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lapack_wrap.F90
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!-----------------------------------------------------------------------
! $Id$
!===============================================================================
module lapack_wrap
! Description:
! Wrappers for the band diagonal and tridiagonal direct matrix
! solvers contained in the LAPACK library.
! References:
! LAPACK--Linear Algebra PACKage
! URL: <http://www.netlib.org/lapack/>
!-----------------------------------------------------------------------
use constants_clubb, only: &
fstderr ! Variable(s)
use clubb_precision, only: &
core_rknd, & ! Variable(s)
dp
implicit none
! Simple routines
public :: tridag_solve, band_solve
! Expert routines
public :: tridag_solvex, band_solvex
private :: lapack_isnan
! A best guess for what the precision of a single precision and double
! precision float is in LAPACK. Hopefully this will work more portably on
! architectures like Itanium than the old code -dschanen 11 Aug 2011
integer, parameter, private :: &
sp = kind ( 0.0 )
private ! Set Default Scope
contains
!-----------------------------------------------------------------------
subroutine tridag_solvex( solve_type, ndim, nrhs, &
supd, diag, subd, rhs, &
solution, rcond )
! Description:
! Solves a tridiagonal system of equations (expert routine).
! References:
! <http://www.netlib.org/lapack/single/sgtsvx.f>
! <http://www.netlib.org/lapack/double/dgtsvx.f>
! Notes:
! More expensive than the simple routine, but tridiagonal
! decomposition is still relatively cheap.
!-----------------------------------------------------------------------
use clubb_precision, only: &
core_rknd ! Variable(s)
use error_code, only: &
clubb_at_least_debug_level, & ! Procedure
err_code, & ! Error Indicator
clubb_fatal_error ! Constants
implicit none
! External
external :: &
sgtsvx, & ! Single-prec. General Tridiagonal Solver eXpert
dgtsvx ! Double-prec. General Tridiagonal Solver eXpert
intrinsic :: kind
! Input variables
character(len=*), intent(in) :: &
solve_type ! Used to write a message if this fails
integer, intent(in) :: &
ndim, & ! N-dimension of matrix
nrhs ! # of right hand sides to back subst. after LU-decomp.
! Input/Output variables
real( kind = core_rknd ), intent(inout), dimension(ndim) :: &
diag, & ! Main diagonal
subd, supd ! Sub and super diagonal
real( kind = core_rknd ), intent(inout), dimension(ndim,nrhs) :: &
rhs ! RHS input
! The estimate of the reciprocal of the condition number on the LHS matrix.
! If rcond is < machine precision the matrix is singular to working
! precision, and info == ndim+1. If rcond == 0, then the LHS matrix
! is singular. This condition is indicated by a return code of info > 0.
real( kind = core_rknd ), intent(out) :: rcond
! Output variables
real( kind = core_rknd ), intent(out), dimension(ndim,nrhs) :: &
solution ! Solution
! Local Variables
! These contain the decomposition of the matrix
real( kind = core_rknd ), dimension(ndim-1) :: dlf, duf
real( kind = core_rknd ), dimension(ndim) :: df
real( kind = core_rknd ), dimension(ndim-2) :: du2
integer, dimension(ndim) :: &
ipivot ! Index of pivots done during decomposition
