C Version 1994-X-18 C This is a new version of WAMP program computing crest-trough wavelength C and amplitude density. C C revised pab 2007 C -moved all common blocks into modules C -renamed from minmax to sp2mmpdfreg + fixed some bugs C revised pab July 2007 ! -renamed from sp2mmpdfreg to cov2mmpdfreg PROGRAM cov2mmpdfreg USE SIZEMOD USE EPSMOD USE CHECKMOD USE MREGMOD IMPLICIT NONE real*8 Q0,SQ0,Q1,SQ1, AA, BB, DAI, AI , U,V,VV, XL0, XL2, XL4 REAL*8 VDERI, CDER,SDER, DER, CONST, F, HHHH,FM, VALUE C INTEGER, PARAMETER :: MMAX = 5, NMAX = 101, RDIM = 10201 REAL*8, DIMENSION(NMAX) :: HHT,T,Ulev,Vlev,VT,UT,Vdd,Udd REAL*8, DIMENSION(RDIM) :: R,R1,R2,R3 REAL*8, DIMENSION(5*NMAX) :: COV REAL*8, DIMENSION(NMAX,NMAX) :: UVdens C DIMENSION UVdens(NMAX,NMAX),HHT(NMAX) C DIMENSION T(NMAX),Ulev(NMAX),Vlev(NMAX) C DIMENSION VT(NMAX),UT(NMAX),Vdd(NMAX),Udd(NMAX) C DIMENSION COV(5*NMAX),R(RDIM),R1(RDIM),R2(RDIM),R3(RDIM) DIMENSION AA(MMAX-2,MMAX-2),BB(MMAX+1),DAI(MMAX),AI((MMAX+1)*NMAX) C C The program computes the joint density of maximum the following minimum C and the distance between Max and min for a zero-mean stationary C Gaussian process with covariance function defined explicitely with 4 C derivatives. The process should be normalized so that the first and C the second spectral moments are equal to 1. The values of Max are taken C as the nodes at Hermite-Quadrature and then integrated out so that C the output is a joint density of wavelength T and amplitude H=Max-min. C The Max values are defined by subroutine Gauss_M with the accuracy C input epsu. The principle is that the integral of the marginal density C of f_Max is computed with sufficient accuracy. C REAL*8, DIMENSION(NMAX) :: B0,DB0,DDB0,B1,DB1,DDB1,DB2,DDB2 REAL*8, DIMENSION(NMAX) :: Q,SQ,VDER,DBI,BI C DIMENSION B0(NMAX),DB0(NMAX),DDB0(NMAX) C DIMENSION B1(NMAX),DB1(NMAX),DDB1(NMAX) C DIMENSION DB2(NMAX),DDB2(NMAX) C DIMENSION Q(NMAX),SQ(NMAX),VDER(NMAX),DBI(NMAX),BI(NMAX) INTEGER :: J,I,I1,I2,I3,IU, IV, NU,NV,NG,N,NIT, NNIT, INF INTEGER :: fffff C REAL*8 EPS0 C INTEGER III01,III11,III21,III31,III41,III51 C *,III61,III71,III81,III91,III101 , III0 C COMMON/CHECK1/III01,III11,III21,III31,III41,III51 C *,III61,III71,III81,III91,III101 C COMMON/CHECKQ/III0 C COMMON /EPS/ EPS,EPSS,CEPSS C C Initiation of all constants and