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Woodbury 2x2 doc kernel passed test.

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This commit is contained in:
Francois Coppens 2023-03-01 18:12:42 +01:00
parent bb8377edc8
commit 17398059d5
1 changed files with 91 additions and 21 deletions
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110
org/qmckl_sherman_morrison_woodbury.org
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@ -1423,7 +1423,7 @@ with Sherman-Morrison and update splitting. Please look at the performance recco
*** Introduction
The Woodbury 2x2 kernel. It is used to apply two rank-1 updates at once. The formula used in
this algorithm is called the Woodbury Matrix Identity
this algorithm is called the Woodbury Matrix Id
\[
(S + U V)^{-1} = S^{-1} - C B^{-1} D
\]
@ -1485,12 +1485,15 @@ integer function qmckl_woodbury_2x2_doc_f(&
real*8 , intent(inout) :: s_inv(dim * lds)
real*8 , intent(inout) :: determinant
real*8 , dimension(lds, 2) :: Updates
real*8 , dimension(dim, lds) :: Inverse
real*8 , dimension(dim, 2) :: C
real*8 , dimension(2, dim) :: D
real*8 :: denominator, idenominator, update
integer*8 :: i, j, l, row
integer*8 , dimension(2, dim) :: V
integer*8 , dimension(2, 2) :: Id
real*8 , dimension(dim, dim) :: Inverse
real*8 , dimension(dim, 2) :: Updates, C
real*8 , dimension(2, 2) :: D, invD
real*8 , dimension(2, dim) :: E, F
real*8 :: detD, idenominator, update
integer*8 :: i, j, k, l
info = QMCKL_FAILURE
@ -1499,18 +1502,85 @@ integer function qmckl_woodbury_2x2_doc_f(&
return
endif
! Construct V(2, dim) matrix
V = 0
V(1, updates_index(1)) = 1
V(2, updates_index(2)) = 1
! Construct Id(2, 2) matrix
Id = 0
Id(1, 1) = 1
Id(2, 2) = 1
! Convert 'upds' and 's_inv' into the more easily readable Fortran
! matrices 'Updates' and 'Inverse'.
call convert(upds, s_inv, Updates, Inverse, int(2,8), lds, dim)
! Compute C(dim, 2) = Inverse(dim, dim) x Updates(dim, 2)
C = 0
do i = 1, dim
do j = 1, dim
C(i,1) = C(i,1) + Inverse(1,j) * Updates(j,1)
C(i,2) = C(i,1) + Inverse(1,j) * Updates(j,2)
do j = 1, 2
do k = 1, dim
C(i, j) = C(i, j) + Inverse(i, k) * Updates(k, j)
end do
end do
end do
! Construct matrix D(2, 2) := I(2, 2) + V(2, dim) x C(dim, 2)
D = 0
do i = 1, 2
do j = 1, 2
do k = 2, dim
D(i, j) = D(i, j) + V(i, k) * C(k, j)
end do
end do
end do
D = Id + D
! Compute determinant := det(D) explicitly
detD = D(1,1) * D(2,2) - D(1,2) * D(2,1)
! Return early if det(D) is too small
if (abs(detD) < breakdown) return
! Update det(S)
determinant = determinant * detD
! Compute inv(D) explicitly
invD(1,1) = D(2,2)
invD(1,2) = - D(1,2)
invD(2,1) = - D(2,1)
invD(2,2) = D(1,1)
invD = invD / detD
! Compute E(2, dim) := V(2, dim) x Inverse(dim, dim)
E = 0
do i = 1, 2
do j = 1, dim
do k = 1, dim
E(i, j) = E(i, j) + V(i, k) * Inverse(k, j)
end do
end do
end do
! Compute F(2, dim) := invD(2, 2) x E(2, dim)
F = 0
do i = 1, 2
do j = 1, dim
do k = 1, 2
F(i, j) = F(i, j) + invD(i, k) * E(k, j)
end do
end do
end do
! Compute Inverse(dim, dim) := Inverse(dim, dim) - C(dim, 2) x F(2, dim)
do i = 1, dim
do j = 1, dim
do k = 1, 2
Inverse(i, j) = Inverse(i, j) - C(i, k) * F(k, j)
end do
end do
end do
! Copy updated inverse and later updates
! back to s_inv and later_upds
@ -1830,16 +1900,7 @@ qmckl_exit_code qmckl_woodbury_2x2(const qmckl_context context,
determinant);
}
#else
// return qmckl_woodbury_2x2_doc(
// context,
// LDS,
// Dim,
// Updates,
// Updates_index,
// breakdown,
// Slater_inv,
// determinant);
return qmckl_woodbury_2x2_hpc(
return qmckl_woodbury_2x2_doc(
context,
LDS,
Dim,
@ -1848,6 +1909,15 @@ qmckl_exit_code qmckl_woodbury_2x2(const qmckl_context context,
breakdown,
Slater_inv,
determinant);
// return qmckl_woodbury_2x2_hpc(
// context,
// LDS,
// Dim,
// Updates,
// Updates_index,
// breakdown,
// Slater_inv,
// determinant);
#endif
return QMCKL_FAILURE;