integer, dimension(ndim) :: &
iwork ! `scrap' array
real( kind = core_rknd ), dimension(nrhs) :: &
ferr, & ! Forward error estimate
berr ! Backward error estimate
real( kind = core_rknd ), dimension(3*ndim) :: &
work ! `Scrap' array
integer :: info ! Diagnostic output
integer :: i ! Array index
!-----------------------------------------------------------------------
! *** The LAPACK Routine ***
! SUBROUTINE SGTSVX( FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF,
! $ DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR,
! $ WORK, IWORK, INFO )
!-----------------------------------------------------------------------
if ( kind( diag(1) ) == dp ) then
call dgtsvx( "Not Factored", "No Transpose lhs", ndim, nrhs, &
subd(2:ndim), diag, supd(1:ndim-1), &
dlf, df, duf, du2, ipivot, &
rhs, ndim, solution, ndim, rcond, &
ferr, berr, work, iwork, info )
else if ( kind( diag(1) ) == sp ) then
call sgtsvx( "Not Factored", "No Transpose lhs", ndim, nrhs, &
subd(2:ndim), diag, supd(1:ndim-1), &
dlf, df, duf, du2, ipivot, &
rhs, ndim, solution, ndim, rcond, &
ferr, berr, work, iwork, info )
else
stop "tridag_solvex: Cannot resolve the precision of real datatype"
end if
! Print diagnostics for when ferr is large
if ( clubb_at_least_debug_level( 2 ) .and. any( ferr > 1.e-3_core_rknd ) ) then
write(fstderr,*) "Warning, large error est. for: " // trim( solve_type )
do i = 1, nrhs, 1
write(fstderr,*) "rhs # ", i, "tridag forward error est. =", ferr(i)
write(fstderr,*) "rhs # ", i, "tridag backward error est. =", berr(i)
end do
write(fstderr,'(2(a20,e15.6))') "rcond est. = ", rcond, &
"machine epsilon = ", epsilon( diag(1) )
end if
select case( info )
case( :-1 )
write(fstderr,*) trim( solve_type )// &
"illegal value in argument", -info
err_code = clubb_fatal_error
case( 0 )
! Success!
if ( lapack_isnan( ndim, nrhs, solution ) ) then
err_code = clubb_fatal_error
end if
case( 1: )
if ( info == ndim+1 ) then
write(fstderr,*) trim( solve_type) // &
" Warning: matrix is singular to working precision."
write(fstderr,'(a,e12.5)') &
"Estimate of the reciprocal of the condition number: ", rcond
else
write(fstderr,*) solve_type// &
" singular matrix."
err_code = clubb_fatal_error
end if
end select
return
end subroutine tridag_solvex
!-----------------------------------------------------------------------
subroutine tridag_solve &
( solve_type, ndim, nrhs, &
supd, diag, subd, rhs, &
solution )
! Description:
! Solves a tridiagonal system of equations (simple routine)
! References:
! <http://www.netlib.org/lapack/single/sgtsv.f>
! <http://www.netlib.org/lapack/double/dgtsv.f>
!-----------------------------------------------------------------------
use clubb_precision, only: &
core_rknd ! Variable(s)
use error_code, only: &
err_code, & ! Error Indicator
clubb_fatal_error ! Constants
implicit none
! External
external :: &
sgtsv, & ! Single-prec. General Tridiagonal Solver eXpert
dgtsv ! Double-prec. General Tridiagonal Solver eXpert
intrinsic :: kind
! Input variables
character(len=*), intent(in) :: &
solve_type ! Used to write a message if this fails
integer, intent(in) :: &
ndim, & ! N-dimension of matrix
nrhs ! # of right hand sides to back subst. after LU-decomp.