integration nodes 'INITINTEG' C CALL INITINTEG(NIT) c c OBS. we are using the variables R,R1,R2 R3 as a temporary storage C for transformation g of the process. c CALL INITLEVELS(Ulev,NU,Vlev,NV,T,HHT,N,R1,R2,NG) IF( R1(1) .gt. R1(ng)) then do 13 I=1,ng R3(I)=R1(I) R(I) =R2(I) 13 continue do 17 i=1,ng R1(i) = R3(ng-i+1) R2(i) = R(ng-i+1) 17 continue end if if(abs(R1(ng)-R1(1))*abs(R2(ng)-R2(1)).lt.0.01d0) then print *,'The transformation g is singular, stop' stop end if DO 14 IV=1,Nv V=Vlev(IV) CALL TRANSF(NG,V,R2,R1,VALUE,DER) VT(IV)=VALUE Vdd(IV)=DER 14 continue DO 16 IU=1,Nu U = Ulev(IU) CALL TRANSF(NG,U,R2,R1,VALUE,DER) UT(IU) = VALUE Udd(IU) = DER do 16 IV=1,Nv UVdens(IU,IV)=0.0d0 16 CONTINUE CALL COVG(XL0,XL2,XL4,COV,R1,R2,R3,T,N) Q0=XL4 IF (Q0.le.1.0D0+EPS) then Print *,'Covariance structure is singular, stop.' stop end if SQ0 = SQRT(Q0) Q1 = XL0-XL2*XL2/XL4 IF (Q1.le.eps) then Print *,'Covariance structure is singular, stop.' stop end if SQ1 = SQRT(Q1) DO 10 I=1,N B0(I) =-COV(I+2*N) DB0(I) =-COV(I+3*N) DDB0(I)=-COV(I+4*N) B1(I) =COV(I)+COV(I+2*N)*(XL2/XL4) DB1(I) =COV(I+N)+COV(I+3*N)*(XL2/XL4) DDB1(I)=COV(I+2*N)+XL2*(COV(I+4*N)/XL4) C C Q(I) contains Var(X(T(i))|X'(0),X''(0),X(0)) C VDER(I) contains Var(X''(T(i))|X'(0),X''(0),X(0)) C Q(I)=XL0 - COV(I+N)*(COV(I+N)/XL2) - B0(I)*(B0(I)/Q0) 1 -B1(I)*(B1(I)/Q1) VDER(I)=XL4 - (COV(I+3*N)*COV(I+3*N))/XL2 - (DDB0(I)*DDB0(I))/Q0 1 - (DDB1(I)*DDB1(I))/Q1 C C DDB2(I) contains Cov(X''(T(i)),X(T(i))|X'(0),X''(0),X(0)) C DDB2(I)=-XL2 - (COV(I+N)*COV(I+3*N))/XL2 - DDB0(I)*(B0(I)/Q0) 1 -DDB1(I)*(B1(I)/Q1) IF(Q(I).LE.eps) then SQ(i) =0.0d0 DDB2(i)=0.0d0 else SQ(I)=SQRT(Q(I)) C C VDER(I) contains Var(X''(T(i))|X'(0),X''(0),X(0),X(T(i)) C VDER(I)=VDER(I) - (DDB2(I)*DDB2(I))/Q(I) end if 10 CONTINUE DO 15 I=1,N DO 15 J=1,N C C R1 contains Cov(X(T(I)),X'(T(J))|X'(0),X''(0),X(0)) C R1(J+(I-1)*N)=R1(J+(I-1)*N) - COV(I+N)*(COV(J+2*N)/XL2) 1 - (B0(I)*DB0(J)/Q0) - (B1(I)*DB1(J)/Q1) C C R2 contains Cov(X'(T(I)),X'(T(J))|X'(0),X''(0),X(0)) C R2(J+(I-1)*N) = -R2(J+(I-1)*N) - COV(I+2*N)*(COV(J+2*N)/XL2) 1 - DB0(I)*DB0(J)/Q0 - DB1(I)*(DB1(J)/Q1) C C R3 contains Cov(X''(T(I)),X'(T(J))|X'(0),X''(0),X(0)) C R3(J+(I-1)*N) = R3(J+(I-1)*N) - COV(I+3*N)*(COV(J+2*N)/XL2) 1 - DB0(J)*(DDB0(I)/Q0) - DDB1(I)*(DB1(J)/Q1) 15 CONTINUE C The initiations are