Scilab 5.5.1
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See the recommended documentation of this function

Scilabヘルプ >> Linear Algebra > Linear Equations > linsolve

# linsolve

### 呼び出し手順

[x0,kerA]=linsolve(A,b [,x0])

### 引数

A

a na x ma 実数行列 (疎行列の場合もあり)

b

na x 1ベクトル (Aの行と同じ次元)

x0

kerA

ma x k 実数行列

### 説明

linsolve は, A*x+b=0の解を全て計算します.

x0 は特解 (存在する場合), kerAAのヌル空間です. 任意のwについてx=x0+kerA*wは, A*x+b=0を満たします.

### 例

A=rand(5,3)*rand(3,8);
b=A*ones(8,1);[x,kerA]=linsolve(A,b);A*x+b   //compatible b
b=ones(5,1);[x,kerA]=linsolve(A,b);A*x+b   //uncompatible b
A=rand(5,5);[x,kerA]=linsolve(A,b), -inv(A)*b  //x is unique
// Benchmark with other linear sparse solver:
b = zeros(size(A,1),1);
tic();
res = umfpack(A,'\',b);
mprintf('\ntime needed to solve the system with umfpack: %.3f\n',toc());
tic();
res = linsolve(A,b);
mprintf('\ntime needed to solve the system with linsolve: %.3f\n',toc());
tic();
res = A\b;
mprintf('\ntime needed to solve the system with the backslash operator: %.3f\n',toc());

### 参照

• inv — 逆行列
• pinv — 擬似逆行列
• colcomp — 列圧縮,カーネル,ヌル空間
• im_inv — 原像
• umfpack — solve sparse linear system
• backslash — (\) 左行列除算.
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