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main.f90subroutine
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main.f90subroutine
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subroutine PCestimate(dim,ndimint,xavgin,xstdin,fctin,fctindxin,DATIN,OSin,orderinitial,orderfinal,statin,probtypeIN,fmeanout,fvarout,fmeanprimeout,fvarprimeout,fmeandbleprimeout,fvardbleprimeout)
use dimpce
implicit none
INCLUDE "collsub.h"
include 'mpif.h'
integer::ndimint
!Input variables
integer,intent(in):: DIM,PROBTYPEIN(20),OSIN
double precision,intent(in) :: xavgin(ndimint),xstdin(ndimint)
integer,intent(in)::fctindxin,fctin,orderfinal,statin,orderinitial
real*8,intent(in)::DATIN(20) ! constants and other values for objective function/constraints
!Export variables
double precision,intent(out)::fmeanout,fvarout,fmeanprimeout(ndimint),fvarprimeout(ndimint),fvardbleprimeout(ndimint,ndimint),fmeandbleprimeout(ndimint,ndimint)
!indices
integer :: i,j,k,ii,jj,kk,fuct
integer::ierr
!Monte Carlo
integer::nmcs,readMCsamples
!flags
integer :: stat,makesamples,solver
!PC vitals
integer::DIMPC,numpc,npts,nterms
real*8 :: coll(MAXPTS,DIM),par(DIM,MAXPAR)
real*8 :: RN(DIM,MAXPTS),DS(2,DIM)
real*8 :: fpcb(MAXPTS),gpcb(DIM,MAXPTS),xcof(MAXTRM),hpcb(dim,dim,maxpts)
integer :: ipar(MAXVAR)
!RandomNumber
integer:: seed
!LU Decomposition
integer :: indx(MAXDAT)
real*8 :: W(MAXDAT),V(MAXDAT,MAXDAT),rhsF(MAXTRM),z(MAXDAT),tmp(MAXTRM)
!Orthogonal Polynomial related
integer::mreg(MAXDAT,DIM)
real*8 :: PL(DIM,0:MAXTRM),DPL(DIM,0:MAXTRM),xmat(MAXDAT,MAXDAT)
!Name related declarations
character*60 :: filename
character*2 :: dimnumber,fctnumber
! Cost func evals
integer::fct
real*8:: fv,gv(DIM),hv(DIM,DIM)
real*8 :: x(DIM)
!!Dynamic samples
real*8::xvec(maxdat,dim)
integer::Randomini,maxorderwant
integer::index,evalfunction
integer::nptsold,ntermsold
integer:: nptstoaddpercyc
! Mixed OUU adaptation vars
real*8::dftmp(ndimint),ftmp
! Dimension of problem
ndimt=ndimint
!Settings
mainprog=.false.
if (dim.ne.ndimt) OUUflag=1 ! mixed uncertainties, need to call optimization at the end
DAT=DATIN
probtype(1:dim)=probtypeIN(1:dim)
filenum= int(DAT(20)) ! 6 for screen, any other number for fort.x
if(id_proc.eq.0) then
write(filenum,*)
write(filenum,*) '======================================================='
write(filenum,*) 'Non-Intrusive Polynomial Chaos (Stochastic Collocation)'
write(filenum,*) '======================================================='
write(filenum,*) 'Author: Komahan Boopathy, University of Dayton, OH'
write(filenum,*) 'Email : komahan.cool@gmail.com'
write(filenum,*) '======================================================='
write(filenum,*)
! write(filenum,'(x,a,i3)')'>> Number of Processors = ',num_proc
end if !master
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++!
! Non-parallel region !
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++!
