VYPER

[GeertD]

VYPER – vector extrusion through cyclic permutations. Extrudes a given Vector by means of all cyclic permutations (the cyclic sequence is invariant).

=LAMBDA(InputVector,LET(
riv,ROWS(InputVector),civ,COLUMNS(InputVector),
IF((riv>1)*(civ>1),"The input needs to be a 1D-vector.",LET(
RowVector,IF(riv=1,InputVector,TRANSPOSE(InputVector)), Cols,COLUMNS(RowVector),
DColdex,MOD(SEQUENCE(,2*Cols,0),Cols)+1,
Rowdex0,SEQUENCE(Cols,,0),
CyclicColdex,INDEX(DColdex,,SEQUENCE(,Cols)+Cols-Rowdex0),
Result,INDEX(RowVector,,CyclicColdex),
IF(riv=1,Result,TRANSPOSE(Result))
))))

VYPER_VectorExtrusionThroughCyclicPermutions.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	AC	AD	AE	AF	AG
1	Input:											Output:											Manual Control:
2	6	3	4	2	8	10	1	5	7	9		6	3	4	2	8	10	1	5	7	9		6	3	4	2	8	10	1	5	7	9
3												9	6	3	4	2	8	10	1	5	7		9	6	3	4	2	8	10	1	5	7
4												7	9	6	3	4	2	8	10	1	5		7	9	6	3	4	2	8	10	1	5
5												5	7	9	6	3	4	2	8	10	1		5	7	9	6	3	4	2	8	10	1
6												1	5	7	9	6	3	4	2	8	10		1	5	7	9	6	3	4	2	8	10
7												10	1	5	7	9	6	3	4	2	8		10	1	5	7	9	6	3	4	2	8
8												8	10	1	5	7	9	6	3	4	2		8	10	1	5	7	9	6	3	4	2
9												2	8	10	1	5	7	9	6	3	4		2	8	10	1	5	7	9	6	3	4
10												4	2	8	10	1	5	7	9	6	3		4	2	8	10	1	5	7	9	6	3
11												3	4	2	8	10	1	5	7	9	6		3	4	2	8	10	1	5	7	9	6
12
13	Input:											Output:
14	5											5	6	3	1	9	8	7	2	4	10
15	10											10	5	6	3	1	9	8	7	2	4
16	4											4	10	5	6	3	1	9	8	7	2
17	2											2	4	10	5	6	3	1	9	8	7
18	7											7	2	4	10	5	6	3	1	9	8
19	8											8	7	2	4	10	5	6	3	1	9
20	9											9	8	7	2	4	10	5	6	3	1
21	1											1	9	8	7	2	4	10	5	6	3
22	3											3	1	9	8	7	2	4	10	5	6
23	6											6	3	1	9	8	7	2	4	10	5
24
25	Input:											Output:
26	3	13										The input needs to be a 1D-vector.
27	5	15
28	1	11
29	6	16
30	7	17
31	9	19
32	2	12
33	4	14
34	8	18
35	10	20
36
VYPER

Cell Formulas
Range	Formula
A2:J2	A2	=SORTBY(SEQUENCE(,10),RANDARRAY(,10,1,10,TRUE))
L2:U11,L26,L14:U23	L2	=LAMBDA(InputVector,LET( riv,ROWS(InputVector),civ,COLUMNS(InputVector), IF((riv>1)*(civ>1),"The input needs to be a 1D-vector.",LET( RowVector,IF(riv=1,InputVector,TRANSPOSE(InputVector)), Cols,COLUMNS(RowVector), DColdex,MOD(SEQUENCE(,2*Cols,0),Cols)+1, Rowdex0,SEQUENCE(Cols,,0), CyclicColdex,INDEX(DColdex,,SEQUENCE(,Cols)+Cols-Rowdex0), Result,INDEX(RowVector,,CyclicColdex), IF(riv=1,Result,TRANSPOSE(Result)) ))))(A2#)
W2:AF2	W2	=A2:J2
W3	W3	=AF2
X3:AF11	X3	=W2
W4	W4	=AE2
W5	W5	=AD2
W6	W6	=AC2
W7	W7	=AB2
W8	W8	=AA2
W9	W9	=Z2
W10	W10	=Y2
W11	W11	=X2
A14:A23	A14	=TRANSPOSE(SORTBY(SEQUENCE(,10),RANDARRAY(,10,1,10,TRUE)))
A26:B35	A26	=TRANSPOSE(SORTBY(SEQUENCE(2,10),RANDARRAY(,10,1,10,TRUE)))
Dynamic array formulas.

