STATUS: unstable Additional math-functions. More...

#include <stdlib.h>
#include <limits.h>
#include <float.h>
#include <math.h>
#include <string.h>
#include <gsl/gsl_spline.h>
#include <gsl/gsl_sf_bessel.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_cblas.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include "helper.h"
#include "definitions.h"
#include "complex.h"

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Defines
#define	_ISOC99_SOURCE
#define	ABS(a) ( ((a)<0) ? (-1*(a)) : (a) )
	absolute value of a number
#define	CHECK_BIT(var, pos) ((var) & (1<<(pos)))
	check whether bit at position pos is 1.
#define	ISODD(x) ((((x)%2)==0)? (0) : (1))
#define	MAX(a, b) ((a) > (b) ? (a):(b))
	maximum of two elements.
#define	MIN(a, b) ((a) < (b) ? (a):(b))
	minimum of two elements.
#define	PI 3.14159265358979323846
#define	SQR(a) ((a)*(a))
	square of a number.
Functions
int	abscmp (const void p1, const void p2)
int	closest_index (const double *v, int n, double c)
int	cmpdouble (double d1, double d2, int precision)
double *	dblp_complex_to_real (const Complex vc, double vr, int n)
double	dblp_euclidean_distance (const double v1, const double v2, int n)
double *	dblp_init (double *v, int n, double val)
double	dblp_max (double v, int n, int idx)
double	dblp_mean (double *v, int n)
double	dblp_min (double v, int n, int idx)
void	dblp_minus_scalar (double *v, int n, double val)
void	dblp_print (double *v, int n)
void	dblp_print_int (int *v, int n)
void	dblp_shuffle_int (int *permut, int n)
void	dblpp_add_dblpp (double m1, const double m2, int N, int n)
void	dblpp_add_scalar (double **m, int N, int n, double s)
void	dblpp_copy (const double src, double dest, int N, int M)
double **	dblpp_delcol (double **m, int N, int n, int col)
double **	dblpp_delrow (double **m, int N, int n, int row)
void	dblpp_divide_scalar (double **m, int N, int n, double s)
void	dblpp_dottimes_dblpp (double m1, const double m2, int N, int M)
void	dblpp_free (double **m, int N)
double **	dblpp_init (int N, int M)
int **	dblpp_init_int (int N, int M)
double	dblpp_max (const double *m, int N, int n, int i1, int *i2)
double	dblpp_min (const double *m, int N, int n, int i1, int *i2)
void	dblpp_mul_scalar (double **m, int N, int n, double s)
void	dblpp_normalize_by_max (double **m, int M, int N)
void	dblpp_print (const double **m, int N, int n)
double **	dblpp_rand (double **m, int N, int M, double lower, double upper)
void	dblpp_sub_dblpp (double dest, const double src, int N, int n)
double	drawsample_nearest_neighbour (const double *v, int n, double x)
Complex *	expand_polynomial_from_roots (const Complex roots, int n, Complex coeffs)
void	fft (double *data, unsigned long nn, int isign)
double *	flip_array (double *v, int n)
double	gaussian (double x, double sigma, double mu)
double	glog (double v, int b)
int	iremainder (double x, double y)
double *	lininterp (const double x1, const double y1, int n1, const double x2, double y2, int n2)
int *	linspace (int first, int last)
double *	linspace_dbl (double first, double last, double step, double v, int n)
double	mad (const double *data, int n)
double	maxel (double *v, int n)
int	maxeli (int *v, int n)
int	next_pow2 (int n)
double *	resample_gsl (const double s, int n, int newn, double news, const gsl_interp_type *method)
double *	resample_linear (const double s, int n, int newn, double news)
double *	resample_nearest_neighbour (const double s, int n, int newn, double news)
double	rmse (const double r, const double d, int n)
double *	sampled_line (double *ntimes, int n, double start, double end)
void	scalar_minus_dblpp (double scalar, double **m, int N, int M)
int	sgn (int x)
double *	sigext_smooth (double *data, int ns, int n)
double *	sigext_sym (double *data, int ns, int n)
double *	sigext_zeros (double *data, int ns, int n)
double *	sigext_zerosr (double *data, int ns, int n)
double	snr (const double r, const double d, int n)
void	swap2d (double v1, double v2)
void	swap2i (int v1, int v2)
double	vnorm (const double *v, int n, int p)
double	weighted_median_from_unsorted (const double d, const double w, int n)

Detailed Description

STATUS: unstable Additional math-functions.

