Computer Science 121 Scientific Computing Winter 2012 Chapter 7 Conditionals.

Computer Science 121

Scientific ComputingWinter 2012

Chapter 7Conditionals

Conditionals: Motivation

• Consider absolute value algorithm:

1. If number is negative, negate it.2. Otherwise, leave it alone.

• We need a way to express “if” and “otherwise”.

7.1 The if Statementfunction res = absvalV1(x)% absolute value, version 1

if x < 0 % the test condition

res = -x; % the YES block

else

res = x; % the NO blockend

• Any amount of code can go inside YES/NO blocks:

function [smaller,bigger] = arrange2(a, b)if a < b

smaller = a;bigger = b;

elsesmaller = b;bigger = a;

end

Style• Don't need as many blank lines as in example:

function res = abs(x)if x < 0

res = -x;else

res = x;end

• But indentation is very important: editor will do this for you automagically (or highlight and use CTRL-I)

7.2 More Than Two Cases• Consider finding max of three numbers a, b, c

Condition Outcome

a ≥ b and a ≥ c ab ≥ a and b ≥ c bc ≥ a and c ≥ b c

• With only if and else, we end up with a lot of indentation (embedding), not reflecting structure of problem (3 cases)....

7.2 More Than Two Cases

function res = max3V0(a, b, c)% max of three inputs, version 0if a >= b && a >= c % why is a here, but ...

res = a;else

if b >= a && b >= c % b and c here?res = b;

elseres = c;

endend

7.2 More Than Two Cases

• We can give each case equal status by using elseif:

function res = max3V1(a, b, c)

if a >= b && a >= cres = a;

elseif b >= a && b >= cres = b;

elseres = c;

end

7.3 Completeness and Exclusivity

• Sometimes we can leave out the “do nothing” case (like abs. val. of a positive number):

function res = absvalV2(x)res = x; % does this have to go first?if x < 0

res = -x;end

• A statement like this is called “incomplete” - no case of the conditional is executed. This can lead to trouble...

A Note on & …

• For logical AND, book uses &, but Matlab now expects you to use && (you’ll get a warning).

• Same for logical OR: use || instead of |

Completeness

function res = max3V2(a, b, c)% © 2008 Stewie Griffin (broken)

if a > b && a > cres = a;

elseif b > a && b > cres = b;

elseres = c;

end

Completeness

>> max3v2(1, 2, 3)ans = 3

>> max3v2(3, 2, 1)ans = 3

>>max3v2(2, 3, 1)ans = 3

>> max3v2(3, 3, 1)ans = 1 % Ruh roh!

• A safer strategy is to make sure that we reach our else case only in an “impossible” situation:

function res = max3V2(a, b, c)% saferif a > b && a > c

res = a;elseif b > a && b > c

res = b;elseif c > a && c > b

res = c;else

error('What the deuce?!')end

Completeness

Completeness

• It might be more sensible to handle the equality case(s) without an error, but the principle is important – make your bugs “shallow”. • Of course, we have to be realistic:

• It is impossible to make anything foolproof, because fools are so ingenious. - Robert Heinlein

• If you make your system more idiot-proof the idiots will build a bigger idiot. - Anonymous

Exclusivity

• Conditionals are exclusive: only one case will be executed

• Again, can lead to problems...

function res = convert_grade_V1(score)% percent to letter-grade conversion

if score >= 90res = 'A';

elseif score >= 80 && score <= 89res = 'B';

elseif score >= 70 && score <= 79res = 'C';

elseif score >= 60 && score <= 69res = 'D';

elsescore = 'F';

end

Exclusivity

Exclusivity

>> convert_grade_V1(89.5)ans = F

• Problem is conflict between exclusivity (computer) and redundancy (human) : people like more information (upper and lower ends of range), but this can be catastrophic when turned into an algorithm.

• Eliminating redundancy can give us a less intuitive, but correct, algorithm....

Exclusivity: Eliminating Redundancy

function res = convert_grade_V2(score)% percent to letter-grade conversion

if score >= 90res = 'A';

elseif score >= 80res = 'B';

elseif score >= 70res = 'C';

elseif score >= 60res = 'D';

elsescore = 'F';

end

Conditionals can get crowded with the repetition of the same operation on the same data:

function res = conversion_factor_meters_V1(unit)% return equivalent one one UNIT in meters

if strcmp(unit, 'yards') | strcmp(unit, 'yd')res = 0.9144;

elseif strcmp(unit, 'inches') | strcmp(unit, 'in')res = 0.0254;

elseif strcmp(unit, 'miles') | strcmp(unit, 'mi')res = 1609.0;

...else

res = 0;end

7.4 Switch / Case

7.4 Switch / Case

Switch / case statement eliminates repetition:

function res = conversion_factor_meters_V2(unit)

switch(unit)case {'yards', 'yd'}

res = 0.9144;case {'inches', 'in'}

res = 0.0254;case {'miles', 'mi'}

res = 1609.0;...otherwise % unrecognized units

res = 0;end

Safety via error

function res = conversion_factor_meters_V3(unit)

switch(unit)case {'yards', 'yd'}

res = 0.9144;case {'inches', 'in'}

res = 0.0254;case {'miles', 'mi'}

res = 1609.0;...otherwise

error('Unrecognized units … ohhhh snap!')end