3dpcp/.svn/pristine/a9/a9eb3942611b4191691a8ce3911926dde1bc0245.svn-base
2012-09-16 14:33:11 +02:00

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//$$ fft.cpp Fast fourier transform
// Copyright (C) 1991,2,3,4,8: R B Davies
#define WANT_MATH
// #define WANT_STREAM
#include "include.h"
#include "newmatap.h"
// #include "newmatio.h"
#ifdef use_namespace
namespace NEWMAT {
#endif
#ifdef DO_REPORT
#define REPORT { static ExeCounter ExeCount(__LINE__,19); ++ExeCount; }
#else
#define REPORT {}
#endif
static void cossin(int n, int d, Real& c, Real& s)
// calculate cos(twopi*n/d) and sin(twopi*n/d)
// minimise roundoff error
{
REPORT
long n4 = n * 4; int sector = (int)floor( (Real)n4 / (Real)d + 0.5 );
n4 -= sector * d;
if (sector < 0) { REPORT sector = 3 - (3 - sector) % 4; }
else { REPORT sector %= 4; }
Real ratio = 1.5707963267948966192 * (Real)n4 / (Real)d;
switch (sector)
{
case 0: REPORT c = cos(ratio); s = sin(ratio); break;
case 1: REPORT c = -sin(ratio); s = cos(ratio); break;
case 2: REPORT c = -cos(ratio); s = -sin(ratio); break;
case 3: REPORT c = sin(ratio); s = -cos(ratio); break;
}
}
static void fftstep(ColumnVector& A, ColumnVector& B, ColumnVector& X,
ColumnVector& Y, int after, int now, int before)
{
REPORT
Tracer trace("FFT(step)");
// const Real twopi = 6.2831853071795864769;
const int gamma = after * before; const int delta = now * after;
// const Real angle = twopi / delta; Real temp;
// Real r_omega = cos(angle); Real i_omega = -sin(angle);
Real r_arg = 1.0; Real i_arg = 0.0;
Real* x = X.Store(); Real* y = Y.Store(); // pointers to array storage
const int m = A.Nrows() - gamma;
for (int j = 0; j < now; j++)
{
Real* a = A.Store(); Real* b = B.Store(); // pointers to array storage
Real* x1 = x; Real* y1 = y; x += after; y += after;
for (int ia = 0; ia < after; ia++)
{
// generate sins & cosines explicitly rather than iteratively
// for more accuracy; but slower
cossin(-(j*after+ia), delta, r_arg, i_arg);
Real* a1 = a++; Real* b1 = b++; Real* x2 = x1++; Real* y2 = y1++;
if (now==2)
{
REPORT int ib = before;
if (ib) for (;;)
{
REPORT
Real* a2 = m + a1; Real* b2 = m + b1; a1 += after; b1 += after;
Real r_value = *a2; Real i_value = *b2;
*x2 = r_value * r_arg - i_value * i_arg + *(a2-gamma);
*y2 = r_value * i_arg + i_value * r_arg + *(b2-gamma);
if (!(--ib)) break;
x2 += delta; y2 += delta;
}
}
else
{
REPORT int ib = before;
if (ib) for (;;)
{
REPORT
Real* a2 = m + a1; Real* b2 = m + b1; a1 += after; b1 += after;
Real r_value = *a2; Real i_value = *b2;
int in = now-1; while (in--)
{
// it should be possible to make this faster
// hand code for now = 2,3,4,5,8
// use symmetry to halve number of operations
a2 -= gamma; b2 -= gamma; Real temp = r_value;
r_value = r_value * r_arg - i_value * i_arg + *a2;
i_value = temp * i_arg + i_value * r_arg + *b2;
}
*x2 = r_value; *y2 = i_value;
if (!(--ib)) break;
x2 += delta; y2 += delta;
}
}
// temp = r_arg;
// r_arg = r_arg * r_omega - i_arg * i_omega;
// i_arg = temp * i_omega + i_arg * r_omega;
}
}
}
void FFTI(const ColumnVector& U, const ColumnVector& V,
ColumnVector& X, ColumnVector& Y)
{
// Inverse transform
Tracer trace("FFTI");
REPORT
FFT(U,-V,X,Y);
const Real n = X.Nrows(); X /= n; Y /= (-n);
}
void RealFFT(const ColumnVector& U, ColumnVector& X, ColumnVector& Y)
{
// Fourier transform of a real series
Tracer trace("RealFFT");
REPORT
const int n = U.Nrows(); // length of arrays
const int n2 = n / 2;
if (n != 2 * n2)
Throw(ProgramException("Vector length not multiple of 2", U));
ColumnVector A(n2), B(n2);
Real* a = A.Store(); Real* b = B.Store(); Real* u = U.Store(); int i = n2;
