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(*************************************************************************
Copyright (c) 2009, Sergey Bochkanov (ALGLIB project).
>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses
>>> END OF LICENSE >>>
*************************************************************************)
unit u_corr;
interface
uses Math, Sysutils, u_ap, u_ftbase, u_fft, u_conv;
procedure CorrC1D(const Signal : TComplex1DArray;
N : Integer;
const Pattern : TComplex1DArray;
M : Integer;
var R : TComplex1DArray);
procedure CorrC1DCircular(const Signal : TComplex1DArray;
M : Integer;
const Pattern : TComplex1DArray;
N : Integer;
var C : TComplex1DArray);
procedure CorrR1D(const Signal : TReal1DArray;
N : Integer;
const Pattern : TReal1DArray;
M : Integer;
var R : TReal1DArray);
procedure CorrR1DCircular(const Signal : TReal1DArray;
M : Integer;
const Pattern : TReal1DArray;
N : Integer;
var C : TReal1DArray);
implementation
(*************************************************************************
1-dimensional complex cross-correlation.
For given Pattern/Signal returns corr(Pattern,Signal) (non-circular).
Correlation is calculated using reduction to convolution. Algorithm with
max(N,N)*log(max(N,N)) complexity is used (see ConvC1D() for more info
about performance).
IMPORTANT:
for historical reasons subroutine accepts its parameters in reversed
order: CorrC1D(Signal, Pattern) = Pattern x Signal (using traditional
definition of cross-correlation, denoting cross-correlation as "x").
INPUT PARAMETERS
Signal - array[0..N-1] - complex function to be transformed,
signal containing pattern
N - problem size
Pattern - array[0..M-1] - complex function to be transformed,
pattern to search withing signal
M - problem size
OUTPUT PARAMETERS
R - cross-correlation, array[0..N+M-2]:
* positive lags are stored in R[0..N-1],
R[i] = sum(conj(pattern[j])*signal[i+j]
* negative lags are stored in R[N..N+M-2],
R[N+M-1-i] = sum(conj(pattern[j])*signal[-i+j]
NOTE:
It is assumed that pattern domain is [0..M-1]. If Pattern is non-zero
on [-K..M-1], you can still use this subroutine, just shift result by K.
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************)
procedure CorrC1D(const Signal : TComplex1DArray;
N : Integer;
const Pattern : TComplex1DArray;
M : Integer;
var R : TComplex1DArray);
var
P : TComplex1DArray;
B : TComplex1DArray;
I : Integer;
i_ : Integer;
i1_ : Integer;
begin
Assert((N>0) and (M>0), 'CorrC1D: incorrect N or M!');
SetLength(P, M);
I:=0;
while I<=M-1 do
begin
P[M-1-I] := Conj(Pattern[I]);
Inc(I);
end;
ConvC1D(P, M, Signal, N, B);
SetLength(R, M+N-1);
i1_ := (M-1) - (0);
for i_ := 0 to N-1 do
begin
R[i_] := B[i_+i1_];
end;
if M+N-2>=N then
begin
i1_ := (0) - (N);
for i_ := N to M+N-2 do
begin
R[i_] := B[i_+i1_];
end;
end;
end;
(*************************************************************************
1-dimensional circular complex cross-correlation.
For given Pattern/Signal returns corr(Pattern,Signal) (circular).
Algorithm has linearithmic complexity for any M/N.
IMPORTANT:
for historical reasons subroutine accepts its parameters in reversed
order: CorrC1DCircular(Signal, Pattern) = Pattern x Signal (using
traditional definition of cross-correlation, denoting cross-correlation
as "x").
INPUT PARAMETERS
Signal - array[0..N-1] - complex function to be transformed,
periodic signal containing pattern
N - problem size
Pattern - array[0..M-1] - complex function to be transformed,
non-periodic pattern to search withing signal
M - problem size
OUTPUT PARAMETERS
R - convolution: A*B. array[0..M-1].
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************)
procedure CorrC1DCircular(const Signal : TComplex1DArray;
M : Integer;
const Pattern : TComplex1DArray;
N : Integer;
var C : TComplex1DArray);
var
P : TComplex1DArray;
B : TComplex1DArray;
I1 : Integer;
I2 : Integer;
I : Integer;
J2 : Integer;
i_ : Integer;
i1_ : Integer;
begin
Assert((N>0) and (M>0), 'ConvC1DCircular: incorrect N or M!');
//
// normalize task: make M>=N,
// so A will be longer (at least - not shorter) that B.
