changed FFT code in graph widget into a more efficient one, with free licence

This commit is contained in:
csoler 2017-04-19 17:16:30 +02:00
parent e95ddb91af
commit 1da89dd70d
2 changed files with 872 additions and 19 deletions

View File

@ -0,0 +1,827 @@
/******************************************************************
Original FFT code Credits:
Copyright Takuya OOURA, 1996-2001
http://www.kurims.kyoto-u.ac.jp/~ooura/fft.html
******************************************************************/
/*
Fast Fourier/Cosine/Sine Transform
dimension :two
data length :power of 2
decimation :frequency
radix :4, 2, row-column
data :inplace
table :use
functions
cdft2d: Complex Discrete Fourier Transform
rdft2d: Real Discrete Fourier Transform
ddct2d: Discrete Cosine Transform
ddst2d: Discrete Sine Transform
function prototypes
void cdft2d(int, int, int, double **, int *, double *);
void rdft2d(int, int, int, double **, int *, double *);
void ddct2d(int, int, int, double **, double **, int *, double *);
void ddst2d(int, int, int, double **, double **, int *, double *);
-------- Complex DFT (Discrete Fourier Transform) --------
[definition]
<case1>
X[k1][k2] = sum_j1=0^n1-1 sum_j2=0^n2-1 x[j1][j2] *
exp(2*pi*i*j1*k1/n1) *
exp(2*pi*i*j2*k2/n2), 0<=k1<n1, 0<=k2<n2
<case2>
X[k1][k2] = sum_j1=0^n1-1 sum_j2=0^n2-1 x[j1][j2] *
exp(-2*pi*i*j1*k1/n1) *
exp(-2*pi*i*j2*k2/n2), 0<=k1<n1, 0<=k2<n2
(notes: sum_j=0^n-1 is a summation from j=0 to n-1)
[usage]
<case1>
ip[0] = 0; // first time only
cdft2d(n1, 2*n2, 1, a, ip, w);
<case2>
ip[0] = 0; // first time only
cdft2d(n1, 2*n2, -1, a, ip, w);
[parameters]
n1 :data length (int)
n1 >= 1, n1 = power of 2
2*n2 :data length (int)
n2 >= 1, n2 = power of 2
a[0...n1-1][0...2*n2-1]
:input/output data (double **)
input data
a[j1][2*j2] = Re(x[j1][j2]),
a[j1][2*j2+1] = Im(x[j1][j2]),
0<=j1<n1, 0<=j2<n2
output data
a[k1][2*k2] = Re(X[k1][k2]),
a[k1][2*k2+1] = Im(X[k1][k2]),
0<=k1<n1, 0<=k2<n2
ip[0...*]
:work area for bit reversal (int *)
length of ip >= 2+sqrt(n)
(n = max(n1, n2))
ip[0],ip[1] are pointers of the cos/sin table.
w[0...*]
:cos/sin table (double *)
length of w >= max(n1/2, n2/2)
w[],ip[] are initialized if ip[0] == 0.
