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43,50145/dapll.ssp
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C DAPL 10
C ..................................................................DAPL 20
C DAPL 30
C SUBROUTINE DAPLL DAPL 40
C PURPOSE DAPL 50
C SET UP NORMAL EQUATIONS FOR A LINEAR LEAST SQUARES FIT DAPL 60
C TO A GIVEN DISCRETE FUNCTION DAPL 70
C DAPL 80
C USAGE DAPL 90
C CALL DAPLL(FFCT,N,IP,P,WORK,DATI,IER) DAPL 100
C SUBROUTINE FFCT REQUIRES AN EXTERNAL STATEMENT DAPL 110
C DAPL 120
C DESCRIPTION OF PARAMETERS DAPL 130
C FFCT - USER CODED SUBROUTINE WHICH MUST BE DECLARED DAPL 140
C EXTERNAL IN THE MAIN PROGRAM. IT IS CALLED DAPL 150
C CALL FFCT(I,N,IP,P,DATI,WGT,IER) AND RETURNS DAPL 160
C THE VALUES OF THE FUNDAMENTAL FUNCTIONS FOR DAPL 170
C THE I-TH ARGUMENT IN P(1) UP TO P(IP) DAPL 180
C FOLLOWED BY THE I-TH FUNCTION VALUE IN P(IP+1) DAPL 190
C N IS THE NUMBER OF ALL POINTS DAPL 200
C P,DATI,WGT MUST BE OF DOUBLE PRECISION. DAPL 210
C DATI IS A DUMMY PARAMETER WHICH IS USED AS ARRAY DAPL 220
C NAME. THE GIVEN DATA SET MAY BE ALLOCATED IN DATI DAPL 230
C WGT IS THE WEIGHT FACTOR FOR THE I-TH POINT DAPL 240
C IER IS USED AS RESULTANT ERROR PARAMETER IN FFCT DAPL 250
C N - NUMBER OF GIVEN POINTS DAPL 260
C IP - NUMBER OF FUNDAMENTAL FUNCTIONS USED FOR LEAST DAPL 270
C SQUARES FIT DAPL 280
C IP SHOULD NOT EXCEED N DAPL 290
C P - WORKING STORAGE OF DIMENSION IP+1, WHICH DAPL 300
C IS USED AS INTERFACE BETWEEN APLL AND THE USER DAPL 310
C CODED SUBROUTINE FFCT DAPL 320
C P MUST BE OF DOUBLE PRECISION. DAPL 330
C WORK - WORKING STORAGE OF DIMENSION (IP+1)*(IP+2)/2. DAPL 340
C ON RETURN WORK CONTAINS THE SYMMETRIC COEFFICIENT DAPL 350
C MATRIX OF THE NORMAL EQUATIONS IN COMPRESSED FORM, DAPL 360
C I.E. UPPER TRINGULAR PART ONLY STORED COLUMNWISE. DAPL 370
C THE FOLLOWING IP POSITIONS CONTAIN THE RIGHT DAPL 380
C HAND SIDE AND WORK((IP+1)*(IP+2)/2) CONTAINS DAPL 390
C THE WEIGHTED SQUARE SUM OF THE FUNCTION VALUES DAPL 400
C WORK MUST BE OF DOUBLE PRECISION. DAPL 410
C DATI - DUMMY ENTRY TO COMMUNICATE AN ARRAY NAME BETWEEN DAPL 420
C MAIN LINE AND SUBROUTINE FFCT. DAPL 430
C DATI MUST BE OF DOUBLE PRECISION. DAPL 440
C IER - RESULTING ERROR PARAMETER DAPL 450
C IER =-1 MEANS FORMAL ERRORS IN SPECIFIED DIMENSIONS DAPL 460
C IER = 0 MEANS NO ERRORS DAPL 470
C IER = 1 MEANS ERROR IN EXTERNAL SUBROUTINE FFCT DAPL 480
C DAPL 490
C REMARKS DAPL 500
C TO ALLOW FOR EASY COMMUNICATION OF INTEGER VALUES DAPL 510
C BETWEEN MAINLINE AND EXTERNAL SUBROUTINE FFCT, THE ERROR DAPL 520
C PARAMETER IER IS TREATED AS A VECTOR OF DIMENSION 1 WITHIN DAPL 530
C SUBROUTINE DAPLL. ADDITIONAL COMPONENTS OF IER MAY BE DAPL 540