while (i--) { *a++ = *u++; *b++ = *u++; }
FFT(A,B,A,B);
int n21 = n2 + 1;
X.ReSize(n21); Y.ReSize(n21);
i = n2 - 1;
a = A.Store(); b = B.Store(); // first els of A and B
Real* an = a + i; Real* bn = b + i; // last els of A and B
Real* x = X.Store(); Real* y = Y.Store(); // first els of X and Y
Real* xn = x + n2; Real* yn = y + n2; // last els of X and Y
*x++ = *a + *b; *y++ = 0.0; // first complex element
*xn-- = *a++ - *b++; *yn-- = 0.0; // last complex element
int j = -1; i = n2/2;
while (i--)
{
Real c,s; cossin(j--,n,c,s);
Real am = *a - *an; Real ap = *a++ + *an--;
Real bm = *b - *bn; Real bp = *b++ + *bn--;
Real samcbp = s * am + c * bp; Real sbpcam = s * bp - c * am;
*x++ = 0.5 * ( ap + samcbp); *y++ = 0.5 * ( bm + sbpcam);
*xn-- = 0.5 * ( ap - samcbp); *yn-- = 0.5 * (-bm + sbpcam);
}
}
void RealFFTI(const ColumnVector& A, const ColumnVector& B, ColumnVector& U)
{
// inverse of a Fourier transform of a real series
Tracer trace("RealFFTI");
REPORT
const int n21 = A.Nrows(); // length of arrays
if (n21 != B.Nrows() || n21 == 0)
Throw(ProgramException("Vector lengths unequal or zero", A, B));
const int n2 = n21 - 1; const int n = 2 * n2; int i = n2 - 1;
ColumnVector X(n2), Y(n2);
Real* a = A.Store(); Real* b = B.Store(); // first els of A and B
Real* an = a + n2; Real* bn = b + n2; // last els of A and B
Real* x = X.Store(); Real* y = Y.Store(); // first els of X and Y
Real* xn = x + i; Real* yn = y + i; // last els of X and Y
Real hn = 0.5 / n2;
*x++ = hn * (*a + *an); *y++ = - hn * (*a - *an);
a++; an--; b++; bn--;
int j = -1; i = n2/2;
while (i--)
{
Real c,s; cossin(j--,n,c,s);
Real am = *a - *an; Real ap = *a++ + *an--;
Real bm = *b - *bn; Real bp = *b++ + *bn--;
Real samcbp = s * am - c * bp; Real sbpcam = s * bp + c * am;
*x++ = hn * ( ap + samcbp); *y++ = - hn * ( bm + sbpcam);
*xn-- = hn * ( ap - samcbp); *yn-- = - hn * (-bm + sbpcam);
}
FFT(X,Y,X,Y); // have done inverting elsewhere
U.ReSize(n); i = n2;
x = X.Store(); y = Y.Store(); Real* u = U.Store();
while (i--) { *u++ = *x++; *u++ = - *y++; }
}
void FFT(const ColumnVector& U, const ColumnVector& V,
ColumnVector& X, ColumnVector& Y)
{
// from Carl de Boor (1980), Siam J Sci Stat Comput, 1 173-8
// but first try Sande and Gentleman
Tracer trace("FFT");
REPORT
const int n = U.Nrows(); // length of arrays
if (n != V.Nrows() || n == 0)
Throw(ProgramException("Vector lengths unequal or zero", U, V));
if (n == 1) { REPORT X = U; Y = V; return; }
// see if we can use the newfft routine
if (!FFT_Controller::OnlyOldFFT && FFT_Controller::CanFactor(n))
{
REPORT
X = U; Y = V;
if ( FFT_Controller::ar_1d_ft(n,X.Store(),Y.Store()) ) return;
}
ColumnVector B = V;
ColumnVector A = U;
X.ReSize(n); Y.ReSize(n);
const int nextmx = 8;
#ifndef ATandT
int prime[8] = { 2,3,5,7,11,13,17,19 };
#else
int prime[8];
prime[0]=2; prime[1]=3; prime[2]=5; prime[3]=7;
prime[4]=11; prime[5]=13; prime[6]=17; prime[7]=19;
#endif
int after = 1; int before = n; int next = 0; bool inzee = true;
int now = 0; int b1; // initialised to keep gnu happy
do
{
for (;;)
{
if (next < nextmx) { REPORT now = prime[next]; }
b1 = before / now; if (b1 * now == before) { REPORT break; }
next++; now += 2;
}
before = b1;
if (inzee) { REPORT fftstep(A, B, X, Y, after, now, before); }
else { REPORT fftstep(X, Y, A, B, after, now, before); }
inzee = !inzee; after *= now;
}
while (before != 1);
if (inzee) { REPORT A.Release(); X = A; B.Release(); Y = B; }
}
// Trigonometric transforms
// see Charles Van Loan (1992) "Computational frameworks for the fast
// Fourier transform" published by SIAM; section 4.4.
