Matrices Built from Shifted Elements
03-06-2019, 01:26 PM
Post: #1 Eddie W. Shore Senior Member Posts: 999 Joined: Dec 2013
Matrices Built from Shifted Elements
The programs LSM (left-shift matrix) and RSM (right-shift matrx) create a n x n matrix based on the elements of a given list. Each row has each of the elements rotated one element.

For LSM, each row has the elements shifted to the left one element.

For RSM, each row has the elements shifted to the right one element.

HP Prime Program: LSM
Code:
 EXPORT LSM(L0) BEGIN // EWS 2019-03-02 // left shift matrix LOCAL L1,N,M0,K; N:=SIZE(L0); L1:=L0; FOR K FROM 1 TO N-1 DO L1:=CONCAT(tail(L1),head(L1)); L0:=CONCAT(L0,L1); END; M0:=list2mat(L0,N); RETURN M0; END;

HP Prime Program: RSM
Code:
 EXPORT RSM(L0) BEGIN // EWS 2019-03-03 // right shift matrix LOCAL L1,N,M0,K; N:=SIZE(L0); L1:=L0; FOR K FROM 1 TO N-1 DO L1:=REVERSE(CONCAT( tail(REVERSE(L1)), head(REVERSE(L1)) )); L0:=CONCAT(L0,L1); END; M0:=list2mat(L0,N); RETURN M0; END;

Note: The program RSM creates a circulant matrix.

Example:

list = {1, 7, 8, -2, 0}

LSM({1, 7, 8, -2, 0} returns:

[ [ 1, 7, 8, -2, 0 ]
[ 7, 8, -2, 0, 1 ]
[ 8, -2, 0, 1, 7 ]
[ -2, 0, 1, 7, 8 ]
[ 0, 1, 7, 8, -2 ] ]

RSM({1,7,8,-2,0}) returns:

[ [ 1, 7, 8, -2, 0 ]
[ 0, 1, 7, 8, -2 ]
[ -2, 0, 1, 7, 8 ]
[ 8, -2, 0, 1, 7 ]
[ 7, 8, -2, 0, 1 ] ]

Blog post: https://edspi31415.blogspot.com/2019/03/...ifted.html
03-06-2019, 04:32 PM
Post: #2
 Didier Lachieze Senior Member Posts: 1,143 Joined: Dec 2013
RE: Matrices Built from Shifted Elements
Interesting topic, another way to do it would be to use MAKEMAT like this:

Code:
EXPORT LSM(L0) BEGIN  LOCAL N:= SIZE(L0);  MAKEMAT(L0((J+I-1) MOD N),N,N);   // left shift matrix END; EXPORT RSM(L0) BEGIN  LOCAL N:= SIZE(L0);  MAKEMAT(L0((J-I+1) MOD N),N,N);   // right shift matrix END;
03-06-2019, 05:41 PM
Post: #3
 John Keith Senior Member Posts: 449 Joined: Dec 2013
RE: Matrices Built from Shifted Elements
Interesting, thanks for posting. As an aside, your left-shifted matrix is a Hankel matrix, useful in linear algebra and integer transforms.
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