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spclibs/examples/driv1.f90
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driv1.f90
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!>
!> @file driv1.f90
!>
!> @brief
!>
!> @copyright
!> Copyright (©) 2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
!> SPC (Swiss Plasma Center)
!>
!> spclibs is free software: you can redistribute it and/or modify it under
!> the terms of the GNU Lesser General Public License as published by the Free
!> Software Foundation, either version 3 of the License, or (at your option)
!> any later version.
!>
!> spclibs is distributed in the hope that it will be useful, but WITHOUT ANY
!> WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
!> FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
!>
!> You should have received a copy of the GNU Lesser General Public License
!> along with this program. If not, see <https://www.gnu.org/licenses/>.
!>
!> @authors
!> (in alphabetical order)
!> @author Trach-Minh Tran <trach-minh.tran@epfl.ch>
!>
PROGRAM main
!
! Basis splines on a 2d grid.
!
USE bsplines
USE futils
IMPLICIT NONE
TYPE(spline1d) :: spx, spy
INTEGER :: nx=10, ny=8, nidbas=2, ngauss=4, npts=1000
DOUBLE PRECISION :: a, b, coefx(5), coefy(5)
DOUBLE PRECISION, ALLOCATABLE :: xgrid(:), ygrid(:), fun(:,:)
DOUBLE PRECISION, ALLOCATABLE :: xp(:), funxp(:,:), yp(:), funyp(:,:)
DOUBLE PRECISION :: dx, dy
INTEGER :: i, j, left
CHARACTER(len=256) :: title
INTEGER :: fid
NAMELIST /newrun/ nx, ny, nidbas, ngauss, a, b, coefx, coefy
!===========================================================================
nidbas = 3
ngauss = 4
nx = 10 ! Number of intevals in x
ny = 8 ! Number of intevals in y
a = 0.0d0 ! Left boundary of interval
b = 1.0d0 ! Right boundary of interval
coefx(1:5) = (/1.0d0, 0.d0, 0.d0, 0.d0, 1.d0/) ! Mesh point distribution function
coefy(1:5) = (/1.0d0, 0.d0, 0.d0, 0.d0, 1.d0/) ! Mesh point distribution function
READ(*,newrun)
WRITE(*,newrun)
!===========================================================================
! 1.0 Set up grids
!
ALLOCATE( xgrid(0:nx) )
xgrid(0) = a
xgrid(nx) = b
CALL meshdist(coefx, xgrid, nx)
!
!!$ dy = 2.d0*pi/REAL(ny)
dy = 1.0d0
ALLOCATE( ygrid(0:ny) )
ygrid(0) = a
ygrid(ny) = b
CALL meshdist(coefy, ygrid, ny)
!===========================================================================
! 2.0 Set up splines on (x,y)
!
CALL set_spline(nidbas, ngauss, xgrid, spx)
CALL set_spline(nidbas, ngauss, ygrid, spy, period=.TRUE.)
WRITE(*,'(/a,i6,a,i6/(10(f8.3)))') 'KNOTS of x-splines', LBOUND(spx%knots), &
& ':',UBOUND(spx%knots), spx%knots
WRITE(*,'(2(a,i5, 2x))') 'NX =', nx, 'DIM =', spx%dim
WRITE(*,'(/a,i6,a,i6/(10(f8.3)))') 'KNOTS of y-splines', LBOUND(spy%knots), &
& ':',UBOUND(spy%knots), spy%knots
WRITE(*,'(2(a,i5, 2x))') 'NY =', ny, 'DIM =', spy%dim
!===========================================================================
! 3.0 Graph the splines on (x,y)
!
ALLOCATE( fun(nidbas+1,1) ) ! Only 0-th derivative
!!$ ALLOCATE( fun(nidbas+1,0:1) ) ! Only 0-th derivative
ALLOCATE( xp(npts), funxp(npts,0:spx%dim-1) )
ALLOCATE( yp(npts-1), funyp(npts-1,0:spy%dim-1) )
!
