ref: ef7df7698cf744f3d43859eb304e4ea4d69d4bfa
dir: /src/mathutils.c/
/*
Copyright (C) 2003 Paul Brossier
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; 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.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
*/
/* see in mathutils.h for doc */
#include "aubio_priv.h"
#include "sample.h"
#include "mathutils.h"
#include "config.h"
void aubio_window(smpl_t *w, uint_t size, aubio_window_type wintype) {
uint_t i;
switch(wintype) {
case aubio_win_rectangle:
for (i=0;i<size;i++)
w[i] = 0.5;
break;
case aubio_win_hamming:
for (i=0;i<size;i++)
w[i] = 0.54 - 0.46 * COS(TWO_PI * i / (size));
break;
case aubio_win_hanning:
for (i=0;i<size;i++)
w[i] = 0.5 - (0.5 * COS(TWO_PI * i / (size)));
break;
case aubio_win_hanningz:
for (i=0;i<size;i++)
w[i] = 0.5 * (1.0 - COS(TWO_PI * i / (size)));
break;
case aubio_win_blackman:
for (i=0;i<size;i++)
w[i] = 0.42
- 0.50 * COS( TWO_PI*i/(size-1.0))
+ 0.08 * COS(2.0*TWO_PI*i/(size-1.0));
break;
case aubio_win_blackman_harris:
for (i=0;i<size;i++)
w[i] = 0.35875
- 0.48829 * COS( TWO_PI*i/(size-1.0))
+ 0.14128 * COS(2.0*TWO_PI*i/(size-1.0))
- 0.01168 * COS(3.0*TWO_PI*i/(size-1.0));
break;
case aubio_win_gaussian:
for (i=0;i<size;i++)
w[i] = EXP(- 1.0 / SQR(size) * SQR(2.0*i-size));
break;
case aubio_win_welch:
for (i=0;i<size;i++)
w[i] = 1.0 - SQR((2*i-size)/(size+1.0));
break;
case aubio_win_parzen:
for (i=0;i<size;i++)
w[i] = 1.0 - ABS((2*i-size)/(size+1.0));
break;
default:
break;
}
}
smpl_t aubio_unwrap2pi(smpl_t phase) {
/* mod(phase+pi,-2pi)+pi */
return phase + TWO_PI * (1. + FLOOR(-(phase+PI)/TWO_PI));
}
smpl_t vec_mean(fvec_t *s) {
uint_t i,j;
smpl_t tmp = 0.0f;
for (i=0; i < s->channels; i++)
for (j=0; j < s->length; j++)
tmp += s->data[i][j];
return tmp/(smpl_t)(s->length);
}
smpl_t vec_sum(fvec_t *s) {
uint_t i,j;
smpl_t tmp = 0.0f;
for (i=0; i < s->channels; i++)
for (j=0; j < s->length; j++)
tmp += s->data[i][j];
return tmp;
}
smpl_t vec_max(fvec_t *s) {
uint_t i,j;
smpl_t tmp = 0.0f;
for (i=0; i < s->channels; i++)
for (j=0; j < s->length; j++)
tmp = (tmp > s->data[i][j])? tmp : s->data[i][j];
return tmp;
}
smpl_t vec_min(fvec_t *s) {
uint_t i,j;
smpl_t tmp = s->data[0][0];
for (i=0; i < s->channels; i++)
for (j=0; j < s->length; j++)
tmp = (tmp < s->data[i][j])? tmp : s->data[i][j] ;
return tmp;
}
uint_t vec_min_elem(fvec_t *s) {
uint_t i,j=0, pos=0.;
smpl_t tmp = s->data[0][0];
for (i=0; i < s->channels; i++)
for (j=0; j < s->length; j++) {
pos = (tmp < s->data[i][j])? pos : j;
tmp = (tmp < s->data[i][j])? tmp : s->data[i][j] ;
}
return pos;
}
uint_t vec_max_elem(fvec_t *s) {
uint_t i,j=0, pos=0.;
smpl_t tmp = 0.0f;