Definition in file mathadd.h.

Define Documentation

#define _ISOC99_SOURCE

Definition at line 29 of file mathadd.h.

#define ABS ( a ) ( ((a)<0) ? (-1*(a)) : (a) )

absolute value of a number

Definition at line 59 of file mathadd.h.

#define CHECK_BIT	(	var,
		pos
	)		((var) & (1<<(pos)))

check whether bit at position pos is 1.

Definition at line 64 of file mathadd.h.

#define ISODD ( x ) ((((x)%2)==0)? (0) : (1))

Definition at line 61 of file mathadd.h.

#define MAX	(	a,
		b
	)		((a) > (b) ? (a):(b))

maximum of two elements.

Definition at line 53 of file mathadd.h.

#define MIN	(	a,
		b
	)		((a) < (b) ? (a):(b))

minimum of two elements.

Definition at line 55 of file mathadd.h.

#define PI 3.14159265358979323846

Definition at line 66 of file mathadd.h.

#define SQR ( a ) ((a)*(a))

square of a number.

Definition at line 57 of file mathadd.h.

Function Documentation

int abscmp	(	const void *	p1,
		const void *	p2
	)

Definition at line 144 of file mathadd.c.

int closest_index	(	const double *	v,
		int	n,
		double	c
	)

return index in vector that is closest to a value

Parameters:

	v	vector to search
	n	length of vector
	c	value to look for

Returns:: index of the value closest to c in v

Definition at line 185 of file mathadd.c.

int cmpdouble	(	double	d1,
		double	d2,
		int	precision
	)

Compare two doubles to a certain precision. cmpdouble()

Parameters:

precision

to which position after comma it is compared

Returns:

-1 if d1<d2
0 if d1==d2
1 if d1>d2

Definition at line 105 of file mathadd.c.

double* dblp_complex_to_real	(	const Complex *	vc,
		double *	vr,
		int	n
	)

return the real part of the complex numbers in vc. If the imaginary part is nonzero, a warning is issued.

Parameters:

	vc	complex vector
	vr	real vector of size n, or ALLOC_IN_FCT

Definition at line 1037 of file mathadd.c.

double dblp_euclidean_distance	(	const double *	v1,
		const double *	v2,
		int	n
	)

calculate $|\vec{v_1} - \vec{v_2}|^2$

Definition at line 390 of file mathadd.c.

double* dblp_init	(	double *	v,
		int	n,
		double	val
	)

Parameters:

	v	- if NULL, own memory is allocated
	n	- length(v)
	val	- set v[i]=val for all i=0,...,n-1

Returns:: v

Definition at line 376 of file mathadd.c.

double dblp_max	(	double *	v,
		int	n,
		int *	idx
	)

find max element in vector.

Parameters:

	v	vector of length n
	idx	the index in v where v[i] is max

Returns:: v[i]

Definition at line 331 of file mathadd.c.

double dblp_mean	(	double *	v,
		int	n
	)

Definition at line 287 of file mathadd.c.

double dblp_min	(	double *	v,
		int	n,
		int *	idx
	)

find minimum element in vector.

Parameters:

	v	vector of length n
	idx	the index in v where v[i] is minimal

Returns:: v[i]

Definition at line 311 of file mathadd.c.

void dblp_minus_scalar	(	double *	v,
		int	n,
		double	val
	)

remove a scalar from all values in a vector.

Definition at line 364 of file mathadd.c.

void dblp_print	(	double *	v,
		int	n
	)

Definition at line 280 of file mathadd.c.

void dblp_print_int	(	int *	v,
		int	n
	)

Definition at line 296 of file mathadd.c.

void dblp_shuffle_int	(	int *	permut,
		int	n
	)

create a random permutation of the elements in permut. This is crude and simple, the function grabs n pairs of indices and swaps them.

