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spclibs/examples/driv4.f90
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driv4.f90
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!>
!> @file driv4.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
!
! Computation of croos mass matrix between two splines sp1 & sp2
! sp1 and sp2 can be splines of any type (i.e. either set up with set_spline or
! set_splcoef) and of any order.
!
USE bsplines
USE matrix
!
IMPLICIT NONE
TYPE(gbmat) :: matm
INTEGER :: mrows, ncols, kl, ku
DOUBLE PRECISION, ALLOCATABLE :: avec(:,:), bvec(:,:), matfull(:,:)
!
TYPE(zgbmat) :: zmatm
DOUBLE COMPLEX, ALLOCATABLE :: zavec(:,:), zbvec(:,:)
DOUBLE PRECISION :: dznrm2
!
TYPE(spline1d) :: sp1, sp2
INTEGER :: nx, nidbas1, nidbas2, ngauss
INTEGER :: i, j
DOUBLE PRECISION :: a, b, coefx(5)
DOUBLE PRECISION, ALLOCATABLE :: xgrid(:)
DOUBLE PRECISION, DIMENSION(:, :), POINTER :: MassMat
LOGICAL :: periodic1, periodic2
NAMELIST /newrun/ nx, a, b, coefx, nidbas1, nidbas2, periodic1, periodic2
!===========================================================================
! 1.0 Set up grids
!
! Read in data specific to run
!
nx = 8 ! Number of intevals in x
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
periodic1 = .FALSE.
periodic2 = .FALSE.
nidbas1 = 3
nidbas2 = 2
READ(*,newrun)
WRITE(*,newrun)
!
! Define grid/knots
!
ALLOCATE(xgrid(0:nx))
xgrid(0 ) = a
xgrid(nx) = b
CALL meshdist(coefx, xgrid, nx)
WRITE(*,'(a/(10f8.3))') 'XGRID', xgrid(0:nx)
!===========================================================================
! 2.0 Set up splines
!
ngauss = 1 ! Gauss points initialized with set_spline are in fact not used
! for computing cross mass matrix
! First spline set up as for solving a PDE with FEMs
CALL set_spline(nidbas1, ngauss, xgrid, sp1, periodic1)
! Second spline set up as for interpolation
!!$ CALL set_splcoef(nidbas2, xgrid, sp2, periodic2)
CALL set_spline(nidbas2, ngauss, xgrid, sp2, periodic2)
WRITE(*,'(/a,i6,a,i6/(10(f8.3)))') 'KNOTS of spline sp1', LBOUND(sp1%knots), &
& ':',UBOUND(sp1%knots), sp1%knots
WRITE(*,'(/a,i6,a,i6/(10(f8.3)))') 'KNOTS of spline sp2', LBOUND(sp2%knots), &
& ':',UBOUND(sp2%knots), sp2%knots
WRITE(*,'(3(a,i5, 2x))') 'NX =', nx, 'DIM sp1 =', sp1%dim, 'DIM sp2 =', sp2%dim
!===========================================================================
! 3.0 Compute cross mass matrix
!
CALL CompMassMatrix(sp1, sp2, a, b, MassMat)
WRITE(*, "(a)") "Cross-mass matrix between splines sp1 & sp2:"
DO i = 1, SIZE(MassMat, 1)
WRITE(*, "(15f10.5)") (MassMat(i, j), j = 1, MIN(SIZE(MassMat, 2), 15))
END DO
!
! Should equal to 1 for splines i "not close to the boundaries":
! p1 .LT. i .LE. N
!
WRITE(*,'(/a/(15f8.5))') 'Sum of cols * NX', SUM(MassMat,dim=2)*REAL(nx,8)
!===========================================================================
! 3.0 Use DGB matrice
!
!!$ mrows = nx+nidbas1
!!$ ncols = nx+nidbas2
CALL get_dim(sp1, mrows)
CALL get_dim(sp2, ncols)
kl = nidbas1
ku = nidbas2
CALL init(kl, ku, ncols, 1, matm, mrows=mrows)
WRITE(*,'(/a, 2i3)') 'Band matrix:, kl, ku =', kl, ku
!
CALL CompMassMatrix(sp1, sp2, a, b, matm)
!
DO i=1,SIZE(matm%val,1)
WRITE(*,'(15f10.5)') matm%val(i,:)
END DO
!
WRITE(*,'(/a)') 'Full matrix'
ALLOCATE(matfull(mrows,ncols))
matfull = 0.0d0
DO i=1,mrows
CALL getrow(matm, i, matfull(i,:))
WRITE(*,'(15f10.5)') matfull(i,:)
END DO
WRITE(*,'(a,1pe12.4)') 'error =', MAXVAL(ABS(matfull-MassMat))
!
! Check VMX
ALLOCATE(avec(ncols,2))
ALLOCATE(bvec(mrows,2))
avec = 1.0d0
bvec = vmx(matm,avec)*REAL(nx,8)
WRITE(*,'(a)') 'M*a, with a=1'
DO j=1,2
WRITE(*,'(15f8.5)') bvec(:,j)
END DO
!===========================================================================
! 4.0 Test complex version
!
CALL init(kl, ku, ncols, 1, zmatm, mrows=mrows)
CALL CompMassMatrix(sp1, sp2, a, b, zmatm)
ALLOCATE(zavec(ncols,2))
ALLOCATE(zbvec(mrows,2))
zavec = (1.0d0,0.0d0)
zbvec = vmx(zmatm,zavec)*REAL(nx,8)
zbvec = zbvec-bvec
WRITE(*,'(/a)') 'Check complex version'
WRITE(*,'(a,2(1pe12.4))') 'Norm of errors =', &
& (dznrm2(mrows, zbvec(1,j), 1), j=1,2)
zmatm%val = zmatm%val-matm%val
WRITE(*,'(a,1pe12.4)') 'Diff of matrix elements =', MAXVAL(ABS(zmatm%val))
!===========================================================================
! 9.0 Epilogue
!
DEALLOCATE(MassMat)
DEALLOCATE(xgrid)
CALL destroy_sp(sp1)
CALL destroy_sp(sp2)
call destroy(matm)
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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