! Input/Output variables
real( kind = core_rknd ), intent(inout), dimension(ndim) :: &
diag, & ! Main diagonal
subd, supd ! Sub and super diagonal
real( kind = core_rknd ), intent(inout), dimension(ndim,nrhs) :: &
rhs ! RHS input
! Output variables
real( kind = core_rknd ), intent(out), dimension(ndim,nrhs) :: &
solution ! Solution
! Local Variables
real( kind = dp ), dimension(ndim) :: &
subd_dp, supd_dp, diag_dp
real( kind = dp ), dimension(ndim,nrhs) :: &
rhs_dp
integer :: info ! Diagnostic output
!-----------------------------------------------------------------------
! *** The LAPACK Routine ***
! SUBROUTINE DGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
!-----------------------------------------------------------------------
if ( kind( diag(1) ) == dp ) then
call dgtsv( ndim, nrhs, subd(2:ndim), diag, supd(1:ndim-1), &
rhs, ndim, info )
else if ( kind( diag(1) ) == sp ) then
call sgtsv( ndim, nrhs, subd(2:ndim), diag, supd(1:ndim-1), &
rhs, ndim, info )
else
!stop "tridag_solve: Cannot resolve the precision of real datatype"
! Eric Raut Aug 2013: Force double precision
subd_dp = real( subd, kind=dp )
diag_dp = real( diag, kind=dp )
supd_dp = real( supd, kind=dp )
rhs_dp = real( rhs, kind=dp )
call dgtsv( ndim, nrhs, subd_dp(2:ndim), diag_dp, supd_dp(1:ndim-1), &
rhs_dp, ndim, info )
subd = real( subd_dp, kind=core_rknd )
diag = real( diag_dp, kind=core_rknd )
supd = real( supd_dp, kind=core_rknd )
rhs = real( rhs_dp, kind=core_rknd )
end if
select case( info )
case( :-1 )
write(fstderr,*) trim( solve_type )// &
" illegal value in argument", -info
err_code = clubb_fatal_error
solution = -999._core_rknd
case( 0 )
! Success!
if ( lapack_isnan( ndim, nrhs, rhs ) ) then
err_code = clubb_fatal_error
end if
solution = rhs
case( 1: )
write(fstderr,*) trim( solve_type )//" singular matrix."
err_code = clubb_fatal_error
solution = -999._core_rknd
end select
return
end subroutine tridag_solve
!-----------------------------------------------------------------------
subroutine band_solvex( solve_type, nsup, nsub, ndim, nrhs, &
lhs, rhs, solution, rcond )
! Description:
! Restructure and then solve a band diagonal system, with
! diagnostic output
! References:
! <http://www.netlib.org/lapack/single/sgbsvx.f>
! <http://www.netlib.org/lapack/double/dgbsvx.f>
! Notes:
! I found that due to the use of sgbcon/dgbcon it is much
! more expensive to use this on most systems than the simple
! driver. Use this version only if you don't case about compute time.
! Also note that this version equilibrates the lhs and does an iterative
! refinement of the solutions, which results in a slightly different answer
! than the simple driver does. -dschanen 24 Sep 2008
!-----------------------------------------------------------------------
use clubb_precision, only: &
core_rknd ! Variable(s)
use error_code, only: &
clubb_at_least_debug_level, & ! Procedure
err_code, & ! Error Indicator
clubb_fatal_error ! Constants
implicit none
! External
external :: &
sgbsvx, & ! Single-prec. General Band Solver eXpert
dgbsvx ! Double-prec. General Band Solver eXpert
intrinsic :: eoshift, kind, trim
! Input Variables
character(len=*), intent(in) :: solve_type
integer, intent(in) :: &
nsup, & ! Number of superdiagonals
nsub, & ! Number of subdiagonals
ndim, & ! The order of the LHS Matrix, i.e. the # of linear equations
nrhs ! Number of RHS's to back substitute for
real( kind = core_rknd ), dimension(nsup+nsub+1,ndim), intent(inout) :: &
lhs ! Left hand side
real( kind = core_rknd ), dimension(ndim,nrhs), intent(inout) :: &
rhs ! Right hand side(s)
! Output Variables
real( kind = core_rknd ), dimension(ndim,nrhs), intent(out) :: &
solution
! The estimate of the reciprocal condition number of matrix
! after equilibration (if done).
