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Merge pull request #4 from Panadestein/as

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Faster gradient and laplacian in 3body Jastrow
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Ramon L. PANADES-BARRUETA 2021-01-23 16:02:43 +01:00 committed by GitHub
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8 changed files with 145 additions and 93 deletions
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2
Makefile
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@ -1,4 +1,4 @@
IRPF90 = irpf90 --codelet=factor_een:100000 #-a -d IRPF90 = irpf90 --codelet=jastrow_full:1000 #-s nelec:10 -s nnuc:2 -s ncord:5 #-a -d
FC = ifort -xHost -g -mkl=sequential FC = ifort -xHost -g -mkl=sequential
FCFLAGS= -O2 -ffree-line-length-none -I . FCFLAGS= -O2 -ffree-line-length-none -I .
NINJA = ninja NINJA = ninja

47
README.org
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@ -4,34 +4,35 @@
Original equation: Original equation:
$$ $$
\sum_{i=2}^{Ne} \sum_{j=1}^i \sum_{pkl} \sum_a^{Nn} c_{apkl}\, r_{ij}^k\, ( R_{ia}^l + R_{ja}^l) ( R_{ia} R_{ja})^m \sum_{i=2}^{Ne} \sum_{j=1}^i \sum_{pkl} \sum_a^{Nn} c_{apkl}\, r_{ij}^k\, ( R_{ia}^l + R_{ja}^l) ( R_{ia} R_{ja})^m
$$ $$
Expanding, one obtains: Expanding, one obtains:
$$ $$
\sum_{i=2}^{Ne} \sum_{j=1}^i \sum_{pkl} \sum_a^{Nn} c_{apkl} R_{ia}^{p-k-l}\, r_{ij}^k\, R_{ja}^{p-k+l} + c_{apkl} R_{ia}^{p-k+l}\, r_{ij}^k\, R_{ja}^{p-k-l} \sum_{i=2}^{Ne} \sum_{j=1}^i \sum_{pkl} \sum_a^{Nn} c_{apkl} R_{ia}^{p-k-l}\, r_{ij}^k\, R_{ja}^{p-k+l} + c_{apkl} R_{ia}^{p-k+l}\, r_{ij}^k\, R_{ja}^{p-k-l}
$$ $$
The equation is symmetric if we exchange $i$ and $j$, so we can rewrite The equation is symmetric if we exchange $i$ and $j$, so we can rewrite
$$ $$
\sum_{i=1}^{Ne} \sum_{j=1}^{Ne} \sum_{pkl} \sum_a^{Nn} c_{apkl} R_{ia}^{p-k-l}\, r_{ij}^k\, R_{ja}^{p-k+l} \sum_{i=1}^{Ne} \sum_{j=1}^{Ne} \sum_{pkl} \sum_a^{Nn} c_{apkl} R_{ia}^{p-k-l}\, r_{ij}^k\, R_{ja}^{p-k+l}
$$ $$
If we reshape $R_{ja}^p$ as a matrix $R_{j,al}$ of size If we reshape $R_{ja}^p$ as a matrix $R_{j,al}$ of size
$N_e \times N_n(N_c+1)$, $N_e \times N_n(N_c+1)$,
for every $k$, we can pre-compute the matrix product for every $k$, we can pre-compute the matrix product
$$ $$
C_{i,al}^{k} = \sum_j r_{ij}^k\, R_{i,al} C_{i,al}^{k} = \sum_j r_{ij}^k\, R_{i,al}
$$ $$
which can be computed efficiently with BLAS. which can be computed efficiently with BLAS.
