SandMatrix Routine of the week: Pseudo-Inverse - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Software Libraries (/forum-10.html) +--- Forum: HP-41C Software Library (/forum-11.html) +--- Thread: SandMatrix Routine of the week: Pseudo-Inverse (/thread-2718.html) SandMatrix Routine of the week: Pseudo-Inverse - Ángel Martin - 12-28-2014 11:37 AM 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. For additional references see: 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 RE: SandMatrix Routine of the week: Pseudo-Inverse - Gene - 12-28-2014 08:48 PM 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!