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1 ## Copyright (C) 1996, 1997 John W. Eaton |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 2, or (at your option) |
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8 ## any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, write to the Free |
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17 ## Software Foundation, 59 Temple Place - Suite 330, Boston, MA |
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18 ## 02111-1307, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} hist (@var{y}, @var{x}, @var{norm}) |
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22 ## Produce histogram counts or plots. |
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23 ## |
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24 ## With one vector input argument, plot a histogram of the values with |
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25 ## 10 bins. The range of the histogram bins is determined by the range |
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26 ## of the data. |
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27 ## |
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28 ## Given a second scalar argument, use that as the number of bins. |
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29 ## |
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30 ## Given a second vector argument, use that as the centers of the bins, |
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31 ## with the width of the bins determined from the adjacent values in |
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32 ## the vector. |
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33 ## |
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34 ## If third argument is provided, the histogram is normalised such that |
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35 ## the sum of the bars is equal to @var{norm}. |
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36 ## |
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37 ## Extreme values are lumped in the first and last bins. |
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38 ## |
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39 ## With two output arguments, produce the values @var{nn} and @var{xx} such |
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40 ## that @code{bar (@var{xx}, @var{nn})} will plot the histogram. |
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41 ## @end deftypefn |
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42 ## |
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43 ## @seealso{bar} |
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44 |
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45 ## Author: jwe |
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46 |
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47 function [nn, xx] = hist (y, x, norm) |
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48 |
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49 if (nargin < 1 || nargin > 3) |
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50 usage ("[nn, xx] = hist (y, x, norm)"); |
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51 endif |
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52 |
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53 arg_is_vector = is_vector (y); |
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54 |
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55 if (rows (y) == 1) |
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56 y = y(:); |
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57 endif |
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58 |
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59 if (isreal (y)) |
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60 max_val = max (y); |
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61 min_val = min (y); |
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62 else |
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63 error ("hist: first argument must be a vector"); |
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64 endif |
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65 |
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66 if (nargin == 1) |
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67 n = 10; |
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68 x = [0.5:n]'/n; |
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69 x = x * (max_val - min_val) + ones(size(x)) * min_val; |
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70 else |
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71 ## nargin is either 2 or 3 |
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72 if (isscalar (x)) |
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73 n = x; |
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74 if (n <= 0) |
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75 error ("hist: number of bins must be positive"); |
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76 endif |
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77 x = [0.5:n]'/n; |
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78 x = x * (max_val - min_val) + ones(size(x)) * min_val; |
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79 elseif (isreal (x)) |
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80 if (isvector (x)) |
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81 x = x(:); |
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82 endif |
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83 tmp = sort (x); |
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84 if (any (tmp != x)) |
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85 warning ("hist: bin values not sorted on input"); |
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86 x = tmp; |
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87 endif |
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88 else |
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89 error ("hist: second argument must be a scalar or a vector"); |
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90 endif |
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91 endif |
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92 |
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93 cutoff = (x(1:end-1,:) + x(2:end,:)) / 2; |
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94 n = rows (x); |
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95 if (n < 30 && columns (x) == 1) |
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96 ## The following algorithm works fastest for n less than about 30. |
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97 chist = zeros (n+1, columns (y)); |
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98 for i = 1:n-1 |
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99 chist(i+1,:) = sum (y <= cutoff(i)); |
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100 endfor |
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101 chist(n+1,:) = rows (y); |
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102 else |
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103 ## The following algorithm works fastest for n greater than about 30. |
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104 ## Put cutoff elements between boundaries, integrate over all |
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105 ## elements, keep totals at boundaries. |
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106 [s, idx] = sort ([y; cutoff]); |
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107 len = rows (y); |
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108 chist = cumsum (idx <= len); |
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109 t1 = zeros (1, columns (y)); |
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110 t2 = reshape (chist(idx > len), size (cutoff)); |
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111 t3 = chist(end,:); |
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112 chist = [t1; t2; t3]; |
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113 endif |
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114 |
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115 freq = diff (chist); |
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116 |
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117 if (nargin == 3) |
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118 ## Normalise the histogram. |
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119 freq = freq / rows (y) * norm; |
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120 endif |
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121 |
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122 if (nargout > 0) |
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123 if (arg_is_vector) |
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124 nn = freq'; |
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125 xx = x'; |
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126 else |
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127 nn = freq; |
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128 xx = x; |
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129 endif |
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130 else |
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131 bar (x, freq); |
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132 endif |
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133 |
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134 endfunction |
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135 |
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136 %!test |
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137 %! [nn,xx]=hist([1:4],3); |
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138 %! assert(xx, [1.5,2.5,3.5]); |
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139 %! assert(nn, [2,1,1]); |
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140 %!test |
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141 %! [nn,xx]=hist([1:4]',3); |
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142 %! assert(xx, [1.5,2.5,3.5]'); |
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143 %! assert(nn, [2,1,1]'); |
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144 %!test |
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145 %! [nn,xx]=hist([[1:4]',[1:4]'],3); |
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146 %! assert(xx, [[1.5,2.5,3.5]',[1.5,2.5,3.5]']); |
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147 %! assert(nn, [[2,1,1]',[2,1,1]']); |
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148 %!assert(hist(1,1),1); |
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149 %!test |
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150 %! for n = [10, 30, 100, 1000] |
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151 %! assert( sum(hist([1:n], n)), n ); |
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152 %! assert( sum(hist([1:n], [2:n-1])), n); |
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153 %! assert( sum(hist([1:n], [1:n])), n ); |
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154 %! assert( sum(hist([1:n], 29)), n); |
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155 %! assert( sum(hist([1:n], 30)), n); |
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156 %! endfor |
