matlab introduction v2

7/21/2019 Matlab Introduction v2

http://slidepdf.com/reader/full/matlab-introduction-v2 1/37

Introduction to MATLAB

Michael Schwedler

Institut f ur Strukturmechanik

Bauhaus-Universitat WeimarWeimar, Germany

Finite Element Methods and Structural Dynamics17. Oktober 2011



basics control structures

Outline

1 basics

2 control structures

Schwedler (Bauhaus-Universitat Weimar) Introduction to MATLAB 18.10.2011 2 / 27




it’s a calculator...

MATLAB

1 7+32 21∗43 6/74 7 . 2 −11. 375 3ˆ26 s q r t ( 1 6 )7 x = 3 . 248 y = 7 . 459 z=x+y ;

10 z11 x=x+2;12 z13 z=x+y





input - fundamental data types

In general

Name Size Range Remark

boolean 1 byte true or false

integer 4 bytes signed: -2147483648 to 2147483647

unsigned: 0 to 4294967295

float 4 bytes −3.4 ∗ 1038 to 3.4 ∗ 1038 (∼7 digits) single precisiondouble 8 bytes −1.7 ∗ 10308 to 1.7 ∗ 10308 (∼15 digits) double precision

char 2 bytes 65536 characters 16 bit Unicode

MATLAB - All numbers stored as double

1 35500/1132 f o r m a t l on g e3 a n s4 f o r m a t s h o r t ; f o r m a t l o n g ; f o r m a t s h o r t e ; f o r m a t l o n g e ;


b i l




input - fundamental data types

In general

Name Size Range Remarkboolean 1 byte true or false

integer 4 bytes signed: -2147483648 to 2147483647

unsigned: 0 to 4294967295

float 4 bytes −3.4 ∗ 1038 to 3.4 ∗ 1038 (∼7 digits) single precisiondouble 8 bytes −1.7 ∗ 10308 to 1.7 ∗ 10308 (∼15 digits) double precision

char 2 bytes 65536 characters 16 bit Unicode

MATLAB - All numbers stored as double

1 35500/1132 f o r m a t l on g e3 a n s4 f o r m a t s h o r t ; f o r m a t l o n g ; f o r m a t s h o r t e ; f o r m a t l o n g e ;


b si s nt l st t s




input - matrices

MATLAB - matrix with dimension 1 x 11 n=22 s i z e ( n )

MATLAB - vectors

1 n =[2 3 .7 4 2 . 1 ]2 s i z e ( n )3

4

n = [ 2 , 3 . 7 , 4 , 2 . 1 ]5 s i z e ( n )6

7 n = [ 2 ; 3 . 7 ; 4 ; 2 . 1 ]8 s i z e ( n )






input - matrices

MATLAB - matrices

1 c l e a r2 M=[2 7 5 . 4 6 . 6 ; 2 2 1 . 0 1 2 . 1 ; 3 . 3 2 . 9 4 6 . 9 ]3 M(2 , 3)4 M( 2 , : )5

6 P( 2 , 7) =45.8

MATLAB - turning a vector into a matrix

1 n =[2 3 .7 4 2 . 1 ]2 n ( 2 , : ) =[4 5 . 5 6 2 . 1 ]3 s i z e ( n )





input - matrices - special initialization

MATLAB - built in functions

1 a=z e r o s ( 5 , 6 )2 b=e y e ( 5 )3 c=r a n d ( 4 , 6 )

4 d=z e r o s ( s i z e ( c ) )

MATLAB - first:increment:last

1 x = 1 : 5 : 3 52 x= [ 1 : 5 : 3 5 ] ’3 y =[x ’ ; x ’ ]





input

MATLAB - strings

1 s= ’ T h i s i s a s t r i n g ’2 t= ’Don ’ ’ t wor ry ’3

s (1 )=t ( 1 ) ;4 s

MATLAB - input from keyboard

1 n=i n p u t ( ’ E n t e r a v al u e f o r n : ’ )





calculating

MATLAB1 A = [ 1 , 2 , 3 ; 4 , 5 , 6 ; 7 , 8 , 9 ]2 B = [ 3 , 2 , 1 ; 6 , 4 , 5 ; 8 , 7 , 9 ]3 C = [ 1 ; 2 ; 3 ]