Definition at line 351 of file mathadd.c.

void dblpp_add_dblpp	(	double **	m1,
		const double **	m2,
		int	N,
		int	n
	)

add matrix m2 to matrix m1 (must be of equal dimensions

Definition at line 577 of file mathadd.c.

void dblpp_add_scalar	(	double **	m,
		int	N,
		int	n,
		double	s
	)

Definition at line 639 of file mathadd.c.

void dblpp_copy	(	const double **	src,
		double **	dest,
		int	N,
		int	M
	)

copy matrix src to dest with dimensions N,M

Definition at line 619 of file mathadd.c.

double** dblpp_delcol	(	double **	m,
		int	N,
		int	n,
		int	col
	)

Delete a column in a matrix. Memory remains allocated and everything is moved (deleted column sits at index n). Index runs from 0,...,n-1

Parameters:

	m	- matrix
	N	- num of rows
	n	- num of cols
	col-	num of col to delete

Definition at line 492 of file mathadd.c.

double** dblpp_delrow	(	double **	m,
		int	N,
		int	n,
		int	row
	)

Delete a row in a matrix. Memory remains allocated and the row pointer is moved to the end of the matrix. Index runs from 0,...,N-1

Parameters:

	m	- matrix
	N	- num of rows
	n	- num of cols
	row-	num of row to delete

Definition at line 439 of file mathadd.c.

void dblpp_divide_scalar	(	double **	m,
		int	N,
		int	n,
		double	s
	)

divide all entries in m by s

Definition at line 630 of file mathadd.c.

void dblpp_dottimes_dblpp	(	double **	m1,
		const double **	m2,
		int	N,
		int	M
	)

MatLab's M1.*M2, which is M1[i][j] = M1[i][j]*M2[i][j]; That is, m1 is overwritten with the result from the operation

Parameters:

	m1,m2
	N,M	dimensions of m1 and m2

Definition at line 607 of file mathadd.c.

void dblpp_free	(	double **	m,
		int	N
	)

free matrix memory

Definition at line 662 of file mathadd.c.

double** dblpp_init	(	int	N,
		int	M
	)

return a 0-initialized matrix of dimension NxM

Definition at line 453 of file mathadd.c.

int** dblpp_init_int	(	int	N,
		int	M
	)

return a 0-initialized integer matrix of dimension NxM

Definition at line 468 of file mathadd.c.

double dblpp_max	(	const double **	m,
		int	N,
		int	n,
		int *	i1,
		int *	i2
	)

Get maximum entry from matrix. Set indices accordingly.

Parameters:

	m,N,n	- Nxn matrix
	i1,i2	- pointer to indices of max-element. If NULL, ignored.

Definition at line 536 of file mathadd.c.

double dblpp_min	(	const double **	m,
		int	N,
		int	n,
		int *	i1,
		int *	i2
	)

Get minimum entry from matrix. Set indices accordingly.

Parameters:

	m,N,n	- Nxn matrix
	i1,i2	- pointer to indices of min-element. If NULL, ignored.

Definition at line 510 of file mathadd.c.

void dblpp_mul_scalar	(	double **	m,
		int	N,
		int	n,
		double	s
	)

multiply all entries in m by s

Definition at line 650 of file mathadd.c.

void dblpp_normalize_by_max	(	double **	m,
		int	M,
		int	N
	)

Normalizes matrix by its maximum value:

$\hat{M} = \frac{1}{\mbox{max}(M)} M$

Definition at line 425 of file mathadd.c.

void dblpp_print	(	const double **	m,
		int	N,
		int	n
	)

print a matrix.

Definition at line 561 of file mathadd.c.

double** dblpp_rand	(	double **	m,
		int	N,
		int	M,
		double	lower,
		double	upper
	)

fills m with uniformely drawn random values from [lower, upper].

Definition at line 405 of file mathadd.c.

void dblpp_sub_dblpp	(	double **	dest,
		const double **	src,
		int	N,
		int	n
	)

subtract matrix src from matrix dest (must be of equal dimensions). result is written to dest.

