function?[t?measurement_overhead?measurement_details]?=?timeit（f?num_outputs）
%TIMEIT?Measure?time?required?to?run?function.
%???T?=?TIMEIT（F）?measures?the?time?（in?seconds）?required?to?run?F?which?is?a
%???function?handle.??TIMEIT?calls?F?with?either?no?output?arguments?or?one
%???output?argument?depending?on?nargout（F）.
%
%???T?=?TIMEIT（FN）?calls?F?with?N?output?arguments.??N?can?be?0?1?2?3?or?4.
%
%???TIMEIT?handles?automatically?the?usual?benchmarking?procedures?of?“warming
%???up“?F?figuring?out?how?many?times?to?repeat?F?in?a?timing?loop?etc.
%???TIMEIT?also?compensates?for?the?estimated?time-measurement?overhead
%???associated?with?tic/toc?and?with?calling?function?handles.??TIMEIT?returns
%???the?median?of?several?repeated?measurements.
%
%???Examples
%???--------
%???How?much?time?does?it?take?to?compute?sum（A.‘?.*?B?1）?where?A?is
%???12000-by-400?and?B?is?400-by-12000?
%
%???????A?=?rand（12000?400）;
%???????B?=?rand（400?12000）;
%???????f?=?@（）?sum（A.‘?.*?B?1）;
%???????timeit（f）
%
%???How?much?time?does?it?take?to?call?svd?with?three?output?arguments?
%
%???????X?=?[1?2;?3?4;?5?6;?7?8];
%???????f?=?@（）?svd（X）;
%???????timeit（f?3）
%
%???How?much?time?does?it?take?to?dilate?the?text.png?image?with
%???a?25-by-25?all-ones?structuring?element??（This?example?uses?Image?Processing
%???Toolbox?functions.）
%
%???????bw?=?imread（‘text.png‘）;
%???????se?=?strel（ones（25?25））;
%???????g?=?@（）?imdilate（bw?se）;
%???????timeit（g）

%???Steve?Eddins
%???Copyright?2008-2010?The?MathWorks?Inc.

if?nargin?????num_outputs?=?min（numOutputs（f）?1）;
else
????if?num_outputs?>?4
????????warning（‘MATLAB:timeit:tooManyOutputs‘?...
????????????‘Too?many?function?output?arguments?specified.?timeit?will?call?your?function?with?4?output?arguments.‘）;
????end
end

t_rough?=?roughEstimate（f?num_outputs）;

%?Calculate?the?number?of?inner-loop?repetitions?so?that?the?inner?for-loop
%?takes?at?least?about?1ms?to?execute.
desired_inner_loop_time?=?0.001;
num_inner_iterations?=?max（ceil（desired_inner_loop_time?/?t_rough）?1）;

%?Run?the?outer?loop?enough?times?to?give?a?reasonable?set?of?inputs?to?median.
num_outer_iterations?=?11;

%?If?the?estimated?running?time?for?the?timing?loops?is?too?long
%?reduce?the?number?of?outer?loop?iterations.
estimated_running_time?=?num_outer_iterations?*?num_inner_iterations?*?t_rough;
long_time?=?15;
min_outer_iterations?=?3;
if?estimated_running_time?>?long_time
????num_outer_iterations?=?ceil（long_time?/?（num_inner_iterations?*?t_rough））;
????num_outer_iterations?=?max（num_outer_iterations?min_outer_iterations）;
end

times?=?zeros（num_outer_iterations?1）;

for?k?=?1:num_outer_iterations
????%?Coding?note:?An?earlier?version?of?this?code?constructed?an?“outputs“?cell
????%?array?which?was?used?in?comma-separated?form?for?the?left-hand?side?of
????%?the?call?to?f（）.??It?turned?out?though?that?the?comma-separated?output
????%?argument