cz1102 computing & problem solving lecture 10

8/8/2019 CZ1102 Computing & Problem Solving Lecture 10

1/24

EfficientProgramming

in

Matlab

Week12

ByJI,Hui

BasedonWritingFastMATLABCodeby PascalGetreuer


2/24

Introduction

Matlab isainterpretedlanguage,meaningit

focuseson

the

ease

of

development

with

languageflexibility,interactivedebugging,and

otherconveniences

Itlackstheperformanceofthosecompiled

languageslikeCandC++.WhileMatlab may

notbe

as

fast

as

C,

there

are

ways

to

bring

it

closer.


3/24

Organizationof

your

project

Useaseparatefolderforeachproject.

Writecomments,

especially

write

the

help

commentforfunctions

Savefrequent

console

commands

as

ascript


4/24

Commendsforhelpingmeasuring

efficiency

usethetic/toc stopwatchtimer

tic Startastopwatch

timer

toc Readthestopwatchtimer

Donotuseinputtic/toc indifferentprompts,itwill

count

the

typing

time Usingitinasinglelineoruseitinscript

>>tic;sin(rand(1,10^6));toc

Elapsedtime

is

0.055057

seconds.

>>tic;

>>toc

Elapsedtime

is

0.743795

seconds.


5/24

Oneway

for

array

allocation

Dynamicallocation,thatis,dynamically

augmentrows

and

columns

of

arrays

e.g.

>>a=2

a=

2

>>a(2,6)=1

a=

2 0 0 0 0 0

0 0 0 0 0 1


6/24

(cont)

Matlab willautomaticallyresizethematrix

Internally,the

matrix

data

memory

must

be

reallocated

withlargersize.

Theoverhead(cost)canbesignificantifthematrixis

resized

repeatedly,

e.g.

like

within

a

loop Ittakes1.2secondsinacomputerwithcorei5CPU

clearab

tic

a(1)=1;

b(1)

=0;

fork=2:30000

a(k)=0.99803*a(k1) 0.06279*b(k1);

b(k)=0.06279*a(k1)+0.99803*b(k1);

end;

toc


7/24

Anotherway

for

array

allocation

Preallocate thematrixwiththezeros

commandsto

avoid

frequent

reallocations

e.g. Ittakesonly0.009514secondstorunthe

followingcode,150timesfasterthandynamic

allocation

tic;a =zeros(1,30000);%Preallocation

b=zeros(1,30000);

a(1)

=

1;b(1)

=

0;fork=2:30000

a(k)=0.99803*a(k1)0.06279*b(k1);

b(k)=0.06279*a(k1)+0.99803*b(k1);

end;toc


8/24

Whatif

the

final

array

size

can

vary?

Makingthetradeoffbetweenstorage

efficiencyand

computing

efficiency.

Preallocatealargerarrayandtrimextrazeros.

e.g.3.8525secs vs 0.0213secs

a=zeros(1,50000);%Preallocate

count=0;

fork=1:50000

v=exp(rand*rand);

ifv>0.5

%

Conditionally

add

to

array

count=count+1;

a(count)=v;

end;end

a=a(1:count);


9/24

Vecterization

Acomputationisvectorized bytaking

advantageof

vector

operations.

Avarietyofprogrammingsituationscanbe

vectorized,andoftenimprovingspeedto10

timesfasterorevenbetter.

Vectorization isoneofthemostgeneraland

effectivetechniques

for

writing

fast

Matlab

codes.


10/24

Vectorized Computations

Manystandardmathematicalfunctionsare

vectorizedin

Matlab

theycanoperateonanarrayasifthefunctionhad

beenappliedindividuallytoeveryelement.

>>sqrt([1,4;9,16])

ans=

1

2

3 4

>>abs([0,1,2,5,6,7])

ans=

0

1

2

5

6

7


11/24

Oneexampleofvecterized

computation

Problem:Findthemindistancebetweenaset

ofpoints

and

the

origin

Nonvecterized code

functiond=minDistance1(x,y,z)

%Find

the

min

distance

between

aset

of

points

and

the

origin

nPoints =length(x);

d=zeros(nPoints,1); %Preallocate

fork=1:nPoints %Computedistanceforeverypoint

d(k)=sqrt(x(k)2

+y(k)2

+z(k)2);

end

d=min(d); %Gettheminimumdistance


12/24

(cont)

Vecterized code

Thecomparison:vecterized code30timesfaster

>>featureaccel off; %ForMatlab 7

>>x=rand(1,30000);y=rand(1,30000);z=rand(1,30000);

>>tic;minDistance2(x,y,z);toc;

Elapsedtimeis0.002272seconds.

>>tic;minDistance1(x,y,z);toc

Elapsedtimeis0.060647seconds.

functiond=minDistance2(x,y,z)

%Findthemindistancebetweenasetofpointsandtheorigin

d=sqrt(x.2+y.2+z.2); %Computedistanceforeverypoint

d=min(d); %Gettheminimumdistanc


13/24

Someusefulfunctionsupporting

vecterization

Min

max sum,

cumsum,

prod,

cumprod

sort diff


14/24

Vectorized Logic

Bottleneckcodeofteninvolvesconditional

logic

Likecomputations,Matlab's logicoperators

arealsovectorized:

Twoarraysarecomparedperelement.Logic

operationsreturnlogicalarrayswithbinaryvalues.

>>[1,5,3]


15/24

Threepowerfulcommandsforlogical

arrays

find:Findindicesofnonzeroelements

any:Trueifanyelementofavectorisnonzero

(orpercolumnforamatrix)

>>find([1,5,3]

>any([1,5,3]


16/24

(cont)

all:Trueifallelementsofavectorarenonzero

(orper

column

for

amatrix)

Vecterized logic alsoworksformatrices

>>all([1,5,3]>find(eye(3)==1)

ans =

1

5

9


17/24

Example1

Problem: removenegativeelementsfromthe

array V1:Nonvecterized code

y=x; %Preallocate

count=0;

fork=1:length(x),

if(x(k)>=0)

count=count+1;

y(count)=x(k);end;

end;

y=y(1:count);


18/24

(cont)

V2:Vecterized code

V3:

Further

streamlined

version

Timecomparison inseconds

V1:V2:V3 =0.04:0.0031:0.0010

idx=find(x>0);%Findelementsthatarenonpositive

y =x(idx);

y=x(find(x>0));


19/24


20/24

Referencingoperations

ReferencinginMatlab isvariedandpowerful

enough.

Goodunderstandingofreferencingenables

vectorizing abroaderrangeofprogramming

situations.


21/24

Subscriptsvs.

Indices

Subscriptsarethemostcommonmethod

usedto

refer

to

matrix

elements,

for

example,

A(3,9)referstorow3,column9.

Indicesareanalternativereferencingmethod

formatrix byviewingitasavector

Anindex referstoanelement'spositioninthis

one

dimensional

vector Fora10by10matrix,A(83)alsorefersA(3,9)


22/24


23/24


24/24

DeletingSub

matrices

with

[]

Elementsinamatrixcanbedeletedby

assigningthe

empty

matrix.

A(2,:)=[]deletesthesecondrowofA

A([3,5])=[]deletestheelementA(3,5)fromAand

reshapeA

to

avector

DeletionslikeA(2,1)=[]is illegal.

cz1102 computing & problem solving lecture 10

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