Loren on the Art of MATLAB

Why is Answer to 3 < A < 7 Unexpected? 9

Posted by Loren Shure,

There have been countless (not really!) times on the MATLAB newsgroup where a question of the sort written in the title has been asked (and answered). Let's go through the code to understand what's happening.

DISCLAIMER: It's not my intention in this post to discuss non-scalar behavior.

Contents

Problem Statement

As part of program, suppose we need to see if some value lies between two others. let's say A is the value we are checking at the limits are low=3 and high=7.

low = 3;
high = 7;

Mathematically you might write this as

  low < A < high

Let's try that for A values both inside the range and outside to start. And let me place the expression into an anonymous function so I don't have to keep repeating it.

myExpr = @(x) low < x < high;
inResult = myExpr(pi)
outResult = myExpr(17)
inResult =
     1
outResult =
     1

WHAT???

It can't be true that both pi and 17 lie between 3 and 7. So what's going on? Let's dissect the expression.

First Part of Expression: low < A

Let's look at the first part of the expression.

step1In = low < pi
step1Out = low < 17
step1In =
     1
step1Out =
     1

and we see that this is true for both of our inputs.

Second Part of Expression: previous output < high

The second part of our expression uses the output from the first expression and continues from there.

step2In = step1In < high
step2Out = step1Out < high
step2In =
     1
step2Out =
     1

and we see that we get ones, or true, for both of these. What's going on?

Look at the Types

whos step1*
  Name          Size            Bytes  Class      Attributes

  step1In       1x1                 1  logical              
  step1Out      1x1                 1  logical              

The results from step 1 are logical - are these numbers greater than low? And the answers for both of our values is yes, or true, represented in MATLAB as logical values. When we take these values as inputs in the second step, what happens is the true values are interpreted as numeric inputs with value 1. And then we ask if 1 is less than high. Which it is in both of these cases!

How to Get the Expected Answer

How do we get the expected answer, and it's easy. We simply combine two logical expressions, but in a different way than above.

myExprCorrect = @(x) (low < x) & (x < high)
inResult1 = myExprCorrect(pi)
outResult1 = myExprCorrect(17)
myExprCorrect = 
    @(x)(low<x)&(x<high)
inResult1 =
     1
outResult1 =
     0

What we did is checked first to see if the number was greater than low and separately checked the same number with high. After getting two logical answers, we combine them. They must both be true for numbers that lie between low and high and hence the result should yield true only under those conditions.

For what it's worth, I always use parentheses to group my expressions to make them very readable for me so I don't need to wonder later what I intended to be testing.

Have Compound Expressions Caused You Problems?

Let me know here if you've had trouble with expressions like the one in this post.


Get the MATLAB code

Published with MATLAB® 7.14

9 CommentsOldest to Newest

Loren,

This type of mistake is about as common as two other, related mistaken uses of MATLAB’s logical operators. The first is when the user doesn’t realize that MATLAB does not use the conditional to filter elements for operation inside the IF statement. For example, I have often seen users do this:

x = 1:5;

if x<=3
x = 10;
end

The user expects this result: x = [10 10 10 4 5]

The reason why the user expects this value is the false understanding that only those elements of x that satisfy the conditional statement are operated on inside the IF statement!
As I mentioned before, this is related to the other common mistake. The MATLAB IF conditional only passes through if all of the elements of a non-empty array evaluate to true. Thus the previous example is equivalent to:

x = 1:5;

if all(x<=3)
x = 10;
end

Also note that the statement inside the IF statement reassigns x to a scalar value of 10; it never operates on any subset of elements. Add to these the way MATLAB treats empty arrays and there is enough material for a long blog post (I know you have covered at least some of these topics before).

While low < x < high is valid syntax, I cannot think of a use case where it is desirable. While I do not advocate changing the MATLAB language to accommodate, an mlint warning seems appropriate if there is never a desirable use for the syntax. The same holds for Matt's example.

Better yet, warn on any arithmetic operation on a boolean (or “logical” as MATLAB appears to call that type).

Chris-

That would be a poor choice.

A = 1:4;
sum(A>3)

is a very convenient way to find out how many elements in A are greater than 3. MATLAB has allowed reasonable calculations with logicals for a long time. Taking that out now as a general rule would lead, I think, to incompatibilities that are likely not warranted.

--Loren

These postings are the author's and don't necessarily represent the opinions of MathWorks.