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Conditionals : function which returns max and min in right order

This helpful assistant provides functions to find the maximum and minimum of two numbers, solve quadratic equations, generate random numbers, calculate textual qualification for a given numerical mark, calculate final grades, perform matrix operations, and use various built-in MATLAB functions.

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Conditionals : function which returns max and min in right order

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  1. Conditionals: functionwhichreturnsmax and min in rightorder • function [max, min] = maxmin(x, y) • max = (x+y)/2 + abs(x-y)/2 • min = (x+y)/2 - abs(x-y)/2 • End • Short butnot “natural”, thefollowingismuch more comprehensible • function[max, min] = maxmin(x, y) • if x > y • max = x; min = y; • else • max= y; min = x; • endif • end

  2. Nowwe can be more general in solvingthequadraticequation function [ re1, im1, re2, im2 ] = ec2( a, b, c ) % solves a quadratic equation % Input : % a, b, c: coefficients of equation a*x^2+b*x+c=0 % Output: % re1,im1,re2,im2: real and imaginary parts of the solution % Use: [re1, im1, re2, im2] = ec2(a, b, c) d=b^2-4*a*c; if d>=0 re1=(-b+sqrt(d))/(2*a); re2=(-b-sqrt(d))/(2*a); im1=0; im2=0; else re1=-b/(2*a); re2=re1; im1=sqrt(-d)/(2*a); im2=-im1; end

  3. Usingit >> [r1,i1,r2,i2] = ec2(1,-1,-1) r1 = 1.6180 i1 = 0 r2 = -0.6180 i2 = 0 >> [r1,i1,r2,i2] = ec2(1,-1,1) r1 = 0.5000 i1 = 0.8660 r2 = 0.5000 i2 = -0.8660

  4. If and generatingrandomnumbers % Generate a random number between 1 and 100 a = randi(100); % If it is even, divide by 2 if rem(a, 2) == 1 disp('a is odd') a = a+1; endif b = a/2 % Generate a random number between 0 and 0.999999 a = rand(); if a < 0.5 disp(‘head') else disp(‘tail') endif

  5. Example: The “Examen de grado” in UCH • Dependingonthenumerical grade received in the final examstudentsfromthe Universidad de Chile get a textual qualification in their diploma. Grades gofrom 1.0 (worst) to 7.0 (best). Thenumericl grade G istranslated to textaccording to thefollowing rules: • If G islessthan 4 you do notgetyour diploma • If G isbetween 4 and 4.9 yougetan “aprobado”, • IfG isbetween 5 and 5,9 yougetan “aprobado con distinción” • If G is 6.0 orhigheryougetan “aprobado con distinción máxima”. • Write a script whichreadsthenumericalmark and printsthecorresponding textual qualification

  6. Examen de grado: Solution 1 g = input(“input numerical grade"); if (g < 4) disp(“Reprobado”) else if(g < 5) disp(“Aprobado”) else if(g < 6) disp(“Aprobado con distincion”) else disp(“Aprobado con distincionmaxima”) end end end

  7. Examen de grado: Solution 2 n = input(“input numericalmark"); if (n < 4) disp(“Reprobado”) elseif(n < 5) disp(“Aprobado”) elseif(n < 6) disp(“Aprobado con distincion”) else disp(“Aprobado con distincionmaxima”) end

  8. RemembertheexcerciseforExecl ? • Calculating the final grade of a hypothetical course reading the Test average grade (T), the Assignment average grade (A) and the grade received for participation in class (P). • If both averages T and A are >= 5 then the final status is calculated by considering 50% the test average, 30% the Assignments and 20% the participation • If the average for the tests is less than 5 then the final status should show “no pass” and the final mark is not calculated. • If the average of the tests is >= 5 but the average of the assignments is < 5 then if the participation mark is >= 8 or the average test is >= 8 then the final status is calculated as in 2. Otherwise the final status should show the word “Incomplete” • T = input("Tests average "); • A=input("Assignment average "); • P=input("Participation") • if T >= 5 && A >= 5 • sprintf("Your final grade is %f",T*0.5+A*0.3+P*0.2) • elseif T < 5 • sprintf("No pass") • elseif T >= 8 || P >= 8 • sprintf("incomplete") • endif

  9. Matrices • Transposition: Exchange rows for columns • >> M = [5 3 -1; 0 -2 1] • M = • 5 3 -1 • 0 -2 1 • >> M' • ans = • 5 0 • 3 -2 • -1 1

  10. Elements of a Matrix • Theelement in row i and column j of a matrix A • Isidentified as A(i,j) • >> M = [5 3 -1; 0 -2 1] • 3 -1 • 0 -2 1 • >> M(2,3) • ans = 1 • >> k=1; • >> M(k+1, k*2-1) • ans = 0

  11. Dimensions of a Matrix • >> M = [5 3 -1; 0 -2 1]; • >> dim= size(M) • dim = 2 3 • >> [rows, cols]= size (M) • rows = 2 • cols = 3

  12. A simple example • % crete a matrix S 4x4 withtheupperrighttrianglewith • % includingthe diagonal; therestshould be zeroes • % 1 1 1 1 • % 0 1 1 1 • % 0 0 1 1 • % 0 0 0 1 • S = zeros(4,4); • for i= 1:4 • for j= i:4 • S(i,j) = 1; • end • end

  13. Slices • FromthefollowingMatrix A 2x3: • A = [ 1 2 3 ; 4 5 6 ] • We can to getthesecondrowdoing: • A (2, 1:3) • ans • 4 5 6

  14. silces(2) • Gettingthethirdcolumn: • A (1:2, 3) • ans • 3 • 6

  15. Funciones vistas en la preparación • ForthefollowingMatrix B: • B = [1 2 3; 4 5 6; 7 8 9] • sum(B) • ans = • 12 15 18 • diag(B) • ans = • 1 • 5 • 9

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