☜	$%MTXEQU M[UMPS] by Example					☞

2-Jul–96, 6:54:35
Routine Save for Matrix Mathematics Library function $%MTXEQU^MATH
 ;
 ; Unless otherwise noted, the code below
 ; was approved in document X11/96–26
 ;
 ; If corrections have been applied,
 ; first the original line appears,
 ; with three semicolons at the beginning of the line.
 ;
 ; Then the source of the correction is acknowledged,
 ; then the corrected line appears, followed by a
 ; line containing three semicolons.
 ;
MTXEQU(A,B,R,N,M) ;
 ; Solve matrix equation A [M,M] * R [M,N] = B [M,N]
 IF $GET(M)<1 QUIT ""
 IF $GET(N)<1 QUIT ""
 IF '$%MTXDET^MATH(.A,M) QUIT 0
 ;
 NEW I,I1,J,J1,J2,K,L,T,T1,T2,TEMP,X
 ;
 SET X=$%MTXCOPY^MATH(.A,.T,N,N)
 SET X=$%MTXCOPY^MATH(.B,.R,N,M)
 ;
 ; Reduction of matrix A
 ; Steps of reduction are counted by index K
 ;
 FOR K=1:1:N–1 DO
 . ;
 . ; Search for largest coefficient of T
 . ; (denoted by TEMP)
 . ; in first column of reduced system
 . ;
 . SET TEMP=0,J2=K
 . FOR J1=K:1:N DO
 . . QUIT:$TRANSLATE($GET(T(J1,K)),"-")>$TRANSLATE(TEMP,"-")
 . . SET TEMP=T(J1,K),J2=J1
 . . QUIT
 . ;
 . ; Exchange row number K with row number J2,
 . ; if necessary
 . ;
 . DO:J2'=K
 . . ;
 . . FOR J=K:1:N DO
 . . . SET T1=$GET(T(K,J)),T2=$GET(T(J2,J))
 . . . KILL T(K,J),T(J2,J)
 . . . IF T1'="" SET T(J2,J)=T1
 . . . IF T2'="" SET T(K,J)=T2
 . . . QUIT
 . . FOR J=1:1:M DO
 . . . SET T1=$GET(R(K,J)),T2=$GET(R(J2,J))
 . . . KILL R(K,J),R(J2,J)
 . . . IF T1'="" SET R(J2,J)=T1
 . . . IF T2'="" SET R(K,J)=T2
 . . . QUIT
 . . QUIT
 . ;
 . ; Actual reduction
 . ;
 . FOR I=K+1:1:N DO
 . . FOR J=K+1:1:N DO
 . . . QUIT:'$GET(T(K,K))
 . . . SET T(I,J)=-$GET(T(K,J))*$GET(T(I,K))/T(K,K)+$GET(T(I,J))
 . . . QUIT
 . . FOR J=1:1:M DO
 . . . QUIT:'$GET(T(K,K))
 . . . SET R(I,J)=-$GET(R(K,J))*$GET(T(I,K))/T(K,K)+$GET(R(I,J))
 . . . QUIT
 . . QUIT
 . QUIT
 ;
 ; Backsubstitution
 ;
 FOR J=1:1:M DO
 . IF $GET(T(N,N)) SET R(N,J)=$GET(R(N,J))/T(N,N)
 . IF N–1>0 FOR I1=1:1:N–1 DO
 . . SET I=N-I1
 . . FOR L=I+1:1:N DO
 . . . SET R(I,J)=-$GET(T(I,L))*$GET(R(L,J))+$GET(R(I,J))
 . . . QUIT
 . . IF $GET(T(I,I)) SET R(I,J)=$GET(R(I,J))/$GET(T(I,I))
 . . QUIT
 . QUIT
 QUIT $SELECT(M=N:$%MTXDET^MATH(.R,M),1:1)
 ;===
 ;
 ;
 ;

Copyright © Standard Documents; 1977-2024 MUMPS Development Committee;
Copyright © Examples: 1995-2024 Ed de Moel;
Copyright © Annotations: 2003-2008 Jacquard Systems Research
Copyright © Annotations: 2008-2024 Ed de Moel.

The information in this page is NOT authoritative and subject to be modified at any moment.
Please consult the appropriate (draft) language standard for an authoritative definition.

Some specifications are "approved for inclusion in a future standard". Note that the MUMPS Development Committee cannot guarantee that such future standards will indeed be published.

This page most recently updated on 16-Nov-2023, 16:52:01.

For comments, contact Ed de Moel (demoel@jacquardsystems.com)