Two Field Histograms

The function histograms_2d() records two dimensional histograms of pairs of fields. The file parameters.h contains an array that lists the pairs for which these histograms are to be calculated, as well as two parameters giving the number of bins to use in each direction. The basic structure of this function is similar to histograms(). The minimum and maximum value used in each histogram are given by the parameters histogram2d_min and histogram2d_max or, if these are equal, set dynamically to the minimum and maximum value of each field at that time. Next the bin values are fixed in a two dimensional array between those limiting values. Then the number of grid points in each square of that array is counted. The file histogram2dtimes_ext is similar to histogramtimes from the histogram() function except that for each histogram the file now lists the minimum value of the first field, the bin spacing of the first field, and then the minimum value and bin spacing of the second field. The files histogram2d$<$field1_number$>$_$<$field2_number$>$_ext lists the bin frequencies in a single column. They should be read in the usual C array order. In other words if the histogram has $10$ bins in the second field direction then the first $10$ frequencies represent increasing values of the second field with the first field at its minimum, the next $10$ represent increasing values of the second field with the first field at its next highest value, and so forth.