matlab iteration

8/12/2019 MATLAB Iteration

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ECE 1331

MATLAB: Iteration

ECE 1331ECE 1331

MATLAB: IterationMATLAB: Iterationloops and implied loopsloops and implied loops


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Loops and Implied Loops

loop example


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Loops and Implied Loops "iterate":

to perform again; repeat

Consider the followingproblem:

given vector of numbersnamed data

want to add up values indata greater than somescalar named val

must "iterate" throughvalues in data, comparing

each one to val, thensumming those valuesgreater than val

This is a "loop" operation, asindicated by thepseudocode:

initialize total to zero

for each value in data:if value is greater than val,add value to total


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Loops and Implied Loops

Init total to zero

Is value > val?

Add value to total

next value

For each

value in

data...

no morevalues

No

Yes

Init total to zero

Look at next data

value

Is value > val?

Add value to total

More values in

data?

Yes

Yes

No

No


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Iteration in Spreadsheets

=SUM(B1:B8)

=IF(A8>val,A8,"")11

=IF(A7>val,A7,"")-5

=IF(A6>val,A6,"")6

=IF(A5>val,A5,"")8

=IF(A4>val,A4,"")-3

=IF(A3>val,A3,"")1

=IF(A2>val,A2,"")5

5=IF(A1>val,A1,"")3

Iteration in spreadsheets takesplace when a formula operatingon a value in a column is copieddown so that it similarly

operates on the entire columnof data.

For example: the problem above is solved in

Excel as shown to the right Assume that cell C1 is named

"val"

Look closely and see how this isan implementation of the

flowchart and pseudocode.

=SUM(B1:B8)

=IF(A8>val,A8,"")11

=IF(A7>val,A7,"")-5

=IF(A6>val,A6,"")6

=IF(A5>val,A5,"")8

=IF(A4>val,A4,"")-3

=IF(A3>val,A3,"")1

=IF(A2>val,A2,"")5

5=IF(A1>val,A1,"")3


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Implied Loops in MATLAB Iteration takes place

"automatically" in MATLAB bcuzof the built-in vector operations

solution is implemented two waysso that you can see the pieces

Since data is a vector, theoperation data > val causesautomatic iteration

comparing val to each element ofdata, in turn automatic iteration also takes

place when data is given a vectorsubscript (as shown on the right)

But look carefully and see, again,that this is an implementation ofthe flowchart

data = [3,4,1,-3,8,6,-5,11];

val = 5;

Solution in several explicit steps

% subscripts of values > val

indices = find(data>val);

% actual values > valbigdata = data(indices);

% sum of those values

total = sum(bigdata)

Solution in fewer steps

% sum data values > val

total = sum(data(data>val))


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for Loops for loops in MATLAB (or any other language) are way of explicitly

implementing Loop structure for iteration

more tedious than MATLAB's implied loops, but are also more flexible

The structure of a for loop is:for loop-variable = m:s:n for loop-variable = aVector

statements statements

end end

where m:s:nare the usual expression for generating elements of a vector: m= initial value s= step or increment n= terminating value

In the second form above, aVectorcan already have a set of values

loop-variabletakes on each of the vector values for one pass through theloop, executing the statementsonce during each pass


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Examples:

Fill vector with values of cos(x)

for k = 1:101

x = (k-1)*2*pi/100;

y(k) = cos(x);

end

equivalent to:

x = linspace(0,2*pi,101);

y = cos(x);

Display the square roots of theodd integers from 1 to 9

% using explicit for loopfor n = 1:2:9

disp(sqrt(n))

end

equivalent to:

% using implied loop

n = 1:2:9;

disp(sqrt(n))


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Examples

Display the log of a set of values read

from a file

load data.txt;

for x = datalogval = log(x);

disp(['Log of ', num2str(x), ' is ', num2str(logval)])

end


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Examples Now let's do our earlier iteration example:

data = [3,4,1,-3,8,6,-5,11];val = 5;

% Loop through data

total = 0;

for n = 1:length(data)

if data(n)>val

total = total + data(n);

endend Notice that in this case we can combine the

comparison and the summing in the same pass,whereas the spreadsheet and implied loopsolutions first created a set of values bigger

than val, and then summed them up. A lessefficient for loop implementation could copythat approach