real( kind = core_rknd ), intent(out) :: &
rcond
! Local Variables
! Workspaces
real( kind = core_rknd ), dimension(3*ndim) :: work
integer, dimension(ndim) :: iwork
real( kind = core_rknd ), dimension(2*nsub+nsup+1,ndim) :: &
lulhs ! LU Decomposition of the LHS
integer, dimension(ndim) :: &
ipivot
real( kind = core_rknd ), dimension(nrhs) :: &
ferr, berr ! Forward and backward error estimate
real( kind = core_rknd ), dimension(ndim) :: &
rscale, cscale ! Row and column scale factors for the LHS
integer :: &
info, & ! If this doesn't come back as 0, something went wrong
offset, & ! Loop iterator
imain, & ! Main diagonal of the matrix
i ! Loop iterator
character :: &
equed ! Row equilibration status
!-----------------------------------------------------------------------
! Reorder Matrix to use LAPACK band matrix format (5x6)
! Shift example:
! [ * * lhs(1,1) lhs(1,2) lhs(1,3) lhs(1,4) ] (2)=>
! [ * lhs(2,1) lhs(2,2) lhs(2,3) lhs(2,4) lhs(2,5) ] (1)=>
! [ lhs(3,1) lhs(3,2) lhs(3,3) lhs(3,4) lhs(3,5) lhs(3,6) ]
! <=(1) [ lhs(4,2) lhs(4,3) lhs(4,4) lhs(4,5) lhs(4,6) * ]
! <=(2) [ lhs(5,3) lhs(5,4) lhs(5,5) lhs(5,6) * * ]
! The '*' indicates unreferenced elements.
! For additional bands above and below the main diagonal, the
! shifts to the left or right increases by the distance from the
! main diagonal of the matrix.
!-----------------------------------------------------------------------
imain = nsup + 1
! For the offset, (+) is left, and (-) is right
! Sub diagonals
do offset = 1, nsub, 1
lhs(imain+offset, 1:ndim) &
= eoshift( lhs(imain+offset, 1:ndim), offset )
end do
! Super diagonals
do offset = 1, nsup, 1
lhs(imain-offset, 1:ndim) &
= eoshift( lhs(imain-offset, 1:ndim), -offset )
end do
!-----------------------------------------------------------------------
! *** The LAPACK Routine ***
! SUBROUTINE SGBSVX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
! $ LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
! $ RCOND, FERR, BERR, WORK, IWORK, INFO )
!-----------------------------------------------------------------------
if ( kind( lhs(1,1) ) == dp ) then
call dgbsvx( 'Equilibrate lhs', 'No Transpose lhs', &
ndim, nsub, nsup, nrhs, &
lhs, nsup+nsub+1, lulhs, 2*nsub+nsup+1, &
ipivot, equed, rscale, cscale, &
rhs, ndim, solution, ndim, &
rcond, ferr, berr, work, iwork, info )
else if ( kind( lhs(1,1) ) == sp ) then
call sgbsvx( 'Equilibrate lhs', 'No Transpose lhs', &
ndim, nsub, nsup, nrhs, &
lhs, nsup+nsub+1, lulhs, 2*nsub+nsup+1, &
ipivot, equed, rscale, cscale, &
rhs, ndim, solution, ndim, &
rcond, ferr, berr, work, iwork, info )
else
if ( clubb_at_least_debug_level( 0 ) ) then
write(fstderr,*) "in band_solvex: only single/double precision supported"
stop
end if
end if
! %% debug
! select case ( equed )
! case ('N')
! print *, "No equilib. was required for lhs."
! case ('R')
! print *, "Row equilib. was done on lhs."
! case ('C')
! print *, "Column equilib. was done on lhs."
! case ('B')
! print *, "Row and column equilib. was done on lhs."
! end select
! write(*,'(a,e12.5)') "Row scale : ", rscale
! write(*,'(a,e12.5)') "Column scale: ", cscale
! write(*,'(a,e12.5)') "Estimate of the reciprocal of the "//
! "condition number: ", rcond
! write(*,'(a,e12.5)') "Forward Error Estimate: ", ferr
! write(*,'(a,e12.5)') "Backward Error Estimate: ", berr
! %% end debug
! Diagnostic information
if ( clubb_at_least_debug_level( 2 ) .and. any( ferr > 1.e-3_core_rknd ) ) then
write(fstderr,*) "Warning, large error est. for: " // trim( solve_type )
do i = 1, nrhs, 1
write(fstderr,*) "rhs # ", i, "band_solvex forward error est. =", ferr(i)
write(fstderr,*) "rhs # ", i, "band_solvex backward error est. =", berr(i)
end do
write(fstderr,'(2(a20,e15.6))') "rcond est. = ", rcond, &
"machine epsilon = ", epsilon( lhs(1,1) )
end if
select case( info )
case( :-1 )
write(fstderr,*) "in band_solvex for ", trim( solve_type ), &
": illegal value for argument", -info
write(fstderr,*) "lhs = ", lhs, new_line('c')
write(fstderr,*) "rhs = ", rhs, new_line('c')
err_code = clubb_fatal_error
case( 0 )
! Success!
