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utils.f90
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utils.f90
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! This module contains various utility routines.
!
! The following routines provide formatted output:
!
! prin2 - output an array of doubles with 7 digits displayed
! prind - output an array of doubles with 15 digits displayed
! princ - output an array of complex numbers with 7 digits displayed
! prinz - output an array of complex numbers with 15 digits displayed
! prini - output an array of integers
! prinl - output an array of long integers
! prina - output a string
!
! The following are miscellaneous routines:
!
! elapsed - return the wall clock time in seconds which has elapsed since some
! arbitrary point in the past
! insort - sort an array of real numbers
! insorti - sort an array of integers
! insort2 - sort an array a of real numbers and return an array which describes
! the rearrangment of the the array a
! insorti2 - sort an array ia of integers and return an array which describes
! the rearrangment of the array ia
! iremove - remove from a list of integers all integers which occur in a second
! list of integers
! randperm - return a random permutation in S_n
! iduplicates - remove duplicates from a sorted list of integers
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
module utils
interface prin2
module procedure prin2_0
module procedure prin2_1
module procedure prin2_2
module procedure prin2_3
end interface prin2
interface prind
module procedure prind_0
module procedure prind_1
module procedure prind_2
end interface prind
interface princ
module procedure princ_0
module procedure princ_1
module procedure princ_2
end interface princ
interface prinz
module procedure prinz_0
module procedure prinz_1
module procedure prinz_2
end interface prinz
interface prini
module procedure prini_0
module procedure prini_1
module procedure prini_2
end interface prini
interface prinl
module procedure prinl_0
module procedure prinl_1
module procedure prinl_2
end interface prinl
contains
subroutine prin2_0(str,a)
implicit double precision (a-h,o-z)
double precision a
character(len=*), intent(in) :: str
print *,str
print "(4(2x,e15.7))",a
write (13,*) str
write (13,"(4(2x,e15.7))") a
end subroutine
subroutine prin2_1(str,a)
implicit double precision (a-h,o-z)
double precision, intent (in) :: a(:)
character(len=*), intent(in) :: str
print *,str
print "(4(2x,e15.7))",a
write (13,*) str
write (13,"(4(2x,e15.7))") a
end subroutine
subroutine prin2_2(str,a)
implicit double precision (a-h,o-z)
double precision, intent (in) :: a(:,:)
character(len=*), intent(in) :: str
print *,str
print "(4(2x,e15.7))",a
write (13,*) str
write (13,"(4(2x,e15.7))") a
end subroutine
subroutine prin2_3(str,a)
implicit double precision (a-h,o-z)
double precision, intent (in) :: a(:,:,:)
character(len=*), intent(in) :: str
print *,str
print "(4(2x,e15.7))",a
write (13,*) str
write (13,"(4(2x,e15.7))") a
end subroutine
subroutine prind_0(str,a)
implicit double precision (a-h,o-z)
double precision :: a
character(len=*), intent(in) :: str
print *,str
print "(2(2x,e24.16))",a
write (13,*) str
write (13,"(2(2x,e24.16))") a
end subroutine
subroutine prind_1(str,a)
implicit double precision (a-h,o-z)
double precision,intent(in) :: a(:)
character(len=*), intent(in) :: str
print *,str
print "(2(2x,e24.16))",a
write (13,*) str
write (13,"(2(2x,e24.16))") a
end subroutine
subroutine prind_2(str,a)
implicit double precision (a-h,o-z)
double precision,intent(in) :: a(:,:)
character(len=*), intent(in) :: str
print *,str
