# Get Smart, Be Logical! 1

Posted by **Loren Shure**,

### Contents

#### The Problem

So what's the problem? The customer posed it by way of an example. Given a 3-D array A, generated for this example from a matrix, find the first plane in which some condition is true.A=[1 2; 3 4] M = cat(3, A, A+1, A+2, A+3);

A = 1 2 3 4So the function should work like this:

`IDX = someFunction(M >=5);`

IDX = [NaN 4; 3 2]

IDX = NaN 4 3 2

*And*, the customer wanted this to work for arrays of higher dimensions as well.

#### The Solution

As I said, I mentioned this to Sean. But I had thought for about 2 seconds about it before and I realized I could do a`find`on the entire array, as if it were a vector, get the locations and sort them into their proper locations and find the first one in the correct last dimension. And then Sean said "Max Logical". Here's what a great solution looks like.

catdim = 3; szA = size(A); [mv,midx] = max(M >= 5,[],catdim); IDX = NaN(szA); IDX(mv) = midx(mv)

IDX = NaN 4 3 2Why/how did this work? Well, I use the condition I want met into function

`max`, and it is logical input, meaning only 0s and 1s. And

`max`returns the index where the first condition is met, and I do this along the final dimension. Then create an array of

`NaN`values, and use logical indexing to update this index matrix. Voila!

#### Higher Dimensions

Now let's see if it makes sense in higher dimensions. For simplicity, I again will provide a base array in 1 dimension less than I am ultimately looking, so I can construct something for which I can reasonably easily check the result.A = randi(17, [3 2 1 3]); catdim = ndims(A)+1 M = cat(catdim, A, A+1, A+2, A+3, A+4);

catdim = 5See a slice of M

sliceOfM = M(:,:,:,1)

sliceOfM = 12 2 13 4 8 16Apply the

`max`, logical indexing to

`M`next.

szA = size(A) [mv,midx] = max(M >= 13,[],catdim); IDX = NaN(szA); IDX(mv) = midx(mv)

szA = 3 2 1 3 IDX(:,:,1,1) = 2 NaN 1 NaN NaN 1 IDX(:,:,1,2) = NaN 1 1 NaN 4 NaN IDX(:,:,1,3) = NaN 1 1 1 NaN 1

#### Have You Embraced Logical Indexing?

I have made several posts over the years on indexing that readers have found helpful. Do you have any interesting logical stories to share? Post them here. Published with MATLAB® R2017b**Category:**- Indexing

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