Rewrote Cholesky

src/ao_two_e_ints/cholesky.irp.f

@@ -1,10 +1,28 @@
+BEGIN_PROVIDER [ integer, mini_basis_size, (128) ]
+ implicit none
+ BEGIN_DOC
+ ! Size of the minimal basis set per element
+ END_DOC
+
+ mini_basis_size(1:2) = 1
+ mini_basis_size(3:4) = 2
+ mini_basis_size(5:10) = 5
+ mini_basis_size(11:12) = 6
+ mini_basis_size(13:18) = 9
+ mini_basis_size(19:20) = 13
+ mini_basis_size(21:36) = 18
+ mini_basis_size(37:38) = 22
+ mini_basis_size(39:54) = 27
+ mini_basis_size(55:) = 36
+END_PROVIDER
+
  BEGIN_PROVIDER [ integer, cholesky_ao_num_guess ]
  implicit none
  BEGIN_DOC
  ! Number of Cholesky vectors in AO basis
  END_DOC
 
- cholesky_ao_num_guess = ao_num*ao_num 
+ cholesky_ao_num_guess = ao_num*ao_num !sum(mini_basis_size(int(nucl_charge(:))))
 END_PROVIDER
 
  BEGIN_PROVIDER [ integer, cholesky_ao_num ]
@@ -103,7 +121,9 @@ END_PROVIDER
 
  ! Call Lapack
  cholesky_ao_num = cholesky_ao_num_guess
- call pivoted_cholesky(ao_integrals, cholesky_ao_num, ao_cholesky_threshold, ao_num*ao_num, cholesky_ao)
+! call pivoted_cholesky(ao_integrals, cholesky_ao_num, ao_cholesky_threshold, ao_num*ao_num, cholesky_ao)
+
+ call direct_cholesky(ao_integrals, cholesky_ao_num, ao_cholesky_threshold, ao_num*ao_num, cholesky_ao)
  print *, 'Rank  : ', cholesky_ao_num, '(', 100.d0*dble(cholesky_ao_num)/dble(ao_num*ao_num), ' %)'
 
  ! Remove mmap
@@ -131,3 +151,172 @@ BEGIN_PROVIDER [ double precision, cholesky_ao_transp, (cholesky_ao_num, ao_num,
  enddo
 END_PROVIDER
 
+
+subroutine direct_cholesky( A, rank, tau, ndim, L)
+  implicit none
+  integer                          :: ndim
+  integer, intent(inout)           :: rank
+  double precision, intent(inout)  :: A(ndim, ndim)
+  double precision, intent(out)    :: L(ndim, rank)
+  double precision, intent(in)     :: tau
+
+  double precision, parameter :: s = 1.d-2
+  double precision, parameter :: dscale = 1.d0
+
+  double precision, allocatable :: D(:), Delta(:,:)
+  integer, allocatable :: Lset(:), Dset(:)
+
+  integer :: i,j,k,m,p,q, qj, dj
+  integer :: N, np, nq
+
+  double precision :: Dmax, Dmin, Qmax, f
+  allocate( D(ndim), Lset(ndim), Dset(ndim) )
+
+  L = 0.d0
+
+  ! 1.
+  do i=1,ndim
+    D(i) = A(i,i)
+  enddo
+  Dmax = maxval(D)
+!  print *, '# 1. ', D
+!  print *, '# 1. ', Dmax
+
+  ! 2.
+  np=0
+  do p=1,ndim
+    if ( dscale*dscale*Dmax*D(p) > tau*tau ) then
+      np = np+1
+      Lset(np) = p
+    endif
+  enddo
+!  print *, '# 2. ', Lset(:np)
+
+  ! 3.
+  N = 0
+!  print *, '# 3. ', N
+
+  ! 4. 
+  i = 0
+!  print *, '# 4. ', i
+
+  ! 5. 
+  do while (Dmax > tau)
+    ! a.
+    i = i+1
+!    print *, '# 5.a ', i
+
+    ! b.
+    Dmin = max(s*Dmax, tau)
+!    print *, '# 5.b ', Dmin
+
+    ! c.
+    nq=0
+    do q=1,np
+      if ( D(Lset(q)) > Dmin ) then
+        nq = nq+1
+        Dset(nq) = Lset(q)
+      endif
+    enddo
+!    print *, '# 5.c ', Dset(:nq)
+
+    ! d.
+    allocate(Delta(np,nq))
+    do m=1,nq
+      do k=1,np
+        Delta(k,m) = A(Lset(k), Dset(m))
+      enddo
+    enddo
+!    print *, '# 5.d ', Delta
+
+    ! e.
+    do m=1,nq
+      do k=1,np
+        do p=1,N
+          Delta(k,m) = Delta(k,m) - L(Lset(k),p) * L(Dset(m),p)
+        enddo
+      enddo
+    enddo
+!    print *, '# 5.e ', Delta
+
+    ! f.
+    Qmax = D(Dset(1))
+    do q=1,nq
+      Qmax = max(Qmax, D(Dset(q)))
+    enddo
+!    print *, '# 5.f ', Qmax
+
+    ! g.
+    j = 0
+!    print *, '# 5.g ', j
+
+    do while ( (j <= nq).and.(Qmax > Dmin) )
+      ! i.
+      j = j+1
+      rank = N+j
+!      print *, '# 5.h.i ', j, rank
+
+      ! ii.
+      do dj=1,nq
+        qj = Dset(dj)
+        if (D(qj) == Qmax) then
+          exit
+        endif
+      enddo
+!      print *, ' # 5.h.ii ', qj, dj
+
+      ! iii.
+      f = 1.d0/dsqrt(Qmax)
+      do p=1,np
+        L(Lset(p), rank) = Delta(p,dj) * f
+      enddo
+!      print *, ' # 5.h.iii '
+!      do k=1,20
+!        print *, L(k,1:rank)
+!      enddo
+
+      ! iv.
+      do m=1, nq
+        do k=1, np
+          Delta(k,m) = Delta(k,m) - L(Lset(k),rank) * L(Dset(m),rank)
+        enddo
+      enddo
+
+      do k=1, np
+        D(Lset(k)) = D(Lset(k)) - L(Lset(k),rank) * L(Lset(k),rank)
+      enddo
+
+      Qmax = D(Dset(1))
+      do q=1,np
+        Qmax = max(Qmax, D(Lset(q)))
+      enddo
+!      print *, '# 5.h.iv ', Delta
+!      print *, '# 5.h.iv ', D
+!      print *, '# 5.h.iv ', Qmax
+
+    enddo
+
+    deallocate(Delta)
+
+    ! i.
+    N = N+j
+!    print *, '# 5.i ', N
+
+    ! j.
+    Dmax = D(Lset(1))
+    do p=1,np
+      Dmax = max(Dmax, D(Lset(p)))
+    enddo
+!    print *, '# 5.j ', Dmax
+
+    np=0
+    do p=1,ndim
+      if ( dscale*dscale*Dmax*D(p) > tau*tau ) then
+        np = np+1
+        Lset(np) = p
+      endif
+    enddo
+!    print *, '# k. ', Lset(:np)
+  enddo
+
+end