ref: 700b89d6e8fcfd9c79cea51b153f46547110fb2d
dir: /src/mathutils.c/
/*
Copyright (C) 2003-2014 Paul Brossier <piem@aubio.org>
This file is part of aubio.
aubio 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 3 of the License, or
(at your option) any later version.
aubio 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 aubio. If not, see <http://www.gnu.org/licenses/>.
*/
/* see in mathutils.h for doc */
#include "aubio_priv.h"
#include "fvec.h"
#include "mathutils.h"
#include "musicutils.h"
/** Window types */
typedef enum
{
aubio_win_ones,
aubio_win_rectangle,
aubio_win_hamming,
aubio_win_hanning,
aubio_win_hanningz,
aubio_win_blackman,
aubio_win_blackman_harris,
aubio_win_gaussian,
aubio_win_welch,
aubio_win_parzen,
aubio_win_default = aubio_win_hanningz,
} aubio_window_type;
fvec_t *
new_aubio_window (char_t * window_type, uint_t length)
{
fvec_t * win = new_fvec (length);
uint_t err;
if (win == NULL) {
return NULL;
}
err = fvec_set_window (win, window_type);
if (err != 0) {
del_fvec(win);
return NULL;
}
return win;
}
uint_t fvec_set_window (fvec_t *win, char_t *window_type) {
smpl_t * w = win->data;
uint_t i, size = win->length;
aubio_window_type wintype;
if (window_type == NULL) {
AUBIO_ERR ("window type can not be null.\n");
return 1;
} else if (strcmp (window_type, "ones") == 0)
wintype = aubio_win_ones;
else if (strcmp (window_type, "rectangle") == 0)
wintype = aubio_win_rectangle;
else if (strcmp (window_type, "hamming") == 0)
wintype = aubio_win_hamming;
else if (strcmp (window_type, "hanning") == 0)
wintype = aubio_win_hanning;
else if (strcmp (window_type, "hanningz") == 0)
wintype = aubio_win_hanningz;
else if (strcmp (window_type, "blackman") == 0)
wintype = aubio_win_blackman;
else if (strcmp (window_type, "blackman_harris") == 0)
wintype = aubio_win_blackman_harris;
else if (strcmp (window_type, "gaussian") == 0)
wintype = aubio_win_gaussian;
else if (strcmp (window_type, "welch") == 0)
wintype = aubio_win_welch;
else if (strcmp (window_type, "parzen") == 0)
wintype = aubio_win_parzen;
else if (strcmp (window_type, "default") == 0)
wintype = aubio_win_default;
else {
AUBIO_ERR ("unknown window type `%s`.\n", window_type);
return 1;
}
switch(wintype) {
case aubio_win_ones:
fvec_ones(win);
break;
case aubio_win_rectangle:
fvec_set_all(win, .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:
{
lsmp_t a, b, c = 0.5;
uint_t n;
for (n = 0; n < size; n++)
{
a = (n-c*(size-1))/(SQR(c)*(size-1));
b = -c*SQR(a);
w[n] = EXP(b);
}
}
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.f*i-size)/(size+1.0f));
break;
default:
break;
}
return 0;
}
smpl_t
aubio_unwrap2pi (smpl_t phase)
{
/* mod(phase+pi,-2pi)+pi */
return phase + TWO_PI * (1. + FLOOR (-(phase + PI) / TWO_PI));
}
smpl_t
fvec_mean (fvec_t * s)
{
smpl_t tmp = 0.0;
#if defined(HAVE_INTEL_IPP)