if ( lapack_isnan( ndim, nrhs, solution ) ) then
err_code = clubb_fatal_error
end if
case( 1: )
if ( info == ndim+1 ) then
write(fstderr,*) trim( solve_type )// &
" Warning: matrix singular to working precision."
write(fstderr,'(a,e12.5)') &
"Estimate of the reciprocal of the"// &
" condition number: ", rcond
else
write(fstderr,*) "in band_solvex for", trim( solve_type ), &
": singular matrix, solution not computed"
write(fstderr,*) "lhs = ", lhs, new_line('c')
write(fstderr,*) "rhs = ", rhs, new_line('c')
err_code = clubb_fatal_error
end if
end select
return
end subroutine band_solvex
!-----------------------------------------------------------------------
subroutine band_solve( solve_type, nsup, nsub, ndim, nrhs, &
lhs, rhs, solution )
! Description:
! Restructure and then solve a band diagonal system
! References:
! <http://www.netlib.org/lapack/single/sgbsv.f>
! <http://www.netlib.org/lapack/double/dgbsv.f>
!-----------------------------------------------------------------------
use clubb_precision, only: &
core_rknd ! Variable(s)
use error_code, only: &
clubb_at_least_debug_level, &
err_code, & ! Error Indicator
clubb_fatal_error ! Constants
implicit none
! External
external :: &
sgbsv, & ! Single-prec. General Band Solver
dgbsv ! Double-prec. General Band Solver
intrinsic :: eoshift, kind, trim
! Input Variables
character(len=*), intent(in) :: solve_type
integer, intent(in) :: &
nsup, & ! Number of superdiagonals
nsub, & ! Number of subdiagonals
ndim, & ! The order of the LHS Matrix, i.e. the # of linear equations
nrhs ! Number of RHS's to solve for
! Note: matrix lhs is intent(in), not intent(inout)
! as in the subroutine band_solvex( )
real( kind = core_rknd ), dimension(nsup+nsub+1,ndim), intent(in) :: &
lhs ! Left hand side
real( kind = core_rknd ), dimension(ndim,nrhs), intent(inout) :: &
rhs ! Right hand side(s)
! Output Variables
real( kind = core_rknd ), dimension(ndim,nrhs), intent(out) :: solution
! Local Variables
! Workspaces
real( kind = core_rknd ), dimension(2*nsub+nsup+1,ndim) :: &
lulhs ! LU Decomposition of the LHS
real( kind = dp ), dimension(2*nsub+nsup+1,ndim) :: &
lulhs_dp
real( kind = dp ), dimension(ndim,nrhs) :: &
rhs_dp
integer, dimension(ndim) :: &
ipivot
integer :: &
info, & ! If this doesn't come back as 0, something went wrong
offset, & ! Loop iterator
imain ! Main diagonal of the matrix
integer :: i, j
!-----------------------------------------------------------------------
! Reorder LU Matrix to use LAPACK band matrix format
!
! Shift example for lulhs matrix given a 5x5 lhs matrix
!
!
! lulhs =
! Columns
! 1 2 3 4 5 6 7
! Rows
! 1 [ 0 0 0 0 lhs(3,1) lhs(4,2) lhs(5,3) ]
! 2 [ 0 0 0 lhs(2,1) lhs(3,2) lhs(4,3) lhs(5,4) ]
! 3 [ 0 0 lhs(1,1) lhs(2,2) lhs(3,3) lhs(4,4) lhs(5,5) ]
! 4 [ 0 0 lhs(1,2) lhs(2,3) lhs(3,4) lhs(4,5) 0 ]
! 5 [ 0 0 lhs(1,3) lhs(2,4) lhs(3,5) 0 0 ]
!
