C PROGRAM 3.1 PERIOD C C ... This program computes periodogram ... C C The following inputs are required in READTS. C TITLE: title of the data C N: data length C Y(I): time series C Parameters: C NMAX: adjustable dimension of Y (NMAX.GE.N) C MJ: adjustable dimension of COV C NF: adjustable dimension of PE and SPE C IDEV: input device C JDEV: output device C IWINDW: window type (0: box-car, 1: Hanning, 2: Hamming) C @TEST.PN31: 5/16/89, 12/5/90, 12/21/90, 8/5/91 C PARAMETER( NMAX=200,MJ=NMAX,NF=512,IDEV=1,JDEV=6,IWINDW=1 ) IMPLICIT REAL*8(A-H,O-Z) DIMENSION Y(NMAX), PE(0:NF), SPE(0:NF), COV(0:MJ) DATA OUTMIN/-1.0D30/, OUTMAX/ 1.0D30/ C CALL READTS( IDEV,Y,N ) C IF( IWINDW.EQ.0 ) LAG = MIN0( N-1,MJ ) IF( IWINDW.GT.0 ) LAG = 2*DSQRT( DBLE(N) ) IF( IWINDW.EQ.0 ) NP = (LAG+1)/2 IF( IWINDW.GT.0 ) NP = LAG C CALL PERIOD( Y,N,LAG,OUTMIN,OUTMAX,NP,0,COV,PE ) C CALL WINDOW( PE,NP,IWINDW,SPE ) C CALL PRPER( JEV,PE,SPE,N,NP,IWINDW ) CALL PTPER( SPE,N,LAG,NP,IWINDW ) C STOP E N D SUBROUTINE FOURIE( X,N,M,FC,FS ) C C ... Discrete Fourier transformation by Goertzel method ... C C Inputs: C X(I): data (I=1,N) C N: data length C M: number of Fourier components C FC(J): Fourier cosine transform (J=1,M) C FS(J): Fourier sine transform (J=1,M) C IMPLICIT REAL*8 (A-H,O-Z) DIMENSION X(N), FC(M), FS(M) DATA PI/3.14159265358979D0/ C W = PI/(M-1) DO 20 I=1,M CI = DCOS(W*(I-1)) SI = DSIN(W*(I-1)) T1 = 0.0 T2 = 0.0 DO 10 J=N,2,-1 T0 = 2*CI*T1 - T2 + X(J) T2 = T1 10 T1 = T0 FC(I) = CI*T1 - T2 + X(1) 20 FS(I) = SI*T1 C RETURN E N D SUBROUTINE PERIOD( Y,N,LAG,OUTMIN,OUTMAX,NN,ISW,COV,P ) C C ... Periodogram computation by Fourier transf. of autocovariance ... C C Inputs: C Y(I): time series C N: data length C LAG: maximum lag of autocovariance C NN: number of frequencies C OUTMIN: lower bound for detecting outliers C OUTMAX: upper bound for detecting outliers C ISW = 0: autocovariance is not given C = 1: given C COV: autocovariance (if ISW=1) C Outputs: C COV(I): autocovariance (if ISW=0) C P(I): periodogram (raw spectrum) C IMPLICIT REAL*8(A-H,O-Z) DIMENSION Y(N), COV(0:1024), P(0:512), FC(513), FS(513) C IF( LAG.GE.1023 ) LAG = 1023 IF( ISW.EQ.0 ) CALL AUTCOV( Y,N,LAG,OUTMIN,OUTMAX,COV ) C C ... Fourier transformation by Goertzel method ... C CALL FOURIE( COV(0),LAG+1,NN+1,FC,FS ) C DO 10 I=0,NN 10 P(I) = 2.0D0*FC(I+1) - COV(0) C RETURN E N D SUBROUTINE PRPER( JDEV,PE,SPE,N,MJ,IWINDW ) C C ... This subroutine prints out periodogram ... C C Inputs: C JDEV: output device