!============================================================
! Initial settings
!============================================================
makesamples=1 ! 0=read from file, 1= Make via LHS for building surrogate
! Choice of orthogonal basis
! 1=Legendre
! 2=Hermite
do j=1,DIM
ipar(j)=2
end do
casemode=1 !0=RMSE only, 1=Statistics
!!$ xavg(1:dim)=xavgin(1:dim)
!!$
!!$ do i=1,dim
!!$ if (probtype(i).eq.1) then
!!$ xstd(i)=xstdin(i)
!!$ else if (probtype(i).eq.2) then
!!$ xstd(i)=xavgin(i)*xstdin(i)
!!$ else
!!$ stop"Wrong problem type"
!!$ end if
!!$ end do
xavgt(1:ndimt)=xavgin(1:ndimt)
do i=1,ndimt
if (probtype(i).eq.1) then
xstdt(i)=xstdin(i)
else if (probtype(i).eq.2) then
xstdt(i)=xavgin(i)*xstdin(i)
else
stop"Wrong problem type"
end if
end do
xavg(1:DIM)=xavgt(ndimt-DIM+1:ndimt)
xstd(1:DIM)=xstdt(ndimt-DIM+1:ndimt)
do dynamics=1,1
!===============================
! Main Program
!===============================
DO OS=OSin,OSin ! Ratio of Over Sampling ratio 1 or 2 (2 is recommended)
do stat=statin,statin
!0= Function only
!1= Function + Gradient
!2= Function +Gradient +Hessian
call solvertype(stat,os,solver)
fctindx=fctindxin
do fct=fctin,fctin
!1 : cos(x+y) (Nd)
!2 : 1.0/(1.0+x**2+y**2) (Nd)
!3 : x**2+y**2 (Nd)
!4 : exp(x+y) (Nd)
!5 : x**3+y**3 (Nd)
!6 : Rosenbrock (Nd)
!7 : sin(3x-1.5)+cos(3y-3) (Nd)
!8 : Two bar truss design (3d)
!9 : Short tubular column (3d)
!10: Cantilever beam (2d)
!11: Three bar truss (3d)
!12: Threebar truss (6d)
!20: CFD
!>20: Mixed Uncertainties, calling suboptimization program to find the worst and best case scenarios to fix the corresponsing epistemic vars at extrema, whereas the aleatory vars are sampled within the space spanned by the mean and 3*SD. The surrogate is built on aleatory vars only, with epistemic vars fixed at extrema. F(B*,A_i) is what is given to the surrogate for each corresponding training point location A_i.
!Domain size
if (casemode.eq.0) then !RMSE comparisons only
if (fct.lt.7)then ! Analytic functions
DO j = 1, DIM
par(j,1)=-2.0
par(j,2)=2.0
END DO
else if (Fct.eq.8) then ! Truss design
if (fctindx.gt.3.or.dim.ne.3) stop'Wrong Function Index or Dimension for this Truss test case. Please check'
!0=obj, 1,2,3= constraints
DO j = 1, DIM
par(j,1)=1.0d0
par(j,2)=3.0d0
end do
else if (Fct.eq.9) then ! Short Column
if (fctindx.gt.2.or.dim.ne.3) stop'Wrong Function Index or Dimension for this Truss test case. Please check'
!0=obj, 1,2,3= constraints
DO j = 1, DIM ! Figure out a best range
par(j,1)=1.0d0
par(j,2)=3.0d0
end do
else if (Fct.eq.8) then ! Cantilever beam problem
if (fctindx.gt.3.or.dim.ne.3) stop'Wrong Function Index or Dimension for this Truss test case. Please check'
!0=obj, 1,2,3= constraints
DO j = 1, DIM
par(j,1)=1.0d0
par(j,2)=3.0d0
end do
else if (fct.eq.20) then
call cfdparams(par) !? on all threads?
end if
else if (Casemode.eq.1) then ! stats + rmse domain
! statistics--> construct PC surrogate between mean and 3 SD's
do i=1,dim
par(i,1)=xavg(i)-3.0*xstd(i)
par(i,2)=xavg(i)+3.0*xstd(i)
end do
else
print *, casemode
stop 'Wrong Casemode'
end if
randomflag=1
dyncyccnt=0
do DIMPC =orderinitial,orderfinal !order 5D requires 3003 terms
dyncyccnt=dyncyccnt+1
! Get number of terms in the expansion
call combination(DIM+DIMPC,DIM,nterms)
! Get number of points based on stat,solver,oversamp ratios
call getnpts(solver,stat,dim,nterms,OS,npts)
if (dyncyccnt.eq.1) then
if(id_proc.eq.0) call sampdist(stat,DIM,DIMPC,ipar,par,makesamples,nterms,npts,fct,RN)
else
if (dynamics.eq.1) then
nptstoaddpercyc=abs(npts-nptsold)
! Trick to force a least number of points
!!$ if (nptstoaddpercyc.le.dim) then
!!$ npts=npts+dim
!!$ nptstoaddpercyc=abs(npts-nptsold)
!!$ end if
! Call the dynamic sample routine
if (id_proc.eq.0) then
write(filenum,*)
write(filenum,*) '================================================='
write(filenum,*) ' Dynamic Point Selection '
write(filenum,*) '================================================='
write(filenum,*)
write(filenum,*)' >> NPTS to add this cycle:',nptstoaddpercyc
end if
call dynsampdist(stat,DIM,DIMPC,ipar,par,makesamples,ntermsold,nterms,nptsold,npts,nptstoaddpercyc,fct,fpcb,gpcb,hpcb,xcof,RN)
else ! random points again call the same routine
if(id_proc.eq.0) call sampdist(stat,DIM,DIMPC,ipar,par,makesamples,nterms,npts,fct,RN)
end if !dynamics
end if ! dyncyccnt
call MPI_Barrier(MPI_COMM_WORLD,ierr) ! All wait until master gets here
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++!
