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◆ Dtbtrs()
| Sub Dtbtrs |
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Uplo As |
String, |
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Trans As |
String, |
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Diag As |
String, |
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N As |
Long, |
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Kd As |
Long, |
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Ab() As |
Double, |
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B() As |
Double, |
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Info As |
Long, |
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Optional Nrhs As |
Long = 1 |
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連立一次方程式 AX = B または ATX = B の解 (三角帯行列)
- 目的
- 本ルーチンは三角行列の連立一次方程式
A * X = B または A^T * X = B
- 引数
-
| [in] | Uplo | = "U": Aは上三角行列.
= "L": Aは下三角行列. |
| [in] | Trans | 連立方程式の形を指定.
= "N": A * X = B. (転置なし)
= "T", "C": A^T * X = B. (転置あり) |
| [in] | Diag | = "N": Aは単位三角行列ではない.
= "U": Aは単位三角行列である. (Ab()の対角要素を参照せず, 1とみなす) |
| [in] | N | 行列Aの行および列数. (N >= 0) (N = 0 の場合, 処理を行わずに戻る) |
| [in] | Kd | 三角帯行列Aの上または下帯幅. (Kd >= 0) |
| [in] | Ab() | 配列 Ab(LAb1 - 1, LAb2 - 1) (LAb1 >= Kd + 1, LAb2 >= N)
Kd+1×N対称帯行列形式のN×N三角帯行列 A. Uploに従って上または下三角部分を格納. |
| [in,out] | B() | 配列 B(LB1 - 1, LB2 - 1) (LB1 >= max(1, N), LB2 >= Nrhs) (2次元配列) または B(LB - 1) (LB >= max(1, N), Nrhs = 1) (1次元配列)
[in] N×Nrhs右辺行列 B.
[out] Info = 0 の場合, N×Nrhs解行列 X. |
| [out] | Info | = 0: 正常終了.
= -1: パラメータ Uplo の誤り. (Uplo <> "U"および"L")
= -2: パラメータ Trans の誤り. (Trans <> "N", "T"および"C")
= -3: パラメータ Diag の誤り. (Diag <> "N"および"U")
= -4: パラメータ N の誤り. (N < 0)
= -5: パラメータ Kd の誤り. (Kd < 0)
= -6: パラメータ Ab() の誤り.
= -7: パラメータ B() の誤り.
= -9: パラメータ Nrhs の誤り. (Nrhs < 0)
= i > 0: Aのi番目の対角要素が0, すなわち, 行列が特異であり解Xは計算されなかった. |
| [in] | Nrhs | (省略可)
右辺の数, すなわち, 行列Bの列数. (Nrhs >= 0) (Nrhs = 0 の場合, 処理を行わずに戻る) (省略時 = 1) |
- 出典
- LAPACK
- 使用例
- 連立一次方程式 Ax = B を解き, 同時にAの条件数の逆数の推定値(RCond)を求める. ただし,
( -0.40 0 0 ) ( -0.0800 )
A = ( 2.06 0.52 0 ), B = ( 0.6616 )
( 0 -0.74 -2.72 ) ( -0.9264 )
Sub Ex_Dtbtrs()
Const N = 3, Kd = 1
Dim Ab(Kd, N - 1) As Double, B(N - 1) As Double
Dim RCond As Double, Info As Long
Ab(0, 0) = -0.4: Ab(0, 1) = 0.52: Ab(0, 2) = -2.72
Ab(1, 0) = 2.06: Ab(1, 1) = -0.74
B(0) = -0.08: B(1) = 0.6616: B(2) = -0.9264
Call Dtbtrs("L", "N", "N", N, Kd, Ab(), B(), Info) If Info = 0 Then Call Dtbcon("1", "L", "N", N, Kd, Ab(), RCond, Info) Debug.Print "X =", B(0), B(1), B(2)
Debug.Print "RCond =", RCond
Debug.Print "Info =", Info
End Sub
Sub Dtbcon(Norm As String, Uplo As String, Diag As String, N As Long, Kd As Long, Ab() As Double, RCond As Double, Info As Long) 行列の条件数 (三角帯行列) Sub Dtbtrs(Uplo As String, Trans As String, Diag As String, N As Long, Kd As Long, Ab() As Double, B() As Double, Info As Long, Optional Nrhs As Long=1) 連立一次方程式 AX = B または ATX = B の解 (三角帯行列)
- 実行結果
X = 0.2 0.48 0.21
RCond = 2.43502692577851E-02
Info = 0
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1.9.7