!{\src2tex{textfont=tt}}
!!****f* ABINIT/ludcmp
!! NAME
!!  ludcmp
!!
!! FUNCTION
!!
!! COPYRIGHT
!!  Copyright (C) 2014 ABINIT group (XG)
!!  This file is distributed under the terms of the
!!  GNU General Public License, see ~abinit/COPYING
!!  or http://www.gnu.org/copyleft/gpl.txt .
!!
!! INPUTS
!!
!! OUTPUT
!!
!! SIDE EFFECTS
!!
!! NOTES
!!
!! PARENTS
!!
!! CHILDREN
!!
!! SOURCE

#if defined HAVE_CONFIG_H
#include "config.h"
#endif

#include "abi_common.h"


SUBROUTINE ludcmp(a,n,np,indx,id,info)

 use defs_basis, only : std_out

!This section has been created automatically by the script Abilint (TD).
!Do not modify the following lines by hand.
#undef ABI_FUNC
#define ABI_FUNC 'ludcmp'
!End of the abilint section

      implicit none

      INTEGER n,np,indx(n),NMAX,id,info
      REAL*8 a(np,np),TINY
      PARAMETER (NMAX=500,TINY=1.0e-20)

!     Given a matrix a(1:n,1:n), with physical dimension np by np, this
!     routine replaces it by the LU decomposition of a rowwise permutation of
!     itself. a and n are input. a is output, arranged as in equation (2.3.14)
!     above; indx(1:n) is an output vector that records the row permutation
!     effected by the partial pivoting; id is output as +- 1 depending on
!     whether the number of row interchanges was even or odd,
!     respectively. This routine is used in combination with lubksb to solve
!     linear equations or invert a matrix.

      INTEGER i,imax,j,k
      REAL*8 aamax,dum,sum,vv(NMAX) 

!      write(std_out,*) 'ENTERING LUDCMP...'
!      write(std_out,*) 'in ludcmp n=',n,' np=',np
!      write(std_out,201) ((a(i,j),j=1,n),i=1,n)
! 201  FORMAT('A in ludcmp ',/,3F16.8,/,3F16.8,/,3F16.8)
      id=1
      info=0
      do i=1,n 
        aamax=0.
        do j=1,n
          if (abs(a(i,j)).gt.aamax) aamax=abs(a(i,j))
        enddo
        if (aamax.eq.0.) then
          write(std_out,*) 'LUDCMP: singular matrix !!!'
          do j=1,3
            write(std_out,*) (a(j,k),k=1,3)
          enddo
          info=1
          return
!          stop 'singular matrix in ludcmp' 
        endif
        vv(i)=1./aamax 
      enddo 
      do j=1,n 
        do i=1,j-1 
          sum=a(i,j)
          do k=1,i-1
            sum=sum-a(i,k)*a(k,j)
          enddo 
          a(i,j)=sum
        enddo 
        aamax=0. 
        do i=j,n 
          sum=a(i,j)
          do k=1,j-1
            sum=sum-a(i,k)*a(k,j)
          enddo 
          a(i,j)=sum
          dum=vv(i)*abs(sum) 
          if (dum.ge.aamax) then 
            imax=i
            aamax=dum
          endif
        enddo 
        if (j.ne.imax)then 
          do  k=1,n 
            dum=a(imax,k)
            a(imax,k)=a(j,k)
            a(j,k)=dum
          enddo 
          id=-id 
          vv(imax)=vv(j) 
        endif
        indx(j)=imax
        if(a(j,j).eq.0.)a(j,j)=TINY
        if(j.ne.n)then 
          dum=1./a(j,j)
          do i=j+1,n
            a(i,j)=a(i,j)*dum
          enddo
        endif
      enddo 
!      write(std_out,*) 'LEAVING LUDCMP...'
      return
END
!!***

!!****f* ABINIT/lubksb
!! NAME
!!  lubksb
!!
!! FUNCTION
!!
!! COPYRIGHT
!!  Copyright (C) 2014 ABINIT group (XG)
!!  This file is distributed under the terms of the
!!  GNU General Public License, see ~abinit/COPYING
!!  or http://www.gnu.org/copyleft/gpl.txt .
!!
!! INPUTS
!!
!! OUTPUT
!!
!! SIDE EFFECTS
!!
!! NOTES
!!
!! PARENTS
!!
!! CHILDREN
!!
!! SOURCE


SUBROUTINE lubksb(a,n,np,indx,b)

 use m_profiling_abi

!This section has been created automatically by the script Abilint (TD).
!Do not modify the following lines by hand.
#undef ABI_FUNC
#define ABI_FUNC 'lubksb'
!End of the abilint section

      IMPLICIT NONE

      INTEGER n,np,indx(n)
      REAL*8 a(np,np),b(n)

!     Solves the set of n linear equations A . X = B. Here a is input, not as
!     the matrix A but rather as its LU decomposition, determined by the
!     routine ludcmp. indx is input as the permutation vector returned by
!     ludcmp. b(1:n) is input as the right-hand side vector B, and returns
!     with the solution vector X. a, n, np, and indx are not modified by this
!     routine and can be left in place for successive calls with different
!     right-hand sides b. This routine takes into account the possibility that
!     b will begin with many zero elements, so it is efficient for use in
!     matrix inversion.

      INTEGER i,ii,j,ll
      REAL*8 sum
!      write(std_out,*) 'ENTERING LUBKSB...'
!      write(std_out,201) ((a(i,j),j=1,n),i=1,n)
! 201  FORMAT('A in lubksb ',/,3F16.8,/,3F16.8,/,3F16.8)

      ii=0
      do i=1,n
        ll=indx(i)
        sum=b(ll)
        b(ll)=b(i)
        if (ii.ne.0)then
          do j=ii,i-1
            sum=sum-a(i,j)*b(j)
          enddo 
        else if (sum.ne.0.) then
          ii=i 
        endif
        b(i)=sum
      enddo 
      do i=n,1,-1
        sum=b(i)
        do j=i+1,n
          sum=sum-a(i,j)*b(j)
        enddo
        b(i)=sum/a(i,i) 
      enddo
!      write(std_out,*) 'LEAVING LUBKSB...'
      return 
END SUBROUTINE LUBKSB
!!***