! Splines in X (non-peridic)
!
WRITE(*,'(a)') 'Splines in x'
dx = (xgrid(nx)-xgrid(0)) / REAL(NPTS-1)
DO i=1,npts
xp(i) = xgrid(0) + (i-1)*dx
CALL locintv(spx, xp(i), left)
CALL basfun(xp(i), spx, fun, left+1)
funxp(i,left:left+nidbas) = fun(:,1)
END DO
!
! Splines in Y (periodic)
!
WRITE(*,'(a)') 'Splines in y'
dy = (ygrid(ny)-ygrid(0)) / REAL(NPTS-1)
DO i=1,npts-1
yp(i) = ygrid(0) + (i-1)*dy
CALL locintv(spy, yp(i), left)
CALL basfun(yp(i), spy, fun, left+1)
funyp(i,left:left+nidbas) = fun(:,1)
END DO
!
! Create hdf5 file
!
CALL creatf('driv1.h5', fid, real_prec='d')
!
WRITE(title,'(a,i3,5x,a,i6)') 'Splines of degree =', nidbas, 'NX =', nx
CALL putarr(fid, 'X', xp)
CALL putarr(fid, 'KNOTSX', spx%knots)
CALL putarr(fid, 'splinesx', funxp, TRIM(title))
CALL putarr(fid, 'KNOTSY', spy%knots)
!
WRITE(title,'(a,i3,5x,a,i6)') 'Periodic splines of degree =', nidbas, 'NY =', ny
CALL putarr(fid, 'Y', yp)
CALL putarr(fid, 'splinesy', funyp, TRIM(title))
CALL closef(fid)
!===========================================================================
! 9.0 Epilogue
!
DEALLOCATE(fun)
DEALLOCATE(xgrid, ygrid)
DEALLOCATE(xp, funxp)
CALL destroy_sp(spx)
CALL destroy_sp(spy)
END PROGRAM main
!+++
SUBROUTINE meshdist(c, x, nx)
!
! Construct an 1d non-equidistant mesh given a
! mesh distribution function.
!
IMPLICIT NONE
DOUBLE PRECISION, INTENT(in) :: c(5)
INTEGER, INTENT(iN) :: nx
DOUBLE PRECISION, INTENT(inout) :: x(0:nx)
INTEGER :: nintg
DOUBLE PRECISION, DIMENSION(:), ALLOCATABLE :: xint, fint
DOUBLE PRECISION :: a, b, dx, f0, f1, scal
INTEGER :: i, k
!
a=x(0)
b=x(nx)
nintg = 10*nx
ALLOCATE(xint(0:nintg), fint(0:nintg))
!
! Mesh distribution
!
dx = (b-a)/REAL(nintg)
xint(0) = a
fint(0) = 0.0d0
f1 = fdist(xint(0))
DO i=1,nintg
f0 = f1
xint(i) = xint(i-1) + dx
f1 = fdist(xint(i))
fint(i) = fint(i-1) + 0.5*(f0+f1)
END DO
!
! Normalization
!
scal = REAL(nx) / fint(nintg)
fint(0:nintg) = fint(0:nintg) * scal
!!$ WRITE(*,'(a/(10f8.3))') 'FINT', fint
!
! Obtain mesh point by (inverse) interpolation
!
k = 1
DO i=1,nintg-1
IF( fint(i) .GE. REAL(k) ) THEN
x(k) = xint(i) + (xint(i+1)-xint(i))/(fint(i+1)-fint(i)) * &
& (k-fint(i))
k = k+1
END IF
END DO
!
DEALLOCATE(xint, fint)
CONTAINS
DOUBLE PRECISION FUNCTION fdist(x)
DOUBLE PRECISION, INTENT(in) :: x
fdist = c(1) + c(2)*x + c(3)*EXP(-((x-c(4))/c(5))**2)
END FUNCTION fdist
END SUBROUTINE meshdist
!+++
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