C FRIT 10
C ..................................................................FRIT 20
C FRIT 30
C SUBROUTINE FORIT FRIT 40
C FRIT 50
C PURPOSE FRIT 60
C FOURIER ANALYSIS OF A PERIODICALLY TABULATED FUNCTION. FRIT 70
C COMPUTES THE COEFFICIENTS OF THE DESIRED NUMBER OF TERMS FRIT 80
C IN THE FOURIER SERIES F(X)=A(0)+SUM(A(K)COS KX+B(K)SIN KX) FRIT 90
C WHERE K=1,2,...,M TO APPROXIMATE A GIVEN SET OF FRIT 100
C PERIODICALLY TABULATED VALUES OF A FUNCTION. FRIT 110
C FRIT 120
C USAGE FRIT 130
C CALL FORIT(FNT,N,M,A,B,IER) FRIT 140
C FRIT 150
C DESCRIPTION OF PARAMETERS FRIT 160
C FNT-VECTOR OF TABULATED FUNCTION VALUES OF LENGTH 2N+1 FRIT 170
C N -DEFINES THE INTERVAL SUCH THAT 2N+1 POINTS ARE TAKEN FRIT 180
C OVER THE INTERVAL (0,2PI). THE SPACING IS THUS 2PI/2N+1 FRIT 190
C M -MAXIMUM ORDER OF HARMONICS TO BE FITTED FRIT 200
C A -RESULTANT VECTOR OF FOURIER COSINE COEFFICIENTS OF FRIT 210
C LENGTH M+1 FRIT 220
C A SUB 0, A SUB 1,..., A SUB M FRIT 230
C B -RESULTANT VECTOR OF FOURIER SINE COEFFICIENTS OF FRIT 240
C LENGTH M+1 FRIT 250
C B SUB 0, B SUB 1,..., B SUB M FRIT 260
C IER-RESULTANT ERROR CODE WHERE FRIT 270
C IER=0 NO ERROR FRIT 280
C IER=1 N NOT GREATER OR EQUAL TO M FRIT 290
C IER=2 M LESS THAN 0 FRIT 300
C FRIT 310
C REMARKS FRIT 320
C M MUST BE GREATER THAN OR EQUAL TO ZERO FRIT 330
C N MUST BE GREATER THAN OR EQUAL TO M FRIT 340
C THE FIRST ELEMENT OF VECTOR B IS ZERO IN ALL CASES FRIT 350
C FRIT 360
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED FRIT 370
C NONE FRIT 380
C FRIT 390
C METHOD FRIT 400
C USES RECURSIVE TECHNIQUE DESCRIBED IN A. RALSTON, H. WILF, FRIT 410
C 'MATHEMATICAL METHODS FOR DIGITAL COMPUTERS', JOHN WILEY FRIT 420
C AND SONS, NEW YORK, 1960, CHAPTER 24. THE METHOD OF INDEXINGFRIT 430
C THROUGH THE PROCEDURE HAS BEEN MODIFIED TO SIMPLIFY THE FRIT 440
C COMPUTATION. FRIT 450
C FRIT 460
C ..................................................................FRIT 470
C FRIT 480
SUBROUTINE FORIT(FNT,N,M,A,B,IER) FRIT 490
DIMENSION A(1),B(1),FNT(1) FRIT 500
C FRIT 510
C CHECK FOR PARAMETER ERRORS FRIT 520
C FRIT 530
IER=0 FRIT 540
20 IF(M) 30,40,40 FRIT 550
30 IER=2 FRIT 560
RETURN FRIT 570
40 IF(M-N) 60,60,50 FRIT 580
50 IER=1 FRIT 590
RETURN FRIT 600
C FRIT 610
C COMPUTE AND PRESET CONSTANTS FRIT 620
C FRIT 630
60 AN=N FRIT 640
COEF=2.0/(2.0*AN+1.0) FRIT 650
CONST=3.141593*COEF FRIT 660
S1=SIN(CONST) FRIT 670
C1=COS(CONST) FRIT 680
C=1.0 FRIT 690
S=0.0 FRIT 700
J=1 FRIT 710
FNTZ=FNT(1) FRIT 720
70 U2=0.0 FRIT 730
U1=0.0 FRIT 740
I=2*N+1 FRIT 750
C FRIT 760
C FORM FOURIER COEFFICIENTS RECURSIVELY FRIT 770
C FRIT 780
75 U0=FNT(I)+2.0*C*U1-U2 FRIT 790
U2=U1 FRIT 800
U1=U0 FRIT 810
I=I-1 FRIT 820
IF(I-1) 80,80,75 FRIT 830
80 A(J)=COEF*(FNTZ+C*U1-U2) FRIT 840
B(J)=COEF*S*U1 FRIT 850
IF(J-(M+1)) 90,100,100 FRIT 860
90 Q=C1*C-S1*S FRIT 870
S=C1*S+S1*C FRIT 880
C=Q FRIT 890
J=J+1 FRIT 900
GO TO 70 FRIT 910
100 A(1)=A(1)*0.5 FRIT 920
RETURN FRIT 930
END FRIT 940