ref: 39122f04202548d4419e7072c99e07fad41a4579
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" #include "config.h" /** Window types */ typedef enum { 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, "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_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: { 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; #ifndef HAVE_ACCELERATE uint_t j; for (j = 0; j < s->length; j++) { tmp += s->data[j]; } return tmp / (smpl_t) (s->length); #else aubio_vDSP_meanv(s->data, 1, &tmp, s->length); return tmp; #endif /* HAVE_ACCELERATE */ } smpl_t fvec_sum (fvec_t * s) { smpl_t tmp = 0.0; #ifndef HAVE_ACCELERATE uint_t j; for (j = 0; j < s->length; j++) { tmp += s->data[j]; } #else aubio_vDSP_sve(s->data, 1, &tmp, s->length); #endif /* HAVE_ACCELERATE */ return tmp; } smpl_t fvec_max (fvec_t * s) { #ifndef HAVE_ACCELERATE uint_t j; smpl_t tmp = 0.0; for (j = 0; j < s->length; j++) { tmp = (tmp > s->data[j]) ? tmp : s->data[j]; } #else smpl_t tmp = 0.; aubio_vDSP_maxv(s->data, 1, &tmp, s->length); #endif return tmp; } smpl_t fvec_min (fvec_t * s) { #ifndef HAVE_ACCELERATE uint_t j; smpl_t tmp = s->data[0]; for (j = 0; j < s->length; j++) { tmp = (tmp < s->data[j]) ? tmp : s->data[j]; } #else smpl_t tmp = 0.; aubio_vDSP_minv(s->data, 1, &tmp, s->length); #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.; uint_t pos = 0.; aubio_vDSP_minvi(s->data, 1, &tmp, (vDSP_Length *)&pos, s->length); #endif return 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.; uint_t pos = 0.; aubio_vDSP_maxvi(s->data, 1, &tmp, (vDSP_Length *)&pos, s->length); #endif return 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_ATLAS 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_ATLAS 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]); } } } smpl_t aubio_level_lin (const fvec_t * f) { smpl_t energy = 0.; #ifndef HAVE_ATLAS 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_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=0; 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) / 0.69314718055995; 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 * 0.69314718055995); 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 * 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; } 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 (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 = 0; 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 }