We can express the total Jastrow as: We can express the total Jastrow as:
$$
\sum_{i=1}^{Ne} \sum_{pkl} \sum_a^{Nn}
c_{apkl} R_{ia}^{p-k-l}\, C_{i,a(p-k+l)}^k
$$
$$
\sum_{i=1}^{Ne} \sum_{pkl} \sum_a^{Nn}
c_{apkl} R_{ia}^{p-k-l}\, C_{i,a(p-k+l)}^k
$$

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73
el_nuc_el.irp.f
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@ -7,8 +7,6 @@ BEGIN_PROVIDER [ double precision, factor_een ]
END_DOC END_DOC
integer :: i, j, a, p, k, l, lmax, m, n integer :: i, j, a, p, k, l, lmax, m, n
double precision :: cn, accu2, accu double precision :: cn, accu2, accu
double precision :: f(nnuc,0:ncord-2,0:ncord-2)
double precision :: tmp_c(nelec,nnuc,0:ncord,0:ncord-1)
! factor_een = factor_een_blas ! factor_een = factor_een_blas
! return ! return
@ -35,10 +33,9 @@ BEGIN_PROVIDER [ double precision, factor_een ]
do i = 1, nelec do i = 1, nelec
accu = accu + & accu = accu + &
rescale_een_e(i,j,k) * & rescale_een_e(i,j,k) * &
rescale_een_n(i,a,m) * & rescale_een_n(i,a,m)
rescale_een_n(j,a,m+l)
enddo enddo
accu2 = accu2 + accu accu2 = accu2 + accu*rescale_een_n(j,a,m+l)
enddo enddo
factor_een = factor_een + accu2 * cn factor_een = factor_een + accu2 * cn
enddo enddo
@ -50,6 +47,66 @@ BEGIN_PROVIDER [ double precision, factor_een ]
END_PROVIDER END_PROVIDER
BEGIN_PROVIDER [ double precision, factor_een_deriv_e, (4, nelec) ] BEGIN_PROVIDER [ double precision, factor_een_deriv_e, (4, nelec) ]
implicit none
integer :: i, j, a, p, k, l, lmax, m, n
double precision :: cn, accu, accu2, daccu(1:4), daccu2(1:4)
factor_een_deriv_e(1:4,1:nelec) = 0.0d0
do p = 2, ncord
do k = 0, p - 1
if (k /= 0) then
lmax = p - k
else
lmax = p - k - 2
endif
do l = 0, lmax
if ( iand(p - k - l, 1) == 1) cycle
m = (p - k - l) / 2
do a = 1, nnuc
cn = cord_vect_lkp(l, k, p, typenuc_arr(a))
do j = 1, nelec
accu=0.d0
accu2 = 0.d0
daccu (1:4) = 0.d0
daccu2(1:4) = 0.d0
do i = 1, nelec
accu = accu + &
rescale_een_e(i,j,k) * &
rescale_een_n(i,a,m)
accu2 = accu2 + &
rescale_een_e(i,j,k) * &
rescale_een_n(i,a,m+l)
daccu(1:4) = daccu(1:4) + &
rescale_een_e_deriv_e(1:4,j,i,k) * &
rescale_een_n(i,a,m)
daccu2(1:4) = daccu2(1:4) + &
rescale_een_e_deriv_e(1:4,j,i,k) * &
rescale_een_n(i,a,m+l)
enddo
factor_een_deriv_e(1:4,j) = factor_een_deriv_e(1:4,j) + &
(accu * rescale_een_n_deriv_e(1:4,j,a,m+l) + daccu(1:4) * rescale_een_n(j,a,m+l) + &
daccu2(1:4)* rescale_een_n(j,a,m) + accu2*rescale_een_n_deriv_e(1:4,j,a,m)) * cn
factor_een_deriv_e(4,j) = factor_een_deriv_e(4,j) + 2.d0*( &
daccu (1) * rescale_een_n_deriv_e(1,j,a,m+l) + &
daccu (2) * rescale_een_n_deriv_e(2,j,a,m+l) + &
daccu (3) * rescale_een_n_deriv_e(3,j,a,m+l) + &
daccu2(1) * rescale_een_n_deriv_e(1,j,a,m ) + &
daccu2(2) * rescale_een_n_deriv_e(2,j,a,m ) + &
daccu2(3) * rescale_een_n_deriv_e(3,j,a,m ) )*cn
