Mercurial > hg > octave-nkf
changeset 16087:2b994ee38b1c
maint: backout accidental check-in 979ebfdd240d.
author | Rik <rik@octave.org> |
---|---|
date | Thu, 21 Feb 2013 22:31:13 -0800 |
parents | f89760972bf4 |
children | 63163e8eaef3 |
files | scripts/plot/stemleaf.m |
diffstat | 1 files changed, 161 insertions(+), 284 deletions(-) [+] |
line wrap: on
line diff
--- a/scripts/plot/stemleaf.m +++ b/scripts/plot/stemleaf.m @@ -21,53 +21,47 @@ ## -*- texinfo -*- ## @deftypefn {Function File} {} stemleaf (@var{x}) -## @deftypefnx {Function File} {} stemleaf (@var{x}, @var{stem_sz}) -## @deftypefnx {Function File} {@var{plotstr} =} stemleaf (@dots{}) +## @deftypefnx {Function File} {@var{plot} =} stemleaf (@var{x}, @var{opt}) +## ## 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})}. 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 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. -## -## 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 is described in: Ch. 3, @cite{Exploratory -## Data Analysis} by J. W. Tukey, Addison-Wesley, 1977. +## The @var{x} vector is converted to integer by @var{x} = @code{fix} (@var{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. +## The @var{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. +## The leaf digits are not sorted. If sorted leaf values +## are wanted, use @code{sort} (@var{x}) before calling @code{stemleaf} (@var{x}). +## The stem and leaf plot is described in: Ch. 3, +## Exploratory Data Analysis by J. W. Tukey, Addison-Wesley, 1977. ## @seealso{hist, printd} ## @end deftypefn ## Author: Michael D. Godfrey <michaeldgodfrey@gmail.com> ## Description: Compute stem and leaf plot -function plotstr = stemleaf (x, 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 +function varargout = stemleaf (x, stem_unit) + ## 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. + ## The default stem step is 10. If stem_unit is provided the stem + ## step is set to: 10^(stem_unit+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 + ## entries in the original order in the data. We decided in favor or + ## 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), + ## 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 @@ -78,14 +72,14 @@ ## ## 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 + ## 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 + ## 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. @@ -93,133 +87,106 @@ ## 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, + ## 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 < 1 || nargin > 2) - print_usage (); - endif + ## provided. This may best be left to users. - if (! isvector (x)) - error ("stemleaf: X must be a vector"); - endif - - if (isinteger (x)) - ## Avoid use of int32 because rounding rules do not use fix(): - ## floor (int32 (-44)/10) == -4 and 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 + if (nargin >= 2) + stem_step = 10^(stem_unit+1); else - error ("stemleaf: X must be a numeric vector"); - endif - - if (nargin == 1) stem_step = 10; - else - if (isscalar (stem_sz) && stem_sz >= 0 && isreal (stem_sz)) - stem_step = 10^(stem_sz+1); - else - error ("stemleaf: STEM_SZ must be a real integer >= 0"); - endif 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. - - if (issorted (x)) - hsort = "sorted."; - else - hsort = "unsorted."; + if (any (x == int32 (x)) == 0) + printf ('Input vector truncated to integer values.