580 lines
25 KiB
Plaintext
580 lines
25 KiB
Plaintext
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! Copyright © 2022 Dynare Team
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!
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! This file is part of Dynare.
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!
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! Dynare is free software: you can redistribute it and/or modify
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! it under the terms of the GNU General Public License as published by
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! the Free Software Foundation, either version 3 of the License, or
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! (at your option) any later version.
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!
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! Dynare is distributed in the hope that it will be useful,
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! but WITHOUT ANY WARRANTY; without even the implied warranty of
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! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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! GNU General Public License for more details.
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!
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! You should have received a copy of the GNU General Public License
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! along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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! Routines and data structures for multithreading over particles in local_state_space_iteration_3
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module pparticle_3
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use matlab_mex
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use partitions
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implicit none
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type tdata_3
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integer :: n, m, s, q, numthreads, xx_size, uu_size, xxx_size, uuu_size
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real(real64), pointer, contiguous :: yhat3(:,:), &
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&e(:,:), ghx(:,:), ghu(:,:), constant(:), ghxu(:,:), ghxx(:,:), &
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&ghuu(:,:), ghxxx(:,:), ghuuu(:,:), ghxxu(:,:), ghxuu(:,:), ghxss(:,:), &
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&ghuss(:,:), ss(:), y3(:,:)
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real(real64), pointer :: yhat2(:,:), yhat1(:,:), y2(:,:), y1(:,:)
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type(index), pointer, contiguous :: xx_idcs(:), uu_idcs(:), &
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&xxx_idcs(:), uuu_idcs(:)
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end type tdata_3
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type(tdata_3) :: td3
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contains
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! Fills y3 as y3 = ybar + ½ghss + ghx·ŷ+ghu·ε + ½ghxx·ŷ⊗ŷ + ½ghuu·ε⊗ε +
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! ghxu·ŷ⊗ε + (1/6)·ghxxx ŷ⊗ŷ⊗ŷ + (1/6)·ghuuu·ε⊗ε⊗ε +
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! (3/6)·ghxxu·ŷ⊗ŷ⊗ε + (3/6)·ghxuu·ŷ⊗ε⊗ε +
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! (3/6)·ghxss·ŷ + (3/6)·ghuss·ε
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! in td3
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subroutine thread_eval_3(arg) bind(c)
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type(c_ptr), intent(in), value :: arg
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integer, pointer :: ithread
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integer :: is, im, j, k, start, end, q, r
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! Checking that the thread number got passed as argument
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if (.not. c_associated(arg)) then
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call mexErrMsgTxt("No argument was passed to thread_eval_3")
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end if
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call c_f_pointer(arg, ithread)
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! Specifying bounds for the curent thread
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q = td3%s / td3%numthreads
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r = mod(td3%s, td3%numthreads)
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start = (ithread-1)*q+1
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if (ithread < td3%numthreads) then
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end = start+q-1
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else
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end = td3%s
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end if
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do is=start,end
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do im=1,td3%m
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! y3 = ybar + ½ghss
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td3%y3(im,is) = td3%constant(im)
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! y3 += ghx·ŷ+(3/6)·ghxss·ŷ + first n folded indices for ½ghxx·ŷ⊗ŷ
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! + first n folded indices for (1/6)ghxxx·ŷ⊗ŷ⊗ŷ
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do j=1,td3%n
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td3%y3(im,is) = td3%y3(im,is)+&
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&(0.5*td3%ghxss(j,im)+td3%ghx(j,im))*td3%yhat3(j,is)+&
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&(0.5*td3%ghxx(j,im)+(1./6.)*td3%ghxxx(j,im)*td3%yhat3(1, is))*&
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&td3%yhat3(1, is)*td3%yhat3(j,is)
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! y3 += ghxu·ŷ⊗ε
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! + first n*q folded indices of (3/6)·ghxxu·ŷ⊗ŷ⊗ε
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do k=1,td3%q
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td3%y3(im,is) = td3%y3(im,is) + &
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&(td3%ghxu(td3%q*(j-1)+k,im)+&
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&0.5*td3%ghxxu(td3%q*(j-1)+k,im)*td3%yhat3(1, is))*&
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&td3%yhat3(j, is)*td3%e(k, is)
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end do
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end do
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! y3 += ghu·ε+(3/6)·ghuss·ε + first q folded indices of ½ghuu·ε⊗ε
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! + first q folded indices for (1/6)·ghuuu·ε⊗ε⊗ε
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! + first n*q folded indices of (3/6)·ghxuu·ŷ⊗ε⊗ε
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do j=1,td3%q
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td3%y3(im,is) = td3%y3(im,is) + &
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&(0.5*td3%ghuss(j,im)+td3%ghu(j,im))*td3%e(j,is) + &
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&(0.5*td3%ghuu(j,im)+(1./6.)*td3%ghuuu(j,im)*&
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&td3%e(1, is))*td3%e(1, is)*td3%e(j, is)
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do k=1,td3%n
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td3%y3(im,is) = td3%y3(im,is) + &
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&0.5*td3%ghxuu(td3%uu_size*(k-1)+j,im)*&
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&td3%yhat3(k, is)*td3%e(1, is)*td3%e(j, is)
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end do
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end do
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! y3 += remaining ½ghxx·ŷ⊗ŷ terms