finished and we are beginning with 3 loops C on T=T(I), U=Ulevels(IU), V=Ulevels(IV), U>V. DO 20 I=1,N NNIT=NIT IF (Q(I).LE.EPS) GO TO 20 DO 30 I1=1,I DB2(I1)=R1(I1+(I-1)*N) C Cov(X'(T(I1)),X(T(i))|X'(0),X''(0),X(0)) C DDB2(I) contains Cov(X''(T(i)),X(T(i))|X'(0),X''(0),X(0)) 30 CONTINUE DO 50 I3=1,I DBI(I3) = R3(I3+(I-1)*N) - (DDB2(I)*DB2(I3)/Q(I)) BI(I3) = R2(I3+(I-1)*N) - (DB2(I)*DB2(I3)/Q(I)) 50 CONTINUE DO 51 I3=1,I-1 AI(I3)=0.0d0 AI(I3+I-1)=DB0(I3)/SQ0 AI(I3+2*(I-1))=DB1(I3)/SQ1 AI(I3+3*(I-1))=DB2(I3)/SQ(I) 51 CONTINUE VDERI=VDER(I) DAI(1)=0.0d0 DAI(2)=DDB0(I)/SQ0 DAI(3)=DDB1(I)/SQ1 DAI(4)=DDB2(I)/SQ(I) AA(1,1)=DB0(I)/SQ0 AA(1,2)=DB1(I)/SQ1 AA(1,3)=DB2(I)/SQ(I) AA(2,1)=XL2/SQ0 AA(2,2)=SQ1 AA(2,3)=0.0d0 AA(3,1)=B0(I)/SQ0 AA(3,2)=B1(I)/SQ1 AA(3,3)=SQ(I) IF (BI(I).LE.EPS) NNIT=0 IF (NNIT.GT.1) THEN IF(I.LT.1) GO TO 41 DO 40 I1=1,I-1 DO 40 I2=1,I-1 C R contains Cov(X'(T(I1)),X'(T(I2))|X'(0),X''(0),X(0),X(I)) R(I2+(I1-1)*(I-1))=R2(I2+(I1-1)*N)-(DB2(I1)*DB2(I2)/Q(I)) 40 CONTINUE 41 CONTINUE END IF C Here the covariance of the problem would be innitiated INF=0 Print *,' Laps to go:',N-I+1 DO 80 IV=1,Nv V=VT(IV) ! IF (ABS(V).GT.5.0D0) GO TO 80 IF (Vdd(IV).LT.EPS0) GO TO 80 DO 60 IU=1,Nu U=UT(IU) IF (U.LE.V) go to 60 ! IF (ABS(U).GT.5.0D0) GO TO 60 IF (Udd(IU).LT.EPS0) GO TO 60 BB(1)=0.0d0 BB(2)=U BB(3)=V ! if (IV.EQ.2.AND.IU.EQ.1) THEN ! fffff = 10 ! endif CALL MREG(F,R,BI,DBI,AA,BB,AI,DAI,VDERI,3,I-1,NNIT,INF) INF=1 UVdens(IU,IV) = UVdens(IU,IV) + Udd(IU)*Vdd(IV)*HHT(I)*F ! if (F.GT.0.01.AND.U.GT.2.AND.V.LT.-2) THEN ! if (N-I+1 .eq. 38.and.IV.EQ.26.AND.IU.EQ.16) THEN ! if (IV.EQ.32.AND.IU.EQ.8.and.I.eq.11) THEN ! PRINT * ,' R:', R(1:I) ! PRINT * ,' BI:', BI(1:I) ! PRINT * ,' DBI:', DBI(1:I) ! PRINT * ,' DB2:', DB2(1:I) ! PRINT * ,' DB0(1):', DB0(1) ! PRINT * ,' DB1(1):', DB1(1) ! PRINT * ,' DAI:', DAI ! PRINT * ,' BB:', BB ! PRINT * ,' VDERI:', VDERI ! PRINT * ,' F :', F ! PRINT * ,' UVDENS :', UVdens(IU,IV) ! fffff = 10 ! endif 60 CONTINUE 80 continue 20 CONTINUE hhhh=0.0d0 do 90 Iu=1,Nu do 90 Iv=1,Nv WRITE(10,300) Ulev(iu),Vlev(iv),UVdens(iu,iv) hhhh=hhhh+UVdens(iu,iv) 90 continue if (nu.gt.1.and.nv.gt.1) then write(11,*) 'SumSum f_uv *du*dv=' 1,(Ulev(2)-Ulev(1))*(Vlev(2)-Vlev(1))*hhhh end if C sder=sqrt(XL4-XL2*XL2/XL0) C cder=-XL2/sqrt(XL0) C const=1/sqrt(XL0*XL4) C