Python基于高斯消元法计算线性方程组示例

#!/usr/bin/env python
# coding=utf-8
# 以上的信息随自己的需要改动吧
def print_matrix( info, m ): # 输出矩阵
  i = 0; j = 0; l = len(m)
  print info
  for i in range( 0, len( m ) ):
    for j in range( 0, len( m[i] ) ):
      if( j == l ):
        print ' |',
      print '%6.4f' % m[i][j],
    print
  print
def swap( a, b ):
  t = a; a = b; b = t
def solve( ma, b, n ):
  global m; m = ma # 这里主要是方便最后矩阵的显示
  global s;
  i = 0; j = 0; row_pos = 0; col_pos = 0; ik = 0; jk = 0
  mik = 0.0; temp = 0.0
  n = len( m )
  # row_pos 变量标记行循环, col_pos 变量标记列循环
  print_matrix( "一开始 de 矩阵", m )
  while( ( row_pos < n ) and( col_pos < n ) ):
    print "位置：row_pos = %d, col_pos = %d" % (row_pos, col_pos)
    # 选主元
    mik = - 1
    for i in range( row_pos, n ):
      if( abs( m[i][col_pos] ) > mik ):
        mik = abs( m[i][col_pos] )
        ik = i
    if( mik == 0.0 ):
      col_pos = col_pos + 1
      continue
    print_matrix( "选主元", m )
    # 交换两行
    if( ik != row_pos ):
      for j in range( col_pos, n ):
        swap( m[row_pos][j], m[ik][j] )
        swap( m[row_pos][n], m[ik][n] );   # 区域之外？
    print_matrix( "交换两行", m )
    try:
      # 消元
      m[row_pos][n] /= m[row_pos][col_pos]
    except ZeroDivisionError:
      # 除零异常 一般在无解或无穷多解的情况下出现……
      return 0;
    j = n - 1
    while( j >= col_pos ):
      m[row_pos][j] /= m[row_pos][col_pos]
      j = j - 1
    for i in range( 0, n ):
      if( i == row_pos ):
        continue
      m[i][n] -= m[row_pos][n] * m[i][col_pos]
      j = n - 1
      while( j >= col_pos ):
        m[i][j] -= m[row_pos][j] * m[i][col_pos]
        j = j - 1
    print_matrix( "消元", m )
    row_pos = row_pos + 1; col_pos = col_pos + 1
  for i in range( row_pos, n ):
    if( abs( m[i][n] ) == 0.0 ):
      return 0
  return 1
if __name__ == '__main__':
  matrix = [[2.0,  0.0, - 2.0,  0.0],
       [0.0,  2.0, - 1.0,  0.0],
       [0.0,  1.0,  0.0, 10.0]]
  i = 0; j = 0; n = 0
  # 输出方程组
  print_matrix( "一开始的矩阵", matrix )
  # 求解方程组, 并输出方程组的可解信息
  ret = solve( matrix, 0, 0 )
  if( ret!= 0 ):
    print "方程组有解\n"
  else:
    print "方 程组无唯一解或无解\n"
  # 输出方程组及其解
  print_matrix( "方程组及其解", matrix )
  for i in range( 0, len( m ) ):
    print "x[%d] = %6.4f" % (i, m[i][len( m )])

一开始的矩阵
2.0000 0.0000 -2.0000 | 0.0000
0.0000 2.0000 -1.0000 | 0.0000
0.0000 1.0000 0.0000 | 10.0000

一开始 de 矩阵
2.0000 0.0000 -2.0000 | 0.0000
0.0000 2.0000 -1.0000 | 0.0000
0.0000 1.0000 0.0000 | 10.0000

位置：row_pos = 0, col_pos = 0
选主元
2.0000 0.0000 -2.0000 | 0.0000
0.0000 2.0000 -1.0000 | 0.0000
0.0000 1.0000 0.0000 | 10.0000

交换两行
2.0000 0.0000 -2.0000 | 0.0000
0.0000 2.0000 -1.0000 | 0.0000
0.0000 1.0000 0.0000 | 10.0000

消元
1.0000 0.0000 -1.0000 | 0.0000
0.0000 2.0000 -1.0000 | 0.0000
0.0000 1.0000 0.0000 | 10.0000

位置：row_pos = 1, col_pos = 1
选主元
1.0000 0.0000 -1.0000 | 0.0000
0.0000 2.0000 -1.0000 | 0.0000
0.0000 1.0000 0.0000 | 10.0000

交换两行
1.0000 0.0000 -1.0000 | 0.0000
0.0000 2.0000 -1.0000 | 0.0000
0.0000 1.0000 0.0000 | 10.0000

消元
1.0000 0.0000 -1.0000 | 0.0000
0.0000 1.0000 -0.5000 | 0.0000
0.0000 0.0000 0.5000 | 10.0000

位置：row_pos = 2, col_pos = 2
选主元
1.0000 0.0000 -1.0000 | 0.0000
0.0000 1.0000 -0.5000 | 0.0000
0.0000 0.0000 0.5000 | 10.0000

交换两行
1.0000 0.0000 -1.0000 | 0.0000
0.0000 1.0000 -0.5000 | 0.0000
0.0000 0.0000 0.5000 | 10.0000

消元
1.0000 0.0000 0.0000 | 20.0000
0.0000 1.0000 0.0000 | 10.0000
0.0000 0.0000 1.0000 | 20.0000

方程组有解

方程组及其解
1.0000 0.0000 0.0000 | 20.0000
0.0000 1.0000 0.0000 | 10.0000
0.0000 0.0000 1.0000 | 20.0000

x[0] = 20.0000
x[1] = 10.0000
x[2] = 20.0000