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Math::GSL::Histogram(3User Contributed Perl DocumentatiMath::GSL::Histogram(3)

NAME
Math::GSL::Histogram - Create and manipulate histograms of data

SYNOPSIS
use Math::GSL::Histogram qw/:all/;

my \$H = gsl_histogram_alloc(100);
gsl_histogram_set_ranges_uniform(\$H,0,101);
gsl_histogram_increment(\$H, -50 );  # ignored
gsl_histogram_increment(\$H, 70 );
gsl_histogram_increment(\$H, 85.2 );

my \$G = gsl_histogram_clone(\$H);
my \$value = gsl_histogram_get(\$G, 70);
my (\$max,\$min) = (gsl_histogram_min_val(\$H),	gsl_histogram_max_val(\$H) );
my \$sum = gsl_histogram_sum(\$H);

DESCRIPTION
Here is a list of all the functions included in this module :

"gsl_histogram_alloc(\$n)" - This	function allocates memory for a
histogram with \$n bins, and returns a pointer to	a newly	created
gsl_histogram struct. The bins and ranges are not initialized, and
should be prepared using	one of the range-setting functions below in
order to	make the histogram ready for use.
"gsl_histogram_calloc "
"gsl_histogram_calloc_uniform "
"gsl_histogram_free(\$h)"	- This function	frees the histogram \$h and all
of the memory associated	with it.
"gsl_histogram_increment(\$h, \$x)" - This	function updates the histogram
\$h by adding one	(1.0) to the bin whose range contains the coordinate
\$x. If \$x lies in the valid range of the	histogram then the function
returns zero to indicate	success. If \$x is less than the	lower limit of
the histogram then the function returns \$GSL_EDOM, and none of bins are
modified. Similarly, if the value of \$x is greater than or equal	to the
upper limit of the histogram then the function returns \$GSL_EDOM, and
none of the bins	are modified. The error	handler	is not called,
however,	since it is often necessary to compute histograms for a	small
range of	a larger dataset, ignoring the values outside the range	of
interest.
"gsl_histogram_accumulate(\$h, \$x, \$weight)" - This function is similar
to gsl_histogram_increment but increases	the value of the appropriate
bin in the histogram \$h by the floating-point number weight.
"gsl_histogram_find(\$h, \$x)" - This function finds the bin number which
covers the coordinate \$x	in the histogram \$h. The bin is	located	using
a binary	search.	The search includes an optimization for	histograms
with uniform range, and will return the correct bin immediately in this
case. If	\$x is found in the range of the	histogram then the function
returns the bin number and returns \$GSL_SUCCESS.	If \$x lies outside the
valid range of the histogram then the function returns \$GSL_EDOM	and
the error handler is invoked.
"gsl_histogram_get(\$h, \$i)" - This function returns the contents	of the
\$i-th bin of the	histogram \$h. If \$i lies outside the valid range of
indices for the histogram then the error	handler	is called with an
error code of GSL_EDOM and the function returns 0.
"gsl_histogram_get_range(\$h, \$i)" - This	function finds the upper and
lower range limits of the \$i-th bin of the histogram \$h.	If the index
\$i is valid then	the corresponding range	limits are returned after the
0 in this order : lower and then	upper. The lower limit is inclusive
(i.e. events with this coordinate are included in the bin) and the
upper limit is exclusive	(i.e. events with the coordinate of the	upper
limit are excluded and fall in the neighboring higher bin, if it
exists).	The function returns 0 to indicate success. If i lies outside
the valid range of indices for the histogram then the error handler is
called and the function returns an error	code of	\$GSL_EDOM.
"gsl_histogram_max(\$h)" - This function returns the maximum upper limit
of the histogram	\$h. It provides	a way of determining this value
without accessing the gsl_histogram struct directly.
"gsl_histogram_min(\$h)" - This function returns the minimum lower range
limit of	the histogram \$h. It provides a	way of determining this	value
without accessing the gsl_histogram struct directly.
"gsl_histogram_bins(\$h)"	- This function	returns	the number of bins of
the histogram \$h	limit. It provides a way of determining	this value
without accessing the gsl_histogram struct directly.
"gsl_histogram_reset(\$h)" - This	function resets	all the	bins in	the
histogram \$h to zero.
"gsl_histogram_calloc_range"
"gsl_histogram_set_ranges(\$h, \$range, \$size)" - This function sets the
ranges of the existing histogram	\$h using the array \$range of size
\$size. The values of the	histogram bins are reset to zero. The \$range
array should contain the	desired	bin limits. The	ranges can be
arbitrary, subject to the restriction that they are monotonically
increasing. Note	that the size of the \$range array should be defined to
be one element bigger than the number of	bins. The additional element
is required for the upper value of the final bin.
"gsl_histogram_set_ranges_uniform(\$h, \$xmin, \$xmax)" - This function
sets the	ranges of the existing histogram \$h to cover the range \$xmin
to \$xmax	uniformly. The values of the histogram bins are	reset to zero.
The bin ranges are shown	in the table below,
bin corresponds to xmin <= x < xmin +	d
bin corresponds to xmin + d <= x < xmin + 2 d
......
bin[n-1]	corresponds to xmin + (n-1)d <=	x < xmax