void DCT_II(const ColumnVector& U, ColumnVector& V)
{
// Discrete cosine transform, type II, of a real series
Tracer trace("DCT_II");
REPORT
const int n = U.Nrows(); // length of arrays
const int n2 = n / 2; const int n4 = n * 4;
if (n != 2 * n2)
Throw(ProgramException("Vector length not multiple of 2", U));
ColumnVector A(n);
Real* a = A.Store(); Real* b = a + n; Real* u = U.Store();
int i = n2;
while (i--) { *a++ = *u++; *(--b) = *u++; }
ColumnVector X, Y;
RealFFT(A, X, Y); A.CleanUp();
V.ReSize(n);
Real* x = X.Store(); Real* y = Y.Store();
Real* v = V.Store(); Real* w = v + n;
*v = *x;
int k = 0; i = n2;
while (i--)
{
Real c, s; cossin(++k, n4, c, s);
Real xi = *(++x); Real yi = *(++y);
*(++v) = xi * c + yi * s; *(--w) = xi * s - yi * c;
}
}
void DCT_II_inverse(const ColumnVector& V, ColumnVector& U)
{
// Inverse of discrete cosine transform, type II
Tracer trace("DCT_II_inverse");
REPORT
const int n = V.Nrows(); // length of array
const int n2 = n / 2; const int n4 = n * 4; const int n21 = n2 + 1;
if (n != 2 * n2)
Throw(ProgramException("Vector length not multiple of 2", V));
ColumnVector X(n21), Y(n21);
Real* x = X.Store(); Real* y = Y.Store();
Real* v = V.Store(); Real* w = v + n;
*x = *v; *y = 0.0;
int i = n2; int k = 0;
while (i--)
{
Real c, s; cossin(++k, n4, c, s);
Real vi = *(++v); Real wi = *(--w);
*(++x) = vi * c + wi * s; *(++y) = vi * s - wi * c;
}
ColumnVector A; RealFFTI(X, Y, A);
X.CleanUp(); Y.CleanUp(); U.ReSize(n);
Real* a = A.Store(); Real* b = a + n; Real* u = U.Store();
i = n2;
while (i--) { *u++ = *a++; *u++ = *(--b); }
}
void DST_II(const ColumnVector& U, ColumnVector& V)
{
// Discrete sine transform, type II, of a real series
Tracer trace("DST_II");
REPORT
const int n = U.Nrows(); // length of arrays
const int n2 = n / 2; const int n4 = n * 4;
if (n != 2 * n2)
Throw(ProgramException("Vector length not multiple of 2", U));
ColumnVector A(n);
Real* a = A.Store(); Real* b = a + n; Real* u = U.Store();
int i = n2;
while (i--) { *a++ = *u++; *(--b) = -(*u++); }
ColumnVector X, Y;
RealFFT(A, X, Y); A.CleanUp();
V.ReSize(n);
Real* x = X.Store(); Real* y = Y.Store();
Real* v = V.Store(); Real* w = v + n;
*(--w) = *x;
int k = 0; i = n2;
while (i--)
{
Real c, s; cossin(++k, n4, c, s);
Real xi = *(++x); Real yi = *(++y);
*v++ = xi * s - yi * c; *(--w) = xi * c + yi * s;
}
}
void DST_II_inverse(const ColumnVector& V, ColumnVector& U)
{
// Inverse of discrete sine transform, type II
Tracer trace("DST_II_inverse");
REPORT
const int n = V.Nrows(); // length of array
const int n2 = n / 2; const int n4 = n * 4; const int n21 = n2 + 1;
if (n != 2 * n2)
Throw(ProgramException("Vector length not multiple of 2", V));
ColumnVector X(n21), Y(n21);
Real* x = X.Store(); Real* y = Y.Store();
Real* v = V.Store(); Real* w = v + n;