! Non-parallel region !
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++!
if (id_proc.eq.0) then
!==================================================
! SETUP MATRIX
!==================================================
write(filenum,*)
write(filenum,*) '================================================='
write(filenum,*) ' Matrix Setup & Pseudo-Inverse '
write(filenum,*) '================================================='
write(filenum,*)
call setupmat(stat,dim,dimpc,npts,ipar,RN,numpc,xmat)
write(filenum,*)' >> Number of columns in the matrix (nterms):',nterms
write(filenum,*)' >> Number of rows in the matrix (numpc):',numpc
if (solver.eq.1)then
write(filenum,*)' >> Solver : LU Decomposition'
else if (solver.eq.2) then
write(filenum,*)' >> Solver : SV Decomposition'
else
stop'Invalid Solver'
end if
!==============================================================
! Decomposing the matrix to enable to use it for multiple RHS's
!==============================================================
write(filenum,*)' >> Finding Pseudo-Inverse of the matrix . . . '
call pseudoinv(solver,numpc,nterms,xmat,indx,W,V)
write(filenum,*)
write(filenum,*) '================================================='
write(filenum,*) ' RHS Setup '
write(filenum,*) '================================================='
write(filenum,*)
! Evaluates cost and grad and stores them as arrays fpcb(maxpts),gpcb(dim,maxpts)
if (dynamics.eq.0.or.dyncyccnt.eq.1) then
call gather_costfn(dim,fct,stat,npts,RN,fpcb,gpcb,hpcb)
! for further dyncyccnts they are automatically computed within dynsamp routine
end if
!=======================================================
! Setting up RHS
!=======================================================
write(filenum,*)'>> Cost Function Number :',fct
if (stat.eq.0) write(filenum,*)' >> Setting up the RHS with Function evals . . .'
if (stat.eq.1) write(filenum,*)' >> Setting up the RHS with Func+Grad evals . . .'
if (stat.eq.2) write(filenum,*)' >> Setting up the RHS with Func+Grad+Hess evals . . .'
! Put fpcb,gpcb,hpcb all into one rhsF
call setupRHS(stat,dim,npts,fpcb,gpcb,hpcb,numpc,rhsF)
write(filenum,*)' >> Number of RHS entries :',numpc ! Atleast equal to number of coeffients
write(filenum,*)
do i=1,numpc
write(filenum,*)i, rhsF(i)
end do
write(filenum,*)
write(filenum,*) '================================================='
write(filenum,*) ' Solve Linear System '
write(filenum,*) '================================================='
write(filenum,*)
!=======================================================
! Backsubstitute for any RHS (like a black box approach)
!=======================================================
write(filenum,*)'>> Solving for the coefficients . . . '
call backsub(solver,xmat,numpc,nterms,indx,W,V,rhsF,XCOF)
write(filenum,*)'>> Coeffs are succesfully determined . . .'
write(filenum,*)'>> Number of coefficients : ',nterms
write(filenum,*)
end if !master
!-------------------------- Info Sharing -------------------------------!
call MPI_Barrier(MPI_COMM_WORLD,ierr) ! All wait until master gets the coeffs
call MPI_BCAST(npts,1,MPI_INTEGER,0,MPI_COMM_WORLD,ierr)
call MPI_BCAST(numpc,1,MPI_INTEGER,0,MPI_COMM_WORLD,ierr)
call MPI_BCAST(nterms,1,MPI_INTEGER,0,MPI_COMM_WORLD,ierr)
call MPI_BCAST(xcof,maxtrm,MPI_DOUBLE_PRECISION,0,MPI_COMM_WORLD,ierr)
!-------------------------- End Sharing -------------------------------!
