source: src/mathutils.h @ 230101d

feature/autosinkfeature/constantqfeature/pitchshiftfeature/pydocstringsfeature/timestretch
Last change on this file since 230101d was 986131d, checked in by Eduard Müller <mueller.eduard@googlemail.com>, 3 years ago

Intel IPP support for aubio

See emuell/aubio/ intel_ipp2 for details please

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1/*
2  Copyright (C) 2003-2015 Paul Brossier <piem@aubio.org>
3
4  This file is part of aubio.
5
6  aubio is free software: you can redistribute it and/or modify
7  it under the terms of the GNU General Public License as published by
8  the Free Software Foundation, either version 3 of the License, or
9  (at your option) any later version.
10
11  aubio is distributed in the hope that it will be useful,
12  but WITHOUT ANY WARRANTY; without even the implied warranty of
13  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
14  GNU General Public License for more details.
15
16  You should have received a copy of the GNU General Public License
17  along with aubio.  If not, see <http://www.gnu.org/licenses/>.
18
19*/
20
21/** \file
22
23  Various math functions
24
25  \example test-mathutils.c
26  \example test-mathutils-window.c
27
28 */
29
30#ifndef AUBIO_MATHUTILS_H
31#define AUBIO_MATHUTILS_H
32
33#include "fvec.h"
34#include "musicutils.h"
35
36#ifdef __cplusplus
37extern "C" {
38#endif
39
40/** compute the mean of a vector
41
42  \param s vector to compute mean from
43  \return the mean of `v`
44
45*/
46smpl_t fvec_mean (fvec_t * s);
47
48/** find the max of a vector
49
50  \param s vector to get the max from
51
52  \return the value of the minimum of v
53
54*/
55smpl_t fvec_max (fvec_t * s);
56
57/** find the min of a vector
58
59  \param s vector to get the min from
60
61  \return the value of the maximum of v
62
63*/
64smpl_t fvec_min (fvec_t * s);
65
66/** find the index of the min of a vector
67
68  \param s vector to get the index from
69
70  \return the index of the minimum element of v
71
72*/
73uint_t fvec_min_elem (fvec_t * s);
74
75/** find the index of the max of a vector
76
77  \param s vector to get the index from
78
79  \return the index of the maximum element of v
80
81*/
82uint_t fvec_max_elem (fvec_t * s);
83
84/** swap the left and right halves of a vector
85
86  This function swaps the left part of the signal with the right part of the
87signal. Therefore
88
89  \f$ a[0], a[1], ..., a[\frac{N}{2}], a[\frac{N}{2}+1], ..., a[N-1], a[N] \f$
90
91  becomes
92
93  \f$ a[\frac{N}{2}+1], ..., a[N-1], a[N], a[0], a[1], ..., a[\frac{N}{2}] \f$
94
95  This operation, known as 'fftshift' in the Matlab Signal Processing Toolbox,
96can be used before computing the FFT to simplify the phase relationship of the
97resulting spectrum. See Amalia de Götzen's paper referred to above.
98
99*/
100void fvec_shift (fvec_t * v);
101
102/** swap the left and right halves of a vector
103
104  This function swaps the left part of the signal with the right part of the
105signal. Therefore
106
107  \f$ a[0], a[1], ..., a[\frac{N}{2}], a[\frac{N}{2}+1], ..., a[N-1], a[N] \f$
108
109  becomes
110
111  \f$ a[\frac{N}{2}+1], ..., a[N-1], a[N], a[0], a[1], ..., a[\frac{N}{2}] \f$
112
113  This operation, known as 'ifftshift' in the Matlab Signal Processing Toolbox,
114can be used after computing the inverse FFT to simplify the phase relationship
115of the resulting spectrum. See Amalia de Götzen's paper referred to above.
116
117*/
118void fvec_ishift (fvec_t * v);
119
120/** push a new element to the end of a vector, erasing the first element and
121 * sliding all others
122
123  \param in vector to push to
124  \param new_elem new_element to add at the end of the vector
125
126  In numpy words, this is equivalent to: in = np.concatenate([in, [new_elem]])[1:]
127
128*/
129void fvec_push(fvec_t *in, smpl_t new_elem);
130
131/** compute the sum of all elements of a vector
132
133  \param v vector to compute the sum of
134
135  \return the sum of v
136
137*/
138smpl_t fvec_sum (fvec_t * v);
139
140/** compute the High Frequency Content of a vector
141
142  The High Frequency Content is defined as \f$ \sum_0^{N-1} (k+1) v[k] \f$.
143
144  \param v vector to get the energy from
145
146  \return the HFC of v
147
148*/
149smpl_t fvec_local_hfc (fvec_t * v);
150
151/** computes the p-norm of a vector
152
153  Computes the p-norm of a vector for \f$ p = \alpha \f$
154
155  \f$ L^p = ||x||_p = (|x_1|^p + |x_2|^p + ... + |x_n|^p ) ^ \frac{1}{p} \f$
156
157  If p = 1, the result is the Manhattan distance.
158
159  If p = 2, the result is the Euclidean distance.
160
161  As p tends towards large values, \f$ L^p \f$ tends towards the maximum of the
162input vector.
163
164  References:
165
166    - <a href="http://en.wikipedia.org/wiki/Lp_space">\f$L^p\f$ space</a> on
167  Wikipedia
168
169  \param v vector to compute norm from
170  \param p order of the computed norm
171
172  \return the p-norm of v
173
174*/
175smpl_t fvec_alpha_norm (fvec_t * v, smpl_t p);