[remark]
Inverse of
cdft2d(n1, 2*n2, -1, a, ip, w);
is
cdft2d(n1, 2*n2, 1, a, ip, w);
for (j1 = 0; j1 <= n1 - 1; j1++) {
for (j2 = 0; j2 <= 2 * n2 - 1; j2++) {
a[j1][j2] *= 1.0 / (n1 * n2);
}
}
*/
/* -------- initializing routines -------- */
#pragma once
#include <math.h>
class fft
{
public:
static void makewt(int nw, int *ip, double *w)
{
int nwh, j;
double delta, x, y;
ip[0] = nw;
ip[1] = 1;
if (nw > 2) {
nwh = nw >> 1;
delta = atan(1.0) / nwh;
w[0] = 1;
w[1] = 0;
w[nwh] = cos(delta * nwh);
w[nwh + 1] = w[nwh];
for (j = 2; j <= nwh - 2; j += 2) {
sincos(delta*j,&y,&x) ;
//x = cos(delta * j);
//y = sin(delta * j);
w[j] = x;
w[j + 1] = y;
w[nw - j] = y;
w[nw - j + 1] = x;
}
bitrv2(nw, ip + 2, w);
}
}
/* -------- child routines -------- */
static void bitrv2(int n, int *ip, double *a)
{
int j, j1, k, k1, l, m, m2;
double xr, xi;
ip[0] = 0;
l = n;
m = 1;
while ((m << 2) < l) {
l >>= 1;
for (j = 0; j <= m - 1; j++) {
ip[m + j] = ip[j] + l;
}
m <<= 1;
}
if ((m << 2) > l) {
for (k = 1; k <= m - 1; k++) {
for (j = 0; j <= k - 1; j++) {
j1 = (j << 1) + ip[k];
k1 = (k << 1) + ip[j];
xr = a[j1];
xi = a[j1 + 1];
a[j1] = a[k1];
a[j1 + 1] = a[k1 + 1];
a[k1] = xr;
a[k1 + 1] = xi;
}
}
} else {
m2 = m << 1;
for (k = 1; k <= m - 1; k++) {
for (j = 0; j <= k - 1; j++) {
j1 = (j << 1) + ip[k];
k1 = (k << 1) + ip[j];
xr = a[j1];
xi = a[j1 + 1];
a[j1] = a[k1];
a[j1 + 1] = a[k1 + 1];
a[k1] = xr;
a[k1 + 1] = xi;
j1 += m2;
k1 += m2;
xr = a[j1];
xi = a[j1 + 1];
a[j1] = a[k1];
a[j1 + 1] = a[k1 + 1];
a[k1] = xr;
a[k1 + 1] = xi;
}
}
}
}
static void bitrv2col(int n1, int n, int *ip, double **a)
{
int i, j, j1, k, k1, l, m, m2;
double xr, xi;
ip[0] = 0;
l = n;
m = 1;
while ((m << 2) < l) {
l >>= 1;
for (j = 0; j <= m - 1; j++) {
ip[m + j] = ip[j] + l;
}
m <<= 1;
}
if ((m << 2) > l) {
for (i = 0; i <= n1 - 1; i++) {
for (k = 1; k <= m - 1; k++) {
for (j = 0; j <= k - 1; j++) {
j1 = (j << 1) + ip[k];
k1 = (k << 1) + ip[j];
xr = a[i][j1];
xi = a[i][j1 + 1];
a[i][j1] = a[i][k1];
a[i][j1 + 1] = a[i][k1 + 1];
a[i][k1] = xr;
a[i][k1 + 1] = xi;
}
}
}
} else {
m2 = m << 1;
for (i = 0; i <= n1 - 1; i++) {
for (k = 1; k <= m - 1; k++) {
for (j = 0; j <= k - 1; j++) {
j1 = (j << 1) + ip[k];
k1 = (k << 1) + ip[j];
xr = a[i][j1];
xi = a[i][j1 + 1];
a[i][j1] = a[i][k1];
a[i][j1 + 1] = a[i][k1 + 1];
a[i][k1] = xr;
a[i][k1 + 1] = xi;
j1 += m2;
k1 += m2;
xr = a[i][j1];
xi = a[i][j1 + 1];
a[i][j1] = a[i][k1];
a[i][j1 + 1] = a[i][k1 + 1];
a[i][k1] = xr;
a[i][k1 + 1] = xi;
}
}
}
}
}
static void bitrv2row(int n, int n2, int *ip, double **a)
{
int i, j, j1, k, k1, l, m;
double xr, xi;
ip[0] = 0;
l = n;
