Programming Environment

Introduction to Matlab: ProgrammingEnvironment Control Flow S. Awad, Ph.D. M. Corless, M.S.E.E. E.C.E. Department University of Michigan-Dearborn

Control Flow Topics • For Loop • While Loop • If-Elseif-Else-End • Switch

For Loop • For Loop Syntax: for v = expression (or array) … commands … end • To Create Column Vector x = [12 22 32 42]’ » x = zeros(4,1); » for i=1:4 x(i) = i*i; end;

Nested For Loops • Create an m x n Hilbert Matrix

Nested For Loops Code » m = 4;n = 5; » a = zeros(m,n); » for i=1:m, for j=1:n a(i,j)=1/(i+j-1); end end » aa = 1.0000 0.5000 0.3333 0.2500 0.2000 0.5000 0.3333 0.2500 0.2000 0.1667 0.3333 0.2500 0.2000 0.1667 0.1429 0.2500 0.2000 0.1667 0.1429 0.1250

Matlab Code Results For Loop Array Example » data = [3 9 4 5; 7 16 -1 5]; » for n = data x = n(1) - n(2) end x = -4ÞFirst Column in data x = -7ÞSecond Column in data x = 5ÞThird Column in data x = 0ÞFourth Column in data

While Loops • While Loop Syntax: whileexpresion : : commands : end

While Loop Log Example • The MacLaurinseries expansion for log(1+x) (natural log), where |x| < 1, is given by: • Estimate log(1+x) for x=0.5 by summing the series until the term to be added next is less than eps(floating point relative accuracy constant) in absolute value

While Loop Log Code » v=0;x=0.5;k=1; » while abs((x^k)/k) >= eps v = v+(-1)^(k+1)*((x^k)/k); k = k+1; end » v,k=k-1 v = 0.4055 log(1.5) k = 46 Number of Iterations

While Loop Factorial Example • What is the first integer n for which n! (n factorial) is a 100 digit number? » n = 1; » while prod(1:n) < 1.e100 n = n + 1; end= » n n = 70

Factorial Verification • Verify the results » prod(1:n)% n! = 70! ans = 1.1979e+100 » prod(1:n-1)%(n-1)! = 69! ans = 1.7112e+098 • Therefore, n=70 is the first integer where n! is a 100 digit number

One Alternative Expression Syntax One Alternative Example One Alternative If - End if expression : :Commands : end » if a > 1 b=0; c=5; end

Two Alternative Expression Syntax Two Alternative Example If-Else-End Constructions if expression : :Command Set 1 : else expression : :Command Set 2 : end » if a > 0 b=1; else b=-1; end

Several Alternative Expression Syntax If-Elseif-Else-End Constructions if expression Command Set 1 elseif expression Command Set 2 elseif expression Command Set 3 else expression Command Set 4 end

Breaking Out of a Loop • It is possible to break out of for loops & while loops using thebreak command • When the break statement is executed, MATLAB jumps from the current loop in which it appears • In the case of nested for or while loops, MATLAB jumps out of only the current loop

Break eps Example » EPS=1; • Find the value of eps (floating point relative accuracy constant) » for i=1:1000 EPS=EPS/2; if(1+EPS)<=1 EPS=EPS*2; break; end end » EPS EPS = 2.2204e-016 NOTE: i=53

Switch Case Constructions • Used when a sequence of commands must be conditionally evaluated based on repeated use of an equality test with one common argument switch expression casetest_expression_1 command Set 1 casetest_expression_2 command set 2 otherwise command set3 end Scalar or Character string

Switch Example 1 • Display a message based on the variable var » var=3; » switch var case 1 disp('1'); case {2,3,4} disp('2 or 3 or 4'); case 5 disp('5'); otherwise disp('something else'); end 2 or 3 or 4

» x=2.7; units='m'; » switch units » y y = 270 Switch Example 2 • Given measurement x in meters, Convert x to centimeters case {'feet','ft'} y=x*2.54*12; case {'inch','in'} y=x*2.54; case {'meter','m'} y=100*x; case {'centimeter','cm'} y=x; case {'millimeter','mm'} y=x/10; • Results in centimeters: otherwise disp(['Unknown Units:' units]); y=nan; end

Programming Environment