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
! gfortran -W -Wall -pedantic-errors -fbounds-check -Werror -c dsvdc.f mregmodule.f cov2mmpdfreg.f
SUBROUTINE INITINTEG(EPS_,EPSS_,EPS0_,C_,IAC_,ISQ_)
! Initiation of all constants and integration nodes 'INITINTEG'
USE RINTMOD
USE EPSMOD
USE INFCMOD
USE MREGMOD
REAL*8 :: EPS_,EPSS_,EPS0_,C_
INTEGER :: IAC_,ISQ_
Cf2py real*8, optional :: EPS_ = 0.01
Cf2py real*8, optional :: EPSS_ = 0.00005
Cf2py real*8, optional :: EPS0_ = 0.00005
Cf2py real*8, optional :: C_ = 4.5
Cf2py integer, optional :: IAC_ = 1
Cf2py integer, optional :: ISQ_ = 0
! IMPLICIT NONE
C COMMON /RINT/ C,FC
C COMMON /EPS/ EPS,EPSS,CEPSS
C COMMON /INFC/ ISQ,INF,INFO
IAC = IAC_
ISQ = ISQ_
EPS = EPS_
EPSS = EPSS_
EPS0 = EPS0_
C = C_
FC = FI(C)-FI(-C)
! CEPSS = 1.0d0-EPSS
RETURN
END SUBROUTINE INITINTEG
subroutine cov2mmpdfreg(UVdens,t,COV,ULev,VLev,Tg,Xg,Nt,Nu,Nv,Ng,
& NIT)
USE SIZEMOD
USE EPSMOD
USE CHECKMOD
USE MREGMOD
USE INTFCMOD
IMPLICIT NONE
INTEGER, INTENT(IN) :: Nt, Nu, Nv, Ng, NIT
REAL*8, DIMENSION(Nt,5), intent(in):: COV
REAL*8, DIMENSION(Nu,Nv), intent(out):: UVdens
REAL*8, DIMENSION(Nu), intent(in):: ULev
REAL*8, DIMENSION(Nv), intent(in):: VLev
REAL*8, DIMENSION(Ng), intent(in):: Tg, Xg
REAL*8, dimension(Nt), intent(in):: T
Cf2py integer, intent(hide), depend(t) :: Nt = len(t)
Cf2py integer, intent(hide), depend(Ulev) :: Nu = len(Ulev)
Cf2py integer, intent(hide), depend(Vlev) :: Nv = len(Vlev)
Cf2py integer, intent(hide), depend(Tg) :: Ng = len(Tg)
Cf2py integer, optional :: NIT = 2
Cf2py real*8, intent(out), depend(Nu,Nv) :: UVdens
Cf2py depend(Ng) Xg
Cf2py depend(Nt,5) COV
real*8 Q0,SQ0,Q1,SQ1, U,V, XL0, XL2, XL4
REAL*8 VDERI, DER, F, HHHH, VALUE
C REAL*8 VV, CDER,SDER, CONST1, FM
C INTEGER, PARAMETER :: MMAX = 5, NMAX = 101, RDIM = 10201
REAL*8, DIMENSION(NMAX) :: HHT,VT,UT,Vdd,Udd
REAL*8, DIMENSION(RDIM) :: R,R1,R2,R3
REAL*8:: AA(MMAX-2,MMAX-2),AI((MMAX+1)*NMAX)
REAL*8, DIMENSION(MMAX+1) :: BB, DAI
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)
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,N, NNIT, INF
C 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()
! OPEN(UNIT=8,FILE='min.out')
! OPEN(UNIT=9,FILE='Max.out')
! OPEN(UNIT=10,FILE='Maxmin.out')
! OPEN(UNIT=11,FILE='Maxmin.log')
c
c OBS. we are using the variables R,R1,R2 R3 as a temporary storage
C for transformation g of the process.