Definition at line 590 of file mathadd.c.

double drawsample_nearest_neighbour	(	const double *	v,
		int	n,
		double	x
	)

Draw a sample from a discrete distribution (nearest neighbour).

Parameters:

	v,n	the distribution as a funciton of [0,...,n]
	x	a real value from the interval [0,...,n]

Returns:: v(x) by nn-interpolation

Definition at line 701 of file mathadd.c.

Complex* expand_polynomial_from_roots	(	const Complex *	roots,
		int	n,
		Complex *	coeffs
	)

expand a polynomial given in root-form

$p(x) = x_0(x-x_1)(x-x_2)\cdots (x-x_n)$

to find the coefficients a_0, ..., a_n of

$p(x) = a_0 + a_1 x_1 + \cdots + a_n x_n$

Parameters:

	roots	x_0,...,x_n
	coeffs	n+1 numbers to hold the resulting coefficients or ALLOC_IN_FCT

Definition at line 1006 of file mathadd.c.

void fft	(	double *	data,
		unsigned long	nn,
		int	isign
	)

1D Fourier transform (FFT). Taken from Numerical Recipes in C.

Parameters:

	data	- array to be tranformed (input/output); for input, is assumed to be complex, i.e. [ real, imag, real, imag, ... ] data contains nn complex numbers and 2*nn entries.
	nn	- must be a power of two, not checked for!; length(data)=2*nn
	isign	- 1: forward; -1: ifft;

Returns:: data is now the FT in complex numbers

Definition at line 827 of file mathadd.c.

double* flip_array	(	double *	v,
		int	n
	)

Definition at line 804 of file mathadd.c.

double gaussian	(	double	x,
		double	sigma,
		double	mu
	)

$G(x) = \frac{1}{\sigma\sqrt{2\pi}} \exp{\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)}$

Definition at line 975 of file mathadd.c.

double glog	(	double	v,
		int	b
	)

Definition at line 116 of file mathadd.c.

int iremainder	(	double	x,
		double	y
	)

computes remainder of x/y using $r(x,y) = \left\lfloor x - y\left\lfloor \frac{x}{y}\right\rfloor \right\rfloor$

Definition at line 958 of file mathadd.c.

double* lininterp	(	const double *	x1,
		const double *	y1,
		int	n1,
		const double *	x2,
		double *	y2,
		int	n2
	)

performs linear interpolation for the values x2, given x1 and y1. A pointer to the interpolated values y2 is returned. The x2 must ly within the x1, the x1 must be increasing in magnitude.

Definition at line 254 of file mathadd.c.

int* linspace	(	int	first,
		int	last
	)

same as first:last in matlab. Data ist allocated in the function and needs to be freed by the caller.

Definition at line 236 of file mathadd.c.

double* linspace_dbl	(	double	first,
		double	last,
		double	step,
		double *	v,
		int *	n
	)

same as first:step:last in matlab. A sequence first, first+step, first+(2*step), ... ,last is computed. The length of this sequence is $n=\lfloor \frac{last-first}{step} \rfloor+1$

Parameters:

v

either enough free allocated space, or ALLOC_IN_FCT (NULL)

data ist allocated in the function and needs to be freed by the caller.

n

- number of doubles in v (return value)

Definition at line 218 of file mathadd.c.

double mad	(	const double *	data,
		int	n
	)

Definition at line 121 of file mathadd.c.

double maxel	(	double *	v,
		int	n
	)

Definition at line 163 of file mathadd.c.

int maxeli	(	int *	v,
		int	n
	)

Definition at line 171 of file mathadd.c.

int next_pow2 ( int n )

return min_k( 2^k | 2^k>n ).

Definition at line 947 of file mathadd.c.

double* resample_gsl	(	const double *	s,
		int	n,
		int	newn,
		double *	news,
		const gsl_interp_type *	method
	)

Resample a vector to match a new length using GSL's interpolation options:

gsl_interp_linear
gsl_interp_polynomial
gsl_interp_cspline
gsl_interp_cspline_periodic
gsl_interp_akima
gsl_interp_akima_periodic

Assume that s is from [0,...,n] and resample, such that the new x is running from [0,...,newn] where y[newn]=y_old[n].

