This information is part of the Modelica Standard Library maintained by the Modelica Association.

The function cat(k,A,B,C,...)concatenates arrays A,B,C,... along dimension k.

Examples

Real[2,3] r1 = cat(1, {{1.0, 2.0, 3}}, {{4, 5, 6}});
Real[2,6] r2 = cat(2, r1, 2*r1);

Description

The function cat(k,A,B,C,...)concatenates arrays A,B,C,... along dimension k according to the following rules:

• Arrays A, B, C, ... must have the same number of dimensions, i.e., ndims(A) = ndims(B) = ...
• Arrays A, B, C, ... must be type compatible expressions giving the type of the elements of the result. The maximally expanded types should be equivalent. Real and Integer subtypes can be mixed resulting in a Real result array where the Integer numbers have been transformed to Real numbers.
• k has to characterize an existing dimension, i.e., 1 <= k <= ndims(A) = ndims(B) = ndims(C); k shall be an integer number.
• Size matching: Arrays A, B, C, ... must have identical array sizes with the exception of the size of dimension k, i.e., size(A,j) = size(B,j), for 1 <= j <= ndims(A) and j <> k.

Concatenation is formally defined according to:

Let R = cat(k,A,B,C,...), and let n = ndims(A) = ndims(B) = ndims(C) = ...., then
size(R,k) = size(A,k) + size(B,k) + size(C,k) + ...
size(R,j) = size(A,j) = size(B,j) = size(C,j) = ...., for 1 <= j <= n and j <> k.
R[i_1, ..., i_k, ..., i_n] = A[i_1, ..., i_k, ..., i_n], for i_k <= size(A,k),
R[i_1, ..., i_k, ..., i_n] = B[i_1, ..., i_k - size(A,i), ..., i_n], for i_k <= size(A,k) + size(B,k),
....
where 1 <= i_j <= size(R,j) for 1 <= j <= n.