本文實例講述了Python基于高斯消元法計算線性方程組。分享給大家供大家參考，具體如下：
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#!/usr/bin/env python# coding=utf-8# 以上的信息隨自己的需要改動吧def print_matrix( info, m ): # 輸出矩陣 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 # 這里主要是方便最后矩陣的顯示 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 變量標記行循環(huán), col_pos 變量標記列循環(huán) print_matrix( "一開始 de 矩陣", m ) while( ( row_pos < n ) and( col_pos < n ) ): print "位置：row_pos = %d, col_pos = %d" % (row_pos, col_pos) # 選主元 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( "選主元", m ) # 交換兩行 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] ); # 區(qū)域之外？ print_matrix( "交換兩行", m ) try: # 消元 m[row_pos][n] /= m[row_pos][col_pos] except ZeroDivisionError: # 除零異常 一般在無解或無窮多解的情況下出現(xiàn)…… 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 # 輸出方程組 print_matrix( "一開始的矩陣", matrix ) # 求解方程組, 并輸出方程組的可解信息 ret = solve( matrix, 0, 0 ) if( ret!= 0 ): print "方程組有解\n" else: print "方 程組無唯一解或無解\n" # 輸出方程組及其解 print_matrix( "方程組及其解", matrix ) for i in range( 0, len( m ) ): print "x[%d] = %6.4f" % (i, m[i][len( m )]) |
運行結(jié)果：
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一開始的矩陣2.0000 0.0000 -2.0000 | 0.00000.0000 2.0000 -1.0000 | 0.00000.0000 1.0000 0.0000 | 10.0000一開始 de 矩陣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選主元2.0000 0.0000 -2.0000 | 0.00000.0000 2.0000 -1.0000 | 0.00000.0000 1.0000 0.0000 | 10.0000交換兩行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選主元1.0000 0.0000 -1.0000 | 0.00000.0000 2.0000 -1.0000 | 0.00000.0000 1.0000 0.0000 | 10.0000交換兩行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選主元1.0000 0.0000 -1.0000 | 0.00000.0000 1.0000 -0.5000 | 0.00000.0000 0.0000 0.5000 | 10.0000交換兩行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方程組有解方程組及其解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 |
希望本文所述對大家Python程序設(shè)計有所幫助。
原文鏈接：http://blog.csdn.net/zuyuanzhu/article/details/21184723