m = 1;
while ((m << 1) < l) {
l >>= 1;
for (j = 0; j <= m - 1; j++) {
ip[m + j] = ip[j] + l;
}
m <<= 1;
}
if ((m << 1) > l) {
for (k = 1; k <= m - 1; k++) {
for (j = 0; j <= k - 1; j++) {
j1 = j + ip[k];
k1 = k + ip[j];
for (i = 0; i <= n2 - 2; i += 2) {
xr = a[j1][i];
xi = a[j1][i + 1];
a[j1][i] = a[k1][i];
a[j1][i + 1] = a[k1][i + 1];
a[k1][i] = xr;
a[k1][i + 1] = xi;
}
}
}
} else {
for (k = 1; k <= m - 1; k++) {
for (j = 0; j <= k - 1; j++) {
j1 = j + ip[k];
k1 = k + ip[j];
for (i = 0; i <= n2 - 2; i += 2) {
xr = a[j1][i];
xi = a[j1][i + 1];
a[j1][i] = a[k1][i];
a[j1][i + 1] = a[k1][i + 1];
a[k1][i] = xr;
a[k1][i + 1] = xi;
}
j1 += m;
k1 += m;
for (i = 0; i <= n2 - 2; i += 2) {
xr = a[j1][i];
xi = a[j1][i + 1];
a[j1][i] = a[k1][i];
a[j1][i + 1] = a[k1][i + 1];
a[k1][i] = xr;
a[k1][i + 1] = xi;
}
}
}
}
}
static void cftbcol(int n1, int n, double **a, double *w)
{
int i, j, j1, j2, j3, k, k1, ks, l, m;
double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
for (i = 0; i <= n1 - 1; i++) {
l = 2;
while ((l << 1) < n) {
m = l << 2;
for (j = 0; j <= l - 2; j += 2) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
x0r = a[i][j] + a[i][j1];
x0i = a[i][j + 1] + a[i][j1 + 1];
x1r = a[i][j] - a[i][j1];
x1i = a[i][j + 1] - a[i][j1 + 1];
x2r = a[i][j2] + a[i][j3];
x2i = a[i][j2 + 1] + a[i][j3 + 1];
x3r = a[i][j2] - a[i][j3];
x3i = a[i][j2 + 1] - a[i][j3 + 1];
a[i][j] = x0r + x2r;
a[i][j + 1] = x0i + x2i;
a[i][j2] = x0r - x2r;
a[i][j2 + 1] = x0i - x2i;
a[i][j1] = x1r - x3i;
a[i][j1 + 1] = x1i + x3r;
a[i][j3] = x1r + x3i;
a[i][j3 + 1] = x1i - x3r;
}
if (m < n) {
wk1r = w[2];
for (j = m; j <= l + m - 2; j += 2) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
x0r = a[i][j] + a[i][j1];
x0i = a[i][j + 1] + a[i][j1 + 1];
x1r = a[i][j] - a[i][j1];
x1i = a[i][j + 1] - a[i][j1 + 1];
x2r = a[i][j2] + a[i][j3];
x2i = a[i][j2 + 1] + a[i][j3 + 1];
x3r = a[i][j2] - a[i][j3];
x3i = a[i][j2 + 1] - a[i][j3 + 1];
a[i][j] = x0r + x2r;
a[i][j + 1] = x0i + x2i;
a[i][j2] = x2i - x0i;
a[i][j2 + 1] = x0r - x2r;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[i][j1] = wk1r * (x0r - x0i);
a[i][j1 + 1] = wk1r * (x0r + x0i);
x0r = x3i + x1r;
x0i = x3r - x1i;
a[i][j3] = wk1r * (x0i - x0r);
a[i][j3 + 1] = wk1r * (x0i + x0r);
}
k1 = 1;
ks = -1;
for (k = (m << 1); k <= n - m; k += m) {
k1++;
ks = -ks;
wk1r = w[k1 << 1];
wk1i = w[(k1 << 1) + 1];
wk2r = ks * w[k1];
wk2i = w[k1 + ks];
wk3r = wk1r - 2 * wk2i * wk1i;
wk3i = 2 * wk2i * wk1r - wk1i;
for (j = k; j <= l + k - 2; j += 2) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
x0r = a[i][j] + a[i][j1];
x0i = a[i][j + 1] + a[i][j1 + 1];
