◆ Rfft2c()

Sub Rfft2c	(	L As	Long,
		M As	Long,
		R() As	Double,
		C() As	Complex,
		Info As	Long
	)

Rfft2fによるフーリエ変換の2次元複素データ

目的: 本ルーチンは, Rfft2fにより求められた圧縮形式の2次元フーリエ変換を2次元複素データに展開する. 圧縮形式についてはRfft2fの説明を参照せよ.

引数

[in]	L	入力データ行列の行数. (L >= 1)
[in]	M	入力データ行列の列数. (M >= 1)
[in]	R()	配列 R(LR1 - 1, LR2 - 1) (LR1 >= L, LR2 >= M) Rfft2fによりフーリエ変換された圧縮形式の2次元フーリエ変換データ.
[in]	C()	配列 C(LC1 - 1, LC2 - 1) (LC1 >= L, LC2 >= M) R()の圧縮された2次元フーリエ変換データを展開した2次元複素データ.
[out]	Info	= 0: 正常終了. = -1: パラメータ L の誤り. (L < 1) = -2: パラメータ M の誤り. (M < 1) = -3: パラメータ R() の誤り. (配列R()の大きさが不足) = -5: パラメータ C() の誤り. (配列C()の大きさが不足)

使用例: 4行4列の2次元ランダムデータのフーリエ変換をRfft2fにより求め, 結果の圧縮形式データをRfft2cにより2次元複素データに展開する. そのフーリエ逆変換をCfft2bにより求め元のデータと比較する.
Sub Ex_Rfft2c()

Const L = 4, M = 4

Dim Wsave() As Double, R(L - 1, M - 1) As Double, R0(L - 1, M - 1) As Double

Dim C(L - 1, M - 1) As Complex

Dim LWsave As Long, Info As Long, I As Long, J As Long

'-- Initialization

LWsave = L + 3 * M + Log(L) / Log(2) + 2 * Log(M) / Log(2) + 12

ReDim Wsave(LWsave - 1)

Call Rfft2i(L, M, Wsave, Info)

If Info <> 0 Then GoTo Err

'-- Generate test data

For I = 0 To L - 1

For J = 0 To M - 1

R(I, J) = Rnd()

R0(I, J) = R(I, J)

Next

Next

'-- Forward transform

Call Rfft2f(L, M, R(), Wsave(), Info)

If Info <> 0 Then GoTo Err

'-- Convert to full complex data

Call Rfft2c(L, M, R(), C(), Info)

'-- Initialization for Cfft2b

LWsave = 2 * (L + M) + Log(L) / Log(2) + Log(M) / Log(2) + 8

ReDim Wsave(LWsave - 1)

Call Cfft2i(L, M, Wsave, Info)

If Info <> 0 Then GoTo Err

'-- Backward transform by Cfft2b

Call Cfft2b(L, M, C(), Wsave(), Info)

If Info <> 0 Then GoTo Err

'-- Print result

For J = 0 To M - 1

For I = 0 To L - 1

Debug.Print R0(I, J), Creal(C(I, J)), Cimag(C(I, J)), Creal(C(I, J)) - R0(I, J)

Next

Debug.Print

Next

Exit Sub

Err:

Debug.Print "Error in Rfft2i/Rfft2f/Rfft2b: Info =", Info

End Sub

Cimag
Function Cimag(A As Complex) As Double
複素数の虚数部

Creal
Function Creal(A As Complex) As Double
複素数の実数部

Rfft2c
Sub Rfft2c(L As Long, M As Long, R() As Double, C() As Complex, Info As Long)
Rfft2fによるフーリエ変換の2次元複素データ

Rfft2i
Sub Rfft2i(L As Long, M As Long, Wsave() As Double, Info As Long)
Rfft2fおよびRfft2bのための作業データの初期化

Rfft2f
Sub Rfft2f(L As Long, M As Long, R() As Double, Wsave() As Double, Info As Long)
2次元実フーリエ変換

Cfft2b
Sub Cfft2b(L As Long, M As Long, C() As Complex, Wsave() As Double, Info As Long)
2次元複素フーリエ逆変換

Cfft2i
Sub Cfft2i(L As Long, M As Long, Wsave() As Double, Info As Long)
Cfft2fおよびCfft2bのための作業データの初期化

Rfft2b
Sub Rfft2b(L As Long, M As Long, R() As Double, Wsave() As Double, Info As Long)
2次元実フーリエ逆変換

実行結果: 0.902888596057892 0.902888596057892 0 0

0.449173510074615 0.449173510074615 0 0

0.91016560792923 0.91016560792923 0 0

0.415564596652985 0.415564596652985 0 0

0.419061899185181 0.419061899185181 0 0

0.52361536026001 0.52361536026001 0 0

0.356703519821167 0.356703519821167 0 0

0.341727256774902 0.341727256774902 0 0

0.614621579647064 0.614621579647064 0 0

0.320736587047577 0.320736587047577 0 0

0.423278748989105 0.423278748989105 0 0

0.214545428752899 0.214545428752899 0 0

0.733203768730164 0.733203768730164 0 0

0.805532574653625 0.805532574653625 0 0

0.942486166954041 0.942486166954041 0 0

0.579672455787659 0.579672455787659 0 0