行列の計算
本ページではOMRON NX/NJシリーズ向けの行列演算ライブラリを紹介しています。
行列の加算、減算、定数倍、アダマール積、行列積、転置行列、逆行列、行列式の計算などを実装できます。
サンプル一覧
加算 (matADD)
- a
- 行列 [0..9,0..9]
- b
- 行列 [0..9,0..9]
- result
- 行列 [0..9,0..9]
例
- a
- \begin{bmatrix} 1,&2,&3 \\ 2,&3,&4 \\ 3,&4,&5 \\ \end{bmatrix}
- b
- \begin{bmatrix} 3,&2,&1 \\ 4,&3,&2 \\ 5,&4,&3 \\ \end{bmatrix}
- result
- \begin{bmatrix} 4,&4,&4 \\ 6,&6,&6 \\ 8,&8,&8 \\ \end{bmatrix}
計算式
\[ \begin{bmatrix} a_{11} & a_{12} & \ldots & a_{1n} \\ a_{21} & a_{22} & \ldots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{nl} & a_{n2} & \ldots & a_{nn} \end{bmatrix} + \begin{bmatrix} b_{11} & b_{12} & \ldots & b_{1n} \\ b_{21} & b_{22} & \ldots & b_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ b_{nl} & b_{n2} & \ldots & b_{nn} \end{bmatrix} = \begin{bmatrix} a_{11}+b_{11} & a_{12}+b_{12} & \ldots & a_{1n}+b_{1n} \\ a_{21}+b_{21} & a_{22}+b_{22} & \ldots & a_{2n}+b_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{nl}+b_{nl} & a_{n2}+b_{n2} & \ldots & a_{nn}+b_{nn} \end{bmatrix} \]
減算 (vecSUB)
- a
- 行列 [0..9,0..9]
- b
- 行列 [0..9,0..9]
- result
- 行列 [0..9,0..9]
例
- a
- \begin{bmatrix} 1,&2,&3 \\ 2,&3,&4 \\ 3,&4,&5 \\ \end{bmatrix}
- b
- \begin{bmatrix} 3,&2,&1 \\ 4,&3,&2 \\ 5,&4,&3 \\ \end{bmatrix}
- result
- \begin{bmatrix} -2,&0,&2 \\ -2,&0,&2 \\ -2,&0,&2 \\ \end{bmatrix}
計算式
\[ \begin{bmatrix} a_{11} & a_{12} & \ldots & a_{1n} \\ a_{21} & a_{22} & \ldots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{nl} & a_{n2} & \ldots & a_{nn} \end{bmatrix} - \begin{bmatrix} b_{11} & b_{12} & \ldots & b_{1n} \\ b_{21} & b_{22} & \ldots & b_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ b_{nl} & b_{n2} & \ldots & b_{nn} \end{bmatrix} = \begin{bmatrix} a_{11}-b_{11} & a_{12}-b_{12} & \ldots & a_{1n}-b_{1n} \\ a_{21}-b_{21} & a_{22}-b_{22} & \ldots & a_{2n}-b_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{nl}-b_{nl} & a_{n2}-b_{n2} & \ldots & a_{nn}-b_{nn} \end{bmatrix} \]
定数倍 (matMUL)
- k
- 倍率
- a
- 行列 [0..9,0..9]
- result
- 行列 [0..9,0..9]
例
- k
- 2.0
- a
- \begin{bmatrix} 1,&2,&3 \\ 2,&3,&4 \\ 3,&4,&5 \\ \end{bmatrix}
- result
- \begin{bmatrix} 2,&4,&6 \\ 4,&6,&8 \\ 6,&8,&10 \\ \end{bmatrix}
計算式
\[ k \begin{bmatrix} a_{11} & a_{12} & \ldots & a_{1n} \\ a_{21} & a_{22} & \ldots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{nl} & a_{n2} & \ldots & a_{nn} \end{bmatrix} = \begin{bmatrix} ka_{11} & ka_{12} & \ldots & ka_{1n} \\ ka_{21} & ka_{22} & \ldots & ka_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ ka_{nl} & ka_{n2} & \ldots & ka_{nn} \end{bmatrix} \]
アダマール積 (matMultiply)
- a
- 行列 [0..9,0..9]
- b
- 行列 [0..9,0..9]
- result
- 行列 [0..9,0..9]
例
- a
- \begin{bmatrix} 1,&2,&3 \\ 2,&3,&4 \\ 3,&4,&5 \\ \end{bmatrix}
- b
- \begin{bmatrix} 3,&2,&1 \\ 4,&3,&2 \\ 5,&4,&3 \\ \end{bmatrix}
- result
- \begin{bmatrix} 3,&4,&3 \\ 8,&9,&8 \\ 15,&16,&15 \\ \end{bmatrix}
計算式
