Added pivoted cholesky

src/utils/linear_algebra.irp.f

@@ -1983,3 +1983,52 @@ end subroutine diag_nonsym_right
 ! ---
 
 
+subroutine pivoted_cholesky( A, rank, tol, ndim, U)
+!
+! A = U**T * U
+!
+! matrix A is destroyed inside this subroutine
+! Cholesky vectors are stored in U
+! dimension of U: U(1:rank, 1:n)
+! U is allocated inside this subroutine
+! rank is the number of Cholesky vectors depending on tol
+!
+integer :: ndim
+integer, intent(inout)                                        :: rank
+double precision, dimension(ndim, ndim), intent(inout)        :: A
+double precision, dimension(ndim, rank), intent(out)          :: U
+double precision, intent(in)                                  :: tol
+
+integer, dimension(:), allocatable          :: piv
+double precision, dimension(:), allocatable :: work
+character, parameter :: uplo = "U"
+integer :: N, LDA
+integer :: info
+integer :: k, l, rank0
+external :: dpstrf
+
+rank0 = rank
+N = size(A, dim=1)
+LDA = N
+allocate(piv(N))
+allocate(work(2*N))
+call dpstrf(uplo, N, A, LDA, piv, rank, tol, work, info)
+
+if (rank > rank0) then
+  print *, 'Bug: rank > rank0 in pivoted cholesky. Increase rank before calling'
+  stop
+end if
+
+do k = 1, N
+  A(k+1:, k) = 0.00D+0
+end do
+! TODO: It should be possible to use only one vector of size (1:rank) as a buffer
+! to do the swapping in-place
+U = 0.00D+0
+do k = 1, N
+  l = piv(k)
+  U(l, :) = A(1:rank, k)
+end do
+
+end subroutine pivoted_cholesky
+