SandMatrix Routine of the week: Pseudo-Inverse
12-28-2014, 11:37 AM (This post was last modified: 12-28-2014 11:41 AM by Ángel Martin.)
Post: #1
 Ángel Martin Senior Member Posts: 1,319 Joined: Dec 2013
SandMatrix Routine of the week: Pseudo-Inverse
Even if the convergence is finicky, using the BenIsrael-Cohen algorithm it takes a relatively short program to calculate the Moore-Penrose matrix pseudo-inverse. Once the initial estimation is calculated it's a matter of a few iterations until the final result is obtained - although each iteration also takes its time.

http://benisrael.net/COHEN-BI-ITER-GI.pdf

and JM Baillard's page:
http://hp41programs.yolasite.com/pseudoinverse.php

The code is listed below; lots of Alpha stuff as they are the input control strings that drive the matrix operations. Also note three auxiliary matrices are needed - mostly due to the M*M instruction that requires a result matrix different from the operands.

Code:
 01    LBL "MPINV" 02    ASTO O1 03    "|-,#" 04    MAT= 05    DIM? 06    INT 07    I<>J 08    LASTX 09    + 10    "P" 11    MATDIM 12    "#" 13    TRNPS 14    XEQ 00 15    "P" 16    MTRACE 17    "#,X,#" 18    MAT/ 19    FNRM 20    STO 00 21    DIM? 22    "Q" 23    MATDIM 24    LBL 01 25    XEQ 00 26    "#,P,Q" 27    M*M 28    "#" 29    MAT+ 30    "#,Q,#" 31    MAT- 32    FNRM 33    X<> 00 34    RCL- (00) 35    ABS 36    VIEW X 37    E-7 38    X<=Y? 39    GTO 01 40    "P" 41    PURFL 42    "Q" 43    PURFL 44    MNAME? 45    RTN 46    LBL 00 47    CLA 48    ARCL 01 49    "|-,#,P" 50    M*M 51    END

You'll need the SandMatrix for functions I<>J, MTRACE and MAT=

Auxiliary matrices "P" and "Q" are purged upon completion.
The result matrix "#" will not overwrite the initial one.

Cheers,
'AM
12-28-2014, 08:48 PM
Post: #2
 Gene Moderator Posts: 1,250 Joined: Dec 2013
RE: SandMatrix Routine of the week: Pseudo-Inverse
Thanks for this and all the work you have done on the modules for the 41. They make the 41CL a joy to use.

I'm sure the surface hasn't even been scratched with the abilities of the roms you have created. Many thanks!
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