! if (id_proc.eq.0) call TimerStop('PC')
! if (id_proc.eq.0) call TimerReport(ttotal)
!++++++++++++++++
!Parallel Region!
!++++++++++++++++
!================================================================
! Post processing--> RMSE, Output statistics,Tecplot
!================================================================
if (DIMPC.eq.orderfinal) then
if(id_proc.eq.0) then
write(filenum,*)
write(filenum,*) '================================================='
write(filenum,*) ' MONTE-CARLO on Surrogate '
write(filenum,*) '================================================='
write(filenum,*)
end if
call montecarlo(stat,fct,DIM,dimpc,nterms,npts,ipar,xcof)
call MPI_Barrier(MPI_COMM_WORLD,ierr)
end if
!!$ !=======================================================
!!$ ! Calculate RMSE
!!$ !=======================================================
!!$
!!$ if(id_proc.eq.0) then
!!$ write(filenum,*)
!!$ write(filenum,*) '================================================='
!!$ write(filenum,*) ' RMSE on Surrogate '
!!$ write(filenum,*) '================================================='
!!$ write(filenum,*)
!!$ end if
!!$ call MPI_Barrier(MPI_COMM_WORLD,ierr)
!!$ call RMSE_Higher(stat,dim,fct,npts,dimPC,ipar,par,xcof)
!!$ call MPI_Barrier(MPI_COMM_WORLD,ierr)
!!$
!!$ !================================================================
!!$ ! Tecplot output to file
!!$ !================================================================
!!$
!!$ if(id_proc.eq.0) then
!!$ if(dim.le.2) then
!!$ write(filenum,*)
!!$ write(filenum,*) '================================================='
!!$ write(filenum,*) ' Tecplot Output '
!!$ write(filenum,*) '================================================='
!!$ write(filenum,*)
!!$ write(filenum,*)'>> Writing Tecplot output to file . . .'
!!$
!!$ call tecplot(dim,dimpc,ipar,par,fct,npts,xcof)
!!$ end if
!!$ end if
nptsold=npts
ntermsold=nterms
enddo !order
enddo ! fct
enddo ! F or FG (Stat)
end do !Oversamp loop
end do !dynamics loop
!!$ if (id_proc.eq.0) then
!!$ print *, fmean,fmeanprime(1:dim)
!!$ print *,fvar,fvarprime(1:dim)
!!$ end if
! Export out of this subroutine for optimization
! Function values
fmeanout=fmean
fvarout=fvar
if (OUUflag.eq.1) then
if (id_proc.eq.0) then
call epigrads(fct,fctindx,dim,ndimt,xavgt,xstdt,ftmp,dftmp)
do j=1,ndimt-dim
fmeanprimeout(j)=dftmp(j) ! epistemic mean
fvarprimeout(j)=0.0 ! epistemic var assumed to be small
end do
end if
end if
call MPI_Barrier(MPI_COMM_WORLD,ierr)
call MPI_BCAST(fmeanprimeout,ndimt,MPI_DOUBLE_PRECISION,0,MPI_COMM_WORLD,ierr)
call MPI_BCAST(fvarprimeout,ndimt,MPI_DOUBLE_PRECISION,0,MPI_COMM_WORLD,ierr)
!assembling epistemic and aleatory gradients in place
fmeanprimeout(ndimt-dim+1:ndimt)=fmeanprime(1:dim)
fvarprimeout(ndimt-dim+1:ndimt)=fvarprime(1:dim)
! Hessian (need to be worked on)
do i=1,dim
do j=1,dim
fmeandbleprimeout(i,j) = fmeandbleprime(i,j)
fvardbleprimeout(i,j) = fvardbleprime(i,j)
end do
end do
if (id_proc.eq.0) then
! print*,'mean:',fmeanout
! print*,'var:',fvarout
! print*,'fmeanprime:',fmeanprimeout
! print*,'fvarprime:',fvarprimeout
!!$ write(filenum,*)
!!$ write(filenum,'(E15.6)')'>> fmean:',fmeanout
!!$ write(filenum,'(E15.6)')'>> fvar :',fvarout
!!$ write(filenum,*)
!!$ write(filenum,'(99E15.6)')'>> fmeanprime:',fmeanprimeout
!!$ write(filenum,'(99E15.6)')'>> fvarprime :',fvarprimeout
!!$ write(filenum,*)
write(filenum,*)
write(filenum,*)'>> Program call is successful'
write(filenum,*)
end if
call MPI_Barrier(MPI_COMM_WORLD,ierr)
return
end subroutine PCestimate
!+======================================================================
function PHI(dim,x1,x2,scal)
implicit none
integer :: dim,j
real*8 :: x1(dim),x2(dim),phi,x(dim),xnorm,tmp,scal
x(:)=x1(:)-x2(:)
xnorm=0.0
do j=1,dim
xnorm=xnorm+x(j)**2
end do
xnorm=SQRT(xnorm)/scal
tmp=max(1.0-xnorm,0.0)
phi=xnorm**3
RETURN
end function phi
SUBROUTINE OTHPL(KF,N,X,PL,DPL)
!
