◆ Bicg1()

双共役勾配(BICG)法による連立一次方程式 Ax = b の解 (シンプルドライバ)

引数

[in]	N	行列 A の次数. (N >= 0) (N = 0 の場合, 処理を行わずに戻る)
[in]	Val()	配列 Val(LVal - 1) (LVal >= Nnz) (Nnz は行列 A の非ゼロ要素数) 行列 A の非ゼロ要素の値.
[in]	Rowptr()	配列 Rowptr(LRowptr - 1) (LRowptr >= N + 1) 行列 A の行ポインタ.
[in]	Colind()	配列 Colind(LColind - 1) (LColind >= Nnz) 行列 A の列インデクス.
[in]	B()	配列 B(LB - 1) (LB >= N) 右辺ベクトル b.
[in,out]	X()	配列 X(LX - 1) (LX >= N) [in] 解の初期推定値. [out] 求められた近似解.
[out]	Info	(省略可) = 0: 正常終了. = i < 0: (-i)番目の入力パラメータの誤り. = 11: 最大反復回数を超えた. = 12: ブレークダウンが発生した.
[out]	Iter	(省略可) 収束時の反復回数.
[out]	Res	(省略可) 最終的な残差ノルム norm(b - A*x) の値.
[in]	MaxIter	(省略可) 最大反復回数. (MaxIter > 0) (省略時 = 500)
[in]	Tol	(省略可) 収束判定基準値. (省略時 = 1.0e-10) norm(b - Ax) <= Tolnorm(b) であれば収束とみなす. Tol < eps (マシンイプシロン) であれば Tol = eps とみなす.

使用例: 連立一次方程式 Ax = B を解く. ただし,
( 0.2 -0.11 -0.93 ) ( -0.3727 )

A = ( -0.32 0.81 0.37 ), B = ( 0.4319 )

( -0.8 -0.92 -0.29 ) ( -1.4247 )

とする.
Sub Ex_Bicg1()

Const N = 3, Nnz = N * N

Dim A(Nnz - 1) As Double, Ia(N) As Long, Ja(Nnz - 1) As Long

Dim B(N - 1) As Double, X(N - 1) As Double

Dim Iter As Long, Res As Double, Info As Long

A(0) = 0.2: A(1) = -0.11: A(2) = -0.93: A(3) = -0.32: A(4) = 0.81: A(5) = 0.37: A(6) = -0.8: A(7) = -0.92: A(8) = -0.29

Ia(0) = 0: Ia(1) = 3: Ia(2) = 6: Ia(3) = 9

Ja(0) = 0: Ja(1) = 1: Ja(2) = 2: Ja(3) = 0: Ja(4) = 1: Ja(5) = 2: Ja(6) = 0: Ja(7) = 1: Ja(8) = 2

B(0) = -0.3727: B(1) = 0.4319: B(2) = -1.4247

Call Bicg1(N, A(), Ia(), Ja(), B(), X(), Info, Iter, Res)

Debug.Print "X =", X(0), X(1), X(2)

Debug.Print "Iter = " + CStr(Iter) + ", Res = " + CStr(Res) + ", Info = " + CStr(Info)

End Sub

Bicg1
Sub Bicg1(N As Long, Val() As Double, Rowptr() As Long, Colind() As Long, B() As Double, X() As Double, Optional Info As Long, Optional Iter As Long, Optional Res As Double, Optional MaxIter As Long=500, Optional Tol As Double=1.0E-10)
双共役勾配(BICG)法による連立一次方程式 Ax = b の解 (シンプルドライバ)

実行結果: X = 0.86 0.640000000000001 0.509999999999996

Iter = 3, Res = 1.86243126342707E-15, Info = 0