x1r = a[i][j] - a[i][j1];
x1i = a[i][j + 1] - a[i][j1 + 1];
x2r = a[i][j2] + a[i][j3];
x2i = a[i][j2 + 1] + a[i][j3 + 1];
x3r = a[i][j2] - a[i][j3];
x3i = a[i][j2 + 1] - a[i][j3 + 1];
a[i][j] = x0r + x2r;
a[i][j + 1] = x0i + x2i;
x0r -= x2r;
x0i -= x2i;
a[i][j2] = wk2r * x0r - wk2i * x0i;
a[i][j2 + 1] = wk2r * x0i + wk2i * x0r;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[i][j1] = wk1r * x0r - wk1i * x0i;
a[i][j1 + 1] = wk1r * x0i + wk1i * x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
a[i][j3] = wk3r * x0r - wk3i * x0i;
a[i][j3 + 1] = wk3r * x0i + wk3i * x0r;
}
}
}
l = m;
}
if (l < n) {
for (j = 0; j <= l - 2; j += 2) {
j1 = j + l;
x0r = a[i][j] - a[i][j1];
x0i = a[i][j + 1] - a[i][j1 + 1];
a[i][j] += a[i][j1];
a[i][j + 1] += a[i][j1 + 1];
a[i][j1] = x0r;
a[i][j1 + 1] = x0i;
}
}
}
}
static void cftbrow(int n, int n2, double **a, double *w)
{
int i, j, j1, j2, j3, k, k1, ks, l, m;
double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
l = 1;
while ((l << 1) < n) {
m = l << 2;
for (j = 0; j <= l - 1; j++) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
for (i = 0; i <= n2 - 2; i += 2) {
x0r = a[j][i] + a[j1][i];
x0i = a[j][i + 1] + a[j1][i + 1];
x1r = a[j][i] - a[j1][i];
x1i = a[j][i + 1] - a[j1][i + 1];
x2r = a[j2][i] + a[j3][i];
x2i = a[j2][i + 1] + a[j3][i + 1];
x3r = a[j2][i] - a[j3][i];
x3i = a[j2][i + 1] - a[j3][i + 1];
a[j][i] = x0r + x2r;
a[j][i + 1] = x0i + x2i;
a[j2][i] = x0r - x2r;
a[j2][i + 1] = x0i - x2i;
a[j1][i] = x1r - x3i;
a[j1][i + 1] = x1i + x3r;
a[j3][i] = x1r + x3i;
a[j3][i + 1] = x1i - x3r;
}
}
if (m < n) {
wk1r = w[2];
for (j = m; j <= l + m - 1; j++) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
for (i = 0; i <= n2 - 2; i += 2) {
x0r = a[j][i] + a[j1][i];
x0i = a[j][i + 1] + a[j1][i + 1];
x1r = a[j][i] - a[j1][i];
x1i = a[j][i + 1] - a[j1][i + 1];
x2r = a[j2][i] + a[j3][i];
x2i = a[j2][i + 1] + a[j3][i + 1];
x3r = a[j2][i] - a[j3][i];
x3i = a[j2][i + 1] - a[j3][i + 1];
a[j][i] = x0r + x2r;
a[j][i + 1] = x0i + x2i;
a[j2][i] = x2i - x0i;
a[j2][i + 1] = x0r - x2r;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[j1][i] = wk1r * (x0r - x0i);
a[j1][i + 1] = wk1r * (x0r + x0i);
x0r = x3i + x1r;
x0i = x3r - x1i;
a[j3][i] = wk1r * (x0i - x0r);
a[j3][i + 1] = wk1r * (x0i + x0r);
}
}
k1 = 1;
ks = -1;
for (k = (m << 1); k <= n - m; k += m) {
k1++;
ks = -ks;
wk1r = w[k1 << 1];
wk1i = w[(k1 << 1) + 1];
wk2r = ks * w[k1];
wk2i = w[k1 + ks];
wk3r = wk1r - 2 * wk2i * wk1i;
wk3i = 2 * wk2i * wk1r - wk1i;
for (j = k; j <= l + k - 1; j++) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
for (i = 0; i <= n2 - 2; i += 2) {