DO 95 IU=1,NU C U=UT(IU) C FM=Udd(IU)*const*exp(-0.5*U*U/XL0)*PMEAN(-cder*U,sder) C WRITE(9,300) Ulev(IU),FM C 95 continue C DO 105 IV=1,NV C V=VT(IV) C VV=cder*V C Fm=Vdd(IV)*const*exp(-0.5*V*V/XL0)*PMEAN(VV,sder) C WRITE(8,300) Vlev(IV),Fm C 105 continue if (III0.eq.0) III0=1 write(11,*) 'Rate of calls RINDT0:',float(iii01)/float(III0) write(11,*) 'Rate of calls RINDT1:',float(iii11)/float(III0) write(11,*) 'Rate of calls RINDT2:',float(iii21)/float(III0) write(11,*) 'Rate of calls RINDT3:',float(iii31)/float(III0) write(11,*) 'Rate of calls RINDT4:',float(iii41)/float(III0) write(11,*) 'Rate of calls RINDT5:',float(iii51)/float(III0) write(11,*) 'Rate of calls RINDT6:',float(iii61)/float(III0) write(11,*) 'Rate of calls RINDT7:',float(iii71)/float(III0) write(11,*) 'Rate of calls RINDT8:',float(iii81)/float(III0) write(11,*) 'Rate of calls RINDT9:',float(iii91)/float(III0) write(11,*) 'Rate of calls RINDT10:',float(iii101)/float(III0) write(11,*) 'Number of calls of RINDT*',III0 CLOSE(UNIT=8) CLOSE(UNIT=9) CLOSE(UNIT=10) CLOSE(UNIT=11) 300 FORMAT(4(3X,F10.6)) STOP END SUBROUTINE INITLEVELS(ULEVELS,NU,Vlevels,Nv,T,HT,N,TG,XG,NG) USE TBRMOD USE SIZEMOD IMPLICIT NONE C INTEGER, PARAMETER:: NMAX = 101, RDIM = 10201 C DIMENSION ULEVELS(1),Vlevels(1),T(1),HT(1),TG(1),XG(1),HH(101) REAL*8, DIMENSION(NMAX), intent(inout) :: ULEVELS,Vlevels,T,HT REAL*8, DIMENSION(RDIM), intent(inout) :: TG,XG INTEGER, intent(inout) :: NG REAL*8 :: UMIN,UMAX,VMIN,VMAX, HU,HV integer :: N, I, NU, NV C REAL*8, DIMENSION(NMAX) :: HH C COMMON/TBR/HH OPEN(UNIT=2,FILE='transf.in') OPEN(UNIT=4,FILE='Mm.in') OPEN(UNIT=3,FILE='t.in') NG=1 12 READ (2,*,END=11) TG(NG),XG(NG) NG=NG+1 GO TO 12 11 CONTINUE NG=NG-1 IF (NG.GT.501) THEN PRINT *,'Vector defining transformation of data > 501, stop' STOP END IF N=1 32 READ (3,*,END=31) T(N) N=N+1 GO TO 32 31 CONTINUE N=N-1 CLOSE(UNIT=3) IF(N.ge.NMAX) then print *,'The number of wavelength points >',NMAX-1, ' stop' stop end if IF(N.lt.2) then print *,'The number of wavelength points < 2, stop' stop end if HT(1)=0.5d0*(T(2)-T(1)) HT(N)=0.5d0*(T(N)-T(N-1)) HH(1)=-100.0d0 HH(N)=-100.0d0 DO 10 I=2,N-1 HT(I)=0.5d0*(T(I+1)-T(I-1)) HH(I)=-100.0d0 10 CONTINUE READ(4,*) Umin,Umax,NU READ(4,*) Vmin,Vmax,NV IF(NU.gt.NMAX) then print *,'The number of maxima >',NMAX,' stop' stop