Mercurial > octave
view scripts/plot/draw/stemleaf.m @ 32062:ada96a467a28
quiver: Improve plotting with non-float numeric inputs (bug #59695)
* scripts/plot/draw/private/__quiver__.m: Change firstnonnumeric check to look
for char instead of numeric to allow for logical inputs. Recast all inputs
up to firstnonnumeric as doubles. Check if firstnonnumeric element is 'off'
and if so set scale factor to 0 and increment firstnonnumeric.
* scripts/plot/draw/quiver.m: Update docstring to include scaling factor
option 'off'. Add BIST for int and logical input types.
* scripts/plot/draw/quiver3.m: Update docstring to include scaling factor
option 'off'. Add BISTs for too-few inputs.
* etc/NEWS.9.md: Appended details of changes to quiver note under General
Improvements and noted it also applies to quiver3.
| author | Nicholas R. Jankowski <jankowski.nicholas@gmail.com> |
|---|---|
| date | Wed, 26 Apr 2023 17:18:50 -0400 |
| parents | 597f3ee61a48 |
| children | a4506463f341 |
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######################################################################## ## ## Copyright (C) 2013-2023 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## This file is part of Octave. ## ## Octave is free software: you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {} stemleaf (@var{x}, @var{caption}) ## @deftypefnx {} {} stemleaf (@var{x}, @var{caption}, @var{stem_sz}) ## @deftypefnx {} {@var{plotstr} =} stemleaf (@dots{}) ## Compute and display a stem and leaf plot of the vector @var{x}. ## ## The input @var{x} should be a vector of integers. Any non-integer values ## will be converted to integer by @code{@var{x} = fix (@var{x})}. By default ## each element of @var{x} will be plotted with the last digit of the element ## as a leaf value and the remaining digits as the stem. For example, 123 ## will be plotted with the stem @samp{12} and the leaf @samp{3}. The second ## argument, @var{caption}, should be a character array which provides a ## description of the data. It is included as a heading for the output. ## ## The optional input @var{stem_sz} sets the width of each stem. ## The stem width is determined by @code{10^(@var{stem_sz} + 1)}. ## The default stem width is 10. ## ## The output of @code{stemleaf} is composed of two parts: a ## "Fenced Letter Display," followed by the stem-and-leaf plot itself. ## The Fenced Letter Display is described in @cite{Exploratory Data Analysis}. ## Briefly, the entries are as shown: ## ## @example ## @group ## ## Fenced Letter Display ## #% nx|___________________ nx = numel (x) ## M% mi| md | mi median index, md median ## H% hi|hl hu| hs hi lower hinge index, hl,hu hinges, ## 1 |x(1) x(nx)| hs h_spreadx(1), x(nx) first ## _______ and last data value. ## ______|step |_______ step 1.5*h_spread ## f|ifl ifh| inner fence, lower and higher ## |nfl nfh| no.\ of data points within fences ## F|ofl ofh| outer fence, lower and higher ## |nFl nFh| no.\ of data points outside outer ## fences ## @end group ## @end example ## ## The stem-and-leaf plot shows on each line the stem value followed by the ## string made up of the leaf digits. If the @var{stem_sz} is not 1 the ## successive leaf values are separated by ",". ## ## With no return argument, the plot is immediately displayed. If an output ## argument is provided, the plot is returned as an array of strings. ## ## The leaf digits are not sorted. If sorted leaf values are desired, use ## @code{@var{xs} = sort (@var{x})} before calling @code{stemleaf (@var{xs})}. ## ## The stem and leaf plot and associated displays are described in: ## Chapter 3, @cite{Exploratory