x0r = a[j][i] + a[j1][i];
x0i = a[j][i + 1] + a[j1][i + 1];
x1r = a[j][i] - a[j1][i];
x1i = a[j][i + 1] - a[j1][i + 1];
x2r = a[j2][i] + a[j3][i];
x2i = a[j2][i + 1] + a[j3][i + 1];
x3r = a[j2][i] - a[j3][i];
x3i = a[j2][i + 1] - a[j3][i + 1];
a[j][i] = x0r + x2r;
a[j][i + 1] = x0i + x2i;
x0r -= x2r;
x0i -= x2i;
a[j2][i] = wk2r * x0r - wk2i * x0i;
a[j2][i + 1] = wk2r * x0i + wk2i * x0r;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[j1][i] = wk1r * x0r - wk1i * x0i;
a[j1][i + 1] = wk1r * x0i + wk1i * x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
a[j3][i] = wk3r * x0r - wk3i * x0i;
a[j3][i + 1] = wk3r * x0i + wk3i * x0r;
}
}
}
}
l = m;
}
if (l < n) {
for (j = 0; j <= l - 1; j++) {
j1 = j + l;
for (i = 0; i <= n2 - 2; i += 2) {
x0r = a[j][i] - a[j1][i];
x0i = a[j][i + 1] - a[j1][i + 1];
a[j][i] += a[j1][i];
a[j][i + 1] += a[j1][i + 1];
a[j1][i] = x0r;
a[j1][i + 1] = x0i;
}
}
}
}
static void cftfcol(int n1, int n, double **a, double *w)
{
int i, j, j1, j2, j3, k, k1, ks, l, m;
double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
for (i = 0; i <= n1 - 1; i++) {
l = 2;
while ((l << 1) < n) {
m = l << 2;
for (j = 0; j <= l - 2; j += 2) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
x0r = a[i][j] + a[i][j1];
x0i = a[i][j + 1] + a[i][j1 + 1];
x1r = a[i][j] - a[i][j1];
x1i = a[i][j + 1] - a[i][j1 + 1];
x2r = a[i][j2] + a[i][j3];
x2i = a[i][j2 + 1] + a[i][j3 + 1];
x3r = a[i][j2] - a[i][j3];
x3i = a[i][j2 + 1] - a[i][j3 + 1];
a[i][j] = x0r + x2r;
a[i][j + 1] = x0i + x2i;
a[i][j2] = x0r - x2r;
a[i][j2 + 1] = x0i - x2i;
a[i][j1] = x1r + x3i;
a[i][j1 + 1] = x1i - x3r;
a[i][j3] = x1r - x3i;
a[i][j3 + 1] = x1i + x3r;
}
if (m < n) {
wk1r = w[2];
for (j = m; j <= l + m - 2; j += 2) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
x0r = a[i][j] + a[i][j1];
x0i = a[i][j + 1] + a[i][j1 + 1];
x1r = a[i][j] - a[i][j1];
x1i = a[i][j + 1] - a[i][j1 + 1];
x2r = a[i][j2] + a[i][j3];
x2i = a[i][j2 + 1] + a[i][j3 + 1];
x3r = a[i][j2] - a[i][j3];
x3i = a[i][j2 + 1] - a[i][j3 + 1];
a[i][j] = x0r + x2r;
a[i][j + 1] = x0i + x2i;
a[i][j2] = x0i - x2i;
a[i][j2 + 1] = x2r - x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
a[i][j1] = wk1r * (x0i + x0r);
a[i][j1 + 1] = wk1r * (x0i - x0r);
x0r = x3i - x1r;
x0i = x3r + x1i;
a[i][j3] = wk1r * (x0r + x0i);
a[i][j3 + 1] = wk1r * (x0r - x0i);
}
k1 = 1;
ks = -1;
for (k = (m << 1); k <= n - m; k += m) {
k1++;
ks = -ks;
wk1r = w[k1 << 1];
wk1i = w[(k1 << 1) + 1];
wk2r = ks * w[k1];
wk2i = w[k1 + ks];
wk3r = wk1r - 2 * wk2i * wk1i;
wk3i = 2 * wk2i * wk1r - wk1i;