enddo
enddo
enddo
enddo
enddo
END_PROVIDER
BEGIN_PROVIDER [ double precision, factor_een_deriv_e_ref, (4, nelec) ]
implicit none implicit none
BEGIN_DOC BEGIN_DOC
! Dimensions 1-3 : dx, dy, dz ! Dimensions 1-3 : dx, dy, dz
@ -60,7 +117,7 @@ BEGIN_PROVIDER [ double precision, factor_een_deriv_e, (4, nelec) ]
double precision, dimension(4) :: driam, drjam_cn, drial, drjal, drijk double precision, dimension(4) :: driam, drjam_cn, drial, drjal, drijk
double precision :: cn, v1, v2, d1, d2, lap1, lap2 double precision :: cn, v1, v2, d1, d2, lap1, lap2
factor_een_deriv_e = 0.0d0 factor_een_deriv_e_ref = 0.0d0
do p = 2, ncord do p = 2, ncord
do k = 0 , p - 1 do k = 0 , p - 1
@ -105,14 +162,14 @@ BEGIN_PROVIDER [ double precision, factor_een_deriv_e, (4, nelec) ]
d2 = drjam_cn(ii) * riam d2 = drjam_cn(ii) * riam
lap1 = lap1 + d1 * d2 lap1 = lap1 + d1 * d2
lap2 = lap2 + drijk(ii) * drjal(ii) lap2 = lap2 + drijk(ii) * drjal(ii)
factor_een_deriv_e(ii, j) = factor_een_deriv_e(ii, j) + v1 * d2 + d1 * v2 factor_een_deriv_e_ref(ii, j) = factor_een_deriv_e_ref(ii, j) + v1 * d2 + d1 * v2
enddo enddo
! v(x) u''(x) + 2 * u'(x) v'(x) + u(x) v''(x) ! v(x) u''(x) + 2 * u'(x) v'(x) + u(x) v''(x)
ii = 4 ii = 4
d1 = drijk(ii) * rial + rijk * drjal(ii) + lap2 + lap2 d1 = drijk(ii) * rial + rijk * drjal(ii) + lap2 + lap2
d2 = drjam_cn(ii) * riam d2 = drjam_cn(ii) * riam
factor_een_deriv_e(ii, j) = factor_een_deriv_e(ii, j) + v1 * d2 + d1 * v2 + lap1 + lap1 factor_een_deriv_e_ref(ii, j) = factor_een_deriv_e_ref(ii, j) + v1 * d2 + d1 * v2 + lap1 + lap1
enddo enddo
enddo enddo

109
el_nuc_el_blas.irp.f
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@ -57,70 +57,57 @@ BEGIN_PROVIDER [ double precision, factor_een_deriv_e_blas, (4, nelec) ]
! Dimensions 1-3 : dx, dy, dz ! Dimensions 1-3 : dx, dy, dz
! Dimension 4 : d2x + d2y + d2z ! Dimension 4 : d2x + d2y + d2z
END_DOC END_DOC
integer :: i, ii, j, a, p, k, l, lmax, m
double precision :: riam, rjam_cn, rial, rjal, rijk integer :: i, j, a, p, k, l, lmax, m, n
double precision, dimension(4) :: driam, drjam_cn, drial, drjal, drijk double precision :: cn(nnuc), accu(4)
double precision :: cn, v1, v2, d1, d2, lap1, lap2 double precision :: f(nnuc,0:ncord-2,0:ncord-2)
double precision :: tmp_c(nelec,nnuc,0:ncord,0:ncord-1)
double precision :: dtmp_c(4,nelec,nnuc,0:ncord,0:ncord-1)
factor_een_deriv_e_blas = 0.0d0 factor_een_deriv_e_blas = 0.0d0
do p = 2, ncord ! r_{ij}^k . R_{ja}^l -> tmp_c_{ia}^{kl}
do k = 0 , p - 1 do k=0,ncord-1
if (k /= 0) then call dgemm('N','N', nelec, nnuc*(ncord+1), nelec, 1.d0, &
lmax = p - k rescale_een_e(1,1,k), size(rescale_een_e,1), &
else rescale_een_n(1,1,0), size(rescale_een_n,1), 0.d0, &
lmax = p - k - 2 tmp_c(1,1,0,k), size(tmp_c,1))
endif
do l = 0, lmax
