Mercurial > octave-antonio

comparison scripts/testfun/speed.m @ 20162:2645f9ef8c88 stable

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
doc: Update more docstrings to have one sentence summary as first line. Reviewed specfun, special-matrix, testfun, and time script directories. * scripts/specfun/expint.m, scripts/specfun/isprime.m, scripts/specfun/legendre.m, scripts/specfun/primes.m, scripts/specfun/reallog.m, scripts/specfun/realsqrt.m, scripts/special-matrix/gallery.m, scripts/special-matrix/hadamard.m, scripts/special-matrix/hankel.m, scripts/special-matrix/hilb.m, scripts/special-matrix/invhilb.m, scripts/special-matrix/magic.m, scripts/special-matrix/pascal.m, scripts/special-matrix/rosser.m, scripts/special-matrix/toeplitz.m, scripts/special-matrix/vander.m, scripts/special-matrix/wilkinson.m, scripts/testfun/assert.m, scripts/testfun/demo.m, scripts/testfun/example.m, scripts/testfun/fail.m, scripts/testfun/rundemos.m, scripts/testfun/runtests.m, scripts/testfun/speed.m, scripts/time/asctime.m, scripts/time/calendar.m, scripts/time/clock.m, scripts/time/ctime.m, scripts/time/datenum.m, scripts/time/datestr.m, scripts/time/datevec.m, scripts/time/etime.m, scripts/time/is_leap_year.m, scripts/time/now.m, scripts/time/weekday.m: Update more docstrings to have one sentence summary as first line.
author Rik <rik@octave.org>
date Sun, 03 May 2015 17:00:11 -0700
parents 9fc020886ae9
children
comparison
equal deleted inserted replaced
20160:03b9d17a2d95 20162:2645f9ef8c88
19 ## -*- texinfo -*- 19 ## -*- texinfo -*-
20 ## @deftypefn {Function File} {} speed (@var{f}, @var{init}, @var{max_n}, @var{f2}, @var{tol}) 20 ## @deftypefn {Function File} {} speed (@var{f}, @var{init}, @var{max_n}, @var{f2}, @var{tol})
21 ## @deftypefnx {Function File} {[@var{order}, @var{n}, @var{T_f}, @var{T_f2}] =} speed (@dots{}) 21 ## @deftypefnx {Function File} {[@var{order}, @var{n}, @var{T_f}, @var{T_f2}] =} speed (@dots{})
22 ## 22 ##
23 ## Determine the execution time of an expression (@var{f}) for various input 23 ## Determine the execution time of an expression (@var{f}) for various input
24 ## values (@var{n}). The @var{n} are log-spaced from 1 to @var{max_n}. For 24 ## values (@var{n}).
25 ## each @var{n}, an initialization expression (@var{init}) is computed to 25 ##
26 ## create any data needed for the test. If a second expression (@var{f2}) is 26 ## The @var{n} are log-spaced from 1 to @var{max_n}. For each @var{n}, an
27 ## given then the execution times of the two expressions are compared. When 27 ## initialization expression (@var{init}) is computed to create any data needed
28 ## called without output arguments the results are printed to stdout and 28 ## for the test. If a second expression (@var{f2}) is given then the
29 ## displayed graphically. 29 ## execution times of the two expressions are compared. When called without
30 ## output arguments the results are printed to stdout and displayed
31 ## graphically.
30 ## 32 ##
31 ## @table @code 33 ## @table @code
32 ## @item @var{f} 34 ## @item @var{f}
33 ## The code expression to evaluate. 35 ## The code expression to evaluate.
34 ## 36 ##
36 ## The maximum test length to run. The default value is 100. Alternatively, 38 ## The maximum test length to run. The default value is 100. Alternatively,
37 ## use @code{[min_n, max_n]} or specify the @var{n} exactly with 39 ## use @code{[min_n, max_n]} or specify the @var{n} exactly with
38 ## @code{[n1, n2, @dots{}, nk]}. 40 ## @code{[n1, n2, @dots{}, nk]}.