*x = *(--w); *y = 0.0;
int i = n2; int k = 0;
while (i--)
{
Real c, s; cossin(++k, n4, c, s);
Real vi = *v++; Real wi = *(--w);
*(++x) = vi * s + wi * c; *(++y) = - vi * c + wi * s;
}
ColumnVector A; RealFFTI(X, Y, A);
X.CleanUp(); Y.CleanUp(); U.ReSize(n);
Real* a = A.Store(); Real* b = a + n; Real* u = U.Store();
i = n2;
while (i--) { *u++ = *a++; *u++ = -(*(--b)); }
}
void DCT_inverse(const ColumnVector& V, ColumnVector& U)
{
// Inverse of discrete cosine transform, type I
Tracer trace("DCT_inverse");
REPORT
const int n = V.Nrows()-1; // length of transform
const int n2 = n / 2; const int n21 = n2 + 1;
if (n != 2 * n2)
Throw(ProgramException("Vector length not multiple of 2", V));
ColumnVector X(n21), Y(n21);
Real* x = X.Store(); Real* y = Y.Store(); Real* v = V.Store();
Real vi = *v++; *x++ = vi; *y++ = 0.0;
Real sum1 = vi / 2.0; Real sum2 = sum1; vi = *v++;
int i = n2-1;
while (i--)
{
Real vi2 = *v++; sum1 += vi2 + vi; sum2 += vi2 - vi;
*x++ = vi2; vi2 = *v++; *y++ = vi - vi2; vi = vi2;
}
sum1 += vi; sum2 -= vi;
vi = *v; *x = vi; *y = 0.0; vi /= 2.0; sum1 += vi; sum2 += vi;
ColumnVector A; RealFFTI(X, Y, A);
X.CleanUp(); Y.CleanUp(); U.ReSize(n+1);
Real* a = A.Store(); Real* b = a + n; Real* u = U.Store(); v = u + n;
i = n2; int k = 0; *u++ = sum1 / n2; *v-- = sum2 / n2;
while (i--)
{
Real s = sin(1.5707963267948966192 * (++k) / n2);
Real ai = *(++a); Real bi = *(--b);
Real bz = (ai - bi) / 4 / s; Real az = (ai + bi) / 2;
*u++ = az - bz; *v-- = az + bz;
}
}
void DCT(const ColumnVector& U, ColumnVector& V)
{
// Discrete cosine transform, type I
Tracer trace("DCT");
REPORT
DCT_inverse(U, V);
V *= (V.Nrows()-1)/2;
}
void DST_inverse(const ColumnVector& V, ColumnVector& U)
{
// Inverse of discrete sine transform, type I
Tracer trace("DST_inverse");
REPORT
const int n = V.Nrows()-1; // length of transform
const int n2 = n / 2; const int n21 = n2 + 1;
if (n != 2 * n2)
Throw(ProgramException("Vector length not multiple of 2", V));
ColumnVector X(n21), Y(n21);
Real* x = X.Store(); Real* y = Y.Store(); Real* v = V.Store();
Real vi = *(++v); *x++ = 2 * vi; *y++ = 0.0;
int i = n2-1;
while (i--) { *y++ = *(++v); Real vi2 = *(++v); *x++ = vi2 - vi; vi = vi2; }
*x = -2 * vi; *y = 0.0;
ColumnVector A; RealFFTI(X, Y, A);
X.CleanUp(); Y.CleanUp(); U.ReSize(n+1);
Real* a = A.Store(); Real* b = a + n; Real* u = U.Store(); v = u + n;
i = n2; int k = 0; *u++ = 0.0; *v-- = 0.0;
while (i--)
{
Real s = sin(1.5707963267948966192 * (++k) / n2);
Real ai = *(++a); Real bi = *(--b);
Real az = (ai + bi) / 4 / s; Real bz = (ai - bi) / 2;
*u++ = az - bz; *v-- = az + bz;
}
}
void DST(const ColumnVector& U, ColumnVector& V)
{
// Discrete sine transform, type I
Tracer trace("DST");
REPORT
DST_inverse(U, V);
V *= (V.Nrows()-1)/2;
}
#ifdef use_namespace
}
#endif