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Examples

First, create a vector of the big values

k = 0; % counter for large values


if data(n)>val

k = k+1;

bigdata(k) = data(n);

endend

Now add up the big values

total = 0;

for n = 1:length(bigdata)

total = total + bigdata(n);

end


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Standard Loop Structure Programmed loop problems

can be solved with thefollowing general structure: pre-loop initialization

set up the problem, initializevariables, initialize counters,etc.

loop control: initialize,increment/modify, test

usually a loop variable isspecified, along with itsinitial value, increment valuefor each pass through theloop, and a test on thevariable for when to exit theloop)

loop body

the instructions that areexecuted each pass throughthe loop

post-loop cleanup stuff that needs to be done

when the loop is exited

allocate "space" on page for eachsection, and insert instructions intoeach section as necessary

Example: Disp. # of neg. values in data

array

data = [3,4,1,-3,8,6,-5,11];

% pre-loop initializationcounter = 0;

% loop control


% loop body

if data(n)< 0

counter = counter + 1

end

end

% post-loop cleanup

disp('Number of negativevalues is: ')

disp(counter)

data = [3,4,1,-3,8,6,-5,11];

counter = 0;

for n = 1:length(data)if data(n)< 0

counter = counter + 1

endend

disp('Number of negative values is: ')disp(counter)

Well known for Loop


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Well-known for Loopexamples

Find maximum value in a vector

load data.txt;

maximum = data(1); % maximum so farfor n = 2:length(data)

if data(n)>maximum

maximum = data(n); % replace with new maximum

endend

Of course, there is also a quick function for that:

maximum = max(data);

W ll k f L


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Well-known for Loop

examplesSearch for a specific value in a vectorload data.txt;

target = input('Enter value to searchfor:');

found = 0; % Init flag to false


if data(n)==target

found = 1;

break;end

end

% Display result

if(found)

disp('Value was found.')

elsedisp('Value was NOT found.')

end

Again, there is a faster way of

doing this using find():

load data.txt;

target = input('Enter value tosearch for:');

found =length(find(data==target));

% Display result

if(found)

disp('Value was found.')

else

disp('Value was NOTfound.')

end


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for Loop to Vectorize a Function

Recall that we had a problemusing an if statement with avector in a function, so welearned how to insist on ascalar argument:

function y = myabs(x);

% Test for scalar

if length(x)~=1

error('Input variablemust be scalar.')

end

% Input is scalar,proceed.

if x>=0

y = x;

else

y = -x;

end

Now we can use a for loop toprovide the iteration needed

with an if statement:function y = myabs(x);

% Assume x, and thus y, arevectors

for n = 1:length(x)if x(n)>=0

% x(n)is scalar

y(n) = x(n);

elsey(n) = -x(n);

end

end


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for Loop to Vectorize a Function

Another example: Define this function asfilteredpulse(t):

y = 0 for t= a

function y = filteredpulse(t,a);

for n = 1:length(t)

if t(n)0 & t(n)


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while Loops for loop

number of passes through the loop is known in advance controlled by the loop index variable

while loop number of passes through the loop is not known in advance depends on a special condition that is reevaluated after each pass

Loop initialization

Is continuation

condition met?

Perform actions,

including something

that may result in

termination of loop

repeat

No

Yes


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while Loops The MATLAB while statement is:

whi l e logical-expression

statements

end

w.r.t. standard loop structure described earlier, elements of loop controlsection (initialize, increment/modify, test) are now distributed

"initialize" operation must be part of the loop initializationsection "increment/test" operation is done in the loop body while instruction itself contains on the "test" operation.

e.g. a for loop implemented with a while might look like this:

n =m

for loop-variable =m:s:n while loop-variable


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while LoopsConsider the following example:

Input the value N. Startingwith 1, compute and display allof the integer squares up toand including N. Do thiswithout taking a square root.

pseudocode:input N

initialize n to 1as long as n*n is less than

or equal to N, do thefollowing

display n*nincrement n

The MATLAB code is:

% Initialization

N = input('Enter stop

number:');n = 1;

nsq = n*n;

% Loop until N is exceeded

while nsq


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while Loops Another example:

To approximate E, sum the series expansion until the sumchanges by no more than a tolerance value entered by the user

% Initializationtol = input('Enter desired errortolerance:');

sum = 1; % first term for n=0

n = 1;

nfact = 1;

newterm = 1; % addition for n=1 (1/1!)

% Loop computing the series sum

while newterm > tol

sum = sum + newterm;n = n+1;

nfact = n*nfact; % next factorial

newterm = 1/nfact; % next term

enddisp(['E is approximately ', num2str(sum)])


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matlab iteration

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