\[ \begin{bmatrix} a_{11} & a_{12} & \ldots & a_{1n} \\ a_{21} & a_{22} & \ldots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{nl} & a_{n2} & \ldots & a_{nn} \end{bmatrix} \circ \begin{bmatrix} b_{11} & b_{12} & \ldots & b_{1n} \\ b_{21} & b_{22} & \ldots & b_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ b_{nl} & b_{n2} & \ldots & b_{nn} \end{bmatrix} = \begin{bmatrix} a_{11}b_{11} & a_{12}b_{12} & \ldots & a_{1n}b_{1n} \\ a_{21}b_{21} & a_{22}b_{22} & \ldots & a_{2n}b_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{nl}b_{nl} & a_{n2}b_{n2} & \ldots & a_{nn}b_{nn} \end{bmatrix} \]
内積 (matDot)
- a
- 行列 [0..9,0..9]
- b
- 行列 [0..9,0..9]
- out
- 結果
例
- a
- \begin{bmatrix} 1,&2,&3 \\ 2,&3,&4 \\ 3,&4,&5 \\ \end{bmatrix}
- b
- \begin{bmatrix} 3,&2,&1 \\ 4,&3,&2 \\ 5,&4,&3 \\ \end{bmatrix}
- out
- 81
計算式
\[ \begin{bmatrix} a_{11} & a_{12} & \ldots & a_{1n} \\ a_{21} & a_{22} & \ldots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{nl} & a_{n2} & \ldots & a_{nn} \end{bmatrix} \bullet \begin{bmatrix} b_{11} & b_{12} & \ldots & b_{1n} \\ b_{21} & b_{22} & \ldots & b_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ b_{nl} & b_{n2} & \ldots & b_{nn} \end{bmatrix} \]
行列積 (matCross)
- a
- 行列 [0..9,0..9]
- b
- 行列 [0..9,0..9]
- result
- 行列 [0..9,0..9]
例
- a
- \begin{bmatrix} 1,&2,&3 \\ 2,&3,&4 \\ 3,&4,&5 \\ \end{bmatrix}
- b
- \begin{bmatrix} 3,&2,&1 \\ 4,&3,&2 \\ 5,&4,&3 \\ \end{bmatrix}
- result
- \begin{bmatrix} 26,&20,&14 \\ 38,&29,&20 \\ 50,&38,&26 \\ \end{bmatrix}
計算式
\[ \begin{bmatrix} a_{11} & a_{12} & \ldots & a_{1n} \\ a_{21} & a_{22} & \ldots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{nl} & a_{n2} & \ldots & a_{nn} \end{bmatrix} \times \begin{bmatrix} b_{11} & b_{12} & \ldots & b_{1n} \\ b_{21} & b_{22} & \ldots & b_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ b_{nl} & b_{n2} & \ldots & b_{nn} \end{bmatrix} \]
転置行列 (matT)
- a
- 行列 [0..9,0..9]
- result
- 行列 [0..9,0..9]
例
- a
- \begin{bmatrix} 1,&2,&3 \\ 4,&5,&6 \\ 7,&8,&9 \\ \end{bmatrix}
- result
- \begin{bmatrix} 1,&4,&7 \\ 2,&5,&8 \\ 3,&6,&9 \\ \end{bmatrix}
計算式
\[ ^tA= \begin{bmatrix} a_{11} & a_{12} & \ldots & a_{1n} \\ a_{21} & a_{22} & \ldots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{nl} & a_{n2} & \ldots & a_{nn} \end{bmatrix} = \begin{bmatrix} a_{11} & a_{21} & \ldots & a_{nl} \\ a_{12} & a_{22} & \ldots & a_{n2} \\ \vdots & \vdots & \ddots & \vdots \\ a_{1n} & a_{2n} & \ldots & a_{nn} \end{bmatrix} \]
逆行列 (matInv)
- a
- 行列 [0..9,0..9]
- result
- 行列 [0..9,0..9]
例
- a
- \begin{bmatrix} 1,&2,&0 \\ -1,&1,&2 \\ 2,&0,&1 \\ \end{bmatrix}
- result
- \begin{bmatrix} 0.09,&-0.18,&0.36 \\ 0.45,&0.09,&-0.18 \\ -0.18,&0.36,&0.27 \\ \end{bmatrix}
計算式
\[ A^{-1}= \begin{bmatrix} a_{11} & a_{12} & \ldots & a_{1n} \\ a_{21} & a_{22} & \ldots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{nl} & a_{n2} & \ldots & a_{nn} \end{bmatrix} \]
行列式の計算 (matDet)
- a
- 行列 [0..9,0..9]
- out
- 計算結果
例
- a
- \begin{bmatrix} 2,&-2,&4 \\ 2,&-1,&6 \\ 3,&-2,&12 \\ \end{bmatrix}
- out
- 8.0
計算式
\[ \begin{bmatrix} a_{11} & a_{12} & \ldots & a_{1n} \\ a_{21} & a_{22} & \ldots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{nl} & a_{n2} & \ldots & a_{nn} \end{bmatrix} \]