aubio_ippsMean(s->data, (int)s->length, &tmp);
return tmp;
#elif defined(HAVE_ACCELERATE)
aubio_vDSP_meanv(s->data, 1, &tmp, s->length);
return tmp;
#else
uint_t j;
for (j = 0; j < s->length; j++) {
tmp += s->data[j];
}
return tmp / (smpl_t)(s->length);
#endif
}
smpl_t
fvec_sum (fvec_t * s)
{
smpl_t tmp = 0.0;
#if defined(HAVE_INTEL_IPP)
aubio_ippsSum(s->data, (int)s->length, &tmp);
#elif defined(HAVE_ACCELERATE)
aubio_vDSP_sve(s->data, 1, &tmp, s->length);
#else
uint_t j;
for (j = 0; j < s->length; j++) {
tmp += s->data[j];
}
#endif
return tmp;
}
smpl_t
fvec_max (fvec_t * s)
{
#if defined(HAVE_INTEL_IPP)
smpl_t tmp = 0.;
aubio_ippsMax( s->data, (int)s->length, &tmp);
#elif defined(HAVE_ACCELERATE)
smpl_t tmp = 0.;
aubio_vDSP_maxv( s->data, 1, &tmp, s->length );
#else
uint_t j;
smpl_t tmp = s->data[0];
for (j = 1; j < s->length; j++) {
tmp = (tmp > s->data[j]) ? tmp : s->data[j];
}
#endif
return tmp;
}
smpl_t
fvec_min (fvec_t * s)
{
#if defined(HAVE_INTEL_IPP)
smpl_t tmp = 0.;
aubio_ippsMin(s->data, (int)s->length, &tmp);
#elif defined(HAVE_ACCELERATE)
smpl_t tmp = 0.;
aubio_vDSP_minv(s->data, 1, &tmp, s->length);
#else
uint_t j;
smpl_t tmp = s->data[0];
for (j = 1; j < s->length; j++) {
tmp = (tmp < s->data[j]) ? tmp : s->data[j];
}
#endif
return tmp;
}
uint_t
fvec_min_elem (fvec_t * s)
{
#ifndef HAVE_ACCELERATE
uint_t j, pos = 0.;
smpl_t tmp = s->data[0];
for (j = 0; j < s->length; j++) {
pos = (tmp < s->data[j]) ? pos : j;
tmp = (tmp < s->data[j]) ? tmp : s->data[j];
}
#else
smpl_t tmp = 0.;
vDSP_Length pos = 0;
aubio_vDSP_minvi(s->data, 1, &tmp, &pos, s->length);
#endif
return (uint_t)pos;
}
uint_t
fvec_max_elem (fvec_t * s)
{
#ifndef HAVE_ACCELERATE
uint_t j, pos = 0;
smpl_t tmp = 0.0;
for (j = 0; j < s->length; j++) {
pos = (tmp > s->data[j]) ? pos : j;
tmp = (tmp > s->data[j]) ? tmp : s->data[j];
}
#else
smpl_t tmp = 0.;
vDSP_Length pos = 0;
aubio_vDSP_maxvi(s->data, 1, &tmp, &pos, s->length);
#endif
return (uint_t)pos;
}
void
fvec_shift (fvec_t * s)
{
uint_t half = s->length / 2, start = half, j;
// if length is odd, middle element is moved to the end
if (2 * half < s->length) start ++;
#ifndef HAVE_BLAS
for (j = 0; j < half; j++) {
ELEM_SWAP (s->data[j], s->data[j + start]);
}
#else
aubio_cblas_swap(half, s->data, 1, s->data + start, 1);
#endif
if (start != half) {
for (j = 0; j < half; j++) {
ELEM_SWAP (s->data[j + start - 1], s->data[j + start]);
}
}
}
void
fvec_ishift (fvec_t * s)
{
uint_t half = s->length / 2, start = half, j;
// if length is odd, middle element is moved to the beginning
if (2 * half < s->length) start ++;
#ifndef HAVE_BLAS
for (j = 0; j < half; j++) {
ELEM_SWAP (s->data[j], s->data[j + start]);
}
#else
aubio_cblas_swap(half, s->data, 1, s->data + start, 1);
#endif
if (start != half) {
for (j = 0; j < half; j++) {
ELEM_SWAP (s->data[half], s->data[j]);
}
}
}
