These Excel LAMBDA functions partition an array into two thunked parts

excel-lambda-partition.txt

/*
axis is (default) 0 for rows 1 for columns
array is a 2D array
at is a position at which to partition the array on the axis

So this returns two thunks, stacked vertically, the first
of which contains the first 5 rows of the array. The second contains the second
5 rows of the array. 

PARTITION(0)(SEQUENCE(10,10), 5)
*/

// only partitions on rows, always outputs VSTACK'd
PARTITION_1 = LAMBDA(array, n, 
    LET(
        part1, TAKE(array, n),
        part2, DROP(array, n),
        VSTACK(LAMBDA(part1), LAMBDA(part2))
    )
);

// adds partitioning on columns
PARTITION_2 = LAMBDA(array, n, [axis], 
    LET(
        _axis, IF(ISOMITTED(axis), 0, 1), 
        part1, IF(_axis=0, TAKE(array, n), TAKE(array,,n)),
        part2, IF(_axis=0, DROP(array, n), DROP(array,,n)),
        VSTACK(LAMBDA(part1), LAMBDA(part2))
    )
);

// Changes to HSTACK output if axis<>0
PARTITION_3 = LAMBDA(array, n, [axis], 
    LET(
        _axis, IF(ISOMITTED(axis), 0, 1), 
        part1, IF(_axis=0, TAKE(array, n), TAKE(array,,n)),
        part2, IF(_axis=0, DROP(array, n), DROP(array,,n)),
        IF(
            _axis=0,
            VSTACK(LAMBDA(part1), LAMBDA(part2)),
            HSTACK(LAMBDA(part1), LAMBDA(part2))
        )
    )
);

// creates STACK function chooser
PARTITION_4 = LAMBDA(array, n, [axis], 
    LET(
        _axis, IF(ISOMITTED(axis), 0, 1), 
        part1, IF(_axis=0, TAKE(array, n), TAKE(array,,n)),
        part2, IF(_axis=0, DROP(array, n), DROP(array,,n)),
        stack_fn, IF(_axis=0, VSTACK, HSTACK),
        stack_fn(LAMBDA(part1), LAMBDA(part2))
    )
);

// Removes stack_fn definition
PARTITION_5 = LAMBDA(array, n, [axis], 
    LET(
        _axis, IF(ISOMITTED(axis), 0, 1), 
        part1, IF(_axis=0, TAKE(array, n), TAKE(array,,n)),
        part2, IF(_axis=0, DROP(array, n), DROP(array,,n)),
        IF(_axis=0, VSTACK, HSTACK)(LAMBDA(part1), LAMBDA(part2))
    )
);

// Removes _axis definition (omited defaults to zero anyway)
PARTITION_6 = LAMBDA(array, n, [axis], 
    LET(
        part1, IF(axis=0, TAKE(array, n), TAKE(array,,n)),
        part2, IF(axis=0, DROP(array, n), DROP(array,,n)),
        IF(axis=0, VSTACK, HSTACK)(LAMBDA(part1), LAMBDA(part2))
    )
);

// Moves thunking to part definitions
PARTITION_7 = LAMBDA(array, n, [axis], 
    LET(
        part1, LAMBDA(IF(axis=0, TAKE(array, n), TAKE(array,,n))),
        part2, LAMBDA(IF(axis=0, DROP(array, n), DROP(array,,n))),
        IF(axis=0, VSTACK, HSTACK)(part1, part2)
    )
);

// Creates part_fn
PARTITION_8 = LAMBDA(array, n, [axis], 
    LET(
        part_fn, LAMBDA(f, LAMBDA(IF(axis=0, f(array, n), f(array,,n)))),
        part1, part_fn(TAKE),
        part2, part_fn(DROP),
        IF(axis=0, VSTACK, HSTACK)(part1, part2)
    )
);

// Moves the part_fn calls
PARTITION_9 = LAMBDA(array, n, [axis], 
    LET(

        part_fn, LAMBDA(f, LAMBDA(IF(axis=0, f(array, n), f(array,,n)))),
        IF(axis=0, VSTACK, HSTACK)(part_fn(TAKE), part_fn(DROP))
    )
);

// curries the axis parameter
PARTITION = LAMBDA([axis],
    LAMBDA(array, n, 
        MAP(
            IF(axis=0,VSTACK,HSTACK)(TAKE,DROP), 
            LAMBDA(f, LAMBDA(IF(axis=0,f(array,n),f(array,,n))))
        )
    )
);


// partial application of axis argument to PARTITION
PARTITIONROWS = PARTITION(0);
PARTITIONCOLS = PARTITION(1);


// dethunks a partition produced by PARTITION
GETPARTITION = LAMBDA(
    partition_array, 
    partition_no, 
    INDEX(TOCOL(partition_array),partition_no,1)()
);