print "(2(2x,e24.16))",a
write (13,*) str
write (13,"(2(2x,e24.16))") a
end subroutine
subroutine princ_0(str,a)
implicit double precision (a-h,o-z)
double complex :: a
character(len=*), intent(in) :: str
print *,str
print "(2(d15.7,',',d15.7,2X))",a
write (13,*) str
write (13,"(2(d15.7,',',d15.7,2X))") a
end subroutine
subroutine princ_1(str,a)
implicit double precision (a-h,o-z)
double complex,intent(in) :: a(:)
character(len=*), intent(in) :: str
print *,str
print "(2(d15.7,',',d15.7,2X))",a
write (13,*) str
write (13,"(2(d15.7,',',d15.7,2X))") a
end subroutine
subroutine princ_2(str,a)
implicit double precision (a-h,o-z)
double complex,intent(in) :: a(:,:)
character(len=*), intent(in) :: str
print *,str
print "(2(d15.7,',',d15.7,2X))",a
write (13,*) str
write (13,"(2(d15.7,',',d15.7,2X))") a
end subroutine
subroutine prinz_0(str,a)
implicit double precision (a-h,o-z)
double complex :: a
character(len=*), intent(in) :: str
print *,str
print "(2(d24.15,',',d24.15,2X))",a
write (13,*) str
write (13,"(2(d24.15,',',d24.15,2X))") a
end subroutine
subroutine prinz_1(str,a)
implicit double precision (a-h,o-z)
double complex,intent(in) :: a(:)
character(len=*), intent(in) :: str
print *,str
print "(2(d24.15,',',d24.15,2X))",a
write (13,*) str
write (13,"(2(d24.15,',',d24.15,2X))") a
end subroutine
subroutine prinz_2(str,a)
implicit double precision (a-h,o-z)
double complex,intent(in) :: a(:,:)
character(len=*), intent(in) :: str
print *,str
print "(2(d24.15,',',d24.15,2X))",a
write (13,*) str
write (13,"(2(d24.15,',',d24.15,2X))") a
end subroutine
subroutine prini_0(str,a)
implicit double precision (a-h,o-z)
integer,intent(in) :: a
character(len=*), intent(in) :: str
print *,str
print "(8(2x,I9))",a
write (13,*) str
write (13,"(8(2x,I9))") a
end subroutine
subroutine prini_1(str,a)
implicit double precision (a-h,o-z)
integer,intent(in) :: a(:)
character(len=*), intent(in) :: str
print *,str
print "(8(2x,I8))",a
write (13,*) str
write (13,"(8(2x,I8))") a
end subroutine
subroutine prini_2(str,a)
implicit double precision (a-h,o-z)
integer,intent(in) :: a(:,:)
character(len=*), intent(in) :: str
print *,str
print "(8(2x,I8))",a
write (13,*) str
write (13,"(8(2x,I8))") a
end subroutine
subroutine prina(str)
implicit double precision (a-h,o-z)
character(len=*), intent(in) :: str
print *,str
write (13,*) str
end subroutine
subroutine prinl_0(str,a)
implicit double precision (a-h,o-z)
integer,intent(in) :: a
character(len=*), intent(in) :: str
print *,str
print "(6(2x,I13))",a
write (13,*) str
write (13,"(6(2x,I13))") a
end subroutine
subroutine prinl_1(str,a)
implicit double precision (a-h,o-z)
integer,intent(in) :: a(:)
character(len=*), intent(in) :: str
print *,str
print "(6(2x,I13))",a
write (13,*) str
write (13,"(6(2x,I13))") a
end subroutine
subroutine prinl_2(str,a)
implicit double precision (a-h,o-z)
integer,intent(in) :: a(:,:)
character(len=*), intent(in) :: str
print *,str
print "(6(2x,I13))",a
write (13,*) str
write (13,"(6(2x,I13))") a
end subroutine
subroutine elapsed(t)
implicit double precision (a-h,o-z)
integer*8 i,irate
real t1
call system_clock(i,irate)
dd = i
dd = dd/irate
t = dd
return
end subroutine
subroutine insort(k,a)
implicit double precision (a-h,o-z)
integer, intent(in) :: k
double precision, intent (inout) :: a(k)
!
! Sort an array a of k double precision numbers.
!
if (k .le. 1) return
do i=2,k
val=a(i)
j=i-1
do while (j .ge. 1 .AND. a(j) .gt. val)
a(j+1)=a(j)
j=j-1
end do
a(j+1)=val
end do
end subroutine
subroutine insorti(k,ia)
implicit double precision (a-h,o-z)
integer, intent(in) :: k
integer, intent (inout) :: ia(k)
!
