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Merge pull request #4 from Panadestein/as
Faster gradient and laplacian in 3body Jastrow
This commit is contained in:
Ramon L. PANADES-BARRUETA
GitHub
commit
8a884235f0
2
Makefile
2
Makefile
@ -1,4 +1,4 @@
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IRPF90 = irpf90 --codelet=factor_een:100000 #-a -d
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IRPF90 = irpf90 --codelet=jastrow_full:1000 #-s nelec:10 -s nnuc:2 -s ncord:5 #-a -d
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FC = ifort -xHost -g -mkl=sequential
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FCFLAGS= -O2 -ffree-line-length-none -I .
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NINJA = ninja
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47
README.org
47
README.org
@ -4,34 +4,35 @@
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Original equation:
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$$
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\sum_{i=2}^{Ne} \sum_{j=1}^i \sum_{pkl} \sum_a^{Nn} c_{apkl}\, r_{ij}^k\, ( R_{ia}^l + R_{ja}^l) ( R_{ia} R_{ja})^m
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$$
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$$
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\sum_{i=2}^{Ne} \sum_{j=1}^i \sum_{pkl} \sum_a^{Nn} c_{apkl}\, r_{ij}^k\, ( R_{ia}^l + R_{ja}^l) ( R_{ia} R_{ja})^m
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$$
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Expanding, one obtains:
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Expanding, one obtains:
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$$
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\sum_{i=2}^{Ne} \sum_{j=1}^i \sum_{pkl} \sum_a^{Nn} c_{apkl} R_{ia}^{p-k-l}\, r_{ij}^k\, R_{ja}^{p-k+l} + c_{apkl} R_{ia}^{p-k+l}\, r_{ij}^k\, R_{ja}^{p-k-l}
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$$
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$$
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\sum_{i=2}^{Ne} \sum_{j=1}^i \sum_{pkl} \sum_a^{Nn} c_{apkl} R_{ia}^{p-k-l}\, r_{ij}^k\, R_{ja}^{p-k+l} + c_{apkl} R_{ia}^{p-k+l}\, r_{ij}^k\, R_{ja}^{p-k-l}
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$$
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The equation is symmetric if we exchange $i$ and $j$, so we can rewrite
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The equation is symmetric if we exchange $i$ and $j$, so we can rewrite
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$$
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\sum_{i=1}^{Ne} \sum_{j=1}^{Ne} \sum_{pkl} \sum_a^{Nn} c_{apkl} R_{ia}^{p-k-l}\, r_{ij}^k\, R_{ja}^{p-k+l}
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$$
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$$
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\sum_{i=1}^{Ne} \sum_{j=1}^{Ne} \sum_{pkl} \sum_a^{Nn} c_{apkl} R_{ia}^{p-k-l}\, r_{ij}^k\, R_{ja}^{p-k+l}
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$$
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If we reshape $R_{ja}^p$ as a matrix $R_{j,al}$ of size
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$N_e \times N_n(N_c+1)$,
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for every $k$, we can pre-compute the matrix product
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If we reshape $R_{ja}^p$ as a matrix $R_{j,al}$ of size
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$N_e \times N_n(N_c+1)$,
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for every $k$, we can pre-compute the matrix product
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$$
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C_{i,al}^{k} = \sum_j r_{ij}^k\, R_{i,al}
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$$
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which can be computed efficiently with BLAS.
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We can express the total Jastrow as:
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$$
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C_{i,al}^{k} = \sum_j r_{ij}^k\, R_{i,al}
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$$
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which can be computed efficiently with BLAS.
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We can express the total Jastrow as:
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$$
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\sum_{i=1}^{Ne} \sum_{pkl} \sum_a^{Nn}
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c_{apkl} R_{ia}^{p-k-l}\, C_{i,a(p-k+l)}^k
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$$
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$$
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\sum_{i=1}^{Ne} \sum_{pkl} \sum_a^{Nn}
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c_{apkl} R_{ia}^{p-k-l}\, C_{i,a(p-k+l)}^k
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$$
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@ -7,8 +7,6 @@ BEGIN_PROVIDER [ double precision, factor_een ]
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END_DOC
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integer :: i, j, a, p, k, l, lmax, m, n
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double precision :: cn, accu2, accu
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double precision :: f(nnuc,0:ncord-2,0:ncord-2)
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double precision :: tmp_c(nelec,nnuc,0:ncord,0:ncord-1)
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! factor_een = factor_een_blas
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! return
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@ -35,10 +33,9 @@ BEGIN_PROVIDER [ double precision, factor_een ]
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do i = 1, nelec
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accu = accu + &
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rescale_een_e(i,j,k) * &
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rescale_een_n(i,a,m) * &
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rescale_een_n(j,a,m+l)
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rescale_een_n(i,a,m)
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enddo
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accu2 = accu2 + accu
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accu2 = accu2 + accu*rescale_een_n(j,a,m+l)
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enddo
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factor_een = factor_een + accu2 * cn
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enddo
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@ -50,6 +47,66 @@ BEGIN_PROVIDER [ double precision, factor_een ]
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END_PROVIDER
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BEGIN_PROVIDER [ double precision, factor_een_deriv_e, (4, nelec) ]
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implicit none
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integer :: i, j, a, p, k, l, lmax, m, n
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double precision :: cn, accu, accu2, daccu(1:4), daccu2(1:4)
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factor_een_deriv_e(1:4,1:nelec) = 0.0d0
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do p = 2, ncord
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do k = 0, p - 1
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if (k /= 0) then
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lmax = p - k
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else
