Octave 解线性方程组
abellong
posted @ 2012年4月14日 01:00
in 数学
, 5494 阅读
$Octave$ 解线性方程组的能力还没有 $matlab$ 强. 对于方程 \(A\times X=B\), $Octave$ 要求 \(A\) 是方阵, \(B\) 是向量; 而 matlab 并没有这些要求, 假设 \(A\) 是 \(m\times n\), \(B\) 是 \(m\times k\), 则可以用 $matlab$ 算出 \(X\), 它是 \(n\times k\) 的.
$Octave$ 解方程组的式子为 \(A\backslash B\). 下面提供两个例子
octave:1> # octave:1> A=[0,2,0,1;2,2,3,2;4,-3,0,1.;6,1,-6,-5] A = 0 2 0 1 2 2 3 2 4 -3 0 1 6 1 -6 -5 octave:2> B=[0;-2;-7;6] B = 0 -2 -7 6 octave:3> A\B ans = -0.50000 1.00000 0.33333 -2.00000
先生成一个随机方阵 $C$ 和随机向量 $D$ 并解方程 $$C\times x=D$$
octave:1> C=rand(5,5) C = 0.847817 0.122730 0.298340 0.652850 0.985631 0.880412 0.618896 0.590534 0.485949 0.763285 0.358464 0.384306 0.469336 0.909417 0.554835 0.306760 0.672447 0.043989 0.371049 0.692044 0.314791 0.410965 0.487560 0.485444 0.892830 octave:2> D=rand(5,1) D = 0.50708 0.99851 0.31515 0.70781 0.66774 octave:3> C\D ans = 0.32657 0.77660 0.32264 -0.50477 0.37354
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