Discussion for Programming

8/2/2019 Discussion for Programming

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Intro MATLAB

Easy 2-D Graphics

>> x = [0: pi/100: pi]; % [start: increment: end]

>> y = sin(x);

>> plot(x,y), title('Simple Plot')



Intro MATLAB

Adding Another Curve

Line color, style, marker type,all within single quotes; type

>> doc LineSpec

for all available line properties

Line color, style, marker type,

all within single quotes; type

>> doc LineSpec

for all available line properties

>> z = cos(x);

>> plot(x,y,'g.',x,z,'b-.'),title('More complicated')



Intro MATLAB

function [a b c] = myfun(x, y)

b = x * y; a = 100; c = x.^2;

>> myfun(2,3) % called with zero outputsans =

100>> u = myfun(2,3) % called with one outputu =

100>> [u v w] = myfun(2,3) % called with all outputs

u =100

v =

6w =

4

Functions – First Example

Write these two lines to a file

myfun.m and save it on MATLAB’s path

Write these two lines to a file

myfun.m and save it on MATLAB’s

path

Any return value which is not storedin an output variable is simply

discarded

Any return value which is not stored

in an output variable is simply

discarded



Problem 1



Problem 1



Solution 1

function sincomp(x,n)i = 1;tru = sin(x);ser = 0; //Value from Seriesfprintf('\n');fprintf('order true value approximation error\n');

while (1)if i > n, break, end

ser = ser + (-1)^(i - 1) * x^(2*i-1) / factorial(2*i-1);er = (tru - ser) / tru * 100;fprintf ('%3d %14.10f %14.10f %12.8f\n', i, tru, ser,er);

i = i + 1;end



Solution 1

>> sincomp (1.5,8)order true value approximation error1 0.9974949866 1.5000000000 -50.376695642 0.9974949866 0.9375000000 6.014565233 0.9974949866 1.0007812500 -0.329451624 0.9974949866 0.9973911830 0.010406435 0.9974949866 0.9974971226 -0.000214146 0.9974949866 0.9974949557 0.000003107 0.9974949866 0.9974949869 -0.00000003

8 0.9974949866 0.9974949866 0.00000000



Problem 2



Problem 2



Problem 2

l i



Solution 2function [r, th] = polar(x, y)r = sqrt(x .^ 2 + y .^ 2);

if x < 0

if y > 0 // second quadrant conditionth = atan(y / x) + pi;

elseif y < 0 // third quadrant conditionth = atan(y / x) - pi;

else

th = pi;end else if y > 0

th = pi / 2; elseif y < 0

th = -pi / 2; else

th = 0;end

end

th = th * 180 / pi;

bl 3



Problem 3

P bl 3



Problem 3



Solution 3

function Manning(A)

A(:,5) = sqrt(A(:,2))./A(:,1).*(A(:,3).*A(:,4)./(A(:,3)

+2*A(:,4))).^(2/3);

fprintf('\n n S B H U\n');

fprintf('%8.3f %8.4f %10.2f %10.2f %10.4f\n',A');



Solution 3A =

0.0350 0.0001 10.0000 2.00000.0200 0.0002 8.0000 1.00000.0150 0.0010 20.0000 1.50000.0300 0.0007 24.0000 3.00000.0220 0.0003 15.0000 2.5000

>> Manning(A)

n S B H U0.035 0.0001 10.00 2.00 0.36240.020 0.0002 8.00 1.00 0.60940.015 0.0010 20.00 1.50 2.51670.030 0.0007 24.00 3.00 1.58090.022 0.0003 15.00 2.50 1.1971

>>



Problem 4

• Economic formulas are available tocompute annual payments for loans.Suppose that you borrow an amount

of money P and agree to repay it inn annual payments at an interestrate of i. The formula to compute the

annual payment A is



Problem 4 (Contd..)

• Write an M-file to compute A. Test it with P = Rs.1,00,000.00 and aninterest rate of 6% (i = 0.06).

Compute results for n = 1, 2, 3, 4, and5 and display the results as a tablewith headings and columns for n and

A.



Solution 4

function annualpayment(P, i, n)nn = 1:n;A = P*i*(1+i).^nn./((1+i).^nn-1);

y = [nn;A];fprintf('\n year annualpayment\n');fprintf('%5d %14.2f\n',y);



Intro MATLAB

Variable Argument Lists (cont.)

• Consider the m-file:

function [s, varargout] = mysize(x)

nout = max(nargout,1) - 1;

s = size(x);

for k = 1:nout, varargout(k) = {s(k)}; end

• The following

>> [s,rows,cols] =mysize(rand(4,5))

returnss = [4 5], rows = 4, cols = 5

pack all outputvalues

into varargout cell

array

pack all outputvalues

into varargout cellarray

nargout: number of output

arguments in function call

nargout: number of output

arguments in function call

MATLAB FUN TI N F R BI E TI N



MATLAB FUN TI N F R BI E TI NMETHOD

function[root,fx,ea,iter]=bisection(func,xl,xu,es,maxit,varargin)% bisect: root location zeroes%[root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,p1,p2,...):

% uses bisection method to find the root of func% input:% func = name of function% xl, xu = lower and upper guesses

% es = desired relative error (default = 0.00001%)% maxit = maximum allowable iterations (default =50)% p1,p2,... = additional parameters used by func% output:

% root = real root




MATLAB FUN TI N F R BI E TI NMETHOD

if nargin<3,error('at least 3 input arguments

required'),endtest =func(xl,varargin{:})*func(xu,varargin{:});

cont=0;while (cont==0)

if (test>0)s= input (' Enter new bound type l/u :', 's');xv=input (' Enter value: ');

if (s=='l')

xl=xv;elsexu=xv;endtest =

func(xl,varargin{:})*func(xu,varargin{:});




MATLAB FUN TI N F R BI E TI NMETHODif nargin<4|isempty(es), es=0.0001;end

if nargin<5|isempty(maxit), maxit=50;end

iter = 0; xr = xl; ea = 100; while (1)xrold = xr;xr = (xl + xu)/2;iter = iter + 1;if xr ~= 0,ea = abs((xr - xrold)/xr) * 100;end

test = func(xl,varargin{:})*func(xr,varargin{:});if test < 0

xu = xr;elseif test > 0xl = xr;

elseea = 0;

endif ea <= es | iter >= maxit,break,end

end

root = xr; fx = func(xr, varargin{:});

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