\n') + x = fix (x); endif + ## Avoid use of int32 due to: + + ## floor (int32 (-44)/10) == -4 and floor (int32 (-46)/10) = -5 !!! + ## x = sort (fix (x)); % User can decide about sorting x. + ## x = fix (x); + ## %Adjust scale if too small. + ## while any(abs((fix(x) - x)) >= abs(x/100)) + ## x =10*x; + ## endwhile + + ## 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. + + if (all((sort(x) == x)) == 1) + hsort = 'sorted.'; + else + hsort = 'unsorted.'; + endif + nx = max (size (x)); ## 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) : -1 , -0]; - stems = [stems, 0 : fix(max_x/stem_step)+1 ]; - else # range includes a zero which may be +0 or -0 - if (min_x == 0) - if (any (x == 0 & signbit (x))) - min_x = -0; + if (min(x) < 0) + if (signbit(max(x)) == 0) # max is positive + stems = [fix(min(x)/stem_step)-1 : -1 -0]; + stems = [stems 0 : fix(max(x)/stem_step)+1 ]; + else + if (max(x) < 0) + stems = [(fix(min(x)/stem_step)-1) : fix(max(x)/stem_step)]; else - min_x = +0; + stems = [(fix(min(x)/stem_step)-1) : -1 -0]; + stems = [stems 0 : fix(max(x)/stem_step)]; 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) : -1 , -0]; - endif - if (! signbit (max_x)) - stems = [stems, 0 : fix(max_x/stem_step)+1 ]; - endif + else # All stems are > 0 + stems = [fix(min(x)/stem_step) : fix(max(x)/stem_step) + 1]; endif - - nx = numel (x); - nstems = numel (stems); + ##stems + ##x + nstems = max(size(stems)); ## compute hinges at +- 1.5 * quartiles ## this requires sorted data! - xs = sort (x); # Note that sort preserves -0 - j = fix (nx/4) + 1; + xs = sort (x); # Note that sort preserves -0 + threeh = 1.5; + two = 2.0; + j = idivide(nx, 4, "fix") + 1; # Use F95 truncation. k = nx - j + 1; - hl = xs(j); - hu = xs(k); - ## FIXME: Is this really the only case where we want to average - ## values to determine the quartile? - if ( (nx + 1) == (4 * j) ) - hl = (xs(j + 1) + hl) / 2; - hu = (xs(k - 1) + hu) / 2; + hl = xs (j); + hu = xs (k); + if ( (nx + 1) == (4 * j) ) + hl = (xs (j + 1) + hl) / two; + hu = (xs (k - 1) + hu) / two; endif - ## determine h-spread (dh) and fences + ## :::::::: determine h-spread (dh) and fences :::::::: dh = hu - hl; - fu = hu + 1.5 * dh; - fl = hl - 1.5 * dh; + fu = hu + threeh * dh; + fl = hl - threeh * dh; - ## find value adjacent to lower fence + ## :::::::: find value adjacent to lower fence :::::::: for i = 1:j - if (xs(i) >= fl) - break; + if ( xs (i) >= fl ) + continue; endif endfor - xlo = xs(i); + ilow = i; + xlo = xs (ilow); - ## find value adjacent to upper fence - for i = 1:j - if (xs(nx -i + 1) <= fu) - break; + ## :::::::: find value adjacent to upper fence :::::::: + for i = 1:j + if ( xs (nx -i + 1) <= fu ) + continue; endif endfor - xhi = xs(nx - i + 1); + + ihi = nx - i + 1; + xhi = xs (ihi); - ## Summary at start of output: - plot_out = sprintf ("stem step: %i, data: %s", stem_step, hsort); - plot_out = [plot_out; sprintf("Hinges: lo: %g, hi: %g", xlo, xhi)]; - plot_out = [plot_out; " "]; + ## Heading for output: + plot_out = ""; + plot_out = [plot_out sprintf("stem step: %i, data: %s\nHinges: lo: %g, hi: %g\n", + stem_step, hsort, xlo, xhi)]; ## This may appear to be a good place to use vectorization using the ## stem and data arrays but the