Is there a built-in function to concatenate arrays in the third direction?

Is there an equivalent function to vertcat(..) and horzcat(..) but in the direction of a third index, e.g. pagecat(..)?

I always accomplish this by horizontally concatenating my arrays and then using permute(..), but it would be convenient to be able to do it with a single function call. Better still, add a third operator to "," and ";" as a shortcut to a pagecat(..) function, if there are any symbols left for that purpose.

Answer 1

[John D'Errico]

Logically, one would just use cat. How might you have found this? READ THE HELP!

That is, near the end of the help for all MATLAB functions, they try to list functions which have similar abilities, are related in some way. That will be a see also line.

help horzcat

 HORZCAT Horizontal concatenation.
    [A B] is the horizontal concatenation of matrices A and B.  A and B
    must have the same number of rows.  [A,B] is the same thing.  Any
    number of matrices can be concatenated within one pair of brackets.
    Horizontal and vertical concatenation can be combined together as in
    [1 2;3 4].  
 
    [A B; C] is allowed if the number of rows of A equals the number of
    rows of B and the number of columns of A plus the number of columns
    of B equals the number of columns of C.  The matrices in a
    concatenation expression can themselves by formed via a
    concatenation as in [A B;[C D]].  These rules generalize in a
    hopefully obvious way to allow fairly complicated constructions.
 
    N-D arrays are concatenated along the second dimension. The first and
    remaining dimensions must match.
 
    C = HORZCAT(A,B) is called for the syntax '[A  B]' when A or B is an
    object.
 
    Y = HORZCAT(X1,X2,X3,...) is called for the syntax '[X1 X2 X3 ...]'
    when any of X1, X2, X3, etc. is an object.
 
    See also VERTCAT, CAT.

    Documentation for horzcat
       doc horzcat

    Other uses of horzcat

       Bluetooth/horzcat
       categorical/horzcat
       codistributed/horzcat
       dataset/horzcat
       datetime/horzcat
       dlarray/horzcat
       double/horzcat
       duration/horzcat
       fittype/horzcat
       gpib/horzcat
       gpuArray/horzcat
       i2c/horzcat
       icdevice/horzcat
       icgroup/horzcat
       icsignal/horzcat
       iddata/horzcat
       inline/horzcat
       iviconfigurationstore/horzcat
       laurentPolynomial/horzcat
       laurpoly/horzcat
       matlab.mixin.Heterogeneous/horzcat
       matlab.mixin.indexing.RedefinesParen/horzcat
       opcroot/horzcat
       RandStream/horzcat
       sensingDictionary/horzcat
       serial/horzcat
       sym/horzcat
       symbolic/horzcat
       tabular/horzcat
       tall/horzcat
       tcpip/horzcat
       tokenizedDocument/horzcat
       tscollection/horzcat
       udp/horzcat
       videoinput/horzcat
       visa/horzcat

In the help for hirzcat, for example, you see the line,

See also vertcat, cat.

And while you know what vertcat does, what might cat do?

help cat

 CAT Concatenate arrays.
    CAT(DIM,A,B) concatenates the arrays A and B along
    the dimension DIM.  
    CAT(2,A,B) is the same as [A,B].
    CAT(1,A,B) is the same as [A;B].
 
    B = CAT(DIM,A1,A2,A3,A4,...) concatenates the input
    arrays A1, A2, etc. along the dimension DIM.
 
    When used with comma separated list syntax, CAT(DIM,C{:}) or 
    CAT(DIM,C.FIELD) is a convenient way to concatenate a cell or
    structure array containing numeric matrices into a single matrix.
 
    Examples:
      a = magic(3); b = pascal(3); 
      c = cat(4,a,b)
    produces a 3-by-3-by-1-by-2 result and
      s = {a b};
      for i=1:length(s), 
        siz{i} = size(s{i});
      end
      sizes = cat(1,siz{:})
    produces a 2-by-2 array of size vectors.
      
    See also NUM2CELL.

    Documentation for cat
       doc cat

    Other uses of cat

       calendarDuration/cat    gpuArray/cat
       categorical/cat         inline/cat
       codistributed/cat       InputOutputModel/cat
       dataset/cat             matlab.mixin.Heterogeneous/cat
       datetime/cat            matlab.mixin.indexing.RedefinesParen/cat
       dlarray/cat             RandStream/cat
       double/cat              sym/cat
       duration/cat            tabular/cat
       fittype/cat             tall/cat
       geopoint/cat            tokenizedDocument/cat

Try it out.

A = magic(3);
B = eye(3);
C = cat(3,A,B)

C = 
C(:,:,1) =

     8     1     6
     3     5     7
     4     9     2


C(:,:,2) =

     1     0     0
     0     1     0
     0     0     1

[Bruce Elliott]

Holy cow!! How did I not know that? It's been a very long time since I ever looked for help with vertcat or horzcat, so I think I had completely forgotten that cat exists.

Thank you for the reminder - this is clearly what I was looking for.

[John D'Errico]

Sometimes cats just hide in plain sight. This must have been one of them. :)

[Stephen23]

Schrodinger's cat?

[Dyuman Joshi]

Some cats are like voids, you can only find them if they stare back at you.

[Bruce Elliott]

Thanks to all for giving this question exactly the serious consideration it deserved.

Happy weekend!