C FRIF 10
C ..................................................................FRIF 20
C FRIF 30
C SUBROUTINE FORIF FRIF 40
C FRIF 50
C PURPOSE FRIF 60
C FOURIER ANALYSIS OF A GIVEN PERIODIC FUNCTION IN THE FRIF 70
C RANGE 0-2PI FRIF 80
C COMPUTES THE COEFFICIENTS OF THE DESIRED NUMBER OF TERMS FRIF 90
C IN THE FOURIER SERIES F(X)=A(0)+SUM(A(K)COS KX+B(K)SIN KX) FRIF 100
C WHERE K=1,2,...,M TO APPROXIMATE THE COMPUTED VALUES OF A FRIF 110
C GIVEN FUNCTION SUBPROGRAM FRIF 120
C FRIF 130
C USAGE FRIF 140
C CALL FORIF(FUN,N,M,A,B,IER) FRIF 150
C FRIF 160
C DESCRIPTION OF PARAMETERS FRIF 170
C FUN-NAME OF FUNCTION SUBPROGRAM TO BE USED FOR COMPUTING FRIF 180
C DATA POINTS FRIF 190
C N -DEFINES THE INTERVAL SUCH THAT 2N+1 POINTS ARE TAKEN FRIF 200
C OVER THE INTERVAL (0,2PI). THE SPACING IS THUS 2PI/2N+1 FRIF 210
C M -THE MAXIMUM ORDER OF THE HARMONICS TO BE FITTED FRIF 220
C A -RESULTANT VECTOR OF FOURIER COSINE COEFFICIENTS OF FRIF 230
C LENGTH M+1 FRIF 240
C A SUB 0, A SUB 1,..., A SUB M FRIF 250
C B -RESULTANT VECTOR OF FOURIER SINE COEFFICIENTS OF FRIF 260
C LENGTH M+1 FRIF 270
C B SUB 0, B SUB 1,..., B SUB M FRIF 280
C IER-RESULTANT ERROR CODE WHERE FRIF 290
C IER=0 NO ERROR FRIF 300
C IER=1 N NOT GREATER OR EQUAL TO M FRIF 310
C IER=2 M LESS THAN 0 FRIF 320
C FRIF 330
C REMARKS FRIF 340
C M MUST BE GREATER THAN OR EQUAL TO ZERO FRIF 350
C N MUST BE GREATER THAN OR EQUAL TO M FRIF 360
C THE FIRST ELEMENT IN VECTOR B IS ZERO IN ALL CASES FRIF 370
C FRIF 380
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED FRIF 390
C FUN-NAME OF USER FUNCTION SUBPROGRAM USED FOR COMPUTING FRIF 400
C DATA POINTS FRIF 410
C CALLING PROGRAM MUST HAVE FORTRAN EXTERNAL STATEMENT FRIF 420
C CONTAINING NAMES OF FUNCTION SUBPROGRAMS LISTED IN CALL TO FRIF 430
C FORIF FRIF 440
C FRIF 450
C METHOD FRIF 460
C USES RECURSIVE TECHNIQUE DESCRIBED IN A. RALSTON, H. WILF, FRIF 470
C 'MATHEMATICAL METHODS FOR DIGITAL COMPUTERS', JOHN WILEY FRIF 480
C AND SONS, NEW YORK, 1960, CHAPTER 24. THE METHOD OF FRIF 490
C INDEXING THROUGH THE PROCEDURE HAS BEEN MODIFIED TO FRIF 500
C SIMPLIFY THE COMPUTATION. FRIF 510
C FRIF 520
C ..................................................................FRIF 530
C FRIF 540
SUBROUTINE FORIF(FUN,N,M,A,B,IER) FRIF 550
DIMENSION A(1),B(1) FRIF 560
C FRIF 570
C CHECK FOR PARAMETER ERRORS FRIF 580
C FRIF 590
IER=0 FRIF 600
20 IF(M) 30,40,40 FRIF 610
30 IER=2 FRIF 620
RETURN FRIF 630
40 IF(M-N) 60,60,50 FRIF 640
50 IER=1 FRIF 650
RETURN FRIF 660
C FRIF 670
C COMPUTE AND PRESET CONSTANTS FRIF 680
C FRIF 690
60 AN=N FRIF 700
COEF=2.0/(2.0*AN+1.0) FRIF 710
CONST=3.141593*COEF FRIF 720
S1=SIN(CONST) FRIF 730
C1=COS(CONST) FRIF 740
C=1.0 FRIF 750
S=0.0 FRIF 760
J=1 FRIF 770
FUNZ=FUN(0.0) FRIF 780
70 U2=0.0 FRIF 790
U1=0.0 FRIF 800
AI=2*N FRIF 810
C FRIF 820
C FORM FOURIER COEFFICIENTS RECURSIVELY FRIF 830
C FRIF 840
75 X=AI*CONST FRIF 850
U0=FUN(X)+2.0*C*U1-U2 FRIF 860
U2=U1 FRIF 870
U1=U0 FRIF 880
AI=AI-1.0 FRIF 890
IF(AI) 80,80,75 FRIF 900
80 A(J)=COEF*(FUNZ+C*U1-U2) FRIF 910
B(J)=COEF*S*U1 FRIF 920
IF(J-(M+1)) 90,100,100 FRIF 930
90 Q=C1*C-S1*S FRIF 940
S=C1*S+S1*C FRIF 950
C=Q FRIF 960
J=J+1 FRIF 970
GO TO 70 FRIF 980
100 A(1)=A(1)*0.5 FRIF 990
RETURN FRIF1000
END FRIF1010