Comparisons & Logic

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Colloquia

Yu-Min Chung

• “Computational Topology with Applications in the Natural Sciences”
• Monday, Feb. 27, 2:30 PM

Eleni Panagiotou

• “Quantifying Entanglement in Physical Systems”
• Thursday, March 2, 2:30 PM

Both speakers are faculty candidates

Extra credit for writing a paragraph or so summarizing connections you make between either or both talks and your own interests.

Exam 1

Monday (Feb. 27)

Material since the beginning of the semester (e.g., Matlab arithmetic, functions, variables, scripts, vectors, plotting, matrices, etc.)

3 to 5 short-answer questions (i.e., questions requiring about a paragraph of prose, 5 - 10 lines of code, etc. to answer)

You’ll have the whole class period to do the test

Open book, open notes, open computer to the extent you use the computer as a reference source. But you can’t communicate in real time with anyone except me during the test.

Questions?

Relational and Logical Operators

Comparisons. Given a vector of numbers, count how many of them are negative.

Logical indexing. Given a vector of numbers, pick out the ones that are negative.

Ideas from reading:

• Use relational operators, e.g. less than 0, element-wise
• Add 1 to a count for each element less than 0
• Truth values in Matlab are also numbers, 0 for false and 1 for true

Matlab code that finds, extracts, and counts the negative numbers in a vector:

>> % Count negative numbers in a vector.
>> numbers = [ 1, 5, -3, 0, -9, 6, -3 ]
numbers =
     1     5    -3     0    -9     6    -3
>> numNeg = numbers < 0
numNeg =
     0     0     1     0     1     0     1
>> negValues = numbers( numNeg )
negValues =
    -3    -9    -3
>> % Beware that users can't enter logical values as 0 or 1, users have to
>> % use true and false:
>> numbers( [0 0 0 0 1 0 1] )
Subscript indices must either be real positive integers or logicals. 
>> numbers( [ true, true, false, false, false, true, true ] )
ans =
     1     5     6    -3
>> numNeg
numNeg =
     0     0     1     0     1     0     1
>> sum( numNeg )
ans =
     3

Truth tables (Try 5.2.1). Write Matlab commands that print the final columns of truth tables for and, or, not, and exclusive or.

Reading ideas:

• Reading was confusing with regard to truth value vs number distinctions. 0 and 1 represent false and true.
• Logical operators work on truth values, not numbers.

Matlab code for the the truth tables:

>> % Start with and
>> true & false
ans =
     0
>> [ false false true true ] & [ false true false true ]
ans =
     0     0     0     1
>> % or
>> [ false false true true ] | [ false true false true ]
ans =
     0     1     1     1
>> % exclusive or
>> xor( [ false, false, true, true ], [false true false true] )
ans =
     0     1     1     0
>> % not
>> ~ [false true]
ans =
     1     0

Challenge. Given a vector of numbers, compute a vector of absolute values without using the abs function.

Ideas: we already used the < operator to find places where there are negative numbers. Multiplying those numbers by -1 would yield their absolute values. But we can’t just multiply by the result of the less-than comparison, because that zeros out the positive numbers. Instead, we need to multiply everything that’s not negative by 1. The logical negation of the less-than results provides these ones, which we can add to the vector of negative ones to get something we can multiply the numbers by:

>> numbers
numbers =
     1     5    -3     0    -9     6    -3
>> numNeg
numNeg =
     0     0     1     0     1     0     1
>> negators = - numNeg
negators =
     0     0    -1     0    -1     0    -1
>> numbers .* negators
ans =
     0     0     3     0     9     0     3
>> numPos = ~ numNeg
numPos =
     1     1     0     1     0     1     0
>> flip = negators + numPos
flip =
     1     1    -1     1    -1     1    -1
>> numbers .* flip
ans =
     1     5     3     0     9     6     3

Next

(After exam)

“If” statements

Read sections 11.1 - 11.3 (11.2 and 11.3 are reviews of relational and logical operators, but with examples using “if” statements)

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