◆ ZCsxDsSolve()

Sub ZCsxDsSolve	(	N As	Long,
		D() As	Complex,
		B() As	Complex,
		X() As	Complex,
		Optional Info As	Long
	)

Diagonal scaling preconditioner (Complex matrices) (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
( 0.78+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_ZFgmres_Ds()

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)

Dim D(N - 1) As Complex

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

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

IRev = 0

Do

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

If IRev = 1 Then '- Matvec

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

ElseIf IRev = 3 Then '- Psolve

Call ZCsxDsSolve(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 ="

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

Cmplx
Function Cmplx(R As Double, Optional I As Double=0) As Complex
Building complex number

Cimag
Function Cimag(A As Complex) As Double
Imaginary part of complex number

Creal
Function Creal(A As Complex) As Double
Real part of complex number

CsrZusmv
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 or y <- αAHx + βy (Complex matrices) (CSR)

ZFgmres_r
Sub ZFgmres_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 M As Long=0, Optional MaxIter As Long=500)
Solution of linear system Ax = b using generalized minimum residual (FGMRES) method (Complex matrices...

ZCsxDsSolve
Sub ZCsxDsSolve(N As Long, D() As Complex, B() As Complex, X() As Complex, Optional Info As Long)
Diagonal scaling preconditioner (Complex matrices) (CSC/CSR)

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

Example Results: X =

(0.59,-0.28)

(-0.2,-0.04)

(0.24,-0.49)

Iter = 3, Res = 3.24824839330284E-16, Info = 0