N = Nt
CALL INITLEVELS(T,HHT,Nt,NU,Nv)
C CALL INITLEVELS(Ulev,NU,Vlev,NV,T,HHT,Nt,R1,R2,NG)
IF( Tg(1) .gt. Tg(ng)) then
print *,'Error Tg must be strictly increasing'
return
end if
if(abs(Tg(ng)-Tg(1))*abs(Xg(ng)-Xg(1)).lt.0.01d0) then
print *,'The transformation g is singular, stop'
return
end if
! do IV=1,Nt
! print *, 'Cov', COV(IV,:)
! end do
DO IV=1,Nv
V=Vlev(IV)
CALL TRANSF(NG,V,Xg,Tg,VALUE,DER)
VT(IV)=VALUE
Vdd(IV)=DER
enddo
DO IU=1,Nu
U = Ulev(IU)
CALL TRANSF(NG,U,Xg,Tg,VALUE,DER)
UT(IU) = VALUE
Udd(IU) = DER
do IV=1,Nv
UVdens(IU,IV)=0.0d0
enddo
enddo
CALL COVG(XL0,XL2,XL4,R1,R2,R3,COV,T,Nt)
Q0=XL4
IF (Q0.le.1.0D0+EPS) then
Print *,'Covariance structure is singular, stop.'
return
end if
SQ0 = SQRT(Q0)
Q1 = XL0-XL2*XL2/XL4
IF (Q1.le.EPS) then
Print *,'Covariance structure is singular, stop.'
return
end if
SQ1 = SQRT(Q1)
DO I=1,Nt
B0(I) =-COV(I,3)
DB0(I) =-COV(I,4)
DDB0(I)=-COV(I,5)
B1(I) =COV(I,1)+COV(I,3)*(XL2/XL4)
DB1(I) =COV(I,2)+COV(I,4)*(XL2/XL4)
DDB1(I)=COV(I,3)+XL2*(COV(I,5)/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,2)*(COV(I,2)/XL2) - B0(I)*(B0(I)/Q0)
1 -B1(I)*(B1(I)/Q1)
VDER(I)=XL4 - (COV(I,4)*COV(I,4))/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,2)*COV(I,4))/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
c10 CONTINUE
enddo
DO I=1,Nt
DO J=1,Nt
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,2)*(COV(J,3)/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,3)*(COV(J,3)/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,4)*(COV(J,3)/XL2)
1 - DB0(J)*(DDB0(I)/Q0) - DDB1(I)*(DB1(J)/Q1)
c15 CONTINUE
enddo
enddo
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 I=1,Nt
NNIT=NIT
IF (Q(I).LE.EPS) GO TO 20
DO 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))
enddo
DO 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))
enddo
DO 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)
enddo
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 I1=1,I-1
DO 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))
enddo
enddo
41 CONTINUE
END IF
C Here the covariance of the problem would be initiated
INF=0
Print *,' Laps to go:',Nt-I+1
DO IV=1,Nv
V=VT(IV)
! IF (ABS(V).GT.5.0D0) GO TO 80
IF (Vdd(IV).LT.EPS0) GO TO 80
DO 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
enddo
80 continue
enddo
20 CONTINUE
enddo
hhhh=0.0d0
do Iu=1,Nu
do Iv=1,Nv
! WRITE(10,300) Ulev(iu),Vlev(iv),UVdens(iu,iv)
hhhh=hhhh+UVdens(iu,iv)
enddo
enddo
if (nu.gt.1.and.nv.gt.1) then
VALUE = (Ulev(2)-Ulev(1))*(Vlev(2)-Vlev(1))*hhhh
print *,'SumSum f_uv *du*dv=', VALUE
end if
C sder=sqrt(XL4-XL2*XL2/XL0)
C cder=-XL2/sqrt(XL0)
C const1=1/sqrt(XL0*XL4)
C DO 95 IU=1,NU
C U=UT(IU)
C FM=Udd(IU)*const1*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)*const1*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
PRINT *, 'Rate of calls RINDT0:',float(iii01)/float(III0)
PRINT *, 'Rate of calls RINDT1:',float(iii11)/float(III0)
PRINT *, 'Rate of calls RINDT2:',float(iii21)/float(III0)
PRINT *, 'Rate of calls RINDT3:',float(iii31)/float(III0)
PRINT *, 'Rate of calls RINDT4:',float(iii41)/float(III0)
PRINT *, 'Rate of calls RINDT5:',float(iii51)/float(III0)
PRINT *, 'Rate of calls RINDT6:',float(iii61)/float(III0)
PRINT *, 'Rate of calls RINDT7:',float(iii71)/float(III0)
PRINT *, 'Rate of calls RINDT8:',float(iii81)/float(III0)
PRINT *, 'Rate of calls RINDT9:',float(iii91)/float(III0)
PRINT *, 'Rate of calls RINDT10:',float(iii101)/float(III0)
PRINT *, 'Number of calls of RINDT*',III0
return
END subroutine cov2mmpdfreg