Data Analysis} by @nospell{J. W. Tukey}, ## Addison-Wesley, 1977. ## @seealso{hist, printd} ## @end deftypefn function plotstr = stemleaf (x, caption, stem_sz) ## Compute and display a stem and leaf plot of the vector x. The x ## vector is converted to integer by x = fix(x). If an output argument ## is provided, the plot is returned as an array of strings. The ## first element is the heading followed by an element for each stem. ## ## The default stem step is 10. If stem_sz is provided the stem ## step is set to: 10^(stem_sz+1). The x vector should be integers. ## It will be treated so that the last digit is the leaf value and the ## other digits are the stems. ## ## When we first implemented stem and leaf plots in the early 1960's ## there was some discussion about sorting vs. leaving the leaf ## entries in the original order in the data. We decided in favor of ## sorting the leaves for most purposes. This is the choice ## implemented in the SNAP/IEDA system that was written at that time. ## ## SNAP/IEDA, and particularly its stem and leaf plotting, were further ## developed by Hale Trotter, David Hoagland (at Princeton and MIT), ## and others. ## ## Tukey, in EDA, generally uses unsorted leaves. In addition, he ## described a wide range of additional display formats. This ## implementation does not sort the leaves, but if the x vector is ## sorted then the leaves come out sorted. A simple display format is ## used. ## ## I doubt if providing other options is worthwhile. The code can ## quite easily be modified to provide specific display results. Or, ## the returned output string can be edited. The returned output is an ## array of strings with each row containing a line of the plot ## preceded by the lines of header text as the first row. This ## facilitates annotation. ## ## Note that the code has some added complexity due to the need to ## distinguish both + and - 0 stems. The +- stem values are essential ## for all plots which span 0. After dealing with +-0 stems, the added ## complexity of putting +- data values in the correct stem is minor, ## but the sign of 0 leaves must be checked. And, the cases where the ## stems start or end at +- 0 must also be considered. ## ## The fact that IEEE floating point defines +- 0 helps make this ## easier. ## ## Michael D. Godfrey January 2013 ## More could be implemented for better data scaling. And, of course, ## other options for the kinds of plots described by Tukey could be ## provided. This may best be left to users. if (nargin < 2) print_usage (); endif if (! isvector (x)) error ("stemleaf: X must be a vector"); endif if (isinteger (x)) ## Avoid use of integers because rounding rules do not use fix(): ## Example: floor (int32 (-44)/10) == -4, floor (int32 (-46)/10) = -5 !!! x = single (x); elseif (isfloat (x)) xint = fix (x); if (any (x != xint)) warning ("stemleaf: X truncated to integer values"); x = xint; endif else error ("stemleaf: X must be a numeric vector"); endif if (! ischar (caption)) error ("stemleaf: CAPTION must be a character array"); endif if (nargin == 2) stem_step = 10; else if (! (isscalar (stem_sz) && stem_sz >= 0 && isreal (stem_sz))) error ("stemleaf: STEM_SZ must be a real integer >= 0"); endif stem_sz = fix (stem_sz); stem_step = 10^(stem_sz+1); endif ## Note that IEEE 754 states that -+ 0 should compare equal. This has ## led to C sort (and therefore Octave) treating them as equal. Thus, ## sort([-1 0 -0 1]) yields [-1 0 -0 1], and sort([-1 -0 0 1]) ## yields: [-1 -0 0 1]. This means that stem-and-leaf plotting cannot ## rely on sort to order the data as needed for display. ## This