MATLAB - matrix arithmetic

1

2

3 A∗B4 A/B % A ∗ i n v (B)5 A\B % i n v ( A) ∗ B 6 Aˆ27 A∗C

MATLAB - elementwise

1 A+B2 A−B3 A .∗B4 A . / B %A( i , j ) : B( i , J )5 A .\B %B( i , j ) : A( i , J )6 A . ˆ 27 A .∗C





calculation hierachy

distance = 0.5 × accel × time ˆ 2distance = 0.5 × accel × ( time ˆ 2 )distance = ( 0.5 × accel × time ) ˆ 2

Hierachy of arithmetic

Precedence Operation

1 The contents of all parentheses are evaluated, starting fromthe innermost parentheses and working outward.

2 All exponentials are evaluated, working from left to right.3 All multiplications and divisions are evaluated, working from

left to right.4 All additions and subtractions are evaluated, working from left

to right.





calculation hierachy

distance = 0.5 × accel × time ˆ 2distance = 0.5 × accel × ( time ˆ 2 )distance = ( 0.5 × accel × time ) ˆ 2



1 The contents of all parentheses are evaluated, starting fromthe innermost parentheses and working outward.

2 All exponentials are evaluated, working from left to right.3 All multiplications and divisions are evaluated, working from

left to right.4 All additions and subtractions are evaluated, working from left

to right.





functions

Functions are subprograms stored in text files with .m extension.

Input parameters are passed to the function by an input argument list.Results are returned to the caller by an output argument list.Anything that happes within the function is invisible to the caller.In order to call a function, the .m-file must be stored within the path of MATLAB.The function name must be equal to the file name.

MATLAB

1 f u n c t i o n [ outArg1 , outArg2 , . . . ] = fname ( inA rg1 , inA rg2 , . . . )2 % H1 comment l i n e 3

% o t h er comment l i n e s 4

5 MATLAB c od e6

7 r e t u r n





exercise

Function: dotProduct3

Write a function named dotProduct3 that calculates the dot product of twovectors a and b , , each with length = 3.

a · b = | a| | b | cos( a, b )

Function: crossProduct3

Write a function named crossProduct3 that calculates the cross product of twovectors a and b , each with length = 3.

a × b = (| a| | b | sin θ) n

a · b = a1 b 1 + a2 b 2 + a3 b 3 a × b =

a1

a2

a3

×

b 1b 2b 3

=

a2b 3 − a3b 2a3b 1 − a1b 3a1b 2 − a2b 1





general control structures

The sequence of programs must be controlled. For this purpose three basic typesof program control structures are defined.

sequences

branchesrepetitions

These basic forms are implemented in any programming language by different

constructs.





sequences

A sequence is a series of instructions.

Algorithm

1 s t at e me n t 1 ;2 s t at e me n t 2 ;3 s t at e me n t 3 ;4 . . .





branches

Branching between alternative code sequences (blocks) depends on whether acondition is satisfied. In MATLAB there are variations of the if construct and theswitch construct for this purpose.

To express conditions, relational and logical operators are required.





branches - relational operators

Relational operators determine the relation between two operands (numbers,strings) and return 1, i.e. true or 0, i.e. false , depending on the relation.

Operator Operation

== equal to∼= not equal to> greater than

>= greater than or equal to< less than<= less than or equal to

Examples

Operation Result

3 < 4 13 >= 4 03 == 4 04 <= 4 1’A’<’B ’ 1





branches - logical operators

Logical operators evaluate the logic result of one (unary operator) or two operands(binary operator). They return 1, i.e. true or 0, i.e. false , depending on therelation.

Operator Operation

& logical AND| logical OR

xor logical exclusive OR∼ logical NOT

Examples

Inputs AND OR XOR NOTl 1 l 2 l 1&l 2 l 1|l 2 XOR (l 1, l 2) ∼ l 1

0 0 0 0 0 10 1 0 1 1 11 0 0 1 1 01 1 1 1 0 0

In case of scalars & becomes && and | becomes .Schwedler (Bauhaus-Universitat Weimar) Introduction to MATLAB 18.10.2011 17 / 27




branches - operator hierachy



1The contents of all parentheses are evaluated, starting fromthe innermost parentheses and working outward.

2All exponentials are evaluated, working from left to right.

3All multiplications and divisions are evaluated, working fromleft to right.

4All additions and subtractions are evaluated, working from leftto right.

