ASUBARRAYS

[Xlambda]

ASUBARRAYS extracts subarrays of an array. calls ATEXTJOIN , ASTACK , AUNSTACK
Original idea credits to tboulden , different approach. The core of the formula is a simple concept based on a simple formula that extracts every subarray in rows format:
=LAMBDA(a,r,c,LET(w,ROWS(a),l,COLUMNS(a),x,l-c+1,y,w-r+1,m,SEQUENCE(,r*c),s,SEQUENCE(x*y),INDEX(IF(a<>"",a,""),QUOTIENT(m-1,c)+1+QUOTIENT(s-1,x),MOD(m-1,c)+1+MOD(s-1,x))))
Added to this other 2 formats that could be useful, and an explicit extraction of anyone of them, based on its index. Other functions on minisheet ASELECT , AAGGREGATE

=LAMBDA(a,r,c,f,i,
    LET(w,ROWS(a),l,COLUMNS(a),o,MEDIAN(1,r,w),u,MEDIAN(1,c,l),x,l-u+1,y,w-o+1,m,SEQUENCE(,o*u),s,SEQUENCE(x*y),
       z,INDEX(IF(a<>"",a,IF(f,""," ")),QUOTIENT(m-1,u)+1+QUOTIENT(s-1,x),MOD(m-1,u)+1+MOD(s-1,x)),
       t,ATEXTJOIN(z,"arr "&s&" =",,","),k,ASTACK(AUNSTACK(ASTACK(AUNSTACK(z,1),u),o),x*u),
       n,ASTACK(XLOOKUP(MEDIAN(i,1,x*y),s,z),u),q,SWITCH(f,0,t,1,z,2,k,"check format"),
       IF(i,n,q)
    )
)