176
177/**  alpha normalisation
178
179  This function divides all elements of a vector by the p-norm as computed by
180fvec_alpha_norm().
181
182  \param v vector to compute norm from
183  \param p order of the computed norm
184
185*/
186void fvec_alpha_normalise (fvec_t * v, smpl_t p);
187
188/** add a constant to each elements of a vector
189
190  \param v vector to add constant to
191  \param c constant to add to v
192
193*/
194void fvec_add (fvec_t * v, smpl_t c);
195
196/** remove the minimum value of the vector to each elements
197
198  \param v vector to remove minimum from
199
200*/
201void fvec_min_removal (fvec_t * v);
202
203/** compute moving median threshold of a vector
204
205  This function computes the moving median threshold value of at the given
206position of a vector, taking the median among post elements before and up to
207pre elements after pos.
208
209  \param v input vector
210  \param tmp temporary vector of length post+1+pre
211  \param post length of causal part to take before pos
212  \param pre length of anti-causal part to take after pos
213  \param pos index to compute threshold for
214
215  \return moving median threshold value
216
217*/
218smpl_t fvec_moving_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre,
219    uint_t pos);
220
221/** apply adaptive threshold to a vector
222
223  For each points at position p of an input vector, this function remove the
224moving median threshold computed at p.
225
226  \param v input vector
227  \param tmp temporary vector of length post+1+pre
228  \param post length of causal part to take before pos
229  \param pre length of anti-causal part to take after pos
230
231*/
232void fvec_adapt_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre);
233
234/** returns the median of a vector
235
236  The QuickSelect routine is based on the algorithm described in "Numerical
237recipes in C", Second Edition, Cambridge University Press, 1992, Section 8.5,
238ISBN 0-521-43108-5
239
240  This implementation of the QuickSelect routine is based on Nicolas
241Devillard's implementation, available at http://ndevilla.free.fr/median/median/
242and in the Public Domain.
243
244  \param v vector to get median from
245
246  \return the median of v
247
248*/
249smpl_t fvec_median (fvec_t * v);
250
251/** finds exact peak index by quadratic interpolation
252
253  See [Quadratic Interpolation of Spectral
254  Peaks](https://ccrma.stanford.edu/~jos/sasp/Quadratic_Peak_Interpolation.html),
255  by Julius O. Smith III
256
257  \f$ p_{frac} = \frac{1}{2} \frac {x[p-1] - x[p+1]} {x[p-1] - 2 x[p] + x[p+1]} \in [ -.5, .5] \f$
258
259  \param x vector to get the interpolated peak position from
260  \param p index of the peak in vector `x`
261  \return \f$ p + p_{frac} \f$ exact peak position of interpolated maximum or minimum
262
263*/
264smpl_t fvec_quadratic_peak_pos (const fvec_t * x, uint_t p);
265
266/** finds magnitude of peak by quadratic interpolation
267
268  See [Quadratic Interpolation of Spectral
269  Peaks](https://ccrma.stanford.edu/~jos/sasp/Quadratic_Peak_Interpolation.html),
270  by Julius O. Smith III
271
272  \param x vector to get the magnitude of the interpolated peak position from
273  \param p index of the peak in vector `x`
274  \return magnitude of interpolated peak
275
276*/
277smpl_t fvec_quadratic_peak_mag (fvec_t * x, smpl_t p);
278
279/** Quadratic interpolation using Lagrange polynomial.
280
281  Inspired from ``Comparison of interpolation algorithms in real-time sound
282processing'', Vladimir Arnost,
283
284  \param s0,s1,s2 are 3 consecutive samples of a curve
285  \param pf is the floating point index [0;2]
286
287  \return \f$ s0 + (pf/2.)*((pf-3.)*s0-2.*(pf-2.)*s1+(pf-1.)*s2); \f$
288
289*/
290smpl_t aubio_quadfrac (smpl_t s0, smpl_t s1, smpl_t s2, smpl_t pf);
291
292/** return 1 if v[p] is a peak and positive, 0 otherwise
293
294  This function returns 1 if a peak is found at index p in the vector v. The
295peak is defined as follows:
296
297  - v[p] is positive
298  - v[p-1] < v[p]
299  - v[p] > v[p+1]
300
301  \param v input vector
302  \param p position of supposed for peak
303
304  \return 1 if a peak is found, 0 otherwise
305
306*/
307uint_t fvec_peakpick (const fvec_t * v, uint_t p);
308
309/** return 1 if a is a power of 2, 0 otherwise */
310uint_t aubio_is_power_of_two(uint_t a);
311
312/** return the next power of power of 2 greater than a */
313uint_t aubio_next_power_of_two(uint_t a);
314
315/** return the log2 factor of the given power of 2 value a */
316uint_t aubio_power_of_two_order(uint_t a);
317
318/** compute normalised autocorrelation function
319
320  \param input vector to compute autocorrelation from
321  \param output vector to store autocorrelation function to
322
323*/
324void aubio_autocorr (const fvec_t * input, fvec_t * output);
325
326#ifdef __cplusplus
327}
328#endif
329
330#endif /* AUBIO_MATHUTILS_H */
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