! all lhs lhs lhs lhs lhs
! set to shifted shifted no shifted shifted
! 0 down 2 down 1 shift up 1 up 2
!
! The first nsup columns of lulhs are always set to 0;
! the rest of the columns are set to shifted
! columns of lhs. This can be thought of as taking lhs, never touching the middle column, but
! shifting the columns that are n columns to the left of the middle down by n rows, and then
! shifting the columns that are n columns to the right of the middle up by n rows, finally
! adding nsup columns of zeros onto the left of the array. This results in lulhs.
!-----------------------------------------------------------------------
! Reorder lulhs, omitting the additional 2*nsub bands
! that are used for the LU decomposition of the matrix.
imain = nsub + nsup + 1
! The first nsup rows of lulhs will contain 0s that are end-shifted lhs values. This needs
! to be handled differently so the algorithm to access lhs will not try to use out of bound
! values.
! ... nsup nsup+1 ... imain ...
! \ / \ /
! always | begins with nsup | all lhs values
! 0 0s, and decreases
! by one 0 each row
!
! ... nsup nsup+1 ... imain ...
! lulhs(:,1) = 0 0 0 0 lhs lhs
! lulhs(:,2) = 0 0 0 lhs lhs lhs
!
! Since the first nsup rows are the first rows in lulhs, we're going to access them first to
! avoid out of order memory accesses.
do i = 1, nsup
! Add 0s to first nsup columns, and decreasing number of end-shift affected columns
do j = 1, imain-i
lulhs(j,i) = 0.0_core_rknd
end do
! Copy lhs values into appropriate lulhs spots
do j = imain-i+1, imain+nsub
lulhs(j,i) = lhs(j-nsub,i+j-imain)
end do
end do
! After the first nsup rows are dealt with, the offset lhs values can be copied into lulhs
! until the last nsup rows are reached. This is because the last nsup rows also contain
! end-shifted values, set to 0 in the next loop.
!
! ... nsup nsup+1 ...
! \ /
! always | all lhs values
!
! ... nsup nsup+1 ...
! lulhs(:,nsup+1) = 0 0 lhs lhs
! lulhs(:,ndim-nsub) = 0 0 lhs lhs
!
! For all values not affected by end-shifting
do i = nsup+1, ndim-nsub
! Set first nsup columns to 0
do j = 1, nsub
lulhs(j,i) = 0.0_core_rknd
end do
! Copy lhs values into appropriate lulhs spots
do j = imain-nsub, imain+nsub
lulhs(j,i) = lhs(j-nsub, i+j-imain)
end do
end do
! The last nsup rows of lulhs will contain 0s that are end-shifted lhs values. This needs
! to be handled differently so the algorithm to access lhs will not try to use out of bound
! values.
!
!
! ... nsup nsup+1 ... imain+1 ...
! lulhs(:,ndim-nsub+1) = 0 0 lhs lhs lhs 0
! lulhs(:,ndim) = 0 0 lhs lhs 0 0
!
! | | starts with one 0, then
! always | all lhs values | then increases to nsup 0s
! | | towards ndim
! / \ / \
! ... nsup nsup+1 ... ndim-nsub+1 ... ndim
!