Parameters:

	s,n	the original vector
	newn	the new length of the vector
	news	caller-allocated memory of at least length newn (if NULL, the function allocates own memory)
	method	one of GSL interpolation types (see above)

Returns:: resampled vector in news

Definition at line 774 of file mathadd.c.

double* resample_linear	(	const double *	s,
		int	n,
		int	newn,
		double *	news
	)

Resample a vector to match a new length (linear interpolation).

Parameters:

	s,n	the original vector
	newn	the new length of the vector
	news	caller-allocated memory of at least length newn (if NULL, the function allocates own memory)

Returns:: resampled vector in news

See also:: drawsample_linear()

Definition at line 752 of file mathadd.c.

double* resample_nearest_neighbour	(	const double *	s,
		int	n,
		int	newn,
		double *	news
	)

Resample a vector to match a new length (NN-interpolation). Assume that s is from [0,...,n] and resample, such that the new x is running from [0,...,newn] where y[newn]=y_old[n].

Parameters:

	s,n	the original vector
	newn	the new length of the vector
	news	caller-allocated memory of at least length newn (if NULL, the function allocates own memory)

Returns:: resampled vector in news

See also:: drawsample_nearest_neighbour()

Definition at line 728 of file mathadd.c.

double rmse	(	const double *	r,
		const double *	d,
		int	n
	)

$RMSE = \sqrt{ \frac{1}{\#r} \sum{ (r-d)^2)}}$

Definition at line 74 of file mathadd.c.

double* sampled_line	(	double *	ntimes,
		int	n,
		double	start,
		double	end
	)

Definition at line 198 of file mathadd.c.

void scalar_minus_dblpp	(	double	scalar,
		double **	m,
		int	N,
		int	M
	)

Computes: m[i][j] = scalar-m[i][j]

Definition at line 983 of file mathadd.c.

int sgn ( int x )

signum function

Definition at line 675 of file mathadd.c.

double* sigext_smooth	(	double *	data,
		int	ns,
		int	n
	)

 [1 2 3 - - - - -] -> [1 1 1 2 3 3 3 3]

Definition at line 930 of file mathadd.c.

double* sigext_sym	(	double *	data,
		int	ns,
		int	n
	)

 [1 2 3 - - - - -] -> [2 1 1 2 3 3 2 1]

Definition at line 914 of file mathadd.c.

double* sigext_zeros	(	double *	data,
		int	ns,
		int	n
	)

 [1 2 3 - - -] -> [0 1 2 3 0 0]

Definition at line 889 of file mathadd.c.

double* sigext_zerosr	(	double *	data,
		int	ns,
		int	n
	)

 [1 2 3 - - -] -> [1 2 3 0 0 0]

Definition at line 906 of file mathadd.c.

double snr	(	const double *	r,
		const double *	d,
		int	n
	)

$SNR = 10\log_{10} \frac{\sum{r^2}}{\sum{(r-d)^2}}$

Definition at line 85 of file mathadd.c.

void swap2d	(	double *	v1,
		double *	v2
	)

Definition at line 687 of file mathadd.c.

void swap2i	(	int *	v1,
		int *	v2
	)

Definition at line 680 of file mathadd.c.

double vnorm	(	const double *	v,
		int	n,
		int	p
	)

Definition at line 153 of file mathadd.c.

double weighted_median_from_unsorted	(	const double *	d,
		const double *	w,
		int	n
	)

Weighted Median computation. Formula:

$WM = y_{(k)}\qquad k = \max\left\{h:\sum_{i=h}^n w_{(i)} \ge \frac{1}{2}\sum_{i=1}^{n} w_i\right\}$

Parameters:

	d	- data
	w	- corresponding weights (>=0)

Definition at line 33 of file mathadd.c.

src/mathadd.h File Reference

Defines

Functions

Detailed Description

Define Documentation

Function Documentation