C INTRODUCED BY THE USER FOR COMMUNICATION BACK AND FORTH. DAPL 550
C IN THIS CASE, HOWEVER, THE USER MUST SPECIFY IER AS A DAPL 560
C VECTOR IN HIS MAINLINE. DAPL 570
C EXECUTION OF SUBROUTINE DAPLL IS A PREPARATORY STEP FOR DAPL 580
C CALCULATION OF THE LINEAR LEAST SQUARES FIT. DAPL 590
C NORMALLY IT IS FOLLOWED BY EXECUTION OF SUBROUTINE DAPFS DAPL 600
C DAPL 610
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED DAPL 620
C THE EXTERNAL SUBROUTINE FFCT MUST BE FURNISHED BY THE USER DAPL 630
C DAPL 640
C METHOD DAPL 650
C HANDLING OF THE GIVEN DATA SET (ARGUMENTS,FUNCTION VALUES DAPL 660
C AND WEIGHTS) IS COMPLETELY LEFT TO THE USER DAPL 670
C ESSENTIALLY HE HAS THREE CHOICES DAPL 680
C (1) THE I-TH VALUES OF ARGUMENT, FUNCTION VALUE AND WEIGHT DAPL 690
C ARE CALCULATED WITHIN SUBROUTINE FFCT FOR GIVEN I. DAPL 700
C (2) THE I-TH VALUES OF ARGUMENT, FUNCTION VALUE AND WEIGHT DAPL 710
C ARE DETERMINED BY TABLE LOOK UP. THE STORAGE LOCATIONS DAPL 720
C REQUIRED ARE ALLOCATED WITHIN THE DUMMY ARRAY DATI DAPL 730
C (POSSIBLY IN P TOO, IN EXCESS OF THE SPECIFIED IP + 1 DAPL 740
C LOCATIONS). DAPL 750
C ANOTHER POSSIBILITY WOULD BE TO USE COMMON AS INTERFACE DAPL 760
C BETWEEN MAIN LINE AND SUBROUTINE FFCT AND TO ALLOCATE DAPL 770
C STORAGE FOR THE DATA SET IN COMMON. DAPL 780
C (3) THE I-TH VALUES OF ARGUMENT, FUNCTION VALUE AND WEIGHT DAPL 790
C ARE READ IN FROM AN EXTERNAL DEVICE. THIS MAY BE EASILY DAPL 800
C ACCOMPLISHED SINCE I IS USED STRICTLY INCREASING FROM DAPL 810
C ONE UP TO N WITHIN APLL DAPL 820
C DAPL 830
C ..................................................................DAPL 840
C DAPL 850
SUBROUTINE DAPLL(FFCT,N,IP,P,WORK,DATI,IER) DAPL 860
C DAPL 870
C DAPL 880
C DIMENSIONED DUMMY VARIABLES DAPL 890
DIMENSION P(1),WORK(1),DATI(1),IER(1) DAPL 900
DOUBLE PRECISION P,WORK,DATI,WGT,AUX DAPL 910
C DAPL 920
C CHECK FOR FORMAL ERRORS IN SPECIFIED DIMENSIONS DAPL 930
IF(N)10,10,1 DAPL 940
1 IF(IP)10,10,2 DAPL 950
2 IF(N-IP)10,3,3 DAPL 960
C DAPL 970
C SET WORKING STORAGE AND RIGHT HAND SIDE TO ZERO DAPL 980
3 IPP1=IP+1 DAPL 990
M=IPP1*(IP+2)/2 DAPL1000
IER(1)=0 DAPL1010
DO 4 I=1,M DAPL1020
4 WORK(I)=0.D0 DAPL1030
C DAPL1040
C START GREAT LOOP OVER ALL GIVEN POINTS DAPL1050
DO 8 I=1,N DAPL1060
CALL FFCT(I,N,IP,P,DATI,WGT,IER) DAPL1070
IF(IER(1))9,5,9 DAPL1080
5 J=0 DAPL1090
DO 7 K=1,IPP1 DAPL1100
AUX=P(K)*WGT DAPL1110
DO 6 L=1,K DAPL1120
J=J+1 DAPL1130
6 WORK(J)=WORK(J)+P(L)*AUX DAPL1140
7 CONTINUE DAPL1150
8 CONTINUE DAPL1160
C DAPL1170
C NORMAL RETURN DAPL1180
9 RETURN DAPL1190
C DAPL1200
C ERROR RETURN IN CASE OF FORMAL ERRORS DAPL1210
10 IER(1)=-1 DAPL1220
RETURN DAPL1230
END DAPL1240