Matrix Utilities & Set Operations

Phase 23 adds triangular-matrix extraction, tiling, Kronecker products, vector products, set-theoretic operations on vectors, and index-conversion utilities.

Triangular extraction

A = [1 2 3; 4 5 6; 7 8 9];

triu(A)        % [1 2 3; 0 5 6; 0 0 9]   upper triangular
triu(A, 1)     % [0 2 3; 0 0 6; 0 0 0]   above main diagonal
tril(A)        % [1 0 0; 4 5 0; 7 8 9]   lower triangular
tril(A, -1)    % [0 0 0; 4 0 0; 7 8 0]   below main diagonal

The optional offset k:

`k`	keeps elements where …
`0` (default)	`col − row ≥ 0` (`triu`) / `col − row ≤ 0` (`tril`)
`k > 0`	strictly above the main diagonal
`k < 0`	extends into the sub-diagonals

Tiling and Kronecker product

repmat([1 2; 3 4], 2, 3)            % 4×6 block matrix
kron([1 0; 0 1], [1 2; 3 4])        % 4×4 block-diagonal (identity scaling)

repmat(A, m, n) tiles matrix A in an m × n grid of blocks.

kron(A, B) replaces each scalar element a[i,j] of A with the block a[i,j] * B, producing a (rows_A × rows_B) by (cols_A × cols_B) result.

Vector products

cross([1 0 0], [0 1 0])   % [0 0 1]
cross([1 2 3], [4 5 6])   % [-3 6 -3]

dot([1 2 3], [4 5 6])     % 32

cross(a, b) requires both vectors to have exactly 3 elements. The result orientation (row or column) matches argument a.

dot(a, b) computes the inner product sum(a .* b) and returns a scalar.

Set operations

All set functions return sorted, unique results. NaN is never considered a member (IEEE semantics: NaN ≠ NaN).

intersect([1 3 5 7], [3 5 9])    % [3 5]
union([1 3 5], [3 5 7])          % [1 3 5 7]
setdiff([1 2 3 4 5], [2 4])      % [1 3 5]

ismember(3, [1 2 3 4])           % 1
ismember([1 6 3], [1 2 3 4])     % [1 0 1]  (element-wise)
ismember(nan, [nan])             % 0  (NaN is never a member)

Index conversion

sub2ind and ind2sub convert between row/column subscripts and 1-based column-major linear indices (MATLAB convention).

sub2ind([3 4], 2, 3)            % 8    (scalar)
sub2ind([3 4], [1 2], [1 3])    % [1 8]  (vectorised)

[r, c] = ind2sub([3 4], 8)      % r=2, c=3
[r, c] = ind2sub([3 4], [1 7])  % r=[1 1], c=[1 3]

Element repetition

repelem([1 2 3], 3)          % [1 1 1 2 2 2 3 3 3]
repelem([1 2 3], [2 1 3])    % [1 1 2 3 3 3]  (per-element counts)
repelem([1 2; 3 4], 2, 3)    % 4×6  (each element repeated 2 rows × 3 cols)

repelem(v, n) — repeat each element n times (scalar n).
repelem(v, nv) — repeat v(i) by nv(i) times (vector nv).
repelem(A, m, n) — 2-D form: repeat each element m rows and n columns.

ccalc