! Sort an array ia of k integers.
!
if (k .le. 1) return
do i=2,k
ival=ia(i)
j=i-1
do while (j .ge. 1 .AND. ia(j) .gt. ival)
ia(j+1)=ia(j)
j=j-1
end do
ia(j+1)=ival
end do
end subroutine
subroutine insorti2(k,ia,idxs)
implicit double precision (a-h,o-z)
integer, intent(in) :: k
integer, intent (inout) :: ia(k),idxs(k)
!
! Sort an integer array ia and return a second array idxs
! such that the sorted array is ia(idxs), where ia is the
! original list of indices.
!
do i=1,k
idxs(i) = i
end do
if (k .le. 1) return
do i=2,k
ival = ia(i)
idxval = idxs(i)
j=i-1
do while (j .ge. 1 .AND. ia(j) .gt. ival)
ia(j+1) = ia(j)
idxs(j+1) = idxs(j)
j=j-1
end do
ia(j+1) = ival
idxs(j+1) = idxval
end do
end subroutine
subroutine quicksorti2(n,ia,idxs)
implicit double precision (a-h,o-z)
dimension istack(2,10000),ia(n),idxs(n)
!
! Sort an integer array ia and return a second array idxs
! such that the sorted array is ia(idxs), where ia is the
! original list of unsorted integers.
!
maxstack = 10000
k = 60
do i=1,n
idxs(i) = i
end do
if (n .lt. k) then
call insorti2(n,ia,idxs)
return
endif
!
nstack = 1
istack(1,1) = 1
istack(2,1) = n
!
do while( nstack .gt. 0)
i1 = istack(1,nstack)
i2 = istack(2,nstack)
nstack=nstack-1
!
l = i2-i1+1
if (l .le. k) then
call insorti20(l,ia(i1:i2),idxs(i1:i2))
cycle
endif
!
! Otherwise perform quicksort step
!
call quicksorti20(ia,idxs,i1,i2,i3)
!
! This should never happen, but just in case ...
!
if (nstack+2 .ge. maxstack) then
print *,"quicksort out of memory"
stop
endif
!
! Make sure the smaller half is processed first to reduce storage
! to O(logn).
!
n1 = i3-i1+1
n2 = i2-(i3+1)+1
!
if (n2 .lt. n1) then
!
nstack = nstack+1
istack(1,nstack) = i1
istack(2,nstack) = i3
!
nstack = nstack+1
istack(1,nstack) = i3+1
istack(2,nstack) = i2
!
else
!
nstack=nstack+1
istack(1,nstack) = i3+1
istack(2,nstack) = i2
!
nstack=nstack+1
istack(1,nstack) = i1
istack(2,nstack) = i3
!
endif
!
end do
end subroutine
subroutine insorti20(k,ia,idxs)
implicit double precision (a-h,o-z)
integer, intent(in) :: k
integer, intent (inout) :: ia(k),idxs(k)
if (k .le. 1) return
do i=2,k
ival = ia(i)
idxval = idxs(i)
j=i-1
do while (j .ge. 1 .AND. ia(j) .gt. ival)
ia(j+1) = ia(j)
idxs(j+1) = idxs(j)
j=j-1
end do
ia(j+1) = ival
idxs(j+1) = idxval
end do
end subroutine
subroutine quicksorti20(ivals,ivals2,i1,i2,i3)
implicit double precision (a-h,o-z)
dimension ivals(:),ivals2(:)
!
! Randomly choose a pivot index.
!
call random_number(r)
ipiv = i1+floor((i2-i1)*r)
!
ival = ivals(ipiv)
ival2 = ivals2(ipiv)
!
! Swap the pivot element and the last element.