5 All relational operators (==, ∼=, >, >=, <, <=) are eva-luates, working from left to right.

6 All ∼ operators are evaluated.7 All & and | operators are evaluated, working from left to right.





branches - if construct

control expressions will be

some combination of relationaland logical operatorsthe code block below a controlexpression is execetued, in casethe expression evalutes to ’1’,

i.e. true after the execution of one codeblock (i.e. one branch) theother expressions are notcheckedmultiple elseif clauses areallowed, including zerothere can be at most one else

clauseif constructs can be nested

Algorithm

1 i f c o n t r o l e x p r e s s i o n 12 S t a t e m e n t A13 S t a t e m e n t A24 . . .5 e l s e i f c o n t r o l e x p r e s s i o n 26 S t a t e m e n t B17 S t a t e m e n t B28 . . .9 e l s e

10 S t a t e m e n t C111 S t a t e m e n t C212 . . .13 end





branches - if construct - example

MATLAB

1 % Prompt t h e u s e r f o r t h e c o e f f i c i e n t s o f t h e e q u a t i o n2 d i s p ( ’ T h i s program s o l v e s f o r t h e r o o t s o f a q u a d r a t i c ’ ) ;3 d i s p ( ’ e q ua t io n o f t he form A∗X ˆ 2 + B∗X + C = 0 . ’ ) ;

4 a = i n p u t ( ’ E n t e r t h e c o e f f i c i e n t A : ’ ) ;5 b = i n p u t ( ’ E n t e r t h e c o e f f i c i e n t B : ’ ) ;6 c = i n p u t ( ’ E n t e r t h e c o e f f i c i e n t C : ’ ) ;7

8 % C a l c u l a t e d i s c r i m i n a n t 9 d i s c r i m i n a n t = b ˆ2 − 4 ∗ a ∗ c ;





branches - if construct - example

MATLAB

1

% So l v e f o r t h e r oo ts , d ep e nd in g on t h e d i s c r i m i n a n t 2 i f d i s c r i m i n a n t > 0 % t h e r e a r e two r e a l r o o ts , s o . . .3 x1 = ( −b + s q r t ( d i s c r i m i n a n t ) ) / ( 2 ∗ a ) ;4 x2 = ( −b − s q r t ( d i s c r i m i n a n t ) ) / ( 2 ∗ a ) ;5 d i s p ( ’ T h is e q ua t io n h a s two r e a l r o o t s : ’ ) ;6 f p r i n t f ( ’ x 1 = %f \n ’ , x1 ) ;

7 f p r i n t f ( ’ x 2 = %f \n ’ , x2 ) ;8 e l s e i f d i s c r i m i n a n t == 0 % t h e r e i s one r e p e a t e d r o o t 9 x1 = ( −b ) / ( 2 ∗ a ) ;

10 d i s p ( ’ T h i s e qu at i o n h a s two i d e n t i c a l r e a l r o o t s : ’ ) ;11 f p r i n t f ( ’ x1 = x2 = %f \n ’ , x1 ) ;12 e l s e % t h e r e a r e c om pl ex r o o t s

13 r e a l p a r t = ( −b ) / ( 2 ∗ a ) ;14 i m ag p a rt = s q r t ( a b s ( d i s c r i m i n a n t ) ) / ( 2 ∗ a ) ;15 d i s p ( ’ T hi s e q u at i o n h as c om pl ex r o o t s : ’ ) ;16 f p r i n t f ( ’ x1 = %f + i %f \n ’ , r e a l p a r t , i m ag p a r t ) ;17 f p r i n t f ( ’ x 1 = %f − i %f \n ’ , r e a l p a r t , i m ag p a r t ) ;18 end



b h i h



branches - switch construct

the switch expression mustevaluate to a number,character, or booleanonly the code block below thecase, whichs value list containsthe value equal to theswitch expression is executedthe otherwise code block isoptionalat most one code block isexecuted

switch constructs can benested

Algorithm

1 s w i t c h ( s w i t c h e x p r e s s i o n )2 c a s e { v al u e 1 , v a l u e 2 } ,3 S t a t e m e n t A14 S t a t e m e n t A2

5 . . .6 c a s e v a l u e 3 ,7 S t a t e m e n t B18 S t a t e m e n t B29 . . .

10 o t h e r w i s e ,11 S t a t e m e n t C112 S t a t e m e n t C213 . . .14 end



i i



repetitions

The repetition of a sequence of statemens is generaly achieved through loops.

