◆ CsxDsSolve()

Sub CsxDsSolve	(	N As	Long,
		D() As	Double,
		B() As	Double,
		X() As	Double,
		Optional Info As	Long
	)

Diagonal scaling preconditioner (CSC/CSR)

Purpose: This routine is the diagonal scaling preconditioner for the coefficient matrix A of the sparse linear equations. It solves the equation M*x = b, where M (= diagonal matrix of A) is the preconditioner matrix.

Parameters

[in]	N	Dimension of preconditioner matrix. (N >= 0) (if N = 0, returns without computation)
[in]	D()	Array D(LD) (LD >= N) Diagonal elements of preconditioner matrix M obtained by CSR_SSOR().
[in]	B()	Array B(LB - 1) (LB >= N) Right hand side vector b.
[out]	X()	Array X(LX - 1) (LX >= N) Solution vector x.
[out]	Info	(Optional) = 0: Successful exit. = i < 0: The (-i)-th argument is invalid. = j > 0: Matrix is singular (j-th diagonal element is zero).

Example Program: Solve the system of linear equations Ax = B by FGMRES method with DS preconditioner, where
( 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 )

Sub Ex_Fgmres_Ds()

Const N = 3, Nnz = N * N, Tol = 0.0000000001 '1.0e-10

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 XX(N - 1) As Double, YY(N - 1) As Double

Dim Iter As Long, Res As Double, IRev As Long, 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

Dim D(N - 1) As Double

Call CsxDs(N, A(), Ia(), Ja(), D(), Info)

If Info <> 0 Then Debug.Print "Ds Info =" + Str(Info)

IRev = 0

Do

Call Fgmres_r(N, B(), X(), Info, XX(), YY(), IRev, Iter, Res)

If IRev = 1 Then '- Matvec

Call CsrDusmv("N", N, N, 1, A(), Ia(), Ja(), XX(), 0, YY())

ElseIf IRev = 3 Then '- Psolve

Call CsxDsSolve(N, D(), YY(), XX())

ElseIf IRev = 10 Then '- Check convergence

If Res < Tol Then IRev = 11

End If

Loop While IRev <> 0

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

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

End Sub

CsrDusmv
Sub CsrDusmv(Trans As String, M As Long, N As Long, Alpha As Double, Val() As Double, Rowptr() As Long, Colind() As Long, X() As Double, Beta As Double, Y() As Double, Optional Info As Long, Optional Base As Long=-1, Optional IncX As Long=1, Optional IncY As Long=1)
y <- αAx + βy or y <- αATx + βy (CSR)

Fgmres_r
Sub Fgmres_r(N As Long, B() As Double, X() As Double, Info As Long, XX() As Double, YY() As Double, IRev As Long, Optional Iter As Long, Optional Res As Double, Optional M As Long=0, Optional MaxIter As Long=500)
Solution of linear system Ax = b using generalized minimum residual (FGMRES) method (Reverse communic...

CsxDs
Sub CsxDs(N As Long, Val() As Double, Ptr() As Long, Ind() As Long, D() As Double, Optional Info As Long, Optional Base As Long=-1)
Initialize diagonal scaling preconditioner (CSC/CSR)

CsxDsSolve
Sub CsxDsSolve(N As Long, D() As Double, B() As Double, X() As Double, Optional Info As Long)
Diagonal scaling preconditioner (CSC/CSR)

Example Results: X = 0.86 0.64 0.51

Iter = 3, Res = 2.64570085387889E-16, Info = 0