specification C PE: periodogram (raw spectrum) C SPE: logarithm of smoothed periodogram C N: data length C MJ: number of frequencies C IWINDW: type of specral window C CHARACTER*72 TITLE REAL*8 PE(0:MJ), SPE(0:MJ) COMMON /CMDATA/ TITLE C WRITE(JDEV,600) WRITE(JDEV,610) TITLE WRITE(JDEV,620) N, MJ, IWINDW WRITE(JDEV,630) (PE(I),I=0,MJ) WRITE(JDEV,640) (SPE(I),I=0,MJ) C 600 FORMAT( 1H ,'PROGRAM 3.1: ' ) 610 FORMAT( 1H ,' DATA: ',A72 ) 620 FORMAT( 1H ,' N =',I5,3X,'MJ =',I4,3X,'IWINDW =',I2 ) 630 FORMAT( 1H0,'** PERIODOGRAM: P(I);(I=0,...,MJ) **',/ * (1H ,5D13.5) ) 640 FORMAT( 1H0,'** LOG-PERIODOGRAM: LOG P(I);(I=0,...,MJ) **',/ * (1H ,10F8.3) ) RETURN E N D SUBROUTINE PTPER( PE,N,LAG,NP,IWINDW ) C C ... This subroutine draws log-periodogram ... C C Inputs: C PE(I): log-periodogam C N: data length C LAG: maximum lag of autocovariance C NP: number of frequencies C IWINDW: window type (0: box-car, 1: Hanning, 2: Hamming) C IMPLICIT REAL*8(A-H,O-Z) CHARACTER*8 VNAME(5) DIMENSION PE(0:NP), VALUE(5) WY = 12.0 WX = 16.0 VNAME(1) = 'N = ' VNAME(2) = 'LAG = ' VNAME(3) = 'IWINDW =' VALUE(1) = N VALUE(2) = LAG VALUE(3) = IWINDW C CALL PLOTS C call plots( 1,0,0,1,0 ) C call form( 1 ) C call factor( 10.0 ) CALL HEADER( 'PROGRAM 3.1: PERIODOGRAM',26,3,VNAME,VALUE ) CALL MAXMIN( PE(1),NP,YMIN,YMAX,DY) CALL DRAWY2( 'PERIODOGRAM (IN LOG SCALE)',26,3.0D0,2.0D0, * PE(1),NP,WX,WY,1,2,0.0D0,0.5D0,0.1D0,YMIN,YMAX,DY ) CALL PLOTE C call plot( 0.0,0.0,999 ) RETURN E N D SUBROUTINE WINDOW( PE,NP,IWINDW,SPE ) C C ... Smoothing by spectral window and log-transformation ... C C Inputs: C PE(I): raw specrum C NP: number of frequencies C IWINDW: window type (0: box-car, 1: Hanning, 2: Hamming) C Outputs: C SPE(I): logarithm of smoothed peiodogram C IMPLICIT REAL*8(A-H,O-Z) DIMENSION PE(0:NP), SPE(0:NP) DIMENSION W(0:1,2) DATA W/0.5D0, 0.25D0, 0.54D0, 0.23D0/ C IF( IWINDW.EQ.0 ) THEN PMIN = 1.0D30 DO 10 I=0,NP 10 IF( PE(I).GT.0.0D0 .AND. PE(I).LT.PMIN ) PMIN = PE(I) DO 20 I=0,NP 20 SPE(I) = DMAX1( PE(I),PMIN ) ELSE SPE(0) = W(0,IWINDW)*PE(0) + W(1,IWINDW)*PE(1)*2 SPE(NP)= W(0,IWINDW)*PE(NP)+ W(1,IWINDW)*PE(NP-1)*2 DO 30 I=1,NP-1 30 SPE(I) = W(0,IWINDW)*PE(I) + W(1,IWINDW)*(PE(I-1) + PE(I+1)) END IF DO 50 I=0,NP 50 SPE(I) = DLOG10( SPE(I) ) C RETURN E N D SUBROUTINE AXISXY(X,Y,WX,WY,X0,X1,Y0,Y1,DX,DY,DWC,IBOX,IX,IY) C C ... This subroutine draws X and Y axes. C C Inputs: C X,Y: location of the left bottom of the figure C WX,WY: width and height of the figure C X0,X1: lower and upper bounds