for (j = k; j <= l + k - 2; j += 2) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
x0r = a[i][j] + a[i][j1];
x0i = a[i][j + 1] + a[i][j1 + 1];
x1r = a[i][j] - a[i][j1];
x1i = a[i][j + 1] - a[i][j1 + 1];
x2r = a[i][j2] + a[i][j3];
x2i = a[i][j2 + 1] + a[i][j3 + 1];
x3r = a[i][j2] - a[i][j3];
x3i = a[i][j2 + 1] - a[i][j3 + 1];
a[i][j] = x0r + x2r;
a[i][j + 1] = x0i + x2i;
x0r -= x2r;
x0i -= x2i;
a[i][j2] = wk2r * x0r + wk2i * x0i;
a[i][j2 + 1] = wk2r * x0i - wk2i * x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
a[i][j1] = wk1r * x0r + wk1i * x0i;
a[i][j1 + 1] = wk1r * x0i - wk1i * x0r;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[i][j3] = wk3r * x0r + wk3i * x0i;
a[i][j3 + 1] = wk3r * x0i - wk3i * x0r;
}
}
}
l = m;
}
if (l < n) {
for (j = 0; j <= l - 2; j += 2) {
j1 = j + l;
x0r = a[i][j] - a[i][j1];
x0i = a[i][j + 1] - a[i][j1 + 1];
a[i][j] += a[i][j1];
a[i][j + 1] += a[i][j1 + 1];
a[i][j1] = x0r;
a[i][j1 + 1] = x0i;
}
}
}
}
static void cftfrow(int n, int n2, double **a, double *w)
{
int i, j, j1, j2, j3, k, k1, ks, l, m;
double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
l = 1;
while ((l << 1) < n) {
m = l << 2;
for (j = 0; j <= l - 1; j++) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
for (i = 0; i <= n2 - 2; i += 2) {
x0r = a[j][i] + a[j1][i];
x0i = a[j][i + 1] + a[j1][i + 1];
x1r = a[j][i] - a[j1][i];
x1i = a[j][i + 1] - a[j1][i + 1];
x2r = a[j2][i] + a[j3][i];
x2i = a[j2][i + 1] + a[j3][i + 1];
x3r = a[j2][i] - a[j3][i];
x3i = a[j2][i + 1] - a[j3][i + 1];
a[j][i] = x0r + x2r;
a[j][i + 1] = x0i + x2i;
a[j2][i] = x0r - x2r;
a[j2][i + 1] = x0i - x2i;
a[j1][i] = x1r + x3i;
a[j1][i + 1] = x1i - x3r;
a[j3][i] = x1r - x3i;
a[j3][i + 1] = x1i + x3r;
}
}
if (m < n) {
wk1r = w[2];
for (j = m; j <= l + m - 1; j++) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
for (i = 0; i <= n2 - 2; i += 2) {
x0r = a[j][i] + a[j1][i];
x0i = a[j][i + 1] + a[j1][i + 1];
x1r = a[j][i] - a[j1][i];
x1i = a[j][i + 1] - a[j1][i + 1];
x2r = a[j2][i] + a[j3][i];
x2i = a[j2][i + 1] + a[j3][i + 1];
x3r = a[j2][i] - a[j3][i];
x3i = a[j2][i + 1] - a[j3][i + 1];
a[j][i] = x0r + x2r;
a[j][i + 1] = x0i + x2i;
a[j2][i] = x0i - x2i;
a[j2][i + 1] = x2r - x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
a[j1][i] = wk1r * (x0i + x0r);
a[j1][i + 1] = wk1r * (x0i - x0r);
x0r = x3i - x1r;
x0i = x3r + x1i;
a[j3][i] = wk1r * (x0r + x0i);
a[j3][i + 1] = wk1r * (x0r - x0i);
}
}
k1 = 1;
ks = -1;
for (k = (m << 1); k <= n - m; k += m) {
k1++;
ks = -ks;
wk1r = w[k1 << 1];
wk1i = w[(k1 << 1) + 1];
wk2r = ks * w[k1];
wk2i = w[k1 + ks];
wk3r = wk1r - 2 * wk2i * wk1i;
wk3i = 2 * wk2i * wk1r - wk1i;