where d is the bin spacing, d = (xmax-xmin)/n.

"gsl_histogram_memcpy(\$dest, \$src)" - This function copies the
histogram \$src into the pre-existing histogram \$dest, making \$dest into
an exact	copy of	\$src. The two histograms must be of the	same size.
"gsl_histogram_clone(\$src)" - This function returns a pointer to	a
newly created histogram which is	an exact copy of the histogram \$src.
"gsl_histogram_max_val(\$h)" - This function returns the maximum value
contained in the	histogram bins.
"gsl_histogram_max_bin(\$h)" - This function returns the index of	the
bin containing the maximum value. In the	case where several bins
contain the same	maximum	value the smallest index is returned.
"gsl_histogram_min_val(\$h)" - This function returns the minimum value
contained in the	histogram bins.
"gsl_histogram_min_bin(\$h)" - This function returns the index of	the
bin containing the minimum value. In the	case where several bins
contain the same	maximum	value the smallest index is returned.
"gsl_histogram_equal_bins_p(\$h1,	\$h2)" -	This function returns 1	if the
all of the individual bin ranges	of the two histograms are identical,
and 0 otherwise.
"gsl_histogram_add(\$h1, \$h2)" - This function adds the contents of the
bins in histogram \$h2 to	the corresponding bins of histogram \$h1, i.e.
h'_1(i) = h_1(i)	+ h_2(i). The two histograms must have identical bin
ranges.
"gsl_histogram_sub(\$h1, \$h2)" - This function subtracts the contents of
the bins	in histogram \$h2 from the corresponding	bins of	histogram \$h1,
i.e. h'_1(i) = h_1(i) - h_2(i). The two histograms must have identical
bin ranges.
"gsl_histogram_mul(\$h1, \$h2)" - This function multiplies	the contents
of the bins of histogram	\$h1 by the contents of the corresponding bins
in histogram \$h2, i.e. h'_1(i) =	h_1(i) * h_2(i). The two histograms
must have identical bin ranges.
"gsl_histogram_div(\$h1, \$h2)" - This function divides the contents of
the bins	of histogram \$h1 by the	contents of the	corresponding bins in
histogram \$h2, i.e. h'_1(i) = h_1(i) / h_2(i). The two histograms must
have identical bin ranges.
"gsl_histogram_scale(\$h,	\$scale)" - This	function multiplies the
contents	of the bins of histogram \$h by the constant \$scale, i.e.
h'_1(i) = h_1(i)	* scale.
"gsl_histogram_shift(\$h,	\$offset)" - This function shifts the contents
of the bins of histogram	\$h by the constant \$offset, i.e. h'_1(i) =
h_1(i) +	offset.
"gsl_histogram_sigma(\$h)" - This	function returns the standard
deviation of the	histogrammed variable, where the histogram is regarded
as a probability	distribution. Negative bin values are ignored for the
purposes	of this	calculation. The accuracy of the result	is limited by
the bin width.
"gsl_histogram_mean(\$h)"	- This function	returns	the mean of the
histogrammed variable, where the	histogram is regarded as a probability
distribution. Negative bin values are ignored for the purposes of this
calculation. The	accuracy of the	result is limited by the bin width.
"gsl_histogram_sum(\$h)" - This function returns the sum of all bin
values. Negative	bin values are included	in the sum.
"gsl_histogram_fwrite(\$stream, \$h)" - This function writes the ranges
and bins	of the histogram \$h to the stream \$stream, which has been
opened by the gsl_fopen function	from the Math::GSL module, in binary
format. The return value	is 0 for success and \$GSL_EFAILED if there was
a problem writing to the	file. Since the	data is	written	in the native
binary format it	may not	be portable between different architectures.
"gsl_histogram_fread(\$stream, \$h)" - This function reads	into the
histogram \$h from the open stream \$stream, which	has been opened	by the
gsl_fopen function from the Math::GSL module,  in binary	format.	The
histogram \$h must be preallocated with the correct size since the
function	uses the number	of bins	in \$h to determine how many bytes to
read. The return	value is 0 for success and \$GSL_EFAILED	if there was a
problem reading from the	file. The data is assumed to have been written
in the native binary format on the same architecture.
"gsl_histogram_fprintf(\$stream, \$h, \$range_format, \$bin_format)"	- This
function	writes the ranges and bins of the histogram \$h line-by-line to
the stream \$stream (from	the gsl_fopen function from the	Math::GSL
module) using the format	specifiers \$range_format and \$bin_format.
These should be one of the %g, %e or %f formats for floating point
numbers.	The function returns 0 for success and \$GSL_EFAILED if there
was a problem writing to	the file. The histogram	output is formatted in
three columns, and the columns are separated by spaces, like this,
range range bin
range range bin
range range bin
....
range[n-1] range[n] bin[n-1]

