[Maxima-commits] [git] Maxima CAS branch master updated. branch-5_49-base-503-g328c0e804

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- Log -----------------------------------------------------------------
commit 328c0e8044a1bb7c711974f642be40d304a19169
Author: Robert Dodier <rob...@so...>
Date:   Sat May 9 15:14:16 2026 -0700

    histogram: correct bar height calculation for frequency = density,
    and scale bars by M/N where M is the number of data covered by bins
    and N is the total number of data, for frequency = relative and frequency = percent.
    
    Update the English-language documentation and put in a new example in rtest_statgraph.mac.

diff --git a/doc/info/descriptive.texi b/doc/info/descriptive.texi
index 6254264d9..aeb36572a 100644
--- a/doc/info/descriptive.texi
+++ b/doc/info/descriptive.texi
@@ -3364,10 +3364,30 @@ That is, the right endpoint of one interval is equal to the left endpoint of the
 
 @item
 @code{frequency} (default, @code{absolute}): indicates the scale of the vertical axis.
-Possible values are:  @code{absolute} (heights of bars add up to number of data),
-@code{relative} (heights of bars add up to 1),
-@code{percent} (heights of bars add up to 100),
-and @code{density} (total area of histogram is 1).
+In the following, let @math{M} be the number of data which fall into the bins specified by @code{nclasses},
+and let @math{N} be the total number of data.
+(When all data are covered by @code{nclasses}, @math{M} is equal to @math{N}.)
+Let @math{m[k]} be the number of data falling into the @math{k}'th bin,
+and let @math{w[k]} be the width of the @math{k}'th bin.
+Then the possible values of @code{frequency} are as follows.
+
+@itemize @bullet
+@item
+@code{absolute} Height of each bar is equal to @math{m[k]},
+                and the sum of all heights is @math{M}.
+
+@item
+@code{relative} Height of each bar is equal to @math{m[k]/N},
+                and the sum of all heights is @math{M/N}.
+
+@item
+@code{percent}  Height of each bar is equal to 100 times @math{m[k]/N},
+                and the sum of all heights is 100 times @math{M/N}.
+
+@item
+@code{density}  Height of each bar is equal to @math{m[k]/N/w[k]},
+                and the sum of all bar areas (width times height) is equal to @math{M/N}.
+@end itemize
 
 @item
 @code{htics} (default, @code{auto}): format of tic marks on the horizontal axis.
diff --git a/share/descriptive/descriptive.mac b/share/descriptive/descriptive.mac
index df5d74ea2..9e03e43b7 100644
--- a/share/descriptive/descriptive.mac
+++ b/share/descriptive/descriptive.mac
@@ -960,7 +960,7 @@ make_skyline (xx, yy, fill_color, fill_density) :=
             'points (skyline_points)]);
 
 histogram_description(m,[select]):=
-   block([fr,amp,scen,before,localopts,num_classes,v,lbels, my_fill_color, my_fill_density,
+   block([n_data,fr,amp,scen,before,localopts,num_classes,v,lbels, my_fill_color, my_fill_density,
           /* specific options */
           my_nclasses:10, my_frequency:'absolute, my_htics:'auto, histogram_bars, histogram_drawing],
       [before, localopts]: extract_options (select, 'nclasses, 'frequency, 'htics, 'fill_color, 'fill_density),
@@ -1039,13 +1039,15 @@ histogram_description(m,[select]):=
                  then my_nclasses: num_classes:
                         ceiling(1 + log(length(m)) / 0.6931471805599453), /* <-- log(2) */
                fr: float(continuous_freq(m,my_nclasses)),
+               n_data: length (m),
                if member(my_frequency, ['relative, 'percent])
-                 then fr: [first(fr), second(fr) / apply("+", second(fr))],
+                 then fr: [first(fr), second(fr) / n_data],
                if my_frequency = 'percent
                  then fr[2]: fr[2] * 100.0,
                amp: makelist(fr[1][i+1]-fr[1][i], i, 1, length(fr[1])-1),
                if my_frequency = 'density
-                 then fr: [first(fr), second(fr) / apply("+", second(fr) * amp)],
+                 then block ([listarith: true],
+                             fr: [first(fr), second(fr) / n_data / amp]),
 
                /* histogram tics */
                if my_htics = 'auto
diff --git a/share/descriptive/rtest_statgraph.mac b/share/descriptive/rtest_statgraph.mac
index bef784707..77168fcad 100644
--- a/share/descriptive/rtest_statgraph.mac
+++ b/share/descriptive/rtest_statgraph.mac
@@ -32,7 +32,8 @@
      "boxplot: Windspeed in knots from wind.data",
      "boxplot: Horizontal boxes",
      "histogram: pi digits from pidigits.data",
-     "histogram + explicit: Random data from normal distribution",
+     "histogram + explicit: Random data from normal distribution, uniform bins",
+     "histogram + explicit: Random data from normal distribution, nonuniform bins",
      "piechart: Digit frequencies in pi from pidigits.data",
      "scatterplot: 1-dimensional random data",
      "starplot: Two random samples"
@@ -130,13 +131,26 @@ block([m: 14, s: 2, s2],
   s2: random_normal(m, s, 1000),
   draw2d(
     grid   = true,
-    xrange = [5, 25],
-    title = title_cache ["histogram + explicit: Random data from normal distribution"],
+    title = title_cache ["histogram + explicit: Random data from normal distribution, uniform bins"],
     histogram_description(
       s2,
       nclasses     = 9,
       frequency    = density,
       fill_density = 0.5),
+    xrange = [5, 25],
+    explicit(pdf_normal(x,m,s), x, m - 3*s, m + 3* s)));
+
+block([m: 14, s: 2, s2],
+  s2: random_normal(m, s, 1000),
+  draw2d(
+    grid   = true,
+    title = title_cache ["histogram + explicit: Random data from normal distribution, nonuniform bins"],
+    histogram_description(
+      s2,
+      nclasses     = setify (makelist (float (quantile_normal (k/13, m, s)), k, 1, 12)),
+      frequency    = density,
+      fill_density = 0.5),
+    xrange = [5, 25],
     explicit(pdf_normal(x,m,s), x, m - 3*s, m + 3* s)));
 
 piechart(

-----------------------------------------------------------------------

Summary of changes:
 doc/info/descriptive.texi             | 28 ++++++++++++++++++++++++----
 share/descriptive/descriptive.mac     |  8 +++++---
 share/descriptive/rtest_statgraph.mac | 20 +++++++++++++++++---
 3 files changed, 46 insertions(+), 10 deletions(-)


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