necessary special case treatment of 0 @@ -229,213 +196,123 @@ ## Determine leaves for each stem: for kx = 2:nstems - line = ""; - steml = ""; - ## Build a string of leaf digits for - ## stem(kx) if stem(kx) <= 0, or + line_out = ""; + steml = ""; + ## Build a string of leaf digits for stem(kx) if stem(kx) <= 0, or ## stem(kx-1) if stem(kx) > 0 ## stems -+ 0 have to be handled as special cases. for xi = 1:nx - if (signbit (stems(kx)) != 0) + if(signbit(stems(kx)) != 0) t1 = ((x(xi) <= stems(kx)*10) && (x(xi) > (stems(kx-1)*10))); else t1 = ((x(xi) < stems(kx)*10) && (x(xi) >= (stems(kx-1)*10))); endif ## Special tests for stem -+ 0 - if ((stems(kx) == 0) - && signbit (stems(kx)) && (x(xi) == 0)) && !signbit (x(xi)) + if ((stems(kx) == 0) && signbit(stems(kx)) && (x(xi) == 0)) && !signbit(x(xi)) t1 = 0; endif - if ((stems(kx-1) == 0) - && !signbit (stems(kx-1)) && (x(xi) == 0)) && signbit (x(xi)) + if ((stems(kx-1) == 0) && !signbit(stems(kx-1)) && (x(xi) == 0)) && signbit(x(xi)) t1 = 0; endif ## Create line as a string - if (t1) + if t1 if (stems(kx) <= 0) - xz = abs (x(xi) - stems(kx)*10); + xz = abs (x(xi) - stems(kx)*10); else - xz = abs (x(xi) - stems(kx-1)*10); + xz = abs (x(xi) - stems(kx-1)*10); endif - if ((stems(kx) == 0) && signbit (stems(kx))) + if ((stems(kx) == 0) && signbit(stems(kx))) steml = [steml sprintf("%d", abs(x(xi) - stems(kx)*10))]; else steml = [steml sprintf("%d", xz)]; endif - endif # t1 - endfor # xi = 1:nx + endif % t1 + endfor % xi = 1:nx ## Set correct -0 - if ((stems(kx) == 0) && signbit (stems(kx))) - line = [line sprintf(" -0 | %s", steml)]; # -0 stem. + if ((stems(kx) == 0) && signbit(stems(kx))) + line_out = [line_out sprintf(" -0 | %s", steml)]; % -0 stem. else - if (stems(kx) < 0) - line = [line sprintf("%4d | %s", stems(kx), steml)]; + if( stems(kx) < 0) + line_out = [line_out sprintf("%4d | %s", stems(kx), steml)]; else - if (stems(kx) > 0) - line = [line sprintf("%4d | %s", stems(kx-1), steml)]; + if stems(kx) > 0 + line_out = [line_out sprintf("%4d | %s", stems(kx-1), steml)]; endif endif endif - plot_out = [plot_out; line]; - endfor # kx = 2:nstems - + plot_out = [plot_out; line_out]; + endfor % kx = 2:nstems if (nargout == 0) - disp (plot_out); + rows = size (plot_out)(1); + cols = size (plot_out)(2); + for k = 1:rows + printf("%s\n", plot_out(k,1:cols)); + endfor else - plotstr = plot_out; + varargout{1} = 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); +%! stemleaf (x, 0); %!demo %! ## Sorted leaves: %! x = [-22 12 -28 52 39 -2 12 10 11 11 42 38 44 18 44]; -%! y = sort (x); -%! stemleaf (y); +%! y = sort(x); +%! stemleaf (y, 0); %!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); - -%!demo -%! ## Gaussian leaves: -%! x = fix (30 * randn (300,1)); -%! stemleaf (x); +%! ## More data (sorted) +%! 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, 0); %!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 ( -%! "stem step: 10, data: sorted." , -%! "Hinges: lo: -28, hi: 146" , -%! " " , -%! " -2 | 82" , -%! " -1 | 3" , -%! " -0 | 2" , -%! " 0 | 00177" , -%! " 1 | 00112288" , -%! " 2 | 001133577777899" , -%! " 3 | 000111123456777889" , -%! " 4 | 00122233344456788" , -%! " 5 | 223788" , -%! " 6 | 138" , -%! " 7 | 11" , -%! " 8 | " , -%! " 9 | 69" , -%! " 10 | 04555567999" , -%! " 11 | 0133344455566667777899", -%! " 12 | 0011223444555677788" , -%! " 13 | 1239" , -%! " 14 | 16" ); -%! r = stemleaf (x, 0); -%! assert (r, rexp); - +%! 