end if IF(NV.gt.NMAX) then print *,'The number of minima >',NMAX,' stop' stop end if IF(NU.LT.1) Then print *,'The number of maxima < 1, stop' stop end if IF(NV.LT.1) Then print *,'The number of minima < 1, stop' stop end if Ulevels(1)=Umax IF (NU.lt.2) go to 25 HU=(Umax-Umin)/DBLE(NU-1) DO 20 I=1,NU-1 ULEVELS(I+1)=Umax-DBLE(I)*HU 20 CONTINUE 25 continue Vlevels(1)=Vmax IF (NV.lt.2) go to 35 HV=(Vmax-Vmin)/DBLE(NV-1) DO 30 I=1,Nv-1 VLEVELS(I+1)=Vmax-DBLE(I)*HV 30 CONTINUE 35 continue CLOSE(UNIT=4) RETURN END SUBROUTINE TRANSF(N,T,A,TIMEV,VALUE,DER) C C N number of data points C TIMEV vector of time points C A a vector of values of a function G(TIME) C T independent time point C VALUE is a value of a function at T, i.e. VALUE=G(T). c DER=G'(t) C USE SIZEMOD IMPLICIT NONE REAL*8, intent(inout):: VALUE, DER,T C INTEGER, PARAMETER :: RDIM = 10201 REAL*8, DIMENSION(RDIM), intent(in) :: A,TIMEV integer, intent(in) :: N REAL*8:: T1 integer :: I IF (T.LT.TIMEV(1)) then der=(A(2)-A(1))/(TIMEV(2)-TIMEV(1)) T1=T-TIMEV(1) VALUE=A(1)+T1*DER return end if IF (T.GT.TIMEV(N)) then der = (A(N)-A(N-1))/(TIMEV(N)-TIMEV(N-1)) T1 = T-TIMEV(N) VALUE=A(N)+T1*DER return end if DO 5 I=2,N IF (T.LT.TIMEV(I)) GO TO 10 5 CONTINUE 10 I=I-1 T1=T-TIMEV(I) DER=(A(I+1)-A(I))/(TIMEV(i+1)-TIMEV(I)) VALUE=A(I)+T1*DER RETURN END REAL*8 FUNCTION SPLE(N,T,A,TIMEV) C C N number of data points C TIME vector of time points C A a vector of values of a function G(TIME) C T independent time point C SPLE is a value of a function at T, i.e. SPLE=G(T). C USE SIZEMOD IMPLICIT NONE INTEGER, INTENT(IN):: N REAL*8, INTENT(IN) :: T REAL*8, DIMENSION(5*NMAX), INTENT(IN) :: A,TIMEV REAL*8 :: T1 INTEGER :: I SPLE=-9.9d0 IF (T.LT.TIMEV(1) .OR. T.GT.TIMEV(N)) RETURN DO 5 I=2,N IF (T.LT.TIMEV(I)) GO TO 10 5 CONTINUE 10 I=I-1 T1=T-TIMEV(I) SPLE=A(I)+T1*(A(I+1)-A(I))/(TIMEV(i+1)-TIMEV(I)) RETURN END SUBROUTINE COVG(XL0,XL2,XL4,COV,COV1,COV2,COV3,T,N) C C COVG evaluates: C C XL0,XL2,XL4 - spectral moments. C C Covariance function and its four derivatives for a vector T of length N. C It is saved in a vector COV; COV(1,...,N)=r(T), COV(N+1,...,2N)=r'(T), etc. C The vector COV should be of the length 5*N. C C Covariance matrices COV1=r'(T-T), COV2=r''(T-T) and COV3=r'''(T-T) C Dimension of COV1, COV2 should be N*N. C USE SIZEMOD ! IMPLICIT NONE C INTEGER, PARAMETER:: NMAX = 101, RDIM = 10201 REAL*8, PARAMETER:: ZERO = 0.0d0 REAL*8, intent(inout) :: XL0,XL2,XL4 REAL*8, DIMENSION(5*NMAX), intent(inout) :: COV REAL*8, DIMENSION(5*NMAX) :: A, TIMEV REAL*8, DIMENSION(RDIM), intent(inout) :: COV1,COV2,COV3 REAL*8, DIMENSION(NMAX), intent(in) :: T INTEGER, intent(in) :: N integer :: NT, I, J, II REAL*8 :: TT, T0 OPEN(UNIT=32,FILE='Cd0.in') OPEN(UNIT=33,FILE='Cd1.in') OPEN(UNIT=34,FILE='Cd2.in') OPEN(UNIT=35,FILE='Cd3.in') OPEN(UNIT=36,FILE='Cd4.in') C C COV(Y(T),Y(0)) C NT=1 12 READ (32,*,END=11) TIMEV(NT),A(NT) NT=NT+1 GO TO 12 11 CONTINUE NT=NT-1 XL0=SPLE(NT,ZERO,A,TIMEV) DO 10 I=1,N COV(I)=SPLE(NT,T(I),A,TIMEV) 10 CONTINUE C C DERIVATIVE COV(Y(T),Y(0)) C NT=1 22 READ (33,*,END=21) TIMEV(NT),A(NT) NT=NT+1 GO TO 22 21 CONTINUE NT=NT-1 II=0 DO 20 I=1,N COV(I+N)=SPLE(NT,T(I),A,TIMEV) DO 20 J=1,N II=II+1 T0=T(J)-T(I) TT=ABS(T0) COV1(II)=SPLE(NT,TT,A,TIMEV) IF (T0.LT.0.0d0) COV1(II)=-COV1(II) 20 CONTINUE C 2-DERIVATIVE COV(Y(T),Y(0)) NT=1 32 READ (34,*,END=31) TIMEV(NT),A(NT) NT=NT+1 GO TO 32 31 CONTINUE NT=NT-1 II=0 XL2=-SPLE(NT,ZERO,A,TIMEV) DO 30 I=1,N COV(I+2*N)=SPLE(NT,T(I),A,TIMEV) DO 30 J=1,N II=II+1 TT=ABS(T(J)-T(I)) COV2(II)=SPLE(NT,TT,A,TIMEV) 30 CONTINUE C 3-DERIVATIVE COV(Y(T),Y(0)) NT=1 42 READ (35,*,END=41) TIMEV(NT),A(NT) NT=NT+1 GO TO 42 41 CONTINUE NT=NT-1 II=0 DO 40 I=1,N COV(I+3*N)=SPLE(NT,T(I),A,TIMEV) DO 40 J=1,N II=II+1 T0=T(J)-T(I) TT=ABS(T0) COV3(II)=SPLE(NT,TT,A,TIMEV) IF (T0.LT.0.0d0) COV3(II)=-COV3(II) 40 CONTINUE C 4-DERIVATIVE COV(Y(T),Y(0)) NT=1 52 READ (36,*,END=51) TIMEV(NT),A(NT) NT=NT+1 GO TO 52 51 CONTINUE NT=NT-1 XL4=SPLE(NT,ZERO,A,TIMEV) DO 50 I=1,N COV(I+4*N)=SPLE(NT,T(I),A,TIMEV) 50 CONTINUE CLOSE(UNIT=32) CLOSE(UNIT=33) CLOSE(UNIT=34) CLOSE(UNIT=35) CLOSE(UNIT=36) RETURN END SUBROUTINE INITINTEG(NIT) USE RINTMOD USE EPSMOD USE INFCMOD USE MREGMOD ! IMPLICIT NONE INTEGER, intent(inout) :: NIT ! INTEGER ISQ1 C dimension INF(10),INFO(10) C COMMON /RINT/ C,FC C COMMON /EPS/ EPS,EPSS,CEPSS C COMMON /INFC/ ISQ,INF,INFO OPEN(UNIT=1,FILE='accur.in') OPEN(UNIT=8,FILE='min.out') OPEN(UNIT=9,FILE='Max.out') OPEN(UNIT=10,FILE='Maxmin.out') OPEN(UNIT=11,FILE='Maxmin.log') READ(1,*) NIT,IAC,ISQ READ(1,*) EPS,EPSS,EPS0 CLOSE (UNIT=1) FC=FI(C)-FI(-C) CEPSS=1.0d0-EPSS RETURN END