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◆ ZCgs_r()
| Sub ZCgs_r |
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N As |
Long, |
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B() As |
Complex, |
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X() As |
Complex, |
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Info As |
Long, |
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XX() As |
Complex, |
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YY() As |
Complex, |
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IRev As |
Long, |
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Optional Iter As |
Long, |
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Optional Res As |
Double, |
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Optional MaxIter As |
Long = 500 |
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二乗共役勾配(CGS)法による連立一次方程式 Ax = b の解 (複素行列) (リバースコミュニケーション版)
- 目的
- 前処理付き反復法(二乗共役勾配(CGS)法)により連立一次方程式 Ax = b の解を求める.
- 引数
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| [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] | 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 | = 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. |
| [in,out] | XX() | 配列 XX(LXX - 1) (LXX >= N)
Matvec, MatvecTrans, Psolve および PsolveTrans演算のためのベクトル XX. |
| [in,out] | YY() | 配列 YY(LYY - 1) (LYY >= N)
Matvec, MatvecTrans, Psolve および PsolveTrans演算のためのベクトル YY. |
| [in,out] | IRev | リバースコミュニケーションの制御変数.
[in] 最初の呼び出し時に IRev = 0 に設定しておくこと. それ以降の呼び出し時にはIRevの値を変更してはならない(収束時を除く).
[out] 0 以外のときには下記処理を行ってから再び本ルーチンを呼び出すこと.
= 0: 処理終了. 正常終了かどうかはInfoをチェックすること.
= 1: Matvec演算. A*XX を YY に設定すること. 他の変数を変更してはならない.
= 3: Psolve演算: M*XX = YY の解を XX に設定すること(Mは前処理行列). 他の変数を変更してはならない.
= 10: 収束判定を行うために反復ごとに戻る. 収束時には IRev = 11 として, それ以外のときは IRev を変更せずに再度呼び出すこと. X(), Iter および Res にはその反復時の最新の値が入っているので収束判定のために使用してよい. また, 中間結果出力のために使うこともできる. |
| [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] | M | (省略可)
リスタートパラメータ. (0 < M <= N (省略時 = min(64, N))) |
| [in] | MaxIter | (省略可)
最大反復回数. (MaxIter > 0) (省略時 = 500) |
- 使用例
- 連立一次方程式 Ax = B を解く. ただし,
( 0.78+0.16i -0.9-1.46i 0.48-1.08i )
A = ( 0.73+0.63i 1.58-1.24 -0.41-0.91i )
( 0.23-1.37i 0.79+0.64i -0.73-1.5i )
( 0.2126-0.2904i )
B = ( -0.3028+0.3346i )
( -1.2905-1.0346i )
Sub Ex_ZCgs_r()
Const N = 3, Nnz = N * N, Tol = 0.0000000001 '1.0e-10
Dim A(Nnz - 1) As Complex, Ia(N) As Long, Ja(Nnz - 1) As Long
Dim B(N - 1) As Complex, X(N - 1) As Complex
Dim XX(N - 1) As Complex, YY(N - 1) As Complex
Dim Iter As Long, Res As Double, IRev As Long, Info As Long, I As Long
A(0) = Cmplx(0.78, 0.16): A(1) = Cmplx(-0.9, -1.46): A(2) = Cmplx(0.48, -1.08): A(3) = Cmplx(0.73, 0.63): A(4) = Cmplx(1.58, -1.24): A(5) = Cmplx(-0.41, -0.91): A(6) = Cmplx(0.23, -1.37): A(7) = Cmplx(0.79, 0.64): A(8) = Cmplx(-0.73, -1.5) 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) = Cmplx(0.2126, -0.2904): B(1) = Cmplx(-0.3028, 0.3346): B(2) = Cmplx(-1.2905, -1.0346) IRev = 0
Do
Call ZCgs_r(N, B(), X(), Info, XX(), YY(), IRev, Iter, Res) If IRev = 1 Then '- Matvec
ElseIf IRev = 3 Then '- Psolve
For I = 0 To N - 1
XX(I) = YY(I)
Next
ElseIf IRev = 10 Then '- Check convergence
If Res < Tol Then IRev = 11
End If
Loop While IRev <> 0
Debug.Print "X ="
Debug.Print "(" + CStr( Creal(X(0))) + "," + CStr( Cimag(X(0))) + ")" Debug.Print "(" + CStr( Creal(X(1))) + "," + CStr( Cimag(X(1))) + ")" Debug.Print "(" + CStr( Creal(X(2))) + "," + CStr( Cimag(X(2))) + ")" Debug.Print "Iter =" + Str(Iter) + ", Res =" + Str(Res) + ", Info =" + Str(Info)
End Sub
Function Cmplx(R As Double, Optional I As Double=0) As Complex 複素数の作成 Function Cimag(A As Complex) As Double 複素数の虚数部 Function Creal(A As Complex) As Double 複素数の実数部 Sub CsrZusmv(Trans As String, M As Long, N As Long, Alpha As Complex, Val() As Complex, Rowptr() As Long, Colind() As Long, X() As Complex, Beta As Complex, Y() As Complex, Optional Info As Long, Optional Base As Long=-1, Optional IncX As Long=1, Optional IncY As Long=1) y <- αAx + βy, y <- αATx + βy または y <- αAHx + βy (複素行列) (CSR) Sub ZCgs_r(N As Long, B() As Complex, X() As Complex, Info As Long, XX() As Complex, YY() As Complex, IRev As Long, Optional Iter As Long, Optional Res As Double, Optional MaxIter As Long=500) 二乗共役勾配(CGS)法による連立一次方程式 Ax = b の解 (複素行列) (リバースコミュニケーション版)
- 実行結果
X =
(0.59,-0.279999999999999)
(-0.2,-3.99999999999992E-02)
(0.24,-0.49)
Iter = 3, Res = 3.16839631446882E-15, Info = 0
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1.9.7