! Finish the lulhs setup by accessing the last values last, keeping memory access ordered
do i = ndim-nsub+1, ndim
! Set first nsup columns to 0
do j = 1, nsub
lulhs(j,i) = 0.0_core_rknd
end do
! Copy lhs values into appropriate lulhs spots
do j = imain-nsup, imain-(i-ndim)
lulhs(j,i) = lhs(j-nsub, i+j-imain)
end do
! Set increasing number of end-shift affected columns to 0
do j = imain-(i-ndim)+1, imain+nsub
lulhs(j,i) = 0.0_core_rknd
end do
end do
!-----------------------------------------------------------------------
! *** LAPACK routine ***
! SUBROUTINE DGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
!-----------------------------------------------------------------------
if ( kind( lhs(1,1) ) == dp ) then
call dgbsv( ndim, nsub, nsup, nrhs, lulhs, nsub*2+nsup+1, &
ipivot, rhs, ndim, info )
else if ( kind( lhs(1,1) ) == sp ) then
call sgbsv( ndim, nsub, nsup, nrhs, lulhs, nsub*2+nsup+1, &
ipivot, rhs, ndim, info )
else
!stop "band_solve: Cannot resolve the precision of real datatype"
! One implication of this is that CLUBB cannot be used with quad
! precision variables without a quad precision band diagonal solver
! Eric Raut Aug 2013: force double precision
lulhs_dp = real( lulhs, kind=dp )
rhs_dp = real( rhs, kind=dp )
call dgbsv( ndim, nsub, nsup, nrhs, lulhs_dp, nsub*2+nsup+1, &
ipivot, rhs_dp, ndim, info )
rhs = real( rhs_dp, kind=core_rknd )
end if
select case( info )
case( :-1 )
write(fstderr,*) "in band_solve for ", trim( solve_type ), &
": illegal value for argument", -info
write(fstderr,*) "lhs = ", lhs, new_line('c')
write(fstderr,*) "rhs = ", rhs, new_line('c')
err_code = clubb_fatal_error
case( 0 )
! Success!
if ( clubb_at_least_debug_level( 1 ) ) then
if ( lapack_isnan( ndim, nrhs, rhs ) ) then
err_code = clubb_fatal_error
end if
end if
solution = rhs
case( 1: )
write(fstderr,*) "in band_solve for ", trim( solve_type ), &
": singular matrix, solution not computed"
write(fstderr,*) "lhs = ", lhs, new_line('c')
write(fstderr,*) "rhs = ", rhs, new_line('c')
err_code = clubb_fatal_error
end select
return
end subroutine band_solve
!-----------------------------------------------------------------------
logical function lapack_isnan( ndim, nrhs, variable )
! Description:
! Check for NaN values in a variable using the LAPACK subroutines
! References:
! <http://www.netlib.org/lapack/single/sisnan.f>
! <http://www.netlib.org/lapack/double/disnan.f>
!-----------------------------------------------------------------------
use clubb_precision, only: &
core_rknd ! Variable(s)
implicit none
#ifdef NO_LAPACK_ISNAN /* Used for older LAPACK libraries that don't have sisnan/disnan */
intrinsic :: any
integer, intent(in) :: &
ndim, & ! Size of variable
nrhs ! Number of right hand sides
real( kind = core_rknd ), dimension(ndim,nrhs), intent(in) :: &
variable ! Variable to check
lapack_isnan = any( variable(:,1:nrhs) /= variable(:,1:nrhs) )
#else
logical, external :: sisnan, disnan
integer, intent(in) :: &
ndim, & ! Size of variable
nrhs ! Number of right hand sides
real( kind = core_rknd ), dimension(ndim,nrhs), intent(in) :: &
variable ! Variable to check
integer :: k, j
! ---- Begin Code ----
lapack_isnan = .false.
if ( kind( variable ) == dp ) then
do k = 1, ndim
do j = 1, nrhs
lapack_isnan = disnan( variable(k,j) )
if ( lapack_isnan ) exit
end do
if ( lapack_isnan ) exit
end do
else if ( kind( variable ) == sp ) then
do k = 1, ndim
do j = 1, nrhs
lapack_isnan = sisnan( variable(k,j) )
if ( lapack_isnan ) exit
end do
if ( lapack_isnan ) exit
end do
else
stop "lapack_isnan: Cannot resolve the precision of real datatype"
end if
#endif /* NO_LAPACK_ISNAN */
return
end function lapack_isnan
end module lapack_wrap