if ( iand(p - k - l, 1) == 1) cycle
m = (p - k - l) / 2
do a = 1, nnuc
cn = cord_vect_lkp(l, k, p, typenuc_arr(a))
do j = 1, nelec
rjal = rescale_een_n(j, a, l)
rjam_cn = rescale_een_n(j, a, m) * cn
do ii = 1, 4
drjal(ii) = rescale_een_n_deriv_e(ii, j, a, l)
drjam_cn(ii) = rescale_een_n_deriv_e(ii, j, a, m) * cn
enddo
do i = 1, nelec
rial = rescale_een_n(i, a, l) + rjal
riam = rescale_een_n(i, a, m)
rijk = rescale_een_e(i, j, k)
do ii = 1, 4
drijk(ii) = rescale_een_e_deriv_e(ii, j, i, k)
enddo
v1 = rijk * rial ! v(x)
v2 = rjam_cn * riam ! u(x)
lap1 = 0.0d0
lap2 = 0.0d0
do ii = 1, 3
d1 = drijk(ii) * rial + rijk * drjal(ii)
d2 = drjam_cn(ii) * riam
lap1 = lap1 + d1 * d2
lap2 = lap2 + drijk(ii) * drjal(ii)
factor_een_deriv_e_blas(ii, j) = factor_een_deriv_e_blas(ii, j) + v1 * d2 + d1 * v2
enddo
! v(x) u''(x) + 2 * u'(x) v'(x) + u(x) v''(x)
ii = 4
d1 = drijk(ii) * rial + rijk * drjal(ii) + lap2 + lap2
d2 = drjam_cn(ii) * riam
factor_een_deriv_e_blas(ii, j) = factor_een_deriv_e_blas(ii, j) + v1 * d2 + d1 * v2 + lap1 + lap1
enddo
enddo
enddo
enddo
enddo
enddo enddo
! dr_{ij}^k . R_{ja}^l -> dtmp_c_{ia}^{kl}
do k=0,ncord-1
call dgemm('N','N', 4*nelec, nnuc*(ncord+1), nelec, 1.d0, &
rescale_een_e_deriv_e(1,1,1,k), 4*size(rescale_een_e_deriv_e,2),&
rescale_een_n(1,1,0), size(rescale_een_n,1), 0.d0, &
dtmp_c(1,1,1,0,k), 4*size(dtmp_c,2))
enddo
do p = 2, ncord
do k = 0, p - 1
m = p-k
if (k > 0) then
lmax = m
else
lmax = m - 2
endif
n = shiftr(m,1)
do l = iand(m, 1), lmax, 2
do a = 1, nnuc
cn(a) = cord_vect_lkp(l, k, p, typenuc_arr(a))
enddo
do a = 1, nnuc
do i=1,nelec
accu(1:4) = rescale_een_n(i,a,n) * dtmp_c(1:4,i,a,n+l,k) &
+ rescale_een_n_deriv_e(1:4,i,a,n) * tmp_c(i,a,n+l,k)
factor_een_deriv_e_blas(1:4,i) = factor_een_deriv_e_blas(1:4,i) + accu(1:4) * cn(a)
enddo
enddo
n = n-1
enddo
enddo
enddo
END_PROVIDER END_PROVIDER

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6
jastrow.irp.f
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@ -2,6 +2,12 @@ program jastrow
implicit none implicit none
print *, 'The total Jastrow factor' print *, 'The total Jastrow factor'
print *, jastrow_full print *, jastrow_full
print *, 'REF'
print *, factor_een_deriv_e_ref
print *, 'X'
print *, factor_een_deriv_e
print *, 'BLAS'
print *, factor_een_deriv_e_blas
!PROVIDE jastrow_full !PROVIDE jastrow_full
end program end program

1
rescale.irp.f
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@ -279,6 +279,7 @@ BEGIN_PROVIDER [double precision, rescale_een_e_deriv_e, (4, nelec, nelec, 0:nco
enddo enddo
END_PROVIDER END_PROVIDER
BEGIN_PROVIDER [double precision, elec_dist_deriv_e, (4, nelec, nelec)] BEGIN_PROVIDER [double precision, elec_dist_deriv_e, (4, nelec, nelec)]
BEGIN_DOC BEGIN_DOC
! Derivative of R_{ij} wrt x ! Derivative of R_{ij} wrt x