}
-struct histogram *
-histogram_create (double bin_width, double min, double max)
+static
+double get_slack (double limit, double half_bin_width, int *n_half_bins)
{
- int bins;
- struct histogram *h = xmalloc (sizeof *h);
- struct statistic *stat = &h->parent;
+ double ipart, remainder;
+
+ assert (half_bin_width > 0);
+
+ remainder = modf (limit / half_bin_width, &ipart);
+
+ /* In C modf and % behave in an unexpected (to me at any rate) manner
+ when presented with a negative value
+
+ 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.
+ */
+static int
+adjust_bin_ranges (double bin_width, double min, double max, double *adj_min, double *adj_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;
- /* -1 if the lower end of the range contains more unused space
- than the upper end.
- +1 otherwise. */
- short sparse_end = 0;
-
- double ul, ll;
- double lower_remainder = fabs (modf (min / half_bin_width, &ll));
- double upper_remainder = fabs (modf (max / half_bin_width, &ul));
+ double lower_slack = get_slack (min, half_bin_width, &lower_limit);
+ double upper_slack = -get_slack (max, half_bin_width, &upper_limit);
+ assert (max > min);
- if (max == min)
+ /* 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)
{
- msg (MW, _("Not creating histogram because the data contains less than 2 distinct values"));
- free (h);
- return NULL;
+ lower_limit--;
+ lower_slack += half_bin_width;
}
-
- assert (max > min);
-
- lower_limit = ll;
-
- /* If the minimum value is not aligned on a half bin width,
- then the lower bound must be extended so that the histogram range includes it. */
- if (lower_remainder > 0)
- lower_limit--;
+ assert (lower_limit * half_bin_width <= min);
/* However, the upper bound must be extended regardless, because histogram bins
- span the range [lower, upper) */
- upper_limit = ul + 1;
-
- /* So, in the case of the maximum value coinciding with a half bin width,
- the upper end will be the sparse end (because is got extended by a complete
- half bin width). In other cases, it depends which got the bigger extension. */
- if (upper_remainder == 0)
- sparse_end = +1;
- else
- sparse_end = lower_remainder < upper_remainder ? -1 : +1;
+ span the range [lower, upper). In other words, the upper bound must be
+ greater than max.
+ */
+ upper_limit++;;
+ upper_slack += half_bin_width;
+ assert (upper_limit * half_bin_width > max);
/* The range must be an EVEN number of half bin_widths */
if ( (upper_limit - lower_limit) % 2)
{
/* Extend the range at the end which gives the least unused space */
- if (sparse_end == +1)
- lower_limit--;
+ if (upper_slack > lower_slack)
+ {
+ lower_limit--;
+ lower_slack += half_bin_width;
+ }
else
- upper_limit++;
-
- /* Now the other end has more space */
- sparse_end *= -1;
+ {
+ upper_limit++;
+ upper_slack += half_bin_width;
+ }
}
/* But the range should be aligned to an ODD number of
*/
if ( lower_limit % 2 == 0)
{
- /* Shift the range away from the sparse end, EXCEPT if that is the upper end,
- and it was extended to prevent the maximum value from getting lost */
- if (sparse_end == +1 && upper_remainder > 0)
+ /* 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)
{
+ 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
{
+ 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;
}
}
- bins = (upper_limit - lower_limit) / 2.0;
- /* Force the number of bins to lie in a sensible range.
- FIXME: We should redo the above calculations if this happens! */
- if (bins > 25)
- bins = 25;
+ /* 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)
+ {
+ upper_slack -= 2 * half_bin_width;
+ upper_limit -=2;
+ }
+
+ if (lower_slack >= 2 * half_bin_width)
+ {
+ lower_slack -= 2 * half_bin_width;
+ lower_limit +=2;
+ }
+
+ *adj_min = lower_limit * half_bin_width;
+ *adj_max = upper_limit * half_bin_width;
+
+ assert (*adj_max > max);
+ assert (*adj_min <= min);
+
+ return (upper_limit - lower_limit) / 2.0;
+}
+
+
+
+struct histogram *
+histogram_create (double bin_width, double min, double max)
+{
+ const int MAX_BINS = 25;
+ struct histogram *h;
+ struct statistic *stat;
+ int bins;
+ double adjusted_min, adjusted_max;
+
+ if (max == min)
+ {
+ msg (MW, _("Not creating histogram because the data contains less than 2 distinct values"));
+ return NULL;
+ }
+
+ assert (bin_width > 0);
+
+ bin_width = chart_rounded_tick (bin_width);
+ bins = adjust_bin_ranges (bin_width, min, max, &adjusted_min, &adjusted_max);
+ /* Force the number of bins to lie in a sensible range. */
+ if (bins > MAX_BINS)
+ {
+ bin_width = chart_rounded_tick ((max - min) / (double) (MAX_BINS - 1));
+ bins = adjust_bin_ranges (bin_width,
+ min, max, &adjusted_min, &adjusted_max);
+ }
+
+ /* Can this ever happen? */
if (bins < 1)
bins = 1;
+ h = xmalloc (sizeof *h);
+
h->gsl_hist = gsl_histogram_alloc (bins);
- gsl_histogram_set_ranges_uniform (h->gsl_hist,
- lower_limit * half_bin_width,
- upper_limit * half_bin_width);
+ gsl_histogram_set_ranges_uniform (h->gsl_hist, adjusted_min, adjusted_max);
+ stat = &h->parent;
stat->accumulate = acc;
stat->destroy = destroy;
projects / pspp / blobdiff