for (j = k; j <= l + k - 1; j++) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
for (i = 0; i <= n2 - 2; i += 2) {
x0r = a[j][i] + a[j1][i];
x0i = a[j][i + 1] + a[j1][i + 1];
x1r = a[j][i] - a[j1][i];
x1i = a[j][i + 1] - a[j1][i + 1];
x2r = a[j2][i] + a[j3][i];
x2i = a[j2][i + 1] + a[j3][i + 1];
x3r = a[j2][i] - a[j3][i];
x3i = a[j2][i + 1] - a[j3][i + 1];
a[j][i] = x0r + x2r;
a[j][i + 1] = x0i + x2i;
x0r -= x2r;
x0i -= x2i;
a[j2][i] = wk2r * x0r + wk2i * x0i;
a[j2][i + 1] = wk2r * x0i - wk2i * x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
a[j1][i] = wk1r * x0r + wk1i * x0i;
a[j1][i + 1] = wk1r * x0i - wk1i * x0r;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[j3][i] = wk3r * x0r + wk3i * x0i;
a[j3][i + 1] = wk3r * x0i - wk3i * x0r;
}
}
}
}
l = m;
}
if (l < n) {
for (j = 0; j <= l - 1; j++) {
j1 = j + l;
for (i = 0; i <= n2 - 2; i += 2) {
x0r = a[j][i] - a[j1][i];
x0i = a[j][i + 1] - a[j1][i + 1];
a[j][i] += a[j1][i];
a[j][i + 1] += a[j1][i + 1];
a[j1][i] = x0r;
a[j1][i + 1] = x0i;
}
}
}
}
static int *alloc_1d_int(int n1)
{
int *i;
i = (int *) malloc(sizeof(int) * n1);
return i;
}
static void free_1d_int(int *i) { free(i); }
static double *alloc_1d_double(int n1)
{
double *d;
d = (double *) malloc(sizeof(double) * n1);
return d;
}
static void free_1d_double(double *d) { free(d); }
static double **alloc_2d_double(int n1, int n2)
{
double **dd, *d;
int j;
dd = (double **) malloc(sizeof(double *) * n1);
d = (double *) malloc(sizeof(double) * n1 * n2);
dd[0] = d;
for (j = 1; j < n1; j++) {
dd[j] = dd[j - 1] + n2;
}
return dd;
}
static void free_2d_double(double **dd) { free(dd[0]); free(dd); }
static void cdft2d(int n1, int n2, int isgn, double **a, int *ip, double *w)
{
int n;
n = n1 << 1;
if (n < n2) {
n = n2;
}
if (n > (ip[0] << 2)) {
makewt(n >> 2, ip, w);
}
if (n2 > 4) {
bitrv2col(n1, n2, ip + 2, a);
}
if (n1 > 2) {
bitrv2row(n1, n2, ip + 2, a);
}
if (isgn < 0) {
cftfcol(n1, n2, a, w);
cftfrow(n1, n2, a, w);
} else {
cftbcol(n1, n2, a, w);
cftbrow(n1, n2, a, w);
}
}
};

View File

@ -42,6 +42,7 @@
#include "graphwidget.h" #include "graphwidget.h"
#include "edge.h" #include "edge.h"
#include "node.h" #include "node.h"
#include "fft.h"
#include <iostream> #include <iostream>
#include <QDebug> #include <QDebug>
@ -259,45 +260,70 @@ void GraphWidget::keyPressEvent(QKeyEvent *event)
} }
} }
static void convolveWithGaussian(double *forceMap,unsigned int S,int /*s*/) static void convolveWithForce(double *forceMap,unsigned int S,int /*s*/)
{ {
static double *bf = NULL ; static double **bf = NULL ;
static double **tmp = NULL ;
static int *ip = NULL ;