Cells with Conditional Formatting
Cell	Condition		Cell Format	Stop If True
L27:U35	Other Type	Color scale		NO
A26:J35	Other Type	Color scale		NO
L15:U23,M14:U14	Other Type	Color scale		NO
A14:J23	Other Type	Color scale		NO
L2:U11,L14	Other Type	Color scale		NO
W2:AF11	Other Type	Color scale		NO
A2:J11	Other Type	Color scale		NO

 

[Xlambda]

Hi, , for fun ? :

=LAMBDA(a,LET(r,ROWS(a),c,COLUMNS(a),IF(AND(r>1,c>1),"no 1D",
      LET(x,IF(r=1,c,r),y,MOD(SEQUENCE(x,,x,-1)+SEQUENCE(,x)-1,x)+1,z,INDEX(a,y),
        IF(r=1,z,TRANSPOSE(z))))
        )
)

Book1
	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
1			a													Concept		for 1st example x=clm(a)=10
2			6	3	4	2	8	10	1	5	7	9
3																step1 seq(x,,x,-1)+seq(,x)
4			=VYPER(C2:L2)													=SEQUENCE(10,,10,-1)+SEQUENCE(,10)
5			6	3	4	2	8	10	1	5	7	9				11	12	13	14	15	16	17	18	19	20
6			9	6	3	4	2	8	10	1	5	7				10	11	12	13	14	15	16	17	18	19
7			7	9	6	3	4	2	8	10	1	5				9	10	11	12	13	14	15	16	17	18
8			5	7	9	6	3	4	2	8	10	1				8	9	10	11	12	13	14	15	16	17
9			1	5	7	9	6	3	4	2	8	10				7	8	9	10	11	12	13	14	15	16
10			10	1	5	7	9	6	3	4	2	8				6	7	8	9	10	11	12	13	14	15
11			8	10	1	5	7	9	6	3	4	2				5	6	7	8	9	10	11	12	13	14
12			2	8	10	1	5	7	9	6	3	4				4	5	6	7	8	9	10	11	12	13
13			4	2	8	10	1	5	7	9	6	3				3	4	5	6	7	8	9	10	11	12
14			3	4	2	8	10	1	5	7	9	6				2	3	4	5	6	7	8	9	10	11
15
16																step2 mod(step1-1,x)+1
17	a		=VYPER(A18:A27)													=MOD(P5#-1,10)+1
18	5		5	6	3	1	9	8	7	2	4	10				1	2	3	4	5	6	7	8	9	10
19	10		10	5	6	3	1	9	8	7	2	4				10	1	2	3	4	5	6	7	8	9
20	4		4	10	5	6	3	1	9	8	7	2				9	10	1	2	3	4	5	6	7	8
21	2		2	4	10	5	6	3	1	9	8	7				8	9	10	1	2	3	4	5	6	7
22	7		7	2	4	10	5	6	3	1	9	8				7	8	9	10	1	2	3	4	5	6
23	8		8	7	2	4	10	5	6	3	1	9				6	7	8	9	10	1	2	3	4	5
24	9		9	8	7	2	4	10	5	6	3	1				5	6	7	8	9	10	1	2	3	4
25	1		1	9	8	7	2	4	10	5	6	3				4	5	6	7	8	9	10	1	2	3
26	3		3	1	9	8	7	2	4	10	5	6				3	4	5	6	7	8	9	10	1	2
27	6		6	3	1	9	8	7	2	4	10	5				2	3	4	5	6	7	8	9	10	1
28
29	a															step3 index(a,step2)
30	5	8		=VYPER(A30:B31)												=INDEX(C2:L2,P18#)
31	3	4		no 1D												6	3	4	2	8	10	1	5	7	9
32																9	6	3	4	2	8	10	1	5	7
33																7	9	6	3	4	2	8	10	1	5
34																5	7	9	6	3	4	2	8	10	1
35																1	5	7	9	6	3	4	2	8	10
36																10	1	5	7	9	6	3	4	2	8
37																8	10	1	5	7	9	6	3	4	2
38																2	8	10	1	5	7	9	6	3	4
39																4	2	8	10	1	5	7	9	6	3
40																3	4	2	8	10	1	5	7	9	6
41
42
Sheet1

Cell Formulas
Range	Formula
C4,P30,D30,P17,C17,P4	C4	=FORMULATEXT(C5)
C5:L14	C5	=VYPER(C2:L2)
P5:Y14	P5	=SEQUENCE(10,,10,-1)+SEQUENCE(,10)
C18:L27	C18	=VYPER(A18:A27)
P18:Y27	P18	=MOD(P5#-1,10)+1
D31	D31	=VYPER(A30:B31)
P31:Y40	P31	=INDEX(C2:L2,P18#)
Dynamic array formulas.

 

[GeertD]

That's a one step Cyclic Index. Well done!
Your solution is minimum effort and therefore the best.
Thanks for sharing.

 

[Xlambda]

? Nice to have you back!! ?

 

[GeertD]

Thanks C. Have to admit: I was a little rusty. I had to look up again how to make a post on the Message Board.?
Well, I thought I'd compensate with a bunch of nice colors ('t is the season) and a cool name for the function.