!
ivals(ipiv) = ivals(i2)
ivals2(ipiv) = ivals2(i2)
ivals(i2) = ival
ivals2(i2) = ival2
!
i3 = i1
!
do i=i1,i2-1
if( ivals(i) .lt. ival) then
id = ivals(i)
id2 = ivals2(i)
!
ivals(i) = ivals(i3)
ivals2(i) = ivals2(i3)
ivals(i3) = id
ivals2(i3) = id2
!
i3=i3+1
endif
end do
!
id = ivals(i3)
id2 = ivals2(i3)
ivals(i3) = ivals(i2)
ivals2(i3) = ivals2(i2)
ivals(i2) = id
ivals2(i2) = id2
!
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine quicksorti(n,ia)
implicit double precision (a-h,o-z)
dimension istack(2,10000),ia(n)
!
! Sort an integer array ia
!
maxstack = 10000
k = 60
if (n .lt. k) then
call insorti(n,ia)
return
endif
!
nstack = 1
istack(1,1) = 1
istack(2,1) = n
!
do while( nstack .gt. 0)
i1 = istack(1,nstack)
i2 = istack(2,nstack)
nstack=nstack-1
l = i2-i1+1
if (l .le. k) then
call insorti0(l,ia(i1:i2))
cycle
endif
!
! Otherwise perform quicksort step
!
call quicksorti0(ia,i1,i2,i3)
!
! This should never happen, but just in case ...
!
if (nstack+2 .ge. maxstack) then
print *,"quicksort out of memory"
stop
endif
!
! Make sure the smaller half is processed first to reduce storage
! to O(logn).
!
n1 = i3-i1+1
n2 = i2-(i3+1)+1
!
if (n2 .lt. n1) then
!
nstack = nstack+1
istack(1,nstack) = i1
istack(2,nstack) = i3
!
nstack = nstack+1
istack(1,nstack) = i3+1
istack(2,nstack) = i2
!
else
!
nstack=nstack+1
istack(1,nstack) = i3+1
istack(2,nstack) = i2
!
nstack=nstack+1
istack(1,nstack) = i1
istack(2,nstack) = i3
!
endif
!
end do
end subroutine
subroutine insorti0(k,ia)
implicit double precision (a-h,o-z)
integer, intent(in) :: k
integer, intent (inout) :: ia(k)
if (k .le. 1) return
do i=2,k
ival = ia(i)
j=i-1
do while (j .ge. 1 .AND. ia(j) .gt. ival)
ia(j+1) = ia(j)
j=j-1
end do
ia(j+1) = ival
end do
end subroutine
subroutine quicksorti0(ivals,i1,i2,i3)
implicit double precision (a-h,o-z)
dimension ivals(:)
!
! Randomly choose a pivot index.
!
call random_number(r)
ipiv = i1+floor((i2-i1)*r)
!
ival = ivals(ipiv)
!
! Swap the pivot element and the last element.
!
ivals(ipiv) = ivals(i2)
ivals(i2) = ival
!
i3 = i1
!
do i=i1,i2-1
if( ivals(i) .lt. ival) then
id = ivals(i)
!
ivals(i) = ivals(i3)
ivals(i3) = id
!
i3=i3+1
endif
end do
!
id = ivals(i3)
ivals(i3) = ivals(i2)
ivals(i2) = id
!
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine insort2(k,a,idxs)
implicit double precision (a-h,o-z)
integer, intent(in) :: k
double precision :: a(k)
integer, intent (inout) :: idxs(k)
!
! Sort a double precision array a and return a second array idxs
! such that the sorted array is equal to a(idxs).
!
do i=1,k
idxs(i) = i
end do
if (k .le. 1) return
do i=2,k
val = a(i)
idxval = idxs(i)
j=i-1
do while (j .ge. 1 .AND. a(j) .gt. val)
a(j+1) = a(j)
idxs(j+1) = idxs(j)
j=j-1
end do
a(j+1) = val
idxs(j+1) = idxval
end do
end subroutine
subroutine iremove(n,ia,m,ib)
implicit double precision (a-h,o-z)
dimension ia(n),ib(m)
!
! Remove from the list ia of length n all integers appearing in
! the list ib of length m. Both the list ia and the list ib
! must be sorted before this call is made. The results will
! also be sorted.