In MATLAB, there are

while - loopsfor - loops

The difference between them is in the way the repetitions are controlled.

while-loop:The sequence of statements in the loop is repeated an indefinite number of times,until a specified condition is not satisfied anymore.

for-loop:The number of repetitions is specified before the loop starts.

Loops can be nested.



i i hil l



repetitions - while-loop

as long as the expression is

non-zero, i.e. true , the codesequence within the loop willbe executed

Algorithm

1 w h i l e e x p r e s s i o n2 . . .3 end

MATLAB

1 n =1; s um x = 0;2 x = i n p u t ( ’ E nt er t he n ex t v a l u e : ’ ) ;3 w h i l e x ∼= 04 n = n + 1 ;

5 sum x = s um x + x ;6 x = i n p u t ( ’ E n te r t he n ex t v a l u e : ’ ) ;7 end8 f p r i n t f ( ’ The sum o f t he e n te r ed v a l u e s i s : %f \n ’ , sum x ) ;9 f p r i n t f ( ’ You e n t e r e d %i v a l u e s .\ n ’ , n ) ;



titi hil l



repetitions - while-loop

as long as the expression is

non-zero, i.e. true , the codesequence within the loop willbe executed

Algorithm

1 w h i l e e x p r e s s i o n2 . . .3 end

MATLAB

1 n =1; s um x = 0;2 x = i n p u t ( ’ E nt er t he n ex t v a l u e : ’ ) ;3 w h i l e x ∼= 04 n = n + 1 ;

5 sum x = s um x + x ;6 x = i n p u t ( ’ E n te r t he n ex t v a l u e : ’ ) ;7 end8 f p r i n t f ( ’ The sum o f t he e n te r ed v a l u e s i s : %f \n ’ , sum x ) ;9 f p r i n t f ( ’ You e n t e r e d %i v a l u e s .\ n ’ , n ) ;



titi f l



repetitions - for-loop

expression is ususally a vector or amatrix with n columnsthe code sequence within the loopbody is repeated n timesfor each loop run, the current

column is copied into index index should not be modifiedwithin the loop body

Algorithm

1 f o r i n d e x = e x p r e s s i o n2 . . .3 . . .4 . . .5 end

MATLAB

1 f o r i i = 1 : 1 02 . . .3 end

MATLAB

1 f o r i i = 1 : 2 : 1 02 . . .3 end



repetitions for loop




expression is ususally a vector or amatrix with n columnsthe code sequence within the loopbody is repeated n timesfor each loop run, the current

column is copied into index index should not be modifiedwithin the loop body

Algorithm

1 f o r i n d e x = e x p r e s s i o n2 . . .3 . . .4 . . .5 end

MATLAB

1 f o r i i = 1 : 1 02 . . .3 end

MATLAB

1 f o r i i = 1 : 2 : 1 02 . . .3 end







MATLAB

1 f o r i i = [ 5 9 7 ]2 . . .3 end

MATLAB

1 f o r i i = [ 1 2 3 ; 4 5 6 ]2 . . .3 end

MATLAB1 n=i n p u t ( ’ E nt er t he i n t e g e r f o r w h ic h t he f a c t o r i a l i s t o

be c a l c u l a t e d : ’ ) ;2 n f a c t o r i a l =1;3 f o r i i = n :−1: 1

4 n f a c t o r i a l = n f a c t o r i a l ∗ i i ;5 end6

7 f p r i n t f ( ’ The f a c t o r i a l o f %i (% i ! ) i s %i .\ n ’ , n , n ,n f a c t o r i a l ) ;







MATLAB

1 f o r i i = [ 5 9 7 ]2 . . .3 end

MATLAB

1 f o r i i = [ 1 2 3 ; 4 5 6 ]2 . . .3 end

MATLAB1 n=i n p u t ( ’ E nt er t he i n t e g e r f o r w h ic h t he f a c t o r i a l i s t o

be c a l c u l a t e d : ’ ) ;2 n f a c t o r i a l =1;3 f o r i i = n :−1: 1

4 n f a c t o r i a l = n f a c t o r i a l ∗ i i ;5 end6

7 f p r i n t f ( ’ The f a c t o r i a l o f %i (% i ! ) i s %i .\ n ’ , n , n ,n f a c t o r i a l ) ;



exercise



exercise

Control structures: dotProduct

Modify the function dotProduct3 such, that the dot product of two vectors regardless of their size, can be evaluated.

Make sure, that both vectors received through the inputargument list are of the same size.


matlab introduction v2

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