subarrays.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z	AA	AB
1	sub 3x4							compact format
2	tot subs (5-3+1)*(6-4+1)=3*3=9							arguments r=3,c=4,f=0,i=0		arguments r=3,c=4,f=1,i=0 row format													sum every sub
3								=ASUBARRAYS(A5:F9,3,4,,)		=ASUBARRAYS(A5:F9,3,4,1,)													=AAGGREGATE(J4#,5,)
4	sample 5x6							arr 1 =a,b,2,-3,5,d, ,3,-4,g,0,v		a	b	2	-3	5	d		3	-4	g	0	v		3		max every sub
5	a	b	2	-3	0	c		arr 2 =b,2,-3,0,d, ,3,e,g,0,v,10		b	2	-3	0	d		3	e	g	0	v	10		12		=AAGGREGATE(J4#,1,)
6	5	d		3	e	f		arr 3 =2,-3,0,c, ,3,e,f,0,v,10,x		2	-3	0	c		3	e	f	0	v	10	x		12		5
7	-4	g	0	v	10	x		arr 4 =5,d, ,3,-4,g,0,v,g,9,-4,		5	d		3	-4	g	0	v	g	9	-4			9		10
8	g	9	-4		r	n		arr 5 =d, ,3,e,g,0,v,10,9,-4, ,r		d		3	e	g	0	v	10	9	-4		r		18		10
9	0	s	z	y	8	-2		arr 6 = ,3,e,f,0,v,10,x,-4, ,r,n			3	e	f	0	v	10	x	-4		r	n		9		9
10								arr 7 =-4,g,0,v,g,9,-4, ,0,s,z,y		-4	g	0	v	g	9	-4		0	s	z	y		1		10
11								arr 8 =g,0,v,10,9,-4, ,r,s,z,y,8		g	0	v	10	9	-4		r	s	z	y	8		23		10
12								arr 9 =0,v,10,x,-4, ,r,n,z,y,8,-2		0	v	10	x	-4		r	n	z	y	8	-2		12		9
13																									10
14	also we can acomplish this									arguments r=3,c=4,f=2,i=0 stack format															10
15	with ASELECT									=ASUBARRAYS(A5:F9,3,4,2,)
16	=ASELECT(A5:F9,2,4,,4,)									a	b	2	-3	b	2	-3	0	2	-3	0	c
17	5	d	0	3				-ASUBARRAYS, like ASELECT		5	d		3	d		3	e		3	e	f
18	-4	g	0	v				can be dynamic, but in a		-4	g	0	v	g	0	v	10	0	v	10	x
19	g	9	-4	0				different manner		5	d		3	d		3	e		3	e	f
20										-4	g	0	v	g	0	v	10	0	v	10	x
21	=ASELECT(A5:F9,3,,3,,)									g	9	-4		9	-4		r	-4		r	n
22	0	v	10	x						-4	g	0	v	g	0	v	10	0	v	10	x
23	-4	0	r	n						g	9	-4		9	-4		r	-4		r	n
24	z	y	8	-2						0	s	z	y	s	z	y	8	z	y	8	-2
25										extracts 9th sub array							extracts 4th sub array
26	other functions									arguments r=3,c=4,f=1,i=9							arguments r=3,c=4,f=2,i=4
27	ASELECT									=ASUBARRAYS(A5:F9,3,4,1,9)							=ASUBARRAYS(A5:F9,3,4,2,4)
28	AAGGREGATE							-when i argument >0,		0	v	10	x				5	d		3
29								f argument is ignored		-4		r	n				-4	g	0	v
30								whatever value it has		z	y	8	-2				g	9	-4
31
32								- if we always want last array		=ASUBARRAYS(A5:F9,3,4,,999)
33								we can use a large i value		0	v	10	x
34										-4		r	n
35										z	y	8	-2
36
37								-other sub dim example 5x5
38	=ASUBARRAYS(A5:F9,7,8,2,)									=ASUBARRAYS(A5:F9,5,5,2,)
39	a	b	2	-3	0	c		-if sub dim values exceed		a	b	2	-3	0	b	2	-3	0	c
40	5	d		3	e	f		main array dimensions,(7x8)		5	d		3	e	d		3	e	f
41	-4	g	0	v	10	x		will be downsized to main		-4	g	0	v	10	g	0	v	10	x
42	g	9	-4		r	n		array dimensions		g	9	-4		r	9	-4		r	n
43	0	s	z	y	8	-2		←		0	s	z	y	8	s	z	y	8	-2
44
45										=ASUBARRAYS(A5:F9,5,5,,10)
46										b	2	-3	0	c
47										d		3	e	f
48										g	0	v	10	x
49										9	-4		r	n
50										s	z	y	8	-2
51	=ASUBARRAYS(A5:F9,5,5,1,)
52	a	b	2	-3	0	5	d		3	e	-4	g	0	v	10	g	9	-4		r	0	s	z	y	8
53	b	2	-3	0	c	d		3	e	f	g	0	v	10	x	9	-4		r	n	s	z	y	8	-2
54
Sheet2

Cell Formulas
Range	Formula
J3,A51,J45,J38,A38,J32,Q27,J27,A21,A16,J15,Y5,H3,W3	J3	=FORMULATEXT(J4)
H4:H12	H4	=ASUBARRAYS(A5:F9,3,4,,)
J4:U12	J4	=ASUBARRAYS(A5:F9,3,4,1,)
W4:W12	W4	=AAGGREGATE(J4#,5,)
Y6:Y14	Y6	=AAGGREGATE(J4#,1,)
J16:U24	J16	=ASUBARRAYS(A5:F9,3,4,2,)
A17:D19	A17	=ASELECT(A5:F9,2,4,,4,)
A22:D24	A22	=ASELECT(A5:F9,3,,3,,)
J28:M30	J28	=ASUBARRAYS(A5:F9,3,4,1,9)
Q28:T30	Q28	=ASUBARRAYS(A5:F9,3,4,2,4)
J33:M35	J33	=ASUBARRAYS(A5:F9,3,4,,999)
A39:F43	A39	=ASUBARRAYS(A5:F9,7,8,2,)
J39:S43	J39	=ASUBARRAYS(A5:F9,5,5,2,)
J46:N50	J46	=ASUBARRAYS(A5:F9,5,5,,10)
A52:Y53	A52	=ASUBARRAYS(A5:F9,5,5,1,)
Dynamic array formulas.

 

[tboulden]

Just updated my post to have a non-recursive, formula-based version; recursion depth was limiting factor on larger dimension arrays. Will play around with yours later to see if it suffers from similar limitations.