39 ## 41 ##
40 ## @item @var{init} 42 ## @item @var{init}
41 ## Initialization expression for function argument values. Use @var{k} 43 ## Initialization expression for function argument values. Use @var{k} for
42 ## for the test number and @var{n} for the size of the test. This should 44 ## the test number and @var{n} for the size of the test. This should compute
43 ## compute values for all variables used by @var{f}. Note that @var{init} will 45 ## values for all variables used by @var{f}. Note that @var{init} will be
44 ## be evaluated first for @math{k = 0}, so things which are constant throughout 46 ## evaluated first for @math{k = 0}, so things which are constant throughout
45 ## the test series can be computed once. The default value is 47 ## the test series can be computed once. The default value is
46 ## @code{@var{x} = randn (@var{n}, 1)}. 48 ## @code{@var{x} = randn (@var{n}, 1)}.
47 ## 49 ##
48 ## @item @var{f2} 50 ## @item @var{f2}
49 ## An alternative expression to evaluate, so that the speed of two 51 ## An alternative expression to evaluate, so that the speed of two
54 ## @var{f2}. If @var{tol} is positive, the tolerance is an absolute one. 56 ## @var{f2}. If @var{tol} is positive, the tolerance is an absolute one.
55 ## If @var{tol} is negative, the tolerance is a relative one. The default is 57 ## If @var{tol} is negative, the tolerance is a relative one. The default is
56 ## @code{eps}. If @var{tol} is @code{Inf}, then no comparison will be made. 58 ## @code{eps}. If @var{tol} is @code{Inf}, then no comparison will be made.
57 ## 59 ##
58 ## @item @var{order} 60 ## @item @var{order}
59 ## The time complexity of the expression @math{O(a*n^p)}. This 61 ## The time complexity of the expression @math{O(a*n^p)}. This is a
60 ## is a structure with fields @code{a} and @code{p}. 62 ## structure with fields @code{a} and @code{p}.
61 ## 63 ##
62 ## @item @var{n} 64 ## @item @var{n}
63 ## The values @var{n} for which the expression was calculated @strong{AND} 65 ## The values @var{n} for which the expression was calculated @strong{AND}
64 ## the execution time was greater than zero. 66 ## the execution time was greater than zero.
65 ## 67 ##
70 ## The nonzero execution times recorded for the expression @var{f2} in seconds. 72 ## The nonzero execution times recorded for the expression @var{f2} in seconds.
71 ## If required, the mean time ratio is simply @code{mean (T_f ./ T_f2)}. 73 ## If required, the mean time ratio is simply @code{mean (T_f ./ T_f2)}.
72 ## 74 ##
73 ## @end table 75 ## @end table
74 ## 76 ##
75 ## The slope of the execution time graph shows the approximate 77 ## The slope of the execution time graph shows the approximate power of the
76 ## power of the asymptotic running time @math{O(n^p)}. This 78 ## asymptotic running time @math{O(n^p)}. This power is plotted for the
77 ## power is plotted for the region over which it is approximated 79 ## region over which it is approximated (the latter half of the graph). The
78 ## (the latter half of the graph). The estimated power is not 80 ## estimated power is not very accurate, but should be sufficient to
79 ## very accurate, but should be sufficient to determine the 81 ## determine the general order of an algorithm. It should indicate if, for
80 ## general order of an algorithm. It should indicate if, for 82 ## example, the implementation is unexpectedly @math{O(n^2)} rather than
81 ## example, the implementation is unexpectedly @math{O(n^2)} 83 ## @math{O(n)} because it extends a vector each time through the loop rather
82 ## rather than @math{O(n)} because it extends a vector each 84 ## than pre-allocating storage. In the current version of Octave, the
83 ## time through the loop rather than pre-allocating storage. 85 ## following is not the expected @math{O(n)}.
84 ## In the current version of Octave, the following is not the
85 ## expected @math{O(n)}.