The values of the ranges are	formatted using	range_format and the
value of the	bins are formatted using bin_format. Each line
contains the	lower and upper	limit of the range of the bins and the
value of the	bin itself. Since the upper limit of one bin is	the
lower limit of the next there is duplication	of these values
between lines but this allows the histogram to be manipulated with
line-oriented tools.

"gsl_histogram_fscanf(\$stream, \$h)" - This function reads formatted
data from the stream \$stream, which has been opened by the gsl_fopen
function	from the Math::GSL module, into	the histogram \$h. The data is
assumed to be in	the three-column format	used by	gsl_histogram_fprintf.
The histogram \$h	must be	preallocated with the correct length since the
function	uses the size of \$h to determine how many numbers to read. The
function	returns	0 for success and \$GSL_EFAILED if there	was a problem
reading from the	file.
"gsl_histogram_pdf_alloc(\$n)" - This function allocates memory for a
probability distribution	with \$n	bins and returns a pointer to a	newly
initialized gsl_histogram_pdf struct. If	insufficient memory is
available a null	pointer	is returned and	the error handler is invoked
with an error code of \$GSL_ENOMEM.
"gsl_histogram_pdf_init(\$p, \$h)"	- This function	initializes the
probability distribution	\$p with	the contents of	the histogram \$h. If
any of the bins of \$h are negative then the error handler is invoked
with an error code of \$GSL_EDOM because a probability distribution
cannot contain negative values.
"gsl_histogram_pdf_free(\$p)" - This function frees the probability
distribution function \$p	and all	of the memory associated with it.
"gsl_histogram_pdf_sample(\$p, \$r)" -	This function uses \$r, a
uniform random number between zero and one, to compute a	single random
sample from the probability distribution	\$p. The	algorithm used to
compute the sample s is given by	the following formula, s = range[i] +
delta * (range[i+1] - range[i]) where i is the index which satisfies
sum[i] <= r < sum[i+1] and delta	is (r -	sum[i])/(sum[i+1] - sum[i]).

EXAMPLES
The following example shows how	to create a histogram with logarithmic bins with ranges	[1,10),	[10,100) and [100,1000).

\$h = gsl_histogram_alloc (3);

# bin covers	the range 1 <= x < 10
# bin covers	the range 10 <=	x < 100
# bin covers	the range 100 <= x < 1000

\$range = [ 1.0,	10.0, 100.0, 1000.0 ];

gsl_histogram_set_ranges(\$h, \$range, 4);

AUTHORS
Jonathan	"Duke" Leto <jonathan@leto.net>	and Thierry Moisan
<thierry.moisan@gmail.com>