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This chapter describes functions for creating and manipulating
**ntuples**, sets of values associated with events. The ntuples
are stored in files. Their values can be extracted in any combination
and **booked** in an histogram using a selection function.

The values to be stored are held in a user-defined data structure, and an ntuple is created associating this data structure with a file. The values are then written to the file (normally inside a loop) using the ntuple functions described below.

A histogram can be created from ntuple data by providing a selection function and a value function. The selection function specifies whether an event should be included in the subset to be analyzed or not. The value function computes the entry to be added to the histogram entry for each event.

All the ntuple functions are defined in the header file
``gsl_ntuple.h'`

Ntuples are manipulated using the `gsl_ntuple`

struct. This struct
contains information on the file where the ntuple data is stored, a
pointer to the current ntuple data row and the size of the user-defined
ntuple data struct.

typedef struct { FILE * file; void * ntuple_data; size_t size; } gsl_ntuple;

__Function:__gsl_ntuple ***gsl_ntuple_create***(char **`filename`, void *`ntuple_data`, size_t`size`)-
This function creates a new write-only ntuple file
`filename`for ntuples of size`size`and returns a pointer to the newly created ntuple struct. Any existing file with the same name is truncated to zero length and overwritten. A pointer to memory for the current ntuple row`ntuple_data`must be supplied -- this is used to copy ntuples in and out of the file.

__Function:__gsl_ntuple ***gsl_ntuple_open***(char **`filename`, void *`ntuple_data`, size_t`size`)-
This function opens an existing ntuple file
`filename`for reading and returns a pointer to a corresponding ntuple struct. The ntuples in the file must have size`size`. A pointer to memory for the current ntuple row`ntuple_data`must be supplied -- this is used to copy ntuples in and out of the file.

__Function:__int**gsl_ntuple_write***(gsl_ntuple **`ntuple`)-
This function writes the current ntuple
`ntuple->ntuple_data`of size`ntuple->size`to the corresponding file.

__Function:__int**gsl_ntuple_bookdata***(gsl_ntuple **`ntuple`)-
This function is a synonym for
`gsl_ntuple_write`

__Function:__int**gsl_ntuple_read***(gsl_ntuple **`ntuple`)-
This function reads the current row of the ntuple file for
`ntuple`and stores the values in`ntuple->data`

__Function:__int**gsl_ntuple_close***(gsl_ntuple **`ntuple`)-
This function closes the ntuple file
`ntuple`and frees its associated allocated memory.

Once an ntuple has been created its contents can be histogrammed in
various ways using the function `gsl_ntuple_project`

. Two
user-defined functions must be provided, a function to select events and
a function to compute scalar values. The selection function and the
value function both accept the ntuple row as a first argument and other
parameters as a second argument.

The **selection function** determines which ntuple rows are selected
for histogramming. It is defined by the following struct,

typedef struct { int (* function) (void * ntuple_data, void * params); void * params; } gsl_ntuple_select_fn;

The struct component `function` should return a non-zero value for
each ntuple row that is to be included in the histogram.

The **value function** computes scalar values for those ntuple rows
selected by the selection function,

typedef struct { double (* function) (void * ntuple_data, void * params); void * params; } gsl_ntuple_value_fn;

In this case the struct component `function` should return the value
to be added to the histogram for the ntuple row.

__Function:__int**gsl_ntuple_project***(gsl_histogram **`h`, gsl_ntuple *`ntuple`, gsl_ntuple_value_fn *`value_func`, gsl_ntuple_select_fn *`select_func`)-
This function updates the histogram
`h`from the ntuple`ntuple`using the functions`value_func`and`select_func`. For each ntuple row where the selection function`select_func`is non-zero the corresponding value of that row is computed using the function`value_func`and added to the histogram. Those ntuple rows where`select_func`returns zero are ignored. New entries are added to the histogram, so subsequent calls can be used to accumulate further data in the same histogram.

The following example programs demonstrate the use of ntuples in
managing a large dataset. The first program creates a set of 100,000
simulated "events", each with 3 associated values (x,y,z). These
are generated from a gaussian distribution with unit variance, for
demonstration purposes, and written to the ntuple file ``test.dat'`.

#include <config.h> #include <gsl/gsl_ntuple.h> #include <gsl/gsl_rng.h> #include <gsl/gsl_randist.h> struct data { double x; double y; double z; }; int main (void) { const gsl_rng_type * T; gsl_rng * r; struct data ntuple_row; int i; gsl_ntuple *ntuple = gsl_ntuple_create ("test.dat", &ntuple_row, sizeof (ntuple_row)); gsl_rng_env_setup(); T = gsl_rng_default; r = gsl_rng_alloc (T); for (i = 0; i < 10000; i++) { ntuple_row.x = gsl_ran_ugaussian (r); ntuple_row.y = gsl_ran_ugaussian (r); ntuple_row.z = gsl_ran_ugaussian (r); gsl_ntuple_write (ntuple); } gsl_ntuple_close(ntuple); return 0; }

The next program analyses the ntuple data in the file ``test.dat'`.
The analysis procedure is to compute the squared-magnitude of each
event, E^2=x^2+y^2+z^2, and select only those which exceed a
lower limit of 1.5. The selected events are then histogrammed using
their E^2 values.

#include <config.h> #include <math.h> #include <gsl/gsl_ntuple.h> #include <gsl/gsl_histogram.h> struct data { double x; double y; double z; }; int sel_func (void *ntuple_data, void *params); double val_func (void *ntuple_data, void *params); int main (void) { struct data ntuple_row; int i; gsl_ntuple *ntuple = gsl_ntuple_open ("test.dat", &ntuple_row, sizeof (ntuple_row)); double lower = 1.5; gsl_ntuple_select_fn S; gsl_ntuple_value_fn V; gsl_histogram *h = gsl_histogram_alloc (100); gsl_histogram_set_ranges_uniform(h, 0.0, 10.0); S.function = &sel_func; S.params = &lower; V.function = &val_func; V.params = 0; gsl_ntuple_project (h, ntuple, &V, &S); gsl_histogram_fprintf (stdout, h, "%f", "%f"); gsl_histogram_free (h); gsl_ntuple_close (ntuple); return 0; } int sel_func (void *ntuple_data, void *params) { double x, y, z, E, scale; scale = *(double *) params; x = ((struct data *) ntuple_data)->x; y = ((struct data *) ntuple_data)->y; z = ((struct data *) ntuple_data)->z; E2 = x * x + y * y + z * z; return E2 > scale; } double val_func (void *ntuple_data, void *params) { double x, y, z; x = ((struct data *) ntuple_data)->x; y = ((struct data *) ntuple_data)->y; z = ((struct data *) ntuple_data)->z; return x * x + y * y + z * z; }

The following plot shows the distribution of the selected events. Note the cut-off at the lower bound.

Further information on the use of ntuples can be found in the documentation for the CERN packages PAW and HBOOK (available online).

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