void fvec_push(fvec_t *in, smpl_t new_elem) {
uint_t i;
for (i = 0; i < in->length - 1; i++) {
in->data[i] = in->data[i + 1];
}
in->data[in->length - 1] = new_elem;
}
void fvec_clamp(fvec_t *in, smpl_t absmax) {
uint_t i;
for (i = 0; i < in->length; i++) {
if (in->data[i] > 0 && in->data[i] > ABS(absmax)) {
in->data[i] = absmax;
} else if (in->data[i] < 0 && in->data[i] < -ABS(absmax)) {
in->data[i] = -absmax;
}
}
}
smpl_t
aubio_level_lin (const fvec_t * f)
{
smpl_t energy = 0.;
#ifndef HAVE_BLAS
uint_t j;
for (j = 0; j < f->length; j++) {
energy += SQR (f->data[j]);
}
#else
energy = aubio_cblas_dot(f->length, f->data, 1, f->data, 1);
#endif
return energy / f->length;
}
smpl_t
fvec_local_hfc (fvec_t * v)
{
smpl_t hfc = 0.;
uint_t j;
for (j = 0; j < v->length; j++) {
hfc += (j + 1) * v->data[j];
}
return hfc;
}
void
fvec_min_removal (fvec_t * v)
{
smpl_t v_min = fvec_min (v);
fvec_add (v, - v_min );
}
smpl_t
fvec_alpha_norm (fvec_t * o, smpl_t alpha)
{
uint_t j;
smpl_t tmp = 0.;
for (j = 0; j < o->length; j++) {
tmp += POW (ABS (o->data[j]), alpha);
}
return POW (tmp / o->length, 1. / alpha);
}
void
fvec_alpha_normalise (fvec_t * o, smpl_t alpha)
{
uint_t j;
smpl_t norm = fvec_alpha_norm (o, alpha);
for (j = 0; j < o->length; j++) {
o->data[j] /= norm;
}
}
void
fvec_add (fvec_t * o, smpl_t val)
{
uint_t j;
for (j = 0; j < o->length; j++) {
o->data[j] += val;
}
}
void
fvec_mul (fvec_t *o, smpl_t val)
{
uint_t j;
for (j = 0; j < o->length; j++) {
o->data[j] *= val;
}
}
void fvec_adapt_thres(fvec_t * vec, fvec_t * tmp,
uint_t post, uint_t pre) {
uint_t length = vec->length, j;
for (j=0;j<length;j++) {
vec->data[j] -= fvec_moving_thres(vec, tmp, post, pre, j);
}
}
smpl_t
fvec_moving_thres (fvec_t * vec, fvec_t * tmpvec,
uint_t post, uint_t pre, uint_t pos)
{
uint_t k;
smpl_t *medar = (smpl_t *) tmpvec->data;
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[k + pos - post];
/* the buffer is fully defined */
} else if (pos + pre < length) {
for (k = 0; k < win_length; k++)
medar[k] = vec->data[k + pos - post];
/* pre part of the buffer does not exist */
} else {
for (k = 0; k < length - pos + post; k++)
medar[k] = vec->data[k + pos - post];
for (k = length - pos + post; k < win_length; k++)
medar[k] = 0.; /* 0-padding at the end */
}
return fvec_median (tmpvec);
}
smpl_t fvec_median (fvec_t * input) {
uint_t n = input->length;
smpl_t * arr = (smpl_t *) input->data;
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 fvec_quadratic_peak_pos (const fvec_t * x, uint_t pos) {
smpl_t s0, s1, s2; uint_t x0, x2;
smpl_t half = .5, two = 2.;
if (pos == 0 || pos == x->length - 1) return pos;
x0 = (pos < 1) ? pos : pos - 1;
x2 = (pos + 1 < x->length) ? pos + 1 : pos;
if (x0 == pos) return (x->data[pos] <= x->data[x2]) ? pos : x2;
if (x2 == pos) return (x->data[pos] <= x->data[x0]) ? pos : x0;
s0 = x->data[x0];