//
if M<N then
begin
SetLength(B, M);
I1:=0;
while I1<=M-1 do
begin
B[I1] := C_Complex(0);
Inc(I1);
end;
I1 := 0;
while I1<N do
begin
I2 := Min(I1+M-1, N-1);
J2 := I2-I1;
i1_ := (I1) - (0);
for i_ := 0 to J2 do
begin
B[i_] := C_Add(B[i_], Pattern[i_+i1_]);
end;
I1 := I1+M;
end;
CorrC1DCircular(Signal, M, B, M, C);
Exit;
end;
//
// Task is normalized
//
SetLength(P, N);
I:=0;
while I<=N-1 do
begin
P[N-1-I] := Conj(Pattern[I]);
Inc(I);
end;
ConvC1DCircular(Signal, M, P, N, B);
SetLength(C, M);
i1_ := (N-1) - (0);
for i_ := 0 to M-N do
begin
C[i_] := B[i_+i1_];
end;
if M-N+1<=M-1 then
begin
i1_ := (0) - (M-N+1);
for i_ := M-N+1 to M-1 do
begin
C[i_] := B[i_+i1_];
end;
end;
end;
(*************************************************************************
1-dimensional real cross-correlation.
For given Pattern/Signal returns corr(Pattern,Signal) (non-circular).
Correlation is calculated using reduction to convolution. Algorithm with
max(N,N)*log(max(N,N)) complexity is used (see ConvC1D() for more info
about performance).
IMPORTANT:
for historical reasons subroutine accepts its parameters in reversed
order: CorrR1D(Signal, Pattern) = Pattern x Signal (using traditional
definition of cross-correlation, denoting cross-correlation as "x").
INPUT PARAMETERS
Signal - array[0..N-1] - real function to be transformed,
signal containing pattern
N - problem size
Pattern - array[0..M-1] - real function to be transformed,
pattern to search withing signal
M - problem size
OUTPUT PARAMETERS
R - cross-correlation, array[0..N+M-2]:
* positive lags are stored in R[0..N-1],
R[i] = sum(pattern[j]*signal[i+j]
* negative lags are stored in R[N..N+M-2],
R[N+M-1-i] = sum(pattern[j]*signal[-i+j]
NOTE:
It is assumed that pattern domain is [0..M-1]. If Pattern is non-zero
on [-K..M-1], you can still use this subroutine, just shift result by K.
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************)
procedure CorrR1D(const Signal : TReal1DArray;
N : Integer;
const Pattern : TReal1DArray;
M : Integer;
var R : TReal1DArray);
var
P : TReal1DArray;
B : TReal1DArray;
I : Integer;
begin
Assert((N>0) and (M>0), 'CorrR1D: incorrect N or M!');
SetLength(P, M);
I:=0;
while I<=M-1 do
begin
P[M-1-I] := Pattern[I];
Inc(I);
end;
ConvR1D(P, M, Signal, N, B);
SetLength(R, M+N-1);
APVMove(@R[0], 0, N-1, @B[0], M-1, M+N-2);
if M+N-2>=N then
begin
APVMove(@R[0], N, M+N-2, @B[0], 0, M-2);
end;
end;
(*************************************************************************
1-dimensional circular real cross-correlation.
For given Pattern/Signal returns corr(Pattern,Signal) (circular).
Algorithm has linearithmic complexity for any M/N.
IMPORTANT:
for historical reasons subroutine accepts its parameters in reversed
order: CorrR1DCircular(Signal, Pattern) = Pattern x Signal (using
traditional definition of cross-correlation, denoting cross-correlation
as "x").
INPUT PARAMETERS
Signal - array[0..N-1] - real function to be transformed,
periodic signal containing pattern
N - problem size
Pattern - array[0..M-1] - real function to be transformed,
non-periodic pattern to search withing signal
M - problem size
OUTPUT PARAMETERS
R - convolution: A*B. array[0..M-1].
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************)
procedure CorrR1DCircular(const Signal : TReal1DArray;
M : Integer;
const Pattern : TReal1DArray;
N : Integer;
var C : TReal1DArray);
var
P : TReal1DArray;
B : TReal1DArray;
I1 : Integer;
I2 : Integer;
I : Integer;
J2 : Integer;
begin
Assert((N>0) and (M>0), 'ConvC1DCircular: incorrect N or M!');
//
// normalize task: make M>=N,
// so A will be longer (at least - not shorter) that B.
//
if M<N then
begin
SetLength(B, M);
I1:=0;
while I1<=M-1 do
begin
B[I1] := 0;
Inc(I1);
end;
I1 := 0;
while I1<N do
begin
I2 := Min(I1+M-1, N-1);
J2 := I2-I1;
APVAdd(@B[0], 0, J2, @Pattern[0], I1, I2);
I1 := I1+M;
end;
CorrR1DCircular(Signal, M, B, M, C);
Exit;
end;
//
// Task is normalized
//
SetLength(P, N);
I:=0;
while I<=N-1 do
begin
P[N-1-I] := Pattern[I];
Inc(I);
end;
ConvR1DCircular(Signal, M, P, N, B);
SetLength(C, M);
APVMove(@C[0], 0, M-N, @B[0], N-1, M-1);
if M-N+1<=M-1 then
begin
APVMove(@C[0], M-N+1, M-1, @B[0], 0, N-2);
end;
end;
end.
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