! ==========================================================
! Purpose: Compute orthogonal polynomials: Hn(x) or Ln(x),
! or Pn(x), and their derivatives
! Input : KF --- Function code
! KF=1 for Legendre polynomials Pn(x)
! KF=2 for Hermite polynomial Hn(x)
! KF=5 for Laguerre polynomial Ln(x)
! n --- Order of orthogonal polynomials
! x --- Argument of orthogonal polynomials
! Output: PL(n) --- Hn(x) or Ln(x) or Pn(x)
! DPL(n)--- Hn'(x) or Ln'(x) or Pn'(x)
! =========================================================
!
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION PL(0:N),DPL(0:N)
Y0=1.0D0
DY0=0.0D0
PL(0)=1.0D0
DPL(0)=0.0D0
IF (KF.EQ.2) THEN
Y1=X
DY1=1.0D0
PL(1)=X
DPL(1)=1.0D0
ELSE IF (KF.EQ.5) THEN
Y1=1.0D0-X
DY1=-1.0D0
PL(1)=1.0D0-X
DPL(1)=-1.0D0
ELSE IF (KF.EQ.1) THEN
Y1=X
PL(1)=X
DPL(1)=1.0D0
ELSE
PRINT *, 'Invalid choice of orthogonal polynomial'
STOP
ENDIF
DO K=2,N
IF (KF.EQ.2) THEN
A=1.0D0
B=0.0D0
C=(K-1.0D0)
ELSE IF (KF.EQ.5) THEN
A=-1.0D0/K
B=2.0D0+A
C=1.0D0+A
ELSE IF (KF.EQ.1) THEN
A=2.0D0-1.0D0/K
B=0.D0
C=1.0D0-1.0D0/K
ENDIF
YN=(A*X+B)*Y1-C*Y0
PL(K)=YN
IF (KF.GE.2) THEN
DYN=A*Y1+(A*X+B)*DY1-C*DY0
DPL(K)=DYN
DY0=DY1
DY1=DYN
ELSE
IF (DABS(X).EQ.1.0D0) THEN
DPL(K)=0.5D0*X**(K+1)*K*(K+1.0D0)
ELSE
DPL(K)=K*(Y1-X*YN)/(1.0D0-X*X)
ENDIF
ENDIF
Y0=Y1
Y1=YN
END DO
RETURN
END SUBROUTINE OTHPL
subroutine i_to_s(intval,s)
use dimpce, only: OS,fctindx
implicit none
integer idig,intval,ipos,ival,i
character (len=*) s
s(:) = ' '
ival = intval
! Working from right to left, strip off the digits of the integer
! and place them into S(1:len ( s )).
!
ipos = len(s)
do while ( ival /= 0 )
idig = mod( ival, 10 )
ival = ival / 10
s(ipos:ipos) = char(idig + 48 )
ipos = ipos - 1
end do
!
! Fill the empties with zeroes.