s1 = x->data[pos];
s2 = x->data[x2];
return pos + half * (s0 - s2 ) / (s0 - two * s1 + s2);
}
smpl_t fvec_quadratic_peak_mag (fvec_t *x, smpl_t pos) {
smpl_t x0, x1, x2;
uint_t index = (uint_t)(pos - .5) + 1;
if (pos >= x->length || pos < 0.) return 0.;
if ((smpl_t)index == pos) return x->data[index];
x0 = x->data[index - 1];
x1 = x->data[index];
x2 = x->data[index + 1];
return x1 - .25 * (x0 - x2) * (pos - index);
}
uint_t fvec_peakpick(const fvec_t * onset, uint_t pos) {
uint_t tmp;
tmp = (onset->data[pos] > onset->data[pos-1]
&& onset->data[pos] > onset->data[pos+1]
&& onset->data[pos] > 0.);
return tmp;
}
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;
}
smpl_t
aubio_freqtomidi (smpl_t freq)
{
smpl_t midi;
if (freq < 2. || freq > 100000.) return 0.; // avoid nans and infs
/* log(freq/A-2)/log(2) */
midi = freq / 6.875;
midi = LOG (midi) / 0.6931471805599453;
midi *= 12;
midi -= 3;
return midi;
}
smpl_t
aubio_miditofreq (smpl_t midi)
{
smpl_t freq;
if (midi > 140.) return 0.; // avoid infs
freq = (midi + 3.) / 12.;
freq = EXP (freq * 0.6931471805599453);
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 * MAX(bin, 0);
}
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 MAX(freq, 0) * 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);
}
uint_t
aubio_is_power_of_two (uint_t a)
{
if ((a & (a - 1)) == 0) {
return 1;
} else {
return 0;
}
}
uint_t
aubio_next_power_of_two (uint_t a)
{
uint_t i = 1;
while (i < a) i <<= 1;
return i;
}
uint_t
aubio_power_of_two_order (uint_t a)
{
int order = 0;
int temp = aubio_next_power_of_two(a);
while (temp >>= 1) {
++order;
}
return order;
}
smpl_t
aubio_db_spl (const fvec_t * o)
{
return 10. * LOG10 (aubio_level_lin (o));
}
uint_t
aubio_silence_detection (const fvec_t * o, smpl_t threshold)
{
return (aubio_db_spl (o) < threshold);
}
smpl_t
aubio_level_detection (const fvec_t * o, smpl_t threshold)
{
smpl_t db_spl = aubio_db_spl (o);
if (db_spl < threshold) {
return 1.;
} else {
return db_spl;
}
}
smpl_t
aubio_zero_crossing_rate (fvec_t * input)
{
uint_t j;
uint_t zcr = 0;
for (j = 1; j < input->length; j++) {
// previous was strictly negative
if (input->data[j - 1] < 0.) {
// current is positive or null
if (input->data[j] >= 0.) {
zcr += 1;
}
// previous was positive or null
} else {
// current is strictly negative
if (input->data[j] < 0.) {
zcr += 1;
}
}
}
return zcr / (smpl_t) input->length;
}
void
aubio_autocorr (const fvec_t * input, fvec_t * output)
{
uint_t i, j, length = input->length;
smpl_t *data, *acf;
smpl_t tmp;
data = input->data;
acf = output->data;
for (i = 0; i < length; i++) {
tmp = 0.;
for (j = i; j < length; j++) {
tmp += data[j - i] * data[j];
}
acf[i] = tmp / (smpl_t) (length - i);
}
}
void
aubio_cleanup (void)
{
#ifdef HAVE_FFTW3F
fftwf_cleanup ();
#else
#ifdef HAVE_FFTW3
fftw_cleanup ();
#endif
#endif
}