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21.21 Resampling from 2D histograms
As in the onedimensional case, a twodimensional histogram made by counting events can be regarded as a measurement of a probability distribution. Allowing for statistical error, the height of each bin represents the probability of an event where (x,y) falls in the range of that bin. For a twodimensional histogram the probability distribution takes the form p(x,y) dx dy where, In this equation n_{ij} is the number of events in the bin which contains (x,y), A_{ij} is the area of the bin and N is the total number of events. The distribution of events within each bin is assumed to be uniform.
 Data Type: gsl_histogram2d_pdf

size_t nx, ny
This is the number of histogram bins used to approximate the probability distribution function in the x and y directions.

double * xrange
The ranges of the bins in the xdirection are stored in an array of nx + 1 elements pointed to by xrange.

double * yrange
The ranges of the bins in the ydirection are stored in an array of ny + 1 pointed to by yrange.

double * sum
The cumulative probability for the bins is stored in an array of nx*ny elements pointed to by sum.

The following functions allow you to create a gsl_histogram2d_pdf
struct which represents a two dimensional probability distribution and
generate random samples from it.
 Function: gsl_histogram2d_pdf * gsl_histogram2d_pdf_alloc (size_t nx, size_t ny)
This function allocates memory for a twodimensional probability distribution of size nxbyny and returns a pointer to a newly initialized
gsl_histogram2d_pdf
struct. If insufficient memory is available a null pointer is returned and the error handler is invoked with an error code ofGSL_ENOMEM
.
 Function: int gsl_histogram2d_pdf_init (gsl_histogram2d_pdf * p, const gsl_histogram2d * h)
This function initializes the twodimensional probability distribution calculated p from 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.
 Function: void gsl_histogram2d_pdf_free (gsl_histogram2d_pdf * p)
This function frees the twodimensional probability distribution function p and all of the memory associated with it.
 Function: int gsl_histogram2d_pdf_sample (const gsl_histogram2d_pdf * p, double r1, double r2, double * x, double * y)
This function uses two uniform random numbers between zero and one, r1 and r2, to compute a single random sample from the twodimensional probability distribution p.
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