for (i=0; i < s->channels; i++)
for (j=0; j < s->length; j++) {
pos = (tmp > s->data[i][j])? pos : j;
tmp = (tmp > s->data[i][j])? tmp : s->data[i][j] ;
}
return pos;
}
void vec_shift(fvec_t *s) {
uint_t i,j;
//smpl_t tmp = 0.0f;
for (i=0; i < s->channels; i++)
for (j=0; j < s->length / 2 ; j++) {
//tmp = s->data[i][j];
//s->data[i][j] = s->data[i][j+s->length/2];
//s->data[i][j+s->length/2] = tmp;
ELEM_SWAP(s->data[i][j],s->data[i][j+s->length/2]);
}
}
smpl_t vec_local_energy(fvec_t * f) {
smpl_t locE = 0.;
uint_t i,j;
for (i=0;i<f->channels;i++)
for (j=0;j<f->length;j++)
locE+=SQR(f->data[i][j]);
return locE;
}
smpl_t vec_local_hfc(fvec_t * f) {
smpl_t locE = 0.;
uint_t i,j;
for (i=0;i<f->channels;i++)
for (j=0;j<f->length;j++)
locE+=(i+1)*f->data[i][j];
return locE;
}
smpl_t vec_alpha_norm(fvec_t * DF, smpl_t alpha) {
smpl_t tmp = 0.;
uint_t i,j;
for (i=0;i<DF->channels;i++)
for (j=0;j<DF->length;j++)
tmp += POW(ABS(DF->data[i][j]),alpha);
return POW(tmp/DF->length,1./alpha);
}
void vec_dc_removal(fvec_t * mag) {
smpl_t mini = 0.;
uint_t length = mag->length, i=0, j;
mini = vec_min(mag);
for (j=0;j<length;j++) {
mag->data[i][j] -= mini;
}
}
void vec_alpha_normalise(fvec_t * mag, uint_t alpha) {
smpl_t alphan = 1.;
uint_t length = mag->length, i=0, j;
alphan = vec_alpha_norm(mag,alpha);
for (j=0;j<length;j++){
mag->data[i][j] /= alphan;
}
}
void vec_add(fvec_t * mag, smpl_t threshold) {
uint_t length = mag->length, i=0, j;
for (j=0;j<length;j++) {
mag->data[i][j] += threshold;
}
}
void vec_adapt_thres(fvec_t * vec, fvec_t * tmp,
uint_t post, uint_t pre) {
uint_t length = vec->length, i=0, j;
for (j=0;j<length;j++) {
vec->data[i][j] -= vec_moving_thres(vec, tmp, post, pre, j);
}
}
smpl_t vec_moving_thres(fvec_t * vec, fvec_t * tmpvec,
uint_t post, uint_t pre, uint_t pos) {
smpl_t * medar = (smpl_t *)tmpvec->data[0];
uint_t k;
uint_t win_length = post+pre+1;
uint_t length = vec->length;
/* post part of the buffer does not exist */
if (pos<post+1) {
for (k=0;k<post+1-pos;k++)
medar[k] = 0.; /* 0-padding at the beginning */
for (k=post+1-pos;k<win_length;k++)
medar[k] = vec->data[0][k+pos-post];
/* the buffer is fully defined */
} else if (pos+pre<length) {
for (k=0;k<win_length;k++)
medar[k] = vec->data[0][k+pos-post];
/* pre part of the buffer does not exist */
} else {
for (k=0;k<length-pos+post+1;k++)
medar[k] = vec->data[0][k+pos-post];
for (k=length-pos+post+1;k<win_length;k++)
medar[k] = 0.; /* 0-padding at the end */
}
return vec_median(tmpvec);
}
smpl_t vec_median(fvec_t * input) {
uint_t n = input->length;
smpl_t * arr = (smpl_t *) input->data[0];
uint_t low, high ;
uint_t median;
uint_t middle, ll, hh;
