MPINVERT: Moore-Penrose Inverse of a Matrix
|
08-29-2014, 09:30 PM
Post: #1
|
|||
|
|||
MPINVERT: Moore-Penrose Inverse of a Matrix
Also known as a pseudoinverse, the Moore-Penrose inverse of a matrix, denoted by A^+ (capital A with a supersubscript of a plus sign), is an inverse of matrix. Different from the "true" matrix inverse, the Moore-Penrose inverse allows for non-square matrices. Primarily, the Moore-Penrose inverses are calculated is assist in solving linear least-square equations.
Input: MPINVERT(matrix). Execute this from Home or CAS screen. Program: EXPORT MPINVERT(mtx) BEGIN // 2014-08-27 EWS // Moore-Penrose Matrix Inverse LOCAL r,c,d,n; d:=SIZE(mtx); r:=d(1); c:=d(2); n:=RANK(mtx); CASE IF n==c THEN RETURN (TRN(mtx)*mtx)^-1*mtx; END; IF n==r THEN RETURN TRN(mtx)*(mtx*TRN(mtx))^-1; END; DEFAULT RETURN "No Solution Found"; END; END; Examples Matrix: [ [ 1, 2, 3 ] [ 3, 4, 0 ] ] Moore-Penrose Inverse: [ [ -8/229, 31/229 ] [ 6/229, 34/229 ] [ 75/229, -33/229 ] ] Matrix: [ [7, 4, 6, -7] [-1, 5, 3, 3] ] Moore-Penrose Inverse: (to four decimal places) [ [0.0489, -0.0338] [0.0194, 0.1092] [0.0360, 0.0600] [-0.0520, 0.0800] ] |
|||
« Next Oldest | Next Newest »
|
Messages In This Thread |
MPINVERT: Moore-Penrose Inverse of a Matrix - Eddie W. Shore - 08-29-2014 09:30 PM
RE: MPINVERT: Moore-Penrose Inverse of a Matrix - Namir - 09-01-2014, 09:11 PM
RE: MPINVERT: Moore-Penrose Inverse of a Matrix - Han - 02-06-2015, 07:48 PM
RE: MPINVERT: Moore-Penrose Inverse of a Matrix - salvomic - 02-06-2015, 03:09 PM
RE: MPINVERT: Moore-Penrose Inverse of a Matrix - Han - 02-06-2015, 07:38 PM
RE: MPINVERT: Moore-Penrose Inverse of a Matrix - salvomic - 02-06-2015, 08:40 PM
RE: MPINVERT: Moore-Penrose Inverse of a Matrix - Han - 10-27-2015, 06:57 PM
RE: MPINVERT: Moore-Penrose Inverse of a Matrix - salvomic - 10-28-2015, 09:02 AM
|
User(s) browsing this thread: 3 Guest(s)