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lmax = p - k - 2
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endif
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do l = 0, lmax
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if ( iand(p - k - l, 1) == 1) cycle
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m = (p - k - l) / 2
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do a = 1, nnuc
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cn = cord_vect_lkp(l, k, p, typenuc_arr(a))
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do j = 1, nelec
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accu=0.d0
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accu2 = 0.d0
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daccu (1:4) = 0.d0
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daccu2(1:4) = 0.d0
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do i = 1, nelec
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accu = accu + &
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rescale_een_e(i,j,k) * &
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rescale_een_n(i,a,m)
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accu2 = accu2 + &
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rescale_een_e(i,j,k) * &
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rescale_een_n(i,a,m+l)
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daccu(1:4) = daccu(1:4) + &
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rescale_een_e_deriv_e(1:4,j,i,k) * &
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rescale_een_n(i,a,m)
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daccu2(1:4) = daccu2(1:4) + &
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rescale_een_e_deriv_e(1:4,j,i,k) * &
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rescale_een_n(i,a,m+l)
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enddo
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factor_een_deriv_e(1:4,j) = factor_een_deriv_e(1:4,j) + &
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(accu * rescale_een_n_deriv_e(1:4,j,a,m+l) + daccu(1:4) * rescale_een_n(j,a,m+l) + &
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daccu2(1:4)* rescale_een_n(j,a,m) + accu2*rescale_een_n_deriv_e(1:4,j,a,m)) * cn
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factor_een_deriv_e(4,j) = factor_een_deriv_e(4,j) + 2.d0*( &
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daccu (1) * rescale_een_n_deriv_e(1,j,a,m+l) + &
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daccu (2) * rescale_een_n_deriv_e(2,j,a,m+l) + &
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daccu (3) * rescale_een_n_deriv_e(3,j,a,m+l) + &
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daccu2(1) * rescale_een_n_deriv_e(1,j,a,m ) + &
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daccu2(2) * rescale_een_n_deriv_e(2,j,a,m ) + &
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daccu2(3) * rescale_een_n_deriv_e(3,j,a,m ) )*cn
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enddo
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enddo
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enddo
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enddo
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enddo
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END_PROVIDER
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BEGIN_PROVIDER [ double precision, factor_een_deriv_e_ref, (4, nelec) ]
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implicit none
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BEGIN_DOC
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! Dimensions 1-3 : dx, dy, dz
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@ -60,7 +117,7 @@ BEGIN_PROVIDER [ double precision, factor_een_deriv_e, (4, nelec) ]
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double precision, dimension(4) :: driam, drjam_cn, drial, drjal, drijk
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double precision :: cn, v1, v2, d1, d2, lap1, lap2
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factor_een_deriv_e = 0.0d0
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factor_een_deriv_e_ref = 0.0d0
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do p = 2, ncord
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do k = 0 , p - 1
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@ -105,14 +162,14 @@ BEGIN_PROVIDER [ double precision, factor_een_deriv_e, (4, nelec) ]
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d2 = drjam_cn(ii) * riam
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lap1 = lap1 + d1 * d2
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lap2 = lap2 + drijk(ii) * drjal(ii)
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factor_een_deriv_e(ii, j) = factor_een_deriv_e(ii, j) + v1 * d2 + d1 * v2
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factor_een_deriv_e_ref(ii, j) = factor_een_deriv_e_ref(ii, j) + v1 * d2 + d1 * v2
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enddo
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! v(x) u''(x) + 2 * u'(x) v'(x) + u(x) v''(x)
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ii = 4
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d1 = drijk(ii) * rial + rijk * drjal(ii) + lap2 + lap2
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d2 = drjam_cn(ii) * riam
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factor_een_deriv_e(ii, j) = factor_een_deriv_e(ii, j) + v1 * d2 + d1 * v2 + lap1 + lap1
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factor_een_deriv_e_ref(ii, j) = factor_een_deriv_e_ref(ii, j) + v1 * d2 + d1 * v2 + lap1 + lap1
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enddo
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enddo
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@ -57,70 +57,57 @@ BEGIN_PROVIDER [ double precision, factor_een_deriv_e_blas, (4, nelec) ]
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! Dimensions 1-3 : dx, dy, dz
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! Dimension 4 : d2x + d2y + d2z
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END_DOC
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integer :: i, ii, j, a, p, k, l, lmax, m
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double precision :: riam, rjam_cn, rial, rjal, rijk
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double precision, dimension(4) :: driam, drjam_cn, drial, drjal, drijk
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double precision :: cn, v1, v2, d1, d2, lap1, lap2
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integer :: i, j, a, p, k, l, lmax, m, n
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double precision :: cn(nnuc), accu(4)
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double precision :: f(nnuc,0:ncord-2,0:ncord-2)
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double precision :: tmp_c(nelec,nnuc,0:ncord,0:ncord-1)
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double precision :: dtmp_c(4,nelec,nnuc,0:ncord,0:ncord-1)
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factor_een_deriv_e_blas = 0.0d0
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do p = 2, ncord
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do k = 0 , p - 1
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if (k /= 0) then
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lmax = p - k
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else
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lmax = p - k - 2
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endif
