@PeterBartholomew1
Let’s assume, No of rows = m and no of columns = n, m > 1 and n > 1.
For either single column range or array input, giving column no argument of INDEX function as 1 or 0 or omitted is acceptable. For 2D range of m X n, omitting the column no argument results into #REF! error whereas for 2D array of m X n, it returns either entire row or first element of the row depending upon whether or not you are enclosing the row no argument inside curly braces. Logic behind not throwing #REF! error for 2D array input with column no argument omitted is unknown or the Microsoft is only privy to. For a single column of Thunks as an argument for array parameter of INDEX function, column no argument cannot be 0 or omitted and must be 1 to select a single Thunk from the array of Thunks. They could have programmed to allow 0 or omitted but they didn’t.
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I see Thunk as facility for packing and storing the array of raw or processed data.
I don’t understand why even single Thunk packed by BYROW function is required to be selected by INDEX function before it is unpacked or released. This sounds very illogical and incomprehensible. For example,
LET (THUNK, BYROW ({1, 2, 3}, LAMBDA (x, LAMBDA (x))), THUNK()).
This fails to release the THUNK and spill the array on the sheet. For this we need to select the Thunk with INDEX function first before we unpack and spill it on the sheet as is in the below code.
LET (THUNK, BYROW ({1, 2, 3}, LAMBDA (x, LAMBDA (x))), INDEX (THUNK,1, 1)()).
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MAP function can return only one element (single cell value) for each element passed to it. Hence it fails to return n elements of 1 X n array (Packed inside one Thunk by BYROW) for each Thunk passed by it.
LET (THUNK, {1, 2, 3}, BYROW (array, LAMBDA (x, LAMBDA (x))),
MAP (THUNK, LAMBDA (Elementθ, Elementθ()))) fails to return or unpack and spill the 3 elements of 1 X 3 array packed in the single Thunk by BYROW.
LET (THUNK, {1, 2, 3; 4, 5, 6}, BYROW (array, LAMBDA (x, LAMBDA (x))),
MAP (THUNK, LAMBDA (Elementθ, Elementθ()))) fails to return 2 X 3 array from two Thunks each containing 1 X 3 array.
We must make sure that we pass only single cell value to MAP function for each element passed by MAP to LAMBDA in order to get all the elements of m X n array packed inside m no of Thunks by BYROW function. Each Thunk containing 1 X n array. Following formula takes care of this:
LET (THUNK, {1, 2, 3; 4, 5, 6}, BYROW (array, LAMBDA (x, LAMBDA (x))),
MAP (THUNK, LAMBDA (Elementθ, INDEX (Elementθ(), 1, COLUMN(A1)))))
You need to drag this formula around till you get all the elements of m X n array.
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Same is the case with MAKEARRAY. It can only return a single cell value for each (row, column) argument that it passes to LAMBDA. It cannot return n elements of 1 X n array (packed by BYROW into a single Thunk) for one (row, column) argument that it passes to LAMBDA hence following formula fails to spill second Thunk from a 2 X 1 array of Thunks (THUNK) containing two Thunks in a single column.
LET (THUNK, {1, 2, 3; 4, 5, 6}, BYROW (array, LAMBDA (x, LAMBDA (x))),
MAKEARRAY (2, 1, LAMBDA (m, n, INDEX (THUNK, m, n)()))).
We need to make sure that we return a single cell value to MAKEARRAY for each (row, column) argument that it passes to LAMBDA so that it will be able to return or spill that single value on sheet. This is taken care of by following formula:
LET (THUNK, {1, 2, 3; 4, 5, 6}, BYROW (array, LAMBDA (x, LAMBDA (x))),
MAKEARRAY (2, 3, LAMBDA (m, n, INDEX (INDEX (THUNK, m, 1)(), 1, n)))).
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Obviously as a renowned formula guru of this forum you must be cognizant about all this. I just wanted to post my comprehensions. Thanx very much for enlightening me about the concept of Thunk.
