Array Concatenation and Construction

General array concatenation can be done through the array concatenation operator cat(k, A, B, C, ...) that concatenates the arrays A, B, C, .... along the k:th dimension. Concatenating along the first dimension is to concate rows and the second dimension is to concatenate colums.

1 Class Concat

class Concat Real[5] c1 = cat(1, {1, 2}, {10, 12, 13}); // Result: {1, 2, 10, 12, 13} Real[2, 3] c2 = cat(2, {{1, 2}, {3, 4}}, {{10}, {11}}); // Result: {{1, 2, 10}, {3, 4, 11}} end Concat;

1.1 Simulation of Concat

simulate(Concat)
plot(c1[4])

2 More Concatenation

A matrix can be constructed from scalar expressions by separating rows by semicolon and columns by comma. The previous example of concatenation along the second dimension can be expressed like this:

class Concat2 Real[2, 3] c3 = cat(2, [1, 2; 3, 4], [10; 11]); // Same result: {{1, 2, 10}, {3, 4, 11}} end Concat2;

2.1 Simulation of Concat2

simulate(Concat2)
val(c3[2,3],0)
plot({c3[2,3],c3[2,2]})

3 Type Rules for Concatenation

The arrays that is concatenated must have the same number of dimensions. The concatenation dimension k must exist. Arrays must have identical dimension sizes with the exception of the size of dimension k, which is called Size matching. Argument arrays must have equivalent maximally expanded element types. The element type of the result array is the element type of the maximally expanded type of the arguments. These rules make it possible to mix integers and real numbers as in the example below:

class Concat3 Real[2, 3] r1 = cat(1, {{1.0, 2.0, 3}}, {{4, 5, 6}}); Real[2, 6] r2 = cat(2, r1, r1); end Concat3;

3.1 Simulation of Concat3

simulate(Concat3)
plot(r1[2,2])

4 Concatenating Larger Arrays

class Concat4 Real[1, 1, 1] A = {{{1}}}; Real[1, 1, 2] B = {{{2, 3}}}; Real[1, 1, 3] C = {{{4, 5, 6}}}; Real[1, 1, 6] R = cat(3,A,B,C); // Result value: {{{1, 2, 3, 4, 5, 6}}}; end Concat4;

4.1 Simulation of Concat4

simulate(Concat4)
plot({R[1,1,5],B[1,1,2]})