!
do i = 1, ipos
s(i:i) = '0'
end do
return
end subroutine i_to_s
!=================================
subroutine getfilename(dim,fct,dimpc,stat,casemode,filename)
use dimpce,only:OS,fctindx,dynamics
implicit none
character*2 :: dimnumber,fctnumber,ordnumber,OSnumber,fctindxnumber
integer ::lenc,fct,dim,stat,casemode,dimpc
character*60 :: filename
call i_to_s(fct,fctnumber)
call i_to_s(dim,dimnumber)
call i_to_s(dimpc,ordnumber)
call i_to_s(OS,OSnumber)
call i_to_s(fctindx,fctindxnumber)
if (casemode.eq.0) then
filename='norm/errornormdim'
lenc=12+5
else if (Casemode.eq.1) then
filename='stats/statsdim'
lenc=8+6
else if (casemode.eq.55)then !Storing samples
filename='samp/sampdim'
lenc=7+5
else
stop'Wrong flag in case mode'
end if
filename(lenc+1:lenc+2)=dimnumber
lenc=lenc+2
if (casemode.ne.55)then
filename(lenc+1:lenc+3)='fct'
lenc=lenc+3
filename(lenc+1:lenc+2)=fctnumber
lenc=lenc+2
if (fct.eq.20) then
filename(lenc+1:lenc+1)='i'
lenc=lenc+1
filename(lenc+1:lenc+2)=fctindxnumber
lenc=lenc+2
end if
else
filename(lenc+1:lenc+3)='ord'
lenc=lenc+3
filename(lenc+1:lenc+2)=ordnumber
lenc=lenc+2
end if
if (OS.gt.1) then
filename(lenc+1:lenc+3)='Rat'
lenc=lenc+3
filename(lenc+1:lenc+2)=OSnumber
lenc=lenc+2
else
end if
if (stat.eq.2) then
filename(lenc+1:lenc+3)='FGH'
lenc=lenc+3
else if (stat.eq.1) then
filename(lenc+1:lenc+2)='FG'
lenc=lenc+2
else if (stat.eq.0) then
filename(lenc+1:lenc+1)='F'
lenc=lenc+1
else
print *, 'Wrong value in hstat'
stop'Wrong value in stat'
end if
if (dynamics.eq.1) then
filename(lenc+1:lenc+6)='mirdyn'
lenc=lenc+6
end if
return
end subroutine getfilename
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
subroutine ortho(dist,dimpc,x,pl,dpl,ddpl)
implicit none
integer :: dist,dimpc,i
real*8:: x,pl(0:dimpc),dpl(0:dimpc),ddpl(0:dimpc)
if (dist.eq.1) then
do i=0,dimpc
call LEGEN(i,X,pl(i),dpl(i),Ddpl(i))
end do
! call LEGENDRE(dimpc,X,PL,DPL,ddpl) !something wrong in DDPL, DPL
else if (dist.eq.2) then
call hermite(dimpc,X,PL,DPL,ddpl,2)
else
stop'Not implemented yet'
end if
end subroutine ortho
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
subroutine solvertype(stat,os,solver)
implicit none
integer,intent(in)::stat,os
integer,intent(out)::solver
if (stat.eq.0) then
if (OS.eq.1) then
solver=1
else
solver=2
end if
else
solver =2
end if
return
end subroutine solvertype
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
subroutine cfdparams(par)
implicit none
include "collsub.h"
integer,parameter::dim=2
integer::j
real*8,intent(out):: par(DIM,MAXPAR)
double precision :: Initialmach, Finalmach, InitialAOA,FinalAOA
InitialMach=0.5d0
FinalMach=1.5d0
InitialAOA=0.0d0 !degrees
FinalAOA=5.0d0 !degrees
!Domain size
DO j = 1, DIM
if (j.eq.1) then
par(j,1)=InitialAOA*4.0d0*atan(1.0)/180.0 ! in radian
par(j,2)=FinalAOA*4.0d0*atan(1.0)/180.0 ! in radian
else
par(j,1)=InitialMach !initial mach number
par(j,2)=FinalMach !final mach number
end if
END DO
end subroutine cfdparams
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
