#include <config.h>
#include "math/histogram.h"
-#include "math/decimal.h"
#include <gsl/gsl_histogram.h>
#include <math.h>
}
-static
-double get_slack (double limit, double half_bin_width, int *n_half_bins)
-{
- double ipart, remainder;
-
- assert (half_bin_width > 0);
-
- remainder = modf (limit / half_bin_width, &ipart);
+/* Find a bin width which is adapted to the scaling of the x axis
+In the example here, the binwidth is half of the tick interval.
- /* In C modf and % behave in an unexpected (to me at any rate) manner
- when presented with a negative value
+ binwidth
+ > <
+ |....+....+....+. .+....|
+ LOWER 1 2 3 N_TICKS
+ ^LOWDBL ^HIGHDBL
- For example, modf (-7.0 / 3.0) returns -2.0 R -0.3333
- */
-
-
- *n_half_bins = ipart;
-
- return remainder * half_bin_width;
-}
-
-
-/* This functions adjusts the upper and lower range of the histogram to make them fit BIN_WIDTH
- MIN and MAX are the lowest and highest data to be plotted in the histogram.
- ADJ_MIN and ADJ_MAX are locations of the adjusted values of MIN and MAX (the range will
- always be equal or slightly larger).
- Returns the number of bins.
-
- The "testing_assert" expressions in this function should be algebraically correct.
- However, due to floating point rounding they could fail, especially when small numbers
- are involved. In normal use, therefore, testing_assert does nothing.
- */
+This only works, when the min and max value for the histogram are adapted
+such that (max-min) is a multiple of the binwidth. Then the location of the
+first bin has to be aligned to the ticks.
+*/
static int
-adjust_bin_ranges (double bin_width, double min, double max, double *adj_min, double *adj_max)
+hist_find_pretty_no_of_bins(double bin_width_in, double min, double max,
+ double *adjusted_min, double *adjusted_max)
{
- const double half_bin_width = bin_width / 2.0;
-
- /* The lower and upper limits of the histogram, in units of half
- bin widths */
- int lower_limit, upper_limit;
-
- double lower_slack = get_slack (min, half_bin_width, &lower_limit);
- double upper_slack = -get_slack (max, half_bin_width, &upper_limit);
+ double lower, interval;
+ int n_ticks;
+ double binwidth;
+ int nbins;
- testing_assert (max > min);
+ chart_get_scale (max, min, &lower, &interval, &n_ticks);
- /* If min is negative, then lower_slack may be less than zero.
- In this case, the lower bound must be extended in the negative direction
- so that it is less than OR EQUAL to min.
- */
- if (lower_slack < 0)
+ if (bin_width_in >= 2 * interval)
{
- lower_limit--;
- lower_slack += half_bin_width;
+ binwidth = floor(bin_width_in/interval) * interval;
+ *adjusted_min = lower;
}
- testing_assert (lower_limit * half_bin_width <= min);
-
- /* However, the upper bound must be extended regardless, because histogram bins
- span the range [lower, upper). In other words, the upper bound must be
- greater than max.
- */
- upper_limit++;;
- upper_slack += half_bin_width;
- testing_assert (upper_limit * half_bin_width > max);
-
- /* The range must be an EVEN number of half bin_widths */
- if ( (upper_limit - lower_limit) % 2)
+ else if (bin_width_in >= 1.5 * interval)
{
- /* Extend the range at the end which gives the least unused space */
- if (upper_slack > lower_slack)
- {
- lower_limit--;
- lower_slack += half_bin_width;
- }
+ binwidth = 1.5 * interval;
+ if (min < (lower + 0.5 * interval))
+ *adjusted_min = lower;
else
- {
- upper_limit++;
- upper_slack += half_bin_width;
- }
+ *adjusted_min = lower + 0.5 * interval;
}
-
- /* But the range should be aligned to an ODD number of
- half bin widths, so that the labels are aesthetically pleasing ones.
- Otherwise we are likely to get labels such as -3 -1 1 3 instead of -2 0 2 4
- */
- if ( lower_limit % 2 == 0)
+ else if (bin_width_in >= interval)
{
- /* If there is not enough slack at either end to perform a shift,
- then we must extend the range so that there is. We must extend
- by two half bin widths in order to preserve the EVEN condition
- established above. Also, we extend on the end with the least
- slack, in order to keep things as balanced as possible. */
- if ( upper_slack > lower_slack && upper_slack <= half_bin_width)
- {
- lower_limit -= 2;
- lower_slack += 2 * half_bin_width;
- }
-
- if (lower_slack > upper_slack && lower_slack < half_bin_width)
- {
- upper_limit += 2;
- upper_slack += 2 * half_bin_width;
- }
-
- if (upper_slack > lower_slack)
- {
- testing_assert (upper_slack > half_bin_width);
-
- /* Adjust the range to the left */
- lower_limit --;
- upper_limit --;
- upper_slack -= half_bin_width;
- lower_slack += half_bin_width;
- }
- else
- {
- testing_assert (lower_slack >= half_bin_width);
-
- /* Adjust the range to the right */
- lower_limit ++;
- upper_limit ++;
- lower_slack -= half_bin_width;
- upper_slack += half_bin_width;
- }
+ binwidth = interval;
+ *adjusted_min = lower;
}
-
- /* If there are any completely empty bins, then remove them,
- since empty bins don't really add much information to the histogram.
- */
- if (upper_slack > 2 * half_bin_width)
+ else if (bin_width_in >= (2.0/3.0 * interval))
{
- upper_slack -= 2 * half_bin_width;
- upper_limit -=2;
+ binwidth = (2.0/3.0 * interval);
+ if (min >= lower + binwidth)
+ *adjusted_min = lower + binwidth;
+ else
+ *adjusted_min = lower;
}
-
- if (lower_slack >= 2 * half_bin_width)
+ else
{
- lower_slack -= 2 * half_bin_width;
- lower_limit +=2;
+ int i;
+ for(i = 2; bin_width_in < interval/i; i++);
+ binwidth = interval/i;
+ *adjusted_min = floor((min - lower)/binwidth)*binwidth + lower;
}
- *adj_min = lower_limit * half_bin_width;
- *adj_max = upper_limit * half_bin_width;
-
- testing_assert (*adj_max > max);
- testing_assert (*adj_min <= min);
+ nbins = ceil((max-*adjusted_min)/binwidth);
+ *adjusted_max = nbins*binwidth + *adjusted_min;
- return (upper_limit - lower_limit) / 2.0;
+ return nbins;
}
-
struct histogram *
histogram_create (double bin_width_in, double min, double max)
{
- struct decimal bin_width;
- const int MAX_BINS = 25;
struct histogram *h;
struct statistic *stat;
int bins;
assert (bin_width_in > 0);
- chart_rounded_tick (bin_width_in, &bin_width);
- bins = adjust_bin_ranges (decimal_to_double (&bin_width),
- min, max, &adjusted_min, &adjusted_max);
-
- /* Force the number of bins to lie in a sensible range. */
- if (bins > MAX_BINS)
- {
- chart_rounded_tick ((max - min) / (double) (MAX_BINS - 1), &bin_width);
- bins = adjust_bin_ranges (decimal_to_double (&bin_width),
- min, max, &adjusted_min, &adjusted_max);
- }
-
- /* Can this ever happen? */
- if (bins < 1)
- bins = 1;
+ bins = hist_find_pretty_no_of_bins(bin_width_in, min, max, &adjusted_min, &adjusted_max);
h = xmalloc (sizeof *h);
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