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  printdef swap( a, b ):  t = a; a = b; b = tdef 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 1if __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 | 0.00000.0000 2.0000 -1.0000 | 0.00000.0000 1.0000 0.0000 | 10.0000一开始 de 矩阵2.0000 0.0000 -2.0000 | 0.00000.0000 2.0000 -1.0000 | 0.00000.0000 1.0000 0.0000 | 10.0000位置：row_pos = 0, col_pos = 0选主元2.0000 0.0000 -2.0000 | 0.00000.0000 2.0000 -1.0000 | 0.00000.0000 1.0000 0.0000 | 10.0000交换两行2.0000 0.0000 -2.0000 | 0.00000.0000 2.0000 -1.0000 | 0.00000.0000 1.0000 0.0000 | 10.0000消元1.0000 0.0000 -1.0000 | 0.00000.0000 2.0000 -1.0000 | 0.00000.0000 1.0000 0.0000 | 10.0000位置：row_pos = 1, col_pos = 1选主元1.0000 0.0000 -1.0000 | 0.00000.0000 2.0000 -1.0000 | 0.00000.0000 1.0000 0.0000 | 10.0000交换两行1.0000 0.0000 -1.0000 | 0.00000.0000 2.0000 -1.0000 | 0.00000.0000 1.0000 0.0000 | 10.0000消元1.0000 0.0000 -1.0000 | 0.00000.0000 1.0000 -0.5000 | 0.00000.0000 0.0000 0.5000 | 10.0000位置：row_pos = 2, col_pos = 2选主元1.0000 0.0000 -1.0000 | 0.00000.0000 1.0000 -0.5000 | 0.00000.0000 0.0000 0.5000 | 10.0000交换两行1.0000 0.0000 -1.0000 | 0.00000.0000 1.0000 -0.5000 | 0.00000.0000 0.0000 0.5000 | 10.0000消元1.0000 0.0000 0.0000 | 20.00000.0000 1.0000 0.0000 | 10.00000.0000 0.0000 1.0000 | 20.0000方程组有解方程组及其解1.0000 0.0000 0.0000 | 20.00000.0000 1.0000 0.0000 | 10.00000.0000 0.0000 1.0000 | 20.0000x[0] = 20.0000x[1] = 10.0000x[2] = 20.0000