low = 0 ; high = n-1 ; median = (low + high) / 2;
for (;;) {
if (high <= low) /* One element only */
return arr[median] ;
if (high == low + 1) { /* Two elements only */
if (arr[low] > arr[high])
ELEM_SWAP(arr[low], arr[high]) ;
return arr[median] ;
}
/* Find median of low, middle and high items; swap into position low */
middle = (low + high) / 2;
if (arr[middle] > arr[high]) ELEM_SWAP(arr[middle], arr[high]);
if (arr[low] > arr[high]) ELEM_SWAP(arr[low], arr[high]);
if (arr[middle] > arr[low]) ELEM_SWAP(arr[middle], arr[low]) ;
/* Swap low item (now in position middle) into position (low+1) */
ELEM_SWAP(arr[middle], arr[low+1]) ;
/* Nibble from each end towards middle, swapping items when stuck */
ll = low + 1;
hh = high;
for (;;) {
do ll++; while (arr[low] > arr[ll]) ;
do hh--; while (arr[hh] > arr[low]) ;
if (hh < ll)
break;
ELEM_SWAP(arr[ll], arr[hh]) ;
}
/* Swap middle item (in position low) back into correct position */
ELEM_SWAP(arr[low], arr[hh]) ;
/* Re-set active partition */
if (hh <= median)
low = ll;
if (hh >= median)
high = hh - 1;
}
}
smpl_t vec_quadint(fvec_t * x,uint_t pos) {
uint_t span = 2;
smpl_t step = 1./200.;
/* hack : init resold to - something (in case x[pos+-span]<0)) */
smpl_t res, frac, s0, s1, s2, exactpos = (smpl_t)pos, resold = -1000.;
if ((pos > span) && (pos < x->length-span)) {
s0 = x->data[0][pos-span];
s1 = x->data[0][pos] ;
s2 = x->data[0][pos+span];
/* increase frac */
for (frac = 0.; frac < 2.; frac = frac + step) {
res = aubio_quadfrac(s0, s1, s2, frac);
if (res > resold)
resold = res;
else {
exactpos += (frac-step)*2. - 1.;
break;
}
}
}
return exactpos;
}
smpl_t vec_quadint_min(fvec_t * x,uint_t pos, uint_t span) {
smpl_t step = 1./200.;
/* init resold to - something (in case x[pos+-span]<0)) */
smpl_t res, frac, s0, s1, s2, exactpos = (smpl_t)pos, resold = 100000.;
if ((pos > span) && (pos < x->length-span)) {
s0 = x->data[0][pos-span];
s1 = x->data[0][pos] ;
s2 = x->data[0][pos+span];
/* increase frac */
for (frac = 0.; frac < 2.; frac = frac + step) {
res = aubio_quadfrac(s0, s1, s2, frac);
if (res < resold) {
resold = res;
} else {
exactpos += (frac-step)*span - span/2.;
break;
}
}
}
return exactpos;
}
smpl_t aubio_quadfrac(smpl_t s0, smpl_t s1, smpl_t s2, smpl_t pf) {
smpl_t tmp = s0 + (pf/2.) * (pf * ( s0 - 2.*s1 + s2 ) - 3.*s0 + 4.*s1 - s2);
return tmp;
}
uint_t vec_peakpick(fvec_t * onset, uint_t pos) {
uint_t i=0, tmp=0;
/*for (i=0;i<onset->channels;i++)*/
tmp = (onset->data[i][pos] > onset->data[i][pos-1]
&& onset->data[i][pos] > onset->data[i][pos+1]
&& onset->data[i][pos] > 0.);
return tmp;
}
smpl_t aubio_freqtomidi(smpl_t freq) {
/* log(freq/A-2)/log(2) */
smpl_t midi = freq/6.875;