also applies to min()/max() so these routines can't be relied ## upon if the max or min is -+ 0. ## Compute hinges and fences based on ref: EDA pgs. 33 and 44. ## Note that these outlier estimates are meant to be "distribution free". nx = numel (x); xs = sort (x); # Note that sort preserves -0 mdidx = fix ((nx + 1)/2); # median index hlidx = fix ((mdidx + 1)/2); # lower hinge index huidx = fix (nx + 1 - hlidx); # upper hinge index md = xs(mdidx); # median hl = xs(hlidx); # lower hinge hu = xs(huidx); # upper hinge h_spread = hu - hl; # h_spread: difference between hinges step = fix (1.5*h_spread); # step: 1.5 * h_spread i_fence_l = hl - step; # inner fences: outside hinges + step o_fence_l = hl - 2*step; # outer fences: outside hinges + 2*step i_fence_h = hu + step; o_fence_h = hu + 2*step; n_out_l = sum (x<i_fence_l) - sum (x<o_fence_l); n_out_h = sum (x>i_fence_h) - sum (x>o_fence_h); n_far_l = sum (x<o_fence_l); n_far_h = sum (x>o_fence_h); ## display table similar to that on pg. 33 plot_out = sprintf (" Data: %s", caption); plot_out = [plot_out; sprintf(" ")]; plot_out = [plot_out; sprintf(" Fenced Letter Display")]; plot_out = [plot_out; sprintf(" ")]; plot_out = [plot_out; sprintf(" #%3d|___________________", nx)]; plot_out = [plot_out; sprintf(" M%3d| %5d |", mdidx, md)]; plot_out = [plot_out; sprintf(" H%3d|%5d %5d| %d", hlidx, hl, hu, h_spread)]; plot_out = [plot_out; sprintf(" 1 |%5d %5d|", xs(1), xs(nx))]; plot_out = [plot_out; sprintf(" _______")]; plot_out = [plot_out; sprintf(" ______|%5d|_______",step)]; plot_out = [plot_out; sprintf(" f|%5d %5d|", i_fence_l, i_fence_h)]; plot_out = [plot_out; sprintf(" |%5d %5d| out", n_out_l, n_out_h)]; plot_out = [plot_out; sprintf(" F|%5d %5g|", o_fence_l, o_fence_h)]; plot_out = [plot_out; sprintf(" |%5d %5d| far",n_far_l,n_far_h)]; plot_out = [plot_out; " "]; ## Determine stem values min_x = min (x); max_x = max (x); if (min_x > 0) # all stems > 0 stems = [fix(min(x)/stem_step) : (fix(max(x)/stem_step)+1)]; elseif (max_x < 0) # all stems < 0 stems = [(fix(min_x/stem_step)-1) : fix(max_x/stem_step)]; elseif (min_x < 0 && max_x > 0) # range crosses 0 stems = [(fix(min_x/stem_step)-1) : -0, 0 : fix(max_x/stem_step)+1 ]; else # one endpoint is a zero which may be +0 or -0 if (min_x == 0) if (any (x == 0 & signbit (x))) min_x = -0; else min_x = +0; endif endif if (max_x == 0) if (any (x == 0 & ! signbit (x))) max_x = +0; else max_x = -0; endif endif stems = []; if (signbit (min_x)) stems = [(fix(min_x/stem_step)-1) : -0]; endif if (! signbit (max_x)) stems = [stems, 0 : fix(max_x/stem_step)+1 ]; endif endif ## Vectorized version provided by Rik Wehbring (rik@octave.org) ## Determine leaves for each stem: new_line = 1; for kx = 2 : numel (stems) stem_sign = signbit (stems(kx)); if (stems(kx) <= 0) idx = ((x <= stems(kx)*stem_step) & (x > (stems(kx-1)*stem_step)) & (signbit (x) == stem_sign)); xlf = abs (x(idx) - stems(kx)*stem_step); else idx = ((x < stems(kx)*stem_step) & (x >= (stems(kx-1)*stem_step)) & (signbit (x) == stem_sign)); xlf = abs (x(idx) - stems(kx-1)*stem_step); endif ## Convert leaves to a string if (stem_step == 10) lf_str = sprintf ("%d", xlf); else lf_str = ""; if (! isempty (xlf)) lf_str = sprintf ("%d", xlf(1)); if (numel (xlf) > 1) lf_str = [lf_str sprintf(",%d", xlf(2:end))]; endif endif endif ## Set correct -0 if (stems(kx) == 0 && signbit (stems(kx))) line = sprintf (" -0 | %s", lf_str); # -0 stem. elseif (stems(kx) < 0) line = sprintf ("%4d | %s", stems(kx), lf_str); elseif (stems(kx) > 0) line = sprintf ("%4d | %s", stems(kx-1), lf_str); else line = ""; endif if (! isempty (lf_str) || stems(kx) == 