!
isrc = 1
itar = 1
ii = 1
1000 continue
if (ii .gt. m) goto 2000
if (isrc .gt. n) goto 3000
if (ia(isrc) .gt. ib(ii)) then
ii=ii+1
goto 1000
endif
if (ia(isrc) .lt. ib(ii)) then
ia(itar) = ia(isrc)
itar=itar+1
isrc=isrc+1
goto 1000
endif
isrc=isrc+1
goto 1000
2000 continue
if (isrc .gt. n) goto 3000
ia(itar) = ia(isrc)
itar=itar+1
isrc=isrc+1
goto 2000
3000 continue
n = itar-1
return
end subroutine
subroutine randperm(n,iperm)
implicit double precision (a-h,o-z)
integer :: iperm(n)
!
! Return a random permuation of the integers 1,2,...,n.
!
do i=1,n
iperm(i) = i
end do
do i=1,n-1
call random_number(dd)
j = i+1 + (n-i-1)*dd
ival = iperm(j)
iperm(j) = iperm(i)
iperm(i) = ival
end do
end subroutine
subroutine permute_randomly(n,ilist,ilist2)
implicit double precision (a-h,o-z)
integer :: ilist(n), ilist2(n)
!
! Return a random permuatio nof the list ilist.
!
integer, allocatable :: iperm(:)
allocate(iperm(n))
do i=1,n
iperm(i) = i
end do
do i=1,n-1
call random_number(dd)
j = i+1 + (n-i-1)*dd
ival = iperm(j)
iperm(j) = iperm(i)
iperm(i) = ival
end do
ilist2 = ilist(iperm)
end subroutine
subroutine iduplicates(nin,ilistin,nout,ilistout)
implicit double precision (a-h,o-z)
integer :: ilistin(nin)
integer, allocatable, intent(out) :: ilistout(:)
!
! Remove duplicates from a sorted list of integers.
!
! Input parameters:
!
! Output parameters:
!
integer, allocatable :: ilist(:)
if (nin .eq. 0) then
allocate(ilistout(0))
return
endif
allocate(ilist(nin))
nout = 0
idx = 1
i = ilistin(idx)
nout = 1
ilist(nout) = i
do while(idx .lt. nin)
idx = idx+1
if (ilistin(idx) .ne. i) then
i = ilistin(idx)
nout = nout+1
ilist(nout) = i
endif
end do
allocate(ilistout(nout))
ilistout = ilist(1:nout)
end subroutine
subroutine quicksort(n,vals)
implicit double precision (a-h,o-z)
dimension istack(2,20000)
dimension vals(1),idxs(1)
!
! Sort a list of double precision numbers.
!
k = 60
if (n .lt. k) then
call insort(n,vals)
return
endif
maxstack = 10000
m = 1
istack(1,1) = 1
istack(2,1) = n
!
1000 continue
if (m .eq. 0) goto 1100
i1 = istack(1,m)
i2 = istack(2,m)
m=m-1
!
l = i2-i1+1
if (l .le. k) then
call insort(l,vals(i1))
goto 1000
endif
!
! Otherwise perform quicksort.
!
call quicksort01(vals,i1,i2,i3)
!
! This should never happen, but just in case ...
!
! if (m+2 .ge. maxstack) then
! print *,"quicksort out of memory"
! stop
! endif
!
! Make sure the smaller half is processed first to reduce storage
! to O(logn).
!
n1 = i3-i1+1
n2 = i2-i3
!
if (n2 .lt. n1) then
!
m = m+1
istack(1,m) = i1
istack(2,m) = i3
!
m = m+1
istack(1,m) = i3+1
istack(2,m) = i2
!
else
!
m = m+1
istack(1,m) = i3+1
istack(2,m) = i2
!
m = m+1
istack(1,m) = i1
istack(2,m) = i3
!
endif
!
goto 1000
1100 continue
end subroutine
subroutine quicksort01(vals,i1,i2,i3)
implicit double precision (a-h,o-z)
dimension vals(1)
!
! Randomly choose a pivot index.
!
! call corrand3(1,r)
call random_number(r)
ipiv = i1+floor((i2-i1)*r)
!
! ipiv = i1+(i2-i1)/2