subroutine pseudoinv(solver,numpc,nterms,xmat,indx,W,V)
implicit none
include "collsub.h"
integer,intent(in)::solver,numpc,nterms
integer,intent(out)::indx(MAXDAT)
real*8,intent(in)::xmat(MAXDAT,MAXDAT)
real*8,intent(out)::W(MAXDAT),V(MAXDAT,MAXDAT)
real*8::dd
if (solver.eq.1) then
call ludcmp(xmat,numpc,MAXDAT,indx,dd)
W=0.0d0
V=0.0d0
else
call svdcmp(xmat,numpc,nterms,MAXDAT,MAXDAT,W,V)
indx=0
end if
end subroutine pseudoinv
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
subroutine backsub(solver,xmat,numpc,nterms,indx,W,V,rhsF,XCOF)
use dimpce,only:filenum
implicit none
include "collsub.h"
INTEGER::I,J,K
integer,intent(in)::solver,numpc,nterms
integer,intent(in)::indx(MAXDAT)
real*8,intent(in)::xmat(MAXDAT,MAXDAT),rhsf(MAXDAT)
real*8,intent(in)::W(MAXDAT),V(MAXDAT,MAXDAT)
real*8,intent(out)::XCOF(MAXDAT)
if (solver.eq.1) then
call lubksb(xmat,nterms,MAXDAT,indx,rhsF) !tmp=rhsfunc
xcof=rhsF
else
call svbksb(xmat,W,V,numpc,nterms,MAXDAT,MAXDAT,rhsF,xcof)
end if
do j=1,nterms
write(filenum,*) j,xcof(j)
enddo
end subroutine backsub
!Unused routines
SUBROUTINE HERM(N,X,Y,DY,D2Y)
! *************************************************************
! * COMPUTES THE VALUE OF THE HERMITE POLYNOMIAL OF DEGREE N
! * AND ITS FIRST AND SECOND DERIVATIVES AT A GIVEN POINT
! * N = DEGREE OF THE POLYNOMIAL
! * X = POINT IN WHICH THE COMPUTATION IS PERFORMED
! * Y = VALUE OF THE POLYNOMIAL IN X
! * DY = VALUE OF THE FIRST DERIVATIVE IN X
! * D2Y= VALUE OF THE SECOND DERIVATIVE IN X
! *************************************************************
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
Y = 1.D0
DY = 0.D0
D2Y = 0.D0
IF (N .EQ. 0) RETURN
Y = 2.D0*X
DY = 2.D0
D2Y = 0.D0
IF (N .EQ. 1) RETURN
YP=1.D0
DO 1 K=2,N
DK = DFLOAT(K-1)
YM = Y
Y = 2.D0*X*Y-2.D0*DK*YP
YPM = YP
YP = YM
1 CONTINUE
DN = 2.D0*DFLOAT(N)
DNN = 2.D0*DFLOAT(N-1)
DY = DN*YP
D2Y = DN*DNN*YPM
RETURN
END SUBROUTINE HERM
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
SUBROUTINE LEGEN(N,X,Y,DY,D2Y)
! **************************************************************
! * COMPUTES THE VALUE OF THE LEGENDRE POLYNOMIAL OF DEGREE N
! * AND ITS FIRST AND SECOND DERIVATIVES AT A GIVEN POINT
! * N = DEGREE OF THE POLYNOMIAL
! * X = POINT IN WHICH THE COMPUTATION IS PERFORMED
! * Y = VALUE OF THE POLYNOMIAL IN X
! * DY = VALUE OF THE FIRST DERIVATIVE IN X
! * D2Y= VALUE OF THE SECOND DERIVATIVE IN X
! **************************************************************
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
Y = 1.D0
DY = 0.D0
D2Y = 0.D0
IF (N .EQ. 0) RETURN
Y = X
DY = 1.D0
D2Y = 0.D0
IF(N .EQ. 1) RETURN
YP = 1.D0
DYP = 0.D0
D2YP = 0.D0
DO 1 I=2,N
C1 = DFLOAT(I)
C2 = 2.D0*C1-1.D0
C4 = C1-1.D0
YM = Y
Y = (C2*X*Y-C4*YP)/C1
YP = YM
DYM = DY
DY = (C2*X*DY-C4*DYP+C2*YP)/C1
DYP = DYM
D2YM = D2Y
D2Y = (C2*X*D2Y-C4*D2YP+2.D0*C2*DYP)/C1
D2YP = D2YM
1 CONTINUE
RETURN
! END DO
End SUBROUTINE LEGEN
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
subroutine evalPC(ndim,dimPC,ipar,xcof,x,yhat,yhatprime,yhatdbleprime)