関数columnvector_swap_by_pivot マニュアル

(The documentation of function columnvector_swap_by_pivot)

Last Update: 2021/12/6

◆機能・用途(Purpose)

連立方程式をLU分解で解くために左辺の係数行列の行を交換したのに合わせて右辺の列ベクトルの成分を交換する。
Swap the column vector components in the right hand side of a simultaneous equation, corresponding to swappings of rows of the coefficient matrix in the left hand side for solving the equation by an LU decomposition.

連立方程式

A x = b

(

A

:係数行列、

x

:未知数ベクトル、

b

:既知定数ベクトル)をLU分解で解く場合、ピボット選択のために

A

の行の交換が行われる。これに合わせて

b

の行の交換も必要であり、それを行うのがこの関数である。
Let us consider to solve a simultaneous equation

A x = b

by an LU decomposition, where

A

is a coefficient matrix,

x

is a vector of unknowns, and

b

is a vector of known constants. To solve the equation, rows of

A

are swapped as the pivod selection. Correcponding to it, the rows of

b

must be swapped, which is done by this function.

◆形式(Format)

#include <matrix/inverse.h>
inline struct columnvector columnvector_swap_by_pivot
(const struct columnvector original,const int ∗pivot)

◆引数(Arguments)

original

元の(成分を交換する前の)連立方程式の右辺を表す列ベクトル。
The original column vector before swapping the components, which represents the right hand side of a simultaneous equation.

pivot

連立方程式の左辺の係数行列に対して行った行の交換の情報。行交換後の係数行列の第

i

行成分がもともと存在していた行番号をpivot[i]とする。
Information of the row swappings applied to the coefficient matrix in the left hand side of the simultaneous equation; pivot[i] is defined such that the

i

th row after the row swapping was originally located at the pivot[i]th row.

◆戻り値(Return value)

originalの第pivot[i]成分を第

i

成分とする列ベクトル。
A column vector whose

i

th component is the pivot[i]th component of original.

◆使用例(Example)

struct matrix A;
struct columnvector b;
struct LU A_LU=LU_decomposition(A);
struct columnvector bb=columnvector_swap_by_pivot(b,A_LU.pivot);