of the X axis C Y0,Y1: lower and upper bounds of the Y axis C DX,DY: step width in X and Y axes C DWC: size of characters C IBOX: = 0 draw X and Y axes only C = 1 draw window doundary C IX,IY: number of additional click in each step C Modified: 8/31/90, 11/21/90 C REAL*8 X,Y,WX,WY,X0,X1,Y0,Y1,DX,DY,DWC C FX = X FY = Y FWX = WX FWY = WY FWC = DWC CALL NEWPEN( 2 ) CALL PLOT( FX,FY,-3 ) CALL PLOT( 0.0,FWY,3 ) CALL PLOT( 0.0,0.0,2 ) CALL PLOT( FWX,0.0,2 ) IF ( IBOX.EQ.1 ) THEN CALL PLOT( FWX,FWY,2 ) CALL PLOT( 0.0,FWY,2 ) END IF C C ... draw X axis ... C WC = DWC NX = (X1-X0)/DX + 0.001 NY = (Y1-Y0)/DY + 0.001 MX = -DLOG10( DX ) + 0.001 IF(DX.LT.1.0D0) MX = -DLOG10( DX ) + 0.999 IF( MX.LE.0 ) MX = -1 D = WX*DX/(X1-X0) DO 10 I=1,NX+1 XN = X0 + DX*(I-1) XX = D*(I-1) CALL PLOT( XX,-FWC/2,3 ) CALL PLOT( XX,0.0,2 ) IF( IBOX.EQ.1 ) THEN CALL PLOT( XX,FWY-FWC/2,3 ) CALL PLOT( XX,FWY,2 ) END IF LX = 0 IF(XN.GT.0.0D0) LX = ALOG10( XN ) + 0.001 IF( MX.GT.0 ) XXX = WC*(LX+MX)*0.5 + WC*4/7.0 IF( MX.LT.0 ) XXX = WC*LX*0.5 + WC*4/7.0 CALL NUMBER( XX-XXX,-(1.5*FWC+0.1),FWC,XN,0.0,MX ) 10 CONTINUE IF( IX.GT.1 ) THEN CALL NEWPEN(1) DO 20 I=1,NX+1 DO 20 J=1,IX XX = D*(I-1) + (D*J)/IX IF( XX.LE.WX ) THEN CALL PLOT( XX,FWC/2,3 ) CALL PLOT( XX,0.0,2 ) IF( IBOX.EQ.1 ) THEN CALL PLOT( XX,FWY-FWC/2,3 ) CALL PLOT( XX,FWY,2 ) END IF END IF 20 CONTINUE CALL NEWPEN( 2 ) END IF C C ... draw Y axis ... C D = WY*DY/(Y1-Y0) MY = -DLOG10( DY ) + 0.99999 IF( MY.LE.0 ) MY = -1 DO 30 I=1,NY+1 YN = Y0 + DY*(I-1) YY = D*(I-1) CALL PLOT( -FWC/2,YY,3 ) CALL PLOT( 0.0,YY,2 ) IF( IBOX.EQ.1 ) THEN CALL PLOT( FWX-FWC/2,YY,3 ) CALL PLOT( FWX,YY,2 ) END IF LY = 1 IF(YN.LT. 0.0) LY = 2 IF(YN.GE. 1.0) LY = ALOG10( YN )+1.00001 IF(YN.LE.-1.0) LY = ALOG10(-YN )+2.00001 IF( MY.GT.0 ) YYY = WC*(LY+MY+1) + 0.20 IF( MY.LT.0 ) YYY = WC*LY + 0.20 CALL NUMBER( -YYY,YY-FWC/2,FWC,YN,0.0,MY ) 30 CONTINUE IF( IX.GT.1 ) THEN CALL NEWPEN(1) DO 40 I=1,NY+1 DO 40 J=1,IY YY = D*(I-1) + (D*J)/IY IF( YY.LE.WY ) THEN CALL PLOT( FWC/2,YY,3 ) CALL PLOT( 0.0,YY,2 ) IF( IBOX.EQ.1 ) THEN CALL PLOT( FWX-FWC/2,YY,3 ) CALL PLOT( FWX,YY,2 ) END IF END IF 40 CONTINUE CALL NEWPEN( 2 ) END IF C RETURN E N D SUBROUTINE HEADER( PNAME,NP,M,VNAME,VALUE ) C C ... This subroutine draw title of data, program name, names C and values of parameters ... C C Inputs: C PNAME: program name C NP: number of characters of program name C M: number of parameters C VNAME(I): name of the I-th parameter C VALUE(I): value of the I-th parameter C Input