86 ## 86 ##
87 ## @example 87 ## @example
88 ## speed ("for i = 1:n, y@{i@} = x(i); endfor", "", [1000, 10000]) 88 ## speed ("for i = 1:n, y@{i@} = x(i); endfor", "", [1000, 10000])
89 ## @end example 89 ## @end example
90 ## 90 ##
96 ## speed ("for i = 1:n, y@{i@} = x(i); endfor", ... 96 ## speed ("for i = 1:n, y@{i@} = x(i); endfor", ...
97 ## "x = rand (n, 1); y = cell (size (x));", [1000, 10000]) 97 ## "x = rand (n, 1); y = cell (size (x));", [1000, 10000])
98 ## @end group 98 ## @end group
99 ## @end example 99 ## @end example
100 ## 100 ##
101 ## An attempt is made to approximate the cost of individual 101 ## An attempt is made to approximate the cost of individual operations, but
102 ## operations, but it is wildly inaccurate. You can improve the 102 ## it is wildly inaccurate. You can improve the stability somewhat by doing
103 ## stability somewhat by doing more work for each @code{n}. For 103 ## more work for each @code{n}. For example:
104 ## example:
105 ## 104 ##
106 ## @example 105 ## @example
107 ## speed ("airy(x)", "x = rand (n, 10)", [10000, 100000]) 106 ## speed ("airy(x)", "x = rand (n, 10)", [10000, 100000])
108 ## @end example 107 ## @end example
109 ## 108 ##
110 ## When comparing two different expressions (@var{f}, @var{f2}), the slope 109 ## When comparing two different expressions (@var{f}, @var{f2}), the slope of
111 ## of the line on the speedup ratio graph should be larger than 1 if the new 110 ## the line on the speedup ratio graph should be larger than 1 if the new
112 ## expression is faster. Better algorithms have a shallow slope. Generally, 111 ## expression is faster. Better algorithms have a shallow slope. Generally,
113 ## vectorizing an algorithm will not change the slope of the execution 112 ## vectorizing an algorithm will not change the slope of the execution time
114 ## time graph, but will shift it relative to the original. For 113 ## graph, but will shift it relative to the original. For example:
115 ## example:
116 ## 114 ##
117 ## @example 115 ## @example
118 ## @group 116 ## @group
119 ## speed ("sum (x)", "", [10000, 100000], ... 117 ## speed ("sum (x)", "", [10000, 100000], ...
120 ## "v = 0; for i = 1:length (x), v += x(i); endfor") 118 ## "v = 0; for i = 1:length (x), v += x(i); endfor")
133 ## speed ("xcorr (x, 15)", "x = rand (20+n, 1);", 100, 131 ## speed ("xcorr (x, 15)", "x = rand (20+n, 1);", 100,
134 ## "xcorr_orig (x, n)", -100*eps) 132 ## "xcorr_orig (x, n)", -100*eps)
135 ## @end group 133 ## @end group
136 ## @end example 134 ## @end example
137 ## 135 ##
138 ## Assuming one of the two versions is in xcorr_orig, this 136 ## Assuming one of the two versions is in xcorr_orig, this would compare their
139 ## would compare their speed and their output values. Note that the 137 ## speed and their output values. Note that the FFT version is not exact, so
140 ## FFT version is not exact, so one must specify an acceptable tolerance on 138 ## one must specify an acceptable tolerance on the comparison @code{100*eps}.
141 ## the comparison @code{100*eps}. In this case, the comparison should be 139 ## In this case, the comparison should be computed relatively, as
142 ## computed relatively, as @code{abs ((@var{x} - @var{y}) ./ @var{y})} rather 140 ## @code{abs ((@var{x} - @var{y}) ./ @var{y})} rather than absolutely as
143 ## than absolutely as @code{abs (@var{x} - @var{y})}. 141 ## @code{abs (@var{x} - @var{y})}.
144 ## 142 ##
145 ## Type @kbd{example ("speed")} to see some real examples or 143 ## Type @kbd{example ("speed")} to see some real examples or
146 ## @kbd{demo ("speed")} to run them. 144 ## @kbd{demo ("speed")} to run them.
147 ## @end deftypefn 145 ## @end deftypefn
148 146