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Patrick2788's avatar
Patrick2788
Silver Contributor
Sep 01, 2026

Pairwiseλ is my approach to generating a Cartesian product of 2 sets. Here is a demo with a deck of cards created from rank and suit.

 

The function is written as simply as possible. The goal was to make it fast, efficient, and predictable.

/* [GR06] -------------------------------------------------------------------------
Function:     Pairwiseλ
Category:     Grid Analytics (Categorical Analysis)
Author:       Patrick H.
Version:      1.1
Dependencies: Echoλ, Resizeλ

Description:
    Creates vertical pairs from 1D and scalar inputs. Inputs are flattened with
    TOCOL to normalize orientation. 2D arrays are strictly prohibited.

Parameters:
    vector_1    - 1D vector or scalar.
    vector_2    - 1D vector or scalar.
------------------------------------------------------------------------------*/

Pairwiseλ=
LAMBDA(
    vector_1,
    vector_2,

LET(
    // Flatten inputs
    v,          TOCOL(vector_1),
    v₂,         TOCOL(vector_2),

    // Element counts
    k,          COUNTA(v),
    k₂,         COUNTA(v₂),

    // Halting scenarios
    Is2DInput?, OR(AND(ROWS(vector_1)>1, COLUMNS(vector_1)>1),
                   AND(ROWS(vector_2)>1, COLUMNS(vector_2)>1)),

    Is2Big?,    k * k₂ > 1000000,

IF(Is2DInput?,  #VALUE!,

    IF(Is2Big?,     #NUM!,

LET(
    // Cartesian expansion
    x,      Echoλ(v, k₂),
    y,      Resizeλ(v₂, k),
    pairs,  HSTACK(x, y),

    pairs
    
)))));

 

I have two more functions in the pipeline for the next update:

Triplewiseλ - Cartesian product of 3 sets

Quadwiseλ - Cartesian product of 4 sets

 

These two are of note because they provide an elegant way to generate indices. I'm toying with Windowedλ which extracts overlapping windows (n x n) from a 2D grid in row-major/col-major order. All will be in the next update.

  • m_tarler's avatar
    m_tarler
    Silver Contributor
    Sep 01, 2026

    Hi Patrick2788​ ,  as always I enjoy seeing what you have created.  In light of the above and the comment about going to triple and quad I thought of an alternative to your Pairwise that can handle ROWS so you can just call it multiple times as needed:

    PairRowsλ=
LAMBDA(
    vector_1,
    vector_2,

LET(
    // Element counts
    k,          ROWS(vector_1),
    k₂,         ROWS(vector_2),
    Size,    k * k₂,

IF(Size > 1000000,  #NUM!,

LET(
    // Cartesian expansion
    x,      CHOOSEROWS(vector_1, INT(SEQUENCE(Size,,0)/k₂)+1),
    y,      CHOOSEROWS(vector_2, MOD(SEQUENCE(Size,,0),k₂)+1),
    pairs,  HSTACK(x, y),

    pairs
    
))));

    So instead of being limited to a single column to get repeated it will pair full rows.  Here is an example from your sample sheet where I added Toppings to your icecream...