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); +%! r2 = ["stem step: 10, data: sorted.\nHinges: lo: 30, hi: 116\n";... +%! " -2 | 82";" -1 | 3";" -0 | 2";" 0 | 00177";... +%! " 1 | 00112288";" 2 | 001133577777899";... +%! " 3 | 000111123456777889";" 4 | 00122233344456788";... +%! " 5 | 223788";" 6 | 138";" 7 | 11";" 8 | ";... +%! " 9 | 69";" 10 | 04555567999";" 11 | 0133344455566667777899";... +%! " 12 | 0011223444555677788";" 13 | 1239";" 14 | 16"]; +%! rx = stemleaf (x, 0); +%! assert(r2, rx); %!test %! ## positive values above 0 -%! x = [22 12 28 52 39 12 11 11 42 38 44 18 44]; -%! rexp = char ( -%! "stem step: 10, data: unsorted." , -%! "Hinges: lo: 11, hi: 52" , -%! " " , -%! " 1 | 22118" , -%! " 2 | 28" , -%! " 3 | 98" , -%! " 4 | 244" , -%! " 5 | 2" ); -%! r = stemleaf (x); -%! assert (r, rexp); - +%! x = [22 12 28 52 39 12 11 11 42 38 44 18 44 ]; +%! r2 = ["stem step: 10, data: unsorted.\nHinges: lo: 12, hi: 42\n";... +%! " 1 | 22118";" 2 | 28";" 3 | 98";" 4 | 244";" 5 | 2"]; +%! rx = stemleaf (x, 0); +%! assert(r2, rx); %!test %! ## negative values below 0 -%! x = [22 12 28 52 39 12 11 11 42 38 44 18 44]; +%! x = [22 12 28 52 39 12 11 11 42 38 44 18 44]; %! x = -x; -%! rexp = char ( -%! "stem step: 10, data: unsorted." , -%! "Hinges: lo: -52, hi: -11" , -%! " " , -%! " -5 | 2" , -%! " -4 | 244" , -%! " -3 | 98" , -%! " -2 | 28" , -%! " -1 | 22118" ); -%! r = stemleaf (x); -%! assert (r, rexp); - +%! r2 = ["stem step: 10, data: unsorted.\nHinges: lo: -42, hi: -12\n";... +%! " -5 | 2";" -4 | 244";" -3 | 98";" -2 | 28";" -1 | 22118"]; +%! rx = stemleaf (x, 0); +%! assert(r2, rx); %!test %! ## positive values from 0 -%! x = [22 12 28 52 39 2 12 0 11 11 42 38 44 18 44]; -%! rexp = char ( -%! "stem step: 10, data: unsorted." , -%! "Hinges: lo: 0, hi: 52" , -%! " " , -%! " 0 | 20" , -%! " 1 | 22118" , -%! " 2 | 28" , -%! " 3 | 98" , -%! " 4 | 244" , -%! " 5 | 2" ); -%! r = stemleaf (x); -%! assert (r, rexp); - +%! x = [22 12 28 52 39 2 12 0 11 11 42 38 44 18 44]; +%! r2 = ["stem step: 10, data: unsorted.\nHinges: lo: 11, hi: 42\n";... +%! " 0 | 20";" 1 | 22118";" 2 | 28";" 3 | 98";" 4 | 244";" 5 | 2"]; +%! rx = stemleaf (x, 0); +%! assert(r2, rx); %!test %! ## negative values from 0 -%! x = [22 12 28 52 39 2 12 0 11 11 42 38 44 18 44]; +%! x = [22 12 28 52 39 2 12 0 11 11 42 38 44 18 44]; %! x = -x; -%! rexp = char ( -%! "stem step: 10, data: unsorted." , -%! "Hinges: lo: -52, hi: -0" , -%! " " , -%! " -5 | 2" , -%! " -4 | 244" , -%! " -3 | 98" , -%! " -2 | 28" , -%! " -1 | 22118" , -%! " -0 | 20" ); -%! r = stemleaf (x); -%! assert (r, rexp); +%! r2 = ["stem step: 10, data: unsorted.\nHinges: lo: -42, hi: -11\n";... +%! " -5 | 2";" -4 | 244";" -3 | 98";" -2 | 28";" -1 | 22118";" -0 | 20"]; +%! rx = stemleaf (x, 0); +%! assert(r2, rx); -%!test -%! ## both +0 and -0 present -%! x = [-9 -7 -0 0]; -%! rexp = char ( -%! "stem step: 10, data: sorted." , -%! "Hinges: lo: -9, hi: 0" , -%! " " , -%! " -0 | 970" , -%! " 0 | 0" ); -%! r = stemleaf (x); -%! assert (r, rexp); - -## Test input validation -%!error stemleaf () -%!error stemleaf (1, 2, 3) -%!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") -%!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) -