via common: C TITLE: title of the data set C CHARACTER PNAME*80, TITLE*72 CHARACTER*8 VNAME(M) REAL*8 VALUE DIMENSION VALUE(M), DAY(2), TIME(3) COMMON /CMDATA/ TITLE C CALL NEWPEN( 2 ) CALL DATE( DAY ) CALL CLOCK( TIME,1 ) C CALL SYMBOL( 2.0,18.7,0.25,TITLE,0.0,72 ) CALL SYMBOL( 2.0,18.3,0.20,PNAME,0.0,NP ) CALL NEWPEN( 1 ) CALL SYMBOL( 2.0,17.9,0.20,DAY,0.0,8 ) CALL SYMBOL( 4.0,17.9,0.20,TIME,0.0,12 ) YY = 17.9 DO 10 I=1,M IF( MOD(I,4).EQ.1 ) THEN YY = YY - 0.40 X1 = 2.0 X2 = 3.5 ELSE X1 = X1 + 5.0 X2 = X2 + 5.0 END IF CALL SYMBOL( X1,YY,0.20,VNAME(I),0.0,8 ) 10 CALL NUMBER( X2,YY,0.20,SNGL(VALUE(I)),0.0,6 ) C RETURN E N D SUBROUTINE DRAWY2( FNAME,NC,XO,YO,Y,N,WX,WY,IPOS,ISW,XMIN, * XMAX,DX,YMIN,YMAX,DY ) C C ... This subroutine draws time series data ... C C Inputs: C FNAME: title of the data set C NC: number of charcters of the name C XO,YO: origin of the figure C Y(I): time series C N: data length C WX,WY: width and height of the figure C IPOS: starting position of time series C ISW: = 1 connect data by line C = 2 connect data by dashed line C XMIN,XMAX: minimum and maximum of the X axis C DX: step width of the X axis C YMIN,YMAX: minimum and maximum of the Y axis C DY: step width of the Y axis C IMPLICIT REAL*8(A-H,O-Z) CHARACTER FNAME*80 DIMENSION Y(N) C CALL AXISXY(XO,YO,WX,WY,XMIN,XMAX,YMIN,YMAX,DX,DY,0.25D0,1,10,1) IF( ISW.LE.1 ) CALL PLOTY ( Y,N,YMIN,YMAX,WX,WY,IPOS,1 ) IF( ISW.EQ.1 ) CALL PLOTY2( Y,N,YMIN,YMAX,WX,WY,IPOS,1,0.0D0 ) IF( ISW.EQ.2 ) CALL PLOTY2( Y,N,YMIN,YMAX,WX,WY,IPOS,1,YMIN ) CALL NEWPEN( 1 ) CALL SYMBOL( 0.0,SNGL(WY)+0.2,0.3,FNAME,0.0,NC ) RETURN E N D SUBROUTINE MAXMIN( X,N,XMIN0,XMAX0,DXL ) C C ... This subroutine determines the minimum, the maximum and C the step width ... C C Inputs: C X(I): data C N: data length C Outputs: C XMIN0: the minimum bound for the figure C XMAX0: the maximum bound for the figure C DXL: step width C IMPLICIT REAL*8(A-H,O-Z) DIMENSION X(N) C XMIN = 1.0D30 XMAX =-1.0D30 C DO 10 I=1,N IF( X(I) .LT. XMIN ) XMIN = X(I) 10 IF( X(I) .GT. XMAX ) XMAX = X(I) DX = XMAX-XMIN IF( DLOG10(DX) .GE. 0.0D0 ) DXL = INT( DLOG10(DX) ) IF( DLOG10(DX) .LT. 0.0D0 ) DXL = INT( DLOG10(DX) )-1.0 DXL = 10.0**DXL IF( DX/DXL.GT.6.0D0 ) DXL = DXL*2.0 DIF = INT( DX/DXL ) XMIN0 = INT( XMIN/DXL )*DXL XMAX0 = XMIN0 + DIF*DXL IF( XMIN0 .GT. XMIN ) XMIN0 = XMIN0 - DXL 30 IF( XMAX0 .GE. XMAX ) GO TO 40 XMAX0 = XMAX0 + DXL GO TO 30 40 CONTINUE C RETURN E N D SUBROUTINE PLOTY( Y,N,YMIN,YMAX,WX,WY,IPOS,ISW ) C C ... This subroutine