Enter your search terms Submit search form
	Web pdp-10.trailing-edge.com

SUBROUTINE SIMQ

PURPOSE
   OBTAIN SOLUTION OF A SET OF SIMULTANEOUS LINEAR EQUATIONS,
   AX=B

USAGE
   CALL SIMQ(A,B,N,KS)

DESCRIPTION OF PARAMETERS
   A - MATRIX OF COEFFICIENTS STORED COLUMNWISE.  THESE ARE
       DESTROYED IN THE COMPUTATION.  THE SIZE OF MATRIX A IS
       N BY N.
   B - VECTOR OF ORIGINAL CONSTANTS (LENGTH N). THESE ARE
       REPLACED BY FINAL SOLUTION VALUES, VECTOR X.
   N - NUMBER OF EQUATIONS AND VARIABLES. N MUST BE .GT. ONE.
   KS - OUTPUT DIGIT
	0 FOR A NORMAL SOLUTION
	1 FOR A SINGULAR SET OF EQUATIONS

REMARKS
   MATRIX A MUST BE GENERAL.
   IF MATRIX IS SINGULAR , SOLUTION VALUES ARE MEANINGLESS.
   AN ALTERNATIVE SOLUTION MAY BE OBTAINED BY USING MATRIX
   INVERSION (MINV) AND MATRIX PRODUCT (GMPRD).

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   METHOD OF SOLUTION IS BY ELIMINATION USING LARGEST PIVOTAL
   DIVISOR. EACH STAGE OF ELIMINATION CONSISTS OF INTERCHANGING
   ROWS WHEN NECESSARY TO AVOID DIVISION BY ZERO OR SMALL
   ELEMENTS.
   THE FORWARD SOLUTION TO OBTAIN VARIABLE N IS DONE IN
   N STAGES. THE BACK SOLUTION FOR THE OTHER VARIABLES IS
   CALCULATED BY SUCCESSIVE SUBSTITUTIONS. FINAL SOLUTION
   VALUES ARE DEVELOPED IN VECTOR B, WITH VARIABLE 1 IN B(1),
   VARIABLE 2 IN B(2),........, VARIABLE N IN B(N).
   IF NO PIVOT CAN BE FOUND EXCEEDING A TOLERANCE OF 0.0,
   THE MATRIX IS CONSIDERED SINGULAR AND KS IS SET TO 1. THIS
   TOLERANCE CAN BE MODIFIED BY REPLACING THE FIRST STATEMENT.