static double *w = NULL ;
static uint32_t last_S = 0 ;
if(bf == NULL) if(bf == NULL)
{ {
bf = new double[S*S*2] ; bf = fft::alloc_2d_double(S, 2*S);
for(unsigned int i=0;i<S;++i) for(unsigned int i=0;i<S;++i)
for(unsigned int j=0;j<S;++j) for(unsigned int j=0;j<S;++j)
{ {
int x = (i<S/2)?i:(S-i) ; int x = (i<S/2)?i:(S-i) ;
int y = (j<S/2)?j:(S-j) ; int y = (j<S/2)?j:(S-j) ;
// int l=2*(x*x+y*y);
bf[2*(i+S*j)] = log(sqrtf(0.1 + x*x+y*y)); // linear -> derivative is constant bf[i][j*2+0] = log(sqrtf(0.1 + x*x+y*y)); // linear -> derivative is constant
bf[2*(i+S*j)+1] = 0 ; bf[i][j*2+1] = 0 ;
} }
unsigned long nn[2] = {S,S}; //unsigned long nn[2] = {S,S};
fourn(&bf[-1],&nn[-1],2,1) ; //fourn(&bf[-1],&nn[-1],2,1) ;
ip = fft::alloc_1d_int(2 + (int) sqrt(S + 0.5));
w = fft::alloc_1d_double(S/2+S);
ip[0] = 0;
fft::cdft2d(S, 2*S, 1, bf, ip, w);
} }
unsigned long nn[2] = {S,S}; if(last_S != S)
fourn(&forceMap[-1],&nn[-1],2,1) ; {
if(tmp)
fft::free_2d_double(tmp) ;
tmp = fft::alloc_2d_double(S, 2*S);
last_S = S ;
}
memcpy(tmp[0],forceMap,S*S*2*sizeof(double)) ;
fft::cdft2d(S, 2*S, 1, tmp, ip, w);
//fourn(&forceMap[-1],&nn[-1],2,1) ;
for (unsigned int i=0;i<S;++i) for (unsigned int i=0;i<S;++i)
for (unsigned int j=0;j<S;++j) for (unsigned int j=0;j<S;++j)
{ {
float a = forceMap[2*(i+S*j)]*bf[2*(i+S*j)] - forceMap[2*(i+S*j)+1]*bf[2*(i+S*j)+1] ; float a = tmp[i][2*j+0]*bf[i][2*j+0] - tmp[i][2*j+1]*bf[i][2*j+1] ;
float b = forceMap[2*(i+S*j)]*bf[2*(i+S*j)+1] + forceMap[2*(i+S*j)+1]*bf[2*(i+S*j)] ; float b = tmp[i][2*j+0]*bf[i][2*j+1] + tmp[i][2*j+1]*bf[i][2*j+0] ;
forceMap[2*(i+S*j)] = a ; tmp[i][2*j+0] = a ;
forceMap[2*(i+S*j)+1] = b ; tmp[i][2*j+1] = b ;
} }
fourn(&forceMap[-1],&nn[-1],2,-1) ; fft::cdft2d(S, 2*S,-1, tmp, ip, w);
for(unsigned int i=0;i<S*S*2;++i) //fourn(&forceMap[-1],&nn[-1],2,-1) ;
forceMap[i] /= S*S;
memcpy(forceMap,tmp[0],S*S*2*sizeof(double)) ;
for(uint32_t i=0;i<2*S*S;++i)
forceMap[i] /= S*S;
} }
void GraphWidget::timerEvent(QTimerEvent *event) void GraphWidget::timerEvent(QTimerEvent *event)
@ -322,7 +348,7 @@ void GraphWidget::timerEvent(QTimerEvent *event)
QRectF R(scene()->sceneRect()) ; QRectF R(scene()->sceneRect()) ;
if( (hit++ & 7) == 0) if( (hit++ & 3) == 0)
{ {
memset(forceMap,0,2*S*S*sizeof(double)) ; memset(forceMap,0,2*S*S*sizeof(double)) ;
@ -348,7 +374,7 @@ void GraphWidget::timerEvent(QTimerEvent *event)
} }
// compute convolution with 1/omega kernel. // compute convolution with 1/omega kernel.
convolveWithGaussian(forceMap,S,20) ; convolveWithForce(forceMap,S,20) ;
} }
foreach (Node *node, _nodes) foreach (Node *node, _nodes)