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# N-tuples

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'`

## The ntuple struct

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;

## Creating ntuples

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.

## Opening an existing ntuple 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.

## Writing ntuples

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`

## Reading ntuples

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

## Closing an ntuple file

Function: int gsl_ntuple_close (gsl_ntuple * ntuple)
  This function closes the ntuple file ntuple and frees its associated allocated memory.

## Histogramming ntuple values

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.

## Example programs

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.

## References and Further Reading

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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