Some basic statistical functions

Modules

• Calculate moments (mean, var, kurtosis) for the data in a gsl_vector.
• Calculate moments such as the covariance matrix

Functions

• double * apop_vector_percentiles (gsl_vector *data, char rounding)
• void apop_vector_normalize (gsl_vector *in, gsl_vector **out, const char normalization_type)
• void apop_matrix_normalize (gsl_matrix *data, const char row_or_col, const char normalization)

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Detailed Description

Many of these are just one-line convenience functions for finding moments and normalizing matrices.

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Function Documentation

void apop_matrix_normalize	(	gsl_matrix *	data,
		const char	row_or_col,
		const char	normalization
	)

Normalize each row or column in the given matrix, one by one.

Basically just a convenience fn to iterate through the columns and run apop_vector_normalize for you.

Parameters:

	data	The data set to normalize.
	row_or_col	Either 'r' or 'c'.
	normalization	see apop_vector_normalize.

void apop_vector_normalize	(	gsl_vector *	in,
		gsl_vector **	out,
		const char	normalization_type
	)

This function will normalize a vector, either such that it has mean zero and variance one, or such that it ranges between zero and one, or sums to one.

Parameters:

	in	A gsl_vector which you have already allocated and filled. NULL input gives NULL output. (No default)
	out	If normalizing in place, NULL. If not, the address of a gsl_vector. Do not allocate. (default = NULL.)
	normalization_type	'p': normalized vector will sum to one. E.g., start with a set of observations in bins, end with the percentage of observations in each bin. (the default) 'r': normalized vector will range between zero and one. Replace each X with (X-min) / (max - min). 's': normalized vector will have mean zero and variance one. Replace each X with , where is the sample standard deviation. 'm': normalize to mean zero: Replace each X with

Example

#include <apop.h>

int main(void){
gsl_vector  *in, *out;

in = gsl_vector_calloc(3);
gsl_vector_set(in, 1, 1);
gsl_vector_set(in, 2, 2);

printf("The orignal vector:\n");
apop_vector_show(in);

apop_vector_normalize(in, &out, 's');
printf("Standardized with mean zero and variance one:\n");
apop_vector_show(out);

apop_vector_normalize(in, &out, 'r');
printf("Normalized range with max one and min zero:\n");
apop_vector_show(out);

apop_vector_normalize(in, NULL, 'p');
printf("Normalized into percentages:\n");
apop_vector_show(in);
}

This function uses the Designated initializers syntax for inputs.

double* apop_vector_percentiles	(	gsl_vector *	data,
		char	rounding
	)

Returns a vector of size 101, where returned_vector[95] gives the value of the 95th percentile, for example. Returned_vector[100] is always the maximum value, and returned_vector[0] is always the min (regardless of rounding rule).

Parameters:

	data	a gsl_vector of data. (No default, must not be NULL.)
	rounding	This will either be 'u', 'd', or 'a'. Unless your data is exactly a multiple of 101, some percentiles will be ambiguous. If 'u', then round up (use the next highest value); if 'd' (or anything else), round down to the next lowest value; if 'a', take the mean of the two nearest points. If 'u' or 'a', then you can say "5% or more of the sample is below returned_vector[5]"; if 'd' or 'a', then you can say "5% or more of the sample is above returned_vector[5]". (Default = 'd'.)

This function uses the Designated initializers syntax for inputs.