source: src/mathutils.h @ c0a1906

feature/autosinkfeature/constantqfeature/pitchshiftfeature/timestretch
Last change on this file since c0a1906 was da01353, checked in by Paul Brossier <piem@piem.org>, 7 months ago

[api] add fvec_mul

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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/** multiply each elements of a vector by a scalar
197
198  \param v vector to add constant to
199  \param s constant to scale v with
200
201*/
202void fvec_mul (fvec_t * v, smpl_t s);
203
204/** remove the minimum value of the vector to each elements
205
206  \param v vector to remove minimum from
207
208*/
209void fvec_min_removal (fvec_t * v);
210
211/** compute moving median threshold of a vector
212
213  This function computes the moving median threshold value of at the given
214position of a vector, taking the median among post elements before and up to
215pre elements after pos.
216
217  \param v input vector
218  \param tmp temporary vector of length post+1+pre
219  \param post length of causal part to take before pos
220  \param pre length of anti-causal part to take after pos
221  \param pos index to compute threshold for
222
223  \return moving median threshold value
224
225*/
226smpl_t fvec_moving_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre,
227    uint_t pos);
228
229/** apply adaptive threshold to a vector
230
231  For each points at position p of an input vector, this function remove the
232moving median threshold computed at p.
233
234  \param v input vector
235  \param tmp temporary vector of length post+1+pre
236  \param post length of causal part to take before pos
237  \param pre length of anti-causal part to take after pos
238
239*/
240void fvec_adapt_thres (fvec_t * v, fvec_t * tmp, uint_t post, uint_t pre);
241
242/** returns the median of a vector
243
244  The QuickSelect routine is based on the algorithm described in "Numerical
245recipes in C", Second Edition, Cambridge University Press, 1992, Section 8.5,
246ISBN 0-521-43108-5
247
248  This implementation of the QuickSelect routine is based on Nicolas
249Devillard's implementation, available at http://ndevilla.free.fr/median/median/
250and in the Public Domain.
251
252  \param v vector to get median from
253
254  \return the median of v
255
256*/
257smpl_t fvec_median (fvec_t * v);
258
259/** finds exact peak index by quadratic interpolation
260
261  See [Quadratic Interpolation of Spectral
262  Peaks](https://ccrma.stanford.edu/~jos/sasp/Quadratic_Peak_Interpolation.html),
263  by Julius O. Smith III
264
265  \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$
266
267  \param x vector to get the interpolated peak position from
268  \param p index of the peak in vector `x`
269  \return \f$ p + p_{frac} \f$ exact peak position of interpolated maximum or minimum
270
271*/
272smpl_t fvec_quadratic_peak_pos (const fvec_t * x, uint_t p);
273
274/** finds magnitude of peak by quadratic interpolation
275
276  See [Quadratic Interpolation of Spectral
277  Peaks](https://ccrma.stanford.edu/~jos/sasp/Quadratic_Peak_Interpolation.html),
278  by Julius O. Smith III
279
280  \param x vector to get the magnitude of the interpolated peak position from
281  \param p index of the peak in vector `x`
282  \return magnitude of interpolated peak
283
284*/
285smpl_t fvec_quadratic_peak_mag (fvec_t * x, smpl_t p);
286
287/** Quadratic interpolation using Lagrange polynomial.
288
289  Inspired from ``Comparison of interpolation algorithms in real-time sound
290processing'', Vladimir Arnost,
291
292  \param s0,s1,s2 are 3 consecutive samples of a curve
293  \param pf is the floating point index [0;2]
294
295  \return \f$ s0 + (pf/2.)*((pf-3.)*s0-2.*(pf-2.)*s1+(pf-1.)*s2); \f$
296
297*/
298smpl_t aubio_quadfrac (smpl_t s0, smpl_t s1, smpl_t s2, smpl_t pf);
299
300/** return 1 if v[p] is a peak and positive, 0 otherwise
301
302  This function returns 1 if a peak is found at index p in the vector v. The
303peak is defined as follows:
304
305  - v[p] is positive
306  - v[p-1] < v[p]
307  - v[p] > v[p+1]
308
309  \param v input vector
310  \param p position of supposed for peak
311
312  \return 1 if a peak is found, 0 otherwise
313
314*/
315uint_t fvec_peakpick (const fvec_t * v, uint_t p);
316
317/** return 1 if a is a power of 2, 0 otherwise */
318uint_t aubio_is_power_of_two(uint_t a);
319
320/** return the next power of power of 2 greater than a */
321uint_t aubio_next_power_of_two(uint_t a);
322
323/** return the log2 factor of the given power of 2 value a */
324uint_t aubio_power_of_two_order(uint_t a);
325
326/** compute normalised autocorrelation function
327
328  \param input vector to compute autocorrelation from
329  \param output vector to store autocorrelation function to
330
331*/
332void aubio_autocorr (const fvec_t * input, fvec_t * output);
333
334#ifdef __cplusplus
335}
336#endif
337
338#endif /* AUBIO_MATHUTILS_H */
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