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do l = 0, lmax
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if ( iand(p - k - l, 1) == 1) cycle
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m = (p - k - l) / 2
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do a = 1, nnuc
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cn = cord_vect_lkp(l, k, p, typenuc_arr(a))
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do j = 1, nelec
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rjal = rescale_een_n(j, a, l)
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rjam_cn = rescale_een_n(j, a, m) * cn
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do ii = 1, 4
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drjal(ii) = rescale_een_n_deriv_e(ii, j, a, l)
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drjam_cn(ii) = rescale_een_n_deriv_e(ii, j, a, m) * cn
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enddo
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do i = 1, nelec
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rial = rescale_een_n(i, a, l) + rjal
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riam = rescale_een_n(i, a, m)
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rijk = rescale_een_e(i, j, k)
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do ii = 1, 4
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drijk(ii) = rescale_een_e_deriv_e(ii, j, i, k)
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enddo
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v1 = rijk * rial ! v(x)
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v2 = rjam_cn * riam ! u(x)
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lap1 = 0.0d0
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lap2 = 0.0d0
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do ii = 1, 3
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d1 = drijk(ii) * rial + rijk * drjal(ii)
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d2 = drjam_cn(ii) * riam
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lap1 = lap1 + d1 * d2
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lap2 = lap2 + drijk(ii) * drjal(ii)
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factor_een_deriv_e_blas(ii, j) = factor_een_deriv_e_blas(ii, j) + v1 * d2 + d1 * v2
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enddo
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! v(x) u''(x) + 2 * u'(x) v'(x) + u(x) v''(x)
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ii = 4
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d1 = drijk(ii) * rial + rijk * drjal(ii) + lap2 + lap2
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d2 = drjam_cn(ii) * riam
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factor_een_deriv_e_blas(ii, j) = factor_een_deriv_e_blas(ii, j) + v1 * d2 + d1 * v2 + lap1 + lap1
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enddo
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enddo
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enddo
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enddo
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enddo
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! r_{ij}^k . R_{ja}^l -> tmp_c_{ia}^{kl}
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do k=0,ncord-1
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call dgemm('N','N', nelec, nnuc*(ncord+1), nelec, 1.d0, &
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rescale_een_e(1,1,k), size(rescale_een_e,1), &
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rescale_een_n(1,1,0), size(rescale_een_n,1), 0.d0, &
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tmp_c(1,1,0,k), size(tmp_c,1))
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enddo
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! dr_{ij}^k . R_{ja}^l -> dtmp_c_{ia}^{kl}
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do k=0,ncord-1
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call dgemm('N','N', 4*nelec, nnuc*(ncord+1), nelec, 1.d0, &
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rescale_een_e_deriv_e(1,1,1,k), 4*size(rescale_een_e_deriv_e,2),&
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rescale_een_n(1,1,0), size(rescale_een_n,1), 0.d0, &
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dtmp_c(1,1,1,0,k), 4*size(dtmp_c,2))
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enddo
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do p = 2, ncord
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do k = 0, p - 1
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m = p-k
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if (k > 0) then
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lmax = m
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else
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lmax = m - 2
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endif
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n = shiftr(m,1)
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do l = iand(m, 1), lmax, 2
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do a = 1, nnuc
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cn(a) = cord_vect_lkp(l, k, p, typenuc_arr(a))
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enddo
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do a = 1, nnuc
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do i=1,nelec
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accu(1:4) = rescale_een_n(i,a,n) * dtmp_c(1:4,i,a,n+l,k) &
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+ rescale_een_n_deriv_e(1:4,i,a,n) * tmp_c(i,a,n+l,k)
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factor_een_deriv_e_blas(1:4,i) = factor_een_deriv_e_blas(1:4,i) + accu(1:4) * cn(a)
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enddo
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enddo
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n = n-1
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enddo
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enddo
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enddo
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END_PROVIDER
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@ -2,6 +2,12 @@ program jastrow
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implicit none
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print *, 'The total Jastrow factor'
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print *, jastrow_full
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print *, 'REF'
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print *, factor_een_deriv_e_ref
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print *, 'X'
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print *, factor_een_deriv_e
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print *, 'BLAS'
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print *, factor_een_deriv_e_blas
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!PROVIDE jastrow_full
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end program
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@ -279,6 +279,7 @@ BEGIN_PROVIDER [double precision, rescale_een_e_deriv_e, (4, nelec, nelec, 0:nco
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enddo
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END_PROVIDER
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BEGIN_PROVIDER [double precision, elec_dist_deriv_e, (4, nelec, nelec)]
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BEGIN_DOC
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! Derivative of R_{ij} wrt x
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