C SIMQ 10
C ..................................................................SIMQ 20
C SIMQ 30
C SUBROUTINE SIMQ SIMQ 40
C SIMQ 50
C PURPOSE SIMQ 60
C OBTAIN SOLUTION OF A SET OF SIMULTANEOUS LINEAR EQUATIONS, SIMQ 70
C AX=B SIMQ 80
C SIMQ 90
C USAGE SIMQ 100
C CALL SIMQ(A,B,N,KS) SIMQ 110
C SIMQ 120
C DESCRIPTION OF PARAMETERS SIMQ 130
C A - MATRIX OF COEFFICIENTS STORED COLUMNWISE. THESE ARE SIMQ 140
C DESTROYED IN THE COMPUTATION. THE SIZE OF MATRIX A IS SIMQ 150
C N BY N. SIMQ 160
C B - VECTOR OF ORIGINAL CONSTANTS (LENGTH N). THESE ARE SIMQ 170
C REPLACED BY FINAL SOLUTION VALUES, VECTOR X. SIMQ 180
C N - NUMBER OF EQUATIONS AND VARIABLES. N MUST BE .GT. ONE. SIMQ 190
C KS - OUTPUT DIGIT SIMQ 200
C 0 FOR A NORMAL SOLUTION SIMQ 210
C 1 FOR A SINGULAR SET OF EQUATIONS SIMQ 220
C SIMQ 230
C REMARKS SIMQ 240
C MATRIX A MUST BE GENERAL. SIMQ 250
C IF MATRIX IS SINGULAR , SOLUTION VALUES ARE MEANINGLESS. SIMQ 260
C AN ALTERNATIVE SOLUTION MAY BE OBTAINED BY USING MATRIX SIMQ 270
C INVERSION (MINV) AND MATRIX PRODUCT (GMPRD). SIMQ 280
C SIMQ 290
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED SIMQ 300
C NONE SIMQ 310
C SIMQ 320
C METHOD SIMQ 330
C METHOD OF SOLUTION IS BY ELIMINATION USING LARGEST PIVOTAL SIMQ 340
C DIVISOR. EACH STAGE OF ELIMINATION CONSISTS OF INTERCHANGINGSIMQ 350
C ROWS WHEN NECESSARY TO AVOID DIVISION BY ZERO OR SMALL SIMQ 360
C ELEMENTS. SIMQ 370
C THE FORWARD SOLUTION TO OBTAIN VARIABLE N IS DONE IN SIMQ 380
C N STAGES. THE BACK SOLUTION FOR THE OTHER VARIABLES IS SIMQ 390
C CALCULATED BY SUCCESSIVE SUBSTITUTIONS. FINAL SOLUTION SIMQ 400
C VALUES ARE DEVELOPED IN VECTOR B, WITH VARIABLE 1 IN B(1), SIMQ 410
C VARIABLE 2 IN B(2),........, VARIABLE N IN B(N). SIMQ 420
C IF NO PIVOT CAN BE FOUND EXCEEDING A TOLERANCE OF 0.0, SIMQ 430
C THE MATRIX IS CONSIDERED SINGULAR AND KS IS SET TO 1. THIS SIMQ 440
C TOLERANCE CAN BE MODIFIED BY REPLACING THE FIRST STATEMENT. SIMQ 450
C SIMQ 460
C ..................................................................SIMQ 470
C SIMQ 480
SUBROUTINE SIMQ(A,B,N,KS) SIMQ 490
DIMENSION A(1),B(1) SIMQ 500
C SIMQ 510
C FORWARD SOLUTION SIMQ 520
C SIMQ 530
TOL=0.0 SIMQ 540
KS=0 SIMQ 550
JJ=-N SIMQ 560
DO 65 J=1,N SIMQ 570
JY=J+1 SIMQ 580
JJ=JJ+N+1 SIMQ 590
BIGA=0 SIMQ 600
IT=JJ-J SIMQ 610
DO 30 I=J,N SIMQ 620
C SIMQ 630
C SEARCH FOR MAXIMUM COEFFICIENT IN COLUMN SIMQ 640
C SIMQ 650
IJ=IT+I SIMQ 660
IF(ABS(BIGA)-ABS(A(IJ))) 20,30,30 SIMQ 670
20 BIGA=A(IJ) SIMQ 680
IMAX=I SIMQ 690
30 CONTINUE SIMQ 700
C SIMQ 710
C TEST FOR PIVOT LESS THAN TOLERANCE (SINGULAR MATRIX) SIMQ 720
C SIMQ 730
IF(ABS(BIGA)-TOL) 35,35,40 SIMQ 740
35 KS=1 SIMQ 750
RETURN SIMQ 760
C SIMQ 770
C INTERCHANGE ROWS IF NECESSARY SIMQ 780
C SIMQ 790
40 I1=J+N*(J-2) SIMQ 800
IT=IMAX-J SIMQ 810
DO 50 K=J,N SIMQ 820
I1=I1+N SIMQ 830
I2=I1+IT SIMQ 840
SAVE=A(I1) SIMQ 850
A(I1)=A(I2) SIMQ 860
A(I2)=SAVE SIMQ 870
C SIMQ 880
C DIVIDE EQUATION BY LEADING COEFFICIENT SIMQ 890
C SIMQ 900
50 A(I1)=A(I1)/BIGA SIMQ 910
SAVE=B(IMAX) SIMQ 920
B(IMAX)=B(J) SIMQ 930
B(J)=SAVE/BIGA SIMQ 940
C SIMQ 950
C ELIMINATE NEXT VARIABLE SIMQ 960
C SIMQ 970
IF(J-N) 55,70,55 SIMQ 980
55 IQS=N*(J-1) SIMQ 990
DO 65 IX=JY,N SIMQ1000
IXJ=IQS+IX SIMQ1010
IT=J-IX SIMQ1020
DO 60 JX=JY,N SIMQ1030
IXJX=N*(JX-1)+IX SIMQ1040
JJX=IXJX+IT SIMQ1050
60 A(IXJX)=A(IXJX)-(A(IXJ)*A(JJX)) SIMQ1060
65 B(IX)=B(IX)-(B(J)*A(IXJ)) SIMQ1070
C SIMQ1080
C BACK SOLUTION SIMQ1090
C SIMQ1100
70 NY=N-1 SIMQ1110
IT=N*N SIMQ1120
DO 80 J=1,NY SIMQ1130
IA=IT-J SIMQ1140
IB=N-J SIMQ1150
IC=N SIMQ1160
DO 80 K=1,J SIMQ1170
B(IB)=B(IB)-A(IA)*B(IC) SIMQ1180
IA=IA-N SIMQ1190
80 IC=IC-1 SIMQ1200
RETURN SIMQ1210
END SIMQ1220