Weizmann 2010 © 1

Introduction to Matlab & Data Analysis

Tutorial 10: How to Write Efficient Programs in

MatlabPlease change directory to directory E:\Matlab (cd E:\Matlab;)

From the course website

(http://www.weizmann.ac.il/midrasha/courses/MatlabIntro//course_outline.htm )

Download:matlab_t10.zip ORt10.m, sumConsecutiveKNums.m, sumConsecutiveKNumsFixed.m, writingEfficientCodeExamples.m , computeSinSlowAndFast.m,computeSinFast.m, computeSinSlow.m,twinPeaksExample.m, computeTwinPeaksFunc.m, ,computeTwinPeaksFuncForSinglePoint.m, findPsychoScore.m

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Goals

M-lint Just-In-Time accelerator Profiler Example of efficient vs. non- efficient

algorithm: Binary search

http://www.mathworks.com/matlabcentral/files/5685/matopt.pdfResource:

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Before We Start

Correct code is always more important than

speed

Keep your code readable

Optimize the bottlenecks

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M-lint Check Code Report

edit sumConsecutiveKNums.m Tools -> M lint

-> Show M lint report %#ok – ignore this line Advanced: Preference -> M-lint

The M-Lint Code Check Report displays potential errors and problems,as well as opportunities for improvement in your code

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M-lint Check Code Report – Lets Fix the Example

Fix: sumConsecutiveKNums.m Tools -> M lint -> Show M lint report

Save it as sumConsecutiveKNumsFixed.m Compare the files using:

Tools -> Compare against -> Browse

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Comparing Files – Compare the Fixed File to the Original

sumConsecutiveKNums.m

sumConsecutiveKNumsFixed.m

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More about M-lint

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Accelerating Your Code

Resources: http://www.mathworks.com/access/helpdesk_r13/help/techdoc/matlab_prog/ch7_pe10.html

http://blogs.mathworks.com/loren/2008/06/25/speeding-up-matlab-applications/

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Write Efficient Code by Using Efficient Algorithms and Efficient Implementation

Efficient algorithm Examples:

Binary search Bubble sort

Efficient implementation Examples:

Using vectors manipulation instead of loops

Allocating memory in advance

Matlab tries to accelerate the code running speed…

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Matlab Goal is to Convert the M-code Into the Most Efficient Computer Language Code

Goal:Best computer language code

Computer language

0100110101

Intermediate language

x = linspace(0,2*pi,1000);y = sin(x);

x = linspace(0,2*pi,1000); z = zeros(size(x)); for i=1:length(x) z(i) = sin(x(i));end

==

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Matlab Just-In-Time Accelerator

Improving the speed of M-code functions and scripts, particularly self-contained loops.

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Matlab Just-In-Time Accelerator

Matlab 6.5 and later versions Not supported (not accelerated):

Cell, Structure, sparse matrix Arrays of more than three dimensions Changing the data type or the shape of

an array Calling non built-in functions (M-files) if, elseif, while, and switch – if the logical

expression does not evaluate to a scalar

Matlab can represent sparse matrices . Checkout sparse doc

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Timing a Run

We can time a run by planting in the code, function that measure the run time: tic, toc cputime

Examples:

CPU time – The amount of time a computer program uses in processing on a CPU

prev_cpu_time = cputime;a = rand(1,100000);cur_cpu_time = cputime;cpu_run_time = … cur_cpu_time-prev_cpu_timerun_time = 0.0156Elapsed time is 0.009608

seconds.

tic;

a = rand(1,100000);

toc;

Recommended

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Matlab Profiler Helps us to Focus on the Code Bottlenecks

Profiling - is a way to measure where the program spends its time

Profiling helps to uncover performance problems that you can solve by: Avoiding unnecessary computation. Changing your algorithm to avoid

costly functions Avoiding recomputation by storing

results for future use

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Matlab Can Produce a Graphical Profiling Report

profile('on'); <tested code> profile('viewer'); profsave(profile('info'),…

'example_profile');

Turning the profiler on

Turning the profiler offand presenting the results

Saving the profiler results in HTML format

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Profiler Example - 1 edit writingEfficientCodeExamples.m; Lets run the first example:

profile('on'); vec1 = linspace(0,2*pi,10^4); [vec1_sin_fast vec1_sin_slow] = computeSinSlowAndFast(vec1); profile('viewer'); profsave(profile('info'),'example1_profile');

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Profiler Example 1 – Profile Summary

Dark band – self time

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Profiler Example 1 – Focusing on a Function

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Function listing highlights time consumintg lines

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The Profiler Gives Also the M-lint Analysis

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Profiler Example - 2 Try run the second example:

In function computeTwinPeaksFunc: Try to change to computation of Z to a function:

How does it affect the code? Why? Try saving the profiler results in HTML

format using:

profile('on');twinPeaksExample();profile('viewer');

%Z(i,j) = X(i,j) * exp(X(i,j)^2-Y(i,j)^2);

Z(i,j) = computeTwinPeaksFuncForSinglePoint(X(i,j),Y(i,j));

profsave(profile('info'),'example2_profile');

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Efficient vs. Non- Efficient Algorithm

Binary search (Lecture Reminder)

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Divide and Conquer Paradigm

Since the lion is dangerous we can’t catch him, so we start building fences until we close him in a cage…

First Strategy:

How do you catch a lion in the desert?

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Divide and Conquer Paradigm

Divide and conquer strategy (“lion in the desert”):

How do you catch a lion in the desert?

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Implementation of binary search

We have data sets of last psychometric exam results

We want to write a function that:Given an ID, finds its corresponding score as fast as possible

ID score

1920345

720

1920352

670

1930114

700

… …

Sorted

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We Will Use the “Lion in the Desert” Strategy – Binary Search

Example: Find id 415

101 115 200 304 415 516 550 602 711 808 901 903 980

= compare IDs

= left index / right index

= Requested ID

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Binary Search – IDs example

function [id_index] = local_findIdIndexBinary(ids, id)

%init id_index = NaN;l_ind = 1;r_ind = length(ids);mid_ind = floor((l_ind + r_ind) / 2);

<main loop>

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Binary Search – IDs example

function [id_index] = local_findIdIndexBinary(ids, id) <init>while l_ind < r_ind cur_mid_id = ids(mid_ind); if id == cur_mid_id id_index = mid_ind; return; elseif id < cur_mid_id r_ind = mid_ind; mid_ind = floor((l_ind + r_ind) / 2); else %id > cur_mid_id l_ind = mid_ind; mid_ind = ceil((l_ind + r_ind) / 2); endend

l_ind r_indmid_ind

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Performance Comparison of Linear Search and Binary Search

Check out t10.m and findPsychoScore.m Results for three search of random id:

------------------ test:1 ---------------------------Linear search took 83231 comparisonsLinear search find that the score of ID 83229533 is:440Binary search took 17 comparisonsBinary search find that the score of ID 83229533 is:440------------------ test:2 ---------------------------Linear search took 2702 comparisonsLinear search find that the score of ID 2627259 is:571Binary search took 17 comparisonsBinary search find that the score of ID 2627259 is:571------------------ test:3 ---------------------------Linear search took 23594 comparisonsLinear search find that the score of ID 23657664 is:720Binary search took 17 comparisonsBinary search find that the score of ID 23657664 is:720

Comment:Worst caseAverage case

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Summary

M-lint Just-In-Time accelerator Profiler Example of efficient vs. non- efficient

algorithm: Binary search