= 3.5
a[ 2 ][ 0 ]= 2.0 a[ 2 ][ 1 ]= -1.5 a[ 2 ][ 2 ]= 3.0 a[ 2 ][ 3 ]= 1.0
x1= -1.0 x2= -0.0 x3= 1.0

a[ 0 ][ 0 ]= 0.0 a[ 0 ][ 1 ]= 0.0 a[ 0 ][ 2 ]= 0.0 a[ 0 ][ 3 ]= 4.1263 a[ 0 ][ 4 ]= 4.1263
a[ 1 ][ 0 ]= 0.0 a[ 1 ][ 1 ]= 0.0 a[ 1 ][ 2 ]= 4.7274 a[ 1 ][ 3 ]= -1.759 a[ 1 ][ 4 ]= 2.9685
a[ 2 ][ 0 ]= 0.0 a[ 2 ][ 1 ]= 7.0327 a[ 2 ][ 2 ]= 1.9714 a[ 2 ][ 3 ]= 3.2439 a[ 2 ][ 4 ]= 12.248
a[ 3 ][ 0 ]= 4.01 a[ 3 ][ 1 ]= 1.23 a[ 3 ][ 2 ]= 1.43 a[ 3 ][ 3 ]= -0.73 a[ 3 ][ 4 ]= 5.94
x1= 1.0 x2= 1.0 x3= 1.0 x4= 1.0
>>>