midi = LOG(midi)/0.69314718055995;
midi *= 12;
midi -= 3;
return midi;
}
smpl_t aubio_miditofreq(smpl_t midi) {
smpl_t freq = (midi+3.)/12.;
freq = EXP(freq*0.69314718055995);
freq *= 6.875;
return freq;
}
smpl_t aubio_bintofreq(smpl_t bin, smpl_t samplerate, smpl_t fftsize) {
smpl_t freq = samplerate/fftsize;
return freq*bin;
}
smpl_t aubio_bintomidi(smpl_t bin, smpl_t samplerate, smpl_t fftsize) {
smpl_t midi = aubio_bintofreq(bin,samplerate,fftsize);
return aubio_freqtomidi(midi);
}
smpl_t aubio_freqtobin(smpl_t freq, smpl_t samplerate, smpl_t fftsize) {
smpl_t bin = fftsize/samplerate;
return freq*bin;
}
smpl_t aubio_miditobin(smpl_t midi, smpl_t samplerate, smpl_t fftsize) {
smpl_t freq = aubio_miditofreq(midi);
return aubio_freqtobin(freq,samplerate,fftsize);
}
/** returns 1 if wassilence is 0 and RMS(ibuf)<threshold
* \bug mono
*/
uint_t aubio_silence_detection(fvec_t * ibuf, smpl_t threshold) {
smpl_t loudness = 0;
uint_t i=0,j;
for (j=0;j<ibuf->length;j++) {
loudness += SQR(ibuf->data[i][j]);
}
loudness = SQRT(loudness);
loudness /= (smpl_t)ibuf->length;
loudness = LIN2DB(loudness);
return (loudness < threshold);
}
/** returns level log(RMS(ibuf)) if < threshold, 1 otherwise
* \bug mono
*/
smpl_t aubio_level_detection(fvec_t * ibuf, smpl_t threshold) {
smpl_t loudness = 0;
uint_t i=0,j;
for (j=0;j<ibuf->length;j++) {
loudness += SQR(ibuf->data[i][j]);
}
loudness = SQRT(loudness);
loudness /= (smpl_t)ibuf->length;
loudness = LIN2DB(loudness);
if (loudness < threshold)
return 1.;
else
return loudness;
}
smpl_t aubio_zero_crossing_rate(fvec_t * input) {
uint_t i=0,j;
uint_t zcr = 0;
for ( j = 1; j < input->length; j++ ) {
// previous was negative
if( input->data[i][j-1] <= 0. ) {
if ( input->data[i][j] > 0. ) {
zcr += 1;
}
//previous was positive
} else if ( input->data[i][j] <= 0. ) {
zcr += 1;
}
}
return zcr/(smpl_t)input->length;
}
smpl_t aubio_spectral_centroid(cvec_t * spectrum, smpl_t samplerate) {
uint_t i=0, j;
smpl_t sum = 0., sc = 0.;
for ( j = 0; j < spectrum->length; j++ ) {
sum += spectrum->norm[i][j];
}
if (sum == 0.) return 0.;
for ( j = 0; j < spectrum->length; j++ ) {
sc += (smpl_t)j * spectrum->norm[i][j];
}
return sc / sum * samplerate / (smpl_t)(spectrum->length);
}
void aubio_autocorr(fvec_t * input, fvec_t * output) {
uint_t i = 0, j = 0, length = input->length;
smpl_t * data = input->data[0];
smpl_t * acf = output->data[0];
smpl_t tmp =0.;
for(i=0;i<length;i++){
for(j=i;j<length;j++){
tmp += data[j-i]*data[j];
}
acf[i] = tmp /(smpl_t)(length-i);
tmp = 0.0;
}
}
void aubio_cleanup(void) {
#if FFTW3_SUPPORT
fftw_cleanup();
#else
#if FFTW3F_SUPPORT
fftwf_cleanup();
#endif
#endif
}