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cholesky.f90
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cholesky.f90
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! CARACAL - Ring polymer molecular dynamics and rate constant calculations
! on black-box generated potential energy surfaces
!
! Copyright (c) 2023 by Julien Steffen ([email protected])
! Stefan Grimme ([email protected]) (QMDFF code)
!
! Permission is hereby granted, free of charge, to any person obtaining a
! copy of this software and associated documentation files (the "Software"),
! to deal in the Software without restriction, including without limitation
! the rights to use, copy, modify, merge, publish, distribute, sublicense,
! and/or sell copies of the Software, and to permit persons to whom the
! Software is furnished to do so, subject to the following conditions:
!
! The above copyright notice and this permission notice shall be included in
! all copies or substantial portions of the Software.
!
! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
! IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
! FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
! THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
! LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
! FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
! DEALINGS IN THE SOFTWARE.
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! subroutine cholesky: Compute the brute-force stabilized
! Cholesky decomposition of a square matrix.
! Parameters:
! SST - The matrix to determine the Cholesky decomposition of
! n - The size of the matrix
! Returns:
! S - The computed Cholesky decomposition
! ---> taken from RPMDrate
!
! part of EVB
!
subroutine cholesky(SST, S, n)
integer, intent(in) :: n
real*8, intent(in) :: SST(n,n)
real*8, intent(out) :: S(n,n)
real*8 :: D(n), L(n,n)
integer i,j,k
D = 0.d0
L = 0.d0
do i = 1,n
L(i,i)=1.
D(i)=SST(i,i)
do j=1,i-1
L(i,j)=SST(i,j);
do k=1,j-1
L(i,j)=L(i,j)-L(i,k)*L(j,k)*D(k)
end do
if (D(j).ne.0.) L(i,j)=L(i,j)/D(j)
end do
do k=1,i-1
D(i)=D(i)-L(i,k)*L(i,k)*D(k)
end do
end do
S=0.
do i=1,n
do j=1,i
if (D(j)>0.) S(i,j)=S(i,j)+L(i,j)*sqrt(D(j))
end do
end do
end subroutine cholesky