draws time vs data plot of the data ... C C Inputs: C Y(I): data C N: data length C YMIN: minimum bound for the Y axis C YMAX: maximum bound for the Y axis C WX,WY: width and height of the figure C IPOS: starting position of the data C ISW: = 1 connect data by straight line C = 2 connect data by dashed line C = 3 express data by character (character code=ISW) C Modified: 8/31/90 C REAL*8 Y(N), YMIN, YMAX, WX, WY C DX = WX/(N-1+IPOS) DY = WY/(YMAX - YMIN) C CALL NEWPEN( 1 ) DO 100 I=1,N XX = DX*(I-1+IPOS) YY = (Y(I) - YMIN)*DY IF( I.EQ.1 .AND. ISW.LT.3 ) THEN CALL PLOT( XX,YY,3 ) ELSE IF(ISW.EQ.1) CALL PLOT( XX,YY,2 ) IF(ISW.EQ.2) CALL DASHP( XX,YY,0.2 ) IF(ISW.GE.3) CALL SYMBOL( XX,YY,0.2,ISW,0.0,-1 ) END IF 100 CONTINUE C RETURN E N D SUBROUTINE PLOTY2( Y,N,YMIN,YMAX,WX,WY,IOFF,ISW,YLEVEL ) C C ... This subroutine draws box car graph of the data ... C C Inputs: C Y(I): data C N: data length C YMIN: minimum bound for the Y axis C YMAX: maximum bound for the Y axis C WX,WY: width and height of the figure C IPOS: starting position of the data C ISW: = 1 draw box with thick line C = 2 draw box with thin line C YLEVEL: ground level for the box car C REAL*8 Y(N), YMIN, YMAX, WX, WY, YLEVEL C DX = WX/(N-1+IOFF) DY = WY/(YMAX - YMIN) C CALL NEWPEN( 3 ) IF( N.GT.75 ) CALL NEWPEN( 2 ) IF( N.GT.150) CALL NEWPEN( 1 ) IF( ISW.EQ.2 ) CALL NEWPEN( 1 ) DO 100 I=1,N XX = DX*(I-1+IOFF) YY = (Y(I) - YMIN)*DY Y0 = (YLEVEL-YMIN)*DY CALL PLOT( XX,Y0,3 ) CALL PLOT( XX,YY,2 ) 100 CONTINUE CALL NEWPEN( 2 ) C RETURN E N D SUBROUTINE READTS( IDEV,Y,N ) REAL*8 Y(N) CHARACTER*72 TITLE COMMON /CMDATA/ TITLE C C OPEN( IDEV,FILE='temp.dat' ) READ( IDEV,1 ) TITLE READ( IDEV,* ) N READ( IDEV,* ) (Y(I),I=1,N) C CLOSE( IDEV ) RETURN 1 FORMAT( A72 ) E N D SUBROUTINE AUTCOV( Y,N,MAXLAG,OUTMIN,OUTMAX,C ) C C ... THIS SUBROUTINE COMPUTES SAMPLE AUTOCOVARIANCE ... C C INPUTS: C Y(I): TIME SERIES C N: DATA LENGTH C MAXLAG: MAXIMUM LAG OF AUTOCOVARIANCE C OUTMIN: BOUND FOR OUTLIERS IN LOW SIDE C OUTMAX: BOUND FOR OUTLIERS IN HIGH SIDE C OUTPUT: C C(I): AUTOCOVARIANCE FUNCTION C IMPLICIT REAL*8( A-H,O-Z ) DIMENSION Y(N), C(0:MAXLAG ) C C ... SAMPLE MEAN ... C CALL MEAN( Y,N,OUTMIN,OUTMAX,NSUM,YMEAN ) C C ... SAMPLE AUTOCOVARIANCE ... C DO 20 LAG = 0,MAXLAG SUM = 0.0D0 DO 10 I=LAG+1,N IF( Y(I).GT.OUTMIN .AND. Y(I).LT.OUTMAX ) THEN IF( Y(I-LAG).GT.OUTMIN .AND. Y(I-LAG).LT.OUTMAX ) THEN SUM = SUM + ( Y(I)-YMEAN)*( Y(I-LAG) - YMEAN ) END IF END IF 10 CONTINUE 20 C(LAG) = SUM/NSUM C RETURN E N D