0 || stems(kx-1) == 0) plot_out = [plot_out; line]; new_line = 1; else if (new_line == 1) plot_out = [plot_out; " :"]; # just print one : if no leaves new_line = 0; endif endif endfor # kx = 2: numel (stems) if (nargout == 0) disp (plot_out); else plotstr = plot_out; endif endfunction %!demo %! ## Unsorted plot: %! x = [-22 12 -28 52 39 -2 12 10 11 11 42 38 44 18 44]; %! stemleaf (x, "Unsorted plot"); %!demo %! ## Sorted leaves: %! x = [-22 12 -28 52 39 -2 12 10 11 11 42 38 44 18 44]; %! y = sort (x); %! stemleaf (y, "Sorted leaves"); %!demo %! ## Sorted leaves (large dataset): %! x = [-22 12 -28 52 39 -2 12 10 11 11 42 38 44 18 44 37 113 124 37 48 ... %! 127 36 29 31 125 139 131 115 105 132 104 123 35 113 122 42 117 119 ... %! 58 109 23 105 63 27 44 105 99 41 128 121 116 125 32 61 37 127 29 113 ... %! 121 58 114 126 53 114 96 25 109 7 31 141 46 -13 71 43 117 116 27 7 ... %! 68 40 31 115 124 42 128 52 71 118 117 38 27 106 33 117 116 111 40 ... %! 119 47 105 57 122 109 124 115 43 120 43 27 27 18 28 48 125 107 114 ... %! 34 133 45 120 30 127 31 116 146 21 23 30 10 20 21 30 0 100 110 1 20 ... %! 0]; %! y = sort (x); %! stemleaf (y, "Sorted leaves (large dataset)"); %!demo %! ## Gaussian leaves: %! x = fix (30 * randn (300,1)); %! stemleaf (x, "Gaussian leaves"); %!test %! ## test minus to plus %! x = [-22 12 -28 52 39 -2 12 10 11 11 42 38 44 18 44 37 113 124 37 48 127 ... %! 36 29 31 125 139 131 115 105 132 104 123 35 113 122 42 117 119 58 109 ... %! 23 105 63 27 44 105 99 41 128 121 116 125 32 61 37 127 29 113 121 58 ... %! 114 126 53 114 96 25 109 7 31 141 46 -13 71 43 117 116 27 7 68 40 31 ... %! 115 124 42 128 52 71 118 117 38 27 106 33 117 116 111 40 119 47 105 57 ... %! 122 109 124 115 43 120 43 27 27 18 28 48 125 107 114 34 133 45 120 30 ... %! 127 31 116 146 21 23 30 10 20 21 30 0 100 110 1 20 0]; %! x = sort (x); %! rexp = char ( %! " Data: test minus to plus" , %! " " , %! " Fenced Letter Display" , %! " " , %! " #138|___________________" , %! " M 69| 52 |" , %! " H 35| 30 116| 86" , %! " 1 | -28 146|" , %! " _______" , %! " ______| 129|_______" , %! " f| -99 245|" , %! " | 0 0| out" , %! " F| -228 374|" , %! " | 0 0| far" , %! " " , %! " -2 | 82" , %! " -1 | 3" , %! " -0 | 2" , %! " 0 | 00177" , %! " 1 | 00112288" , %! " 2 | 001133577777899" , %! " 3 | 000111123456777889" , %! " 4 | 00122233344456788" , %! " 5 | 223788" , %! " 6 | 138" , %! " 7 | 11" , %! " : " , %! " 9 | 69" , %! " 10 | 04555567999" , %! " 11 | 0133344455566667777899" , %! " 12 | 0011223444555677788" , %! " 13 | 1239" , %! " 14 | 16" ); %! r = stemleaf (x, "test minus to plus", 0); %! assert (r, rexp); %!test %! ## positive values above 0 %! x = [5 22 12 28 52 39 12 11 11 42 38 44 18 44]; %! rexp = char ( %! " Data: positive values above 0", %! " " , %! " Fenced Letter Display" , %! " " , %! " # 14|___________________" , %! " M 7| 22 |" , %! " H 4| 12 42| 30" , %! " 1 | 5 52|" , %! " _______" , %! " ______| 45|_______" , %! " f| -33 87|" , %! " | 0 0| out" , %! " F| -78 132|" , %! " | 0 0| far" , %! " " , %! " 0 | 5" , %! " 1 | 22118" , %! " 2 | 28" , %! " 3 | 98" , %! " 4 | 244" , %! " 5 | 2" ); %! r = stemleaf (x, "positive values above 0"); %! assert (r, rexp); %!test %! ## negative values below 0 %! x = [5 22 12 28 52 39 12 11 11 42 38 44 18 44]; %! x = -x; %! rexp = char ( %! " Data: negative values below 0", %! " " , %! " Fenced Letter Display" , %! " " , %! " # 14|___________________" , %! " M 7| -28 |" , %! " H 4| -42 -12| 30" , %! " 1 | -52 -5|" , %! " _______" , %! " ______| 45|_______" , %! " f| -87 33|" , %! " | 0 0| out" , %! " F| -132 78|" , %! " | 0 0| far" , %! " " , %! " -5 | 2" , %! " -4 | 244" , %! " -3 | 98" , %! " -2 | 28" , %! " -1 | 22118" , %! " -0 | 5" ); %! r = stemleaf (x, "negative values below 0"); %! assert (r, rexp); %!test %! ## positive values from 0 %! x = [22 12 28 52 39 2 12 0 11 11 42 38 44 18 44]; %! rexp = char ( %! " Data: positive values from 0", %! " " , %! " Fenced Letter Display" , %! " " , %! " # 15|___________________" , %! " M 8| 22 |" , %! " H 4| 11 42| 31" , %! " 1 | 0 52|" , %! " _______" , %! " ______| 46|_______" , %! " f| -35 88|" , %! " | 0 0| out" , %! " F| -81 134|" , %! " | 0 0| far" , %! " " , %! " 0 | 20" , %! " 1 | 22118" , %! " 2 | 28" , %! " 3 | 98" , %! " 4 | 244" , %! " 5 | 2" ); %! r = stemleaf (x, "positive values from 0"); %! assert (r, rexp); %!test %! ## negative values from 0 %! x = [22 12 28 52 39 2 12 0 11 11 42 38 44 18 44]; %! x = -x; %! rexp = char ( %! " Data: negative values from 0", %! " " , %! " Fenced Letter Display" , %! " " , %! " # 15|___________________" , %! " M 8| -22 |" , %! " H 4| -42 -11| 31" , %! " 1 | -52 0|" , %! " _______" , %! " ______| 46|_______" , %! " f| -88 35|" , %! " | 0 0| out" , %! " F| -134 81|" , %! " | 0 0| far" , %! " " , %! " -5 | 2" , %! " -4 | 244" , %! " -3 | 98" , %! " -2 | 28" , %! " -1 | 22118" , %! " -0 | 20" ); %! r = stemleaf (x, "negative values from 0"); %! assert (r, rexp); %!test %! ## both +0 and -0 present %! x = [-9 -7 -0 0 -0]; %! rexp = char ( %! " Data: both +0 and -0 present", %! " " , %! " Fenced Letter Display" , %! " " , %! " # 5|___________________" , %! " M 3| 0 |" , %! " H 2| -7 0| 7" , %! " 1 | -9 0|" , %! " _______" , %! " ______| 10|_______" , %! " f| -17 10|" , %! " | 0 0| out" , %! " F| -27 20|" , %! " | 0 0| far" , %! " " , %! " -0 | 9700" , %! " 0 | 0" ); %! r = stemleaf (x, "both +0 and -0 present"); %! assert (r, rexp); %!test %! ## both <= 0 and -0 present %! x = [-9 -7 0 -0]; %! rexp = char ( %! " Data: both <= 0 and -0 present", %! " " , %! " Fenced Letter Display" , %! " " , %! " # 4|___________________" , %! " M 2| -7 |" , %! " H 1| -9 0| 9" , %! " 1 | -9 0|" , %! " _______" , %! " ______| 13|_______" , %! " f| -22 13|" , %! " | 0 0| out" , %! " F| -35 26|" , %! " | 0 0| far" , %! " " , %! " -0 | 970" , %! " 0 | 0" ); %! r = stemleaf (x, "both <= 0 and -0 present"); %! assert (r, rexp); %!test %! ## Example from EDA: Chevrolet Prices pg. 30 %! x = [150 250 688 695 795 795 895 895 895 ... %! 1099 1166 1333 1499 1693 1699 1775 1995]; %! rexp = char ( %! " Data: Chevrolet Prices EDA pg.30", %! " " , %! " Fenced Letter Display" , %! " " , %! " # 17|___________________" , %! " M 9| 895 |" , %! " H 5| 795 1499| 704" , %! " 1 | 150 1995|" , %! " _______" , %! " ______| 1056|_______" , %! " f| -261 2555|" , %! " | 0 0| out" , %! " F|-1317 3611|" , %! " | 0 0| far" , %! " " , %! " 1 | 50" , %! " 2 | 50" , %! " :" , %! " 6 | 88,95" , %! " 7 | 95,95" , %! " 8 | 95,95,95" , %! " :" , %! " 10 | 99" , %! " 11 | 66" , %! " :" , %! " 13 | 33" , %! " 14 | 99" , %! " :" , %! " 16 | 93,99" , %! " 17 | 75" , %! " :" , %! " 19 | 95" ); %! r = stemleaf (x, "Chevrolet Prices EDA pg.30", 1); %! assert (r, rexp); ## Test input validation %!error <Invalid call> stemleaf () %!error <X must be a vector> stemleaf (ones (2,2), "") %!warning <X truncated to integer values> tmp = stemleaf ([0 0.5 1],""); %!error <X must be a numeric vector> stemleaf ("Hello World", "data") %!error <CAPTION must be a character array> stemleaf (1, 2) %!error <STEM_SZ must be a real integer> stemleaf (1, "", ones (2,2)) %!error <STEM_SZ must be a real integer> stemleaf (1, "", -1) %!error <STEM_SZ must be a real integer> stemleaf (1, "", 1+i)