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! + the next terms starting from n+1 up to xx_size
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! of (1/6)ghxxx·ŷ⊗ŷ⊗ŷ
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! + remaining terms of (3/6)·ghxxu·ŷ⊗ŷ⊗ε
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do j=td3%n+1,td3%xx_size
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td3%y3(im,is) = td3%y3(im,is) + &
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&(0.5*td3%ghxx(j,im)+(1./6.)*td3%ghxxx(j,im)*td3%yhat3(1, is))*&
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&td3%yhat3(td3%xx_idcs(j)%coor(1), is)*&
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&td3%yhat3(td3%xx_idcs(j)%coor(2), is)
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do k=1,td3%q
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td3%y3(im,is) = td3%y3(im,is)+&
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&0.5*td3%ghxxu(td3%q*(j-1)+k,im)*&
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&td3%yhat3(td3%xx_idcs(j)%coor(1), is)*&
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&td3%yhat3(td3%xx_idcs(j)%coor(2), is)*&
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&td3%e(k, is)
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end do
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end do
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! y3 += remaining ½ghuu·ε⊗ε terms
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! + the next uu_size terms starting from q+1
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! of (1/6)·ghuuu·ε⊗ε⊗ε
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! + remaining terms of (3/6)·ghxuu·ŷ⊗ε⊗ε
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do j=td3%q+1,td3%uu_size
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td3%y3(im,is) = td3%y3(im,is) + &
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&(0.5*td3%ghuu(j,im)+(1./6.)*td3%ghuuu(j,im)*td3%e(1, is))*&
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&td3%e(td3%uu_idcs(j)%coor(1), is)*&
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&td3%e(td3%uu_idcs(j)%coor(2), is)
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do k=1,td3%n
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td3%y3(im,is) = td3%y3(im,is) + &
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&0.5*td3%ghxuu(td3%uu_size*(k-1)+j,im)*&
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&td3%yhat3(k, is)*&
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&td3%e(td3%uu_idcs(j)%coor(1), is)*&
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&td3%e(td3%uu_idcs(j)%coor(2), is)
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end do
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end do
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! y3 += remaining (1/6)·ghxxx·ŷ⊗ŷ⊗ŷ terms
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do j=td3%xx_size+1,td3%xxx_size
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td3%y3(im,is) = td3%y3(im,is)+&
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&(1./6.)*td3%ghxxx(j,im)*&
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&td3%yhat3(td3%xxx_idcs(j)%coor(1), is)*&
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&td3%yhat3(td3%xxx_idcs(j)%coor(2), is)*&
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&td3%yhat3(td3%xxx_idcs(j)%coor(3), is)
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end do
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! y3 += remaining (1/6)ghuuu·ε⊗ε⊗ε terms
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do j=td3%uu_size+1,td3%uuu_size
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td3%y3(im,is) = td3%y3(im,is) + &
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&(1./6.)*td3%ghuuu(j,im)*&
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&td3%e(td3%uuu_idcs(j)%coor(1), is)*&
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&td3%e(td3%uuu_idcs(j)%coor(2), is)*&
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&td3%e(td3%uuu_idcs(j)%coor(3), is)
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end do
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end do
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end do
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end subroutine thread_eval_3
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! Fills y1 and y2 as
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! y1 = ybar + ghx·ŷ1 + ghu·ε
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! y2 = ybar + ½ghss + ghx·ŷ2 + ghu·ε + ½ghxx·ŷ1⊗ŷ1 + ½ghuu·ε⊗ε + ghxu·ŷ1⊗ε
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! y3 = ybar + ghx·ŷ3 + ghu·ε + ghxx·ŷ1⊗ŷ2 + ghuu·ε⊗ε + ghxu·ŷ1⊗ε + ghxu·ŷ2⊗ε
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! + (1/6)·ghxxx·ŷ1⊗ŷ1⊗ŷ1 + (1/6)·ghuuu·ε⊗ε⊗ε + (3/6)·ghxxu·ŷ1⊗ŷ1⊗ε
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! + (3/6)·ghxuu·ŷ1⊗ε⊗ε + (3/6)·ghxss·ŷ1 + (3/6)·ghuss·ε
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! in td3
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subroutine thread_eval_3_pruning(arg) bind(c)
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type(c_ptr), intent(in), value :: arg
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integer, pointer :: ithread
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integer :: is, im, j, k, start, end, q, r
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real(real64) :: x, y
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! Checking that the thread number got passed as argument
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if (.not. c_associated(arg)) then
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call mexErrMsgTxt("No argument was passed to thread_eval")
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end if
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call c_f_pointer(arg, ithread)
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! Specifying bounds for the curent thread
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q = td3%s / td3%numthreads
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r = mod(td3%s, td3%numthreads)
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start = (ithread-1)*q+1
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if (ithread < td3%numthreads) then
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end = start+q-1
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else
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end = td3%s
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end if
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do is=start,end
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do im=1,td3%m
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! y1 = ybar
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! y2 = ybar + ½ghss
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! y3 = ybar
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td3%y1(im,is) = td3%ss(im)
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td3%y2(im,is) = td3%constant(im)
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td3%y3(im,is) = td3%ss(im)
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! y1 += ghx·ŷ1
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! y2 += ghx·ŷ2 + first n folded indices for ½ghxx·ŷ1⊗ŷ1
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! y3 += ghx·ŷ3 +(3/6)·ghxss·ŷ
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! + first n folded indices for ghxx·ŷ1⊗ŷ2
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! + first n folded indices for (1/6)ghxxx·ŷ1⊗ŷ1⊗ŷ1
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do j=1,td3%n
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td3%y1(im,is) = td3%y1(im,is) + td3%ghx(j,im)*td3%yhat1(j,is)
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td3%y2(im,is) = td3%y2(im,is) + td3%ghx(j,im)*td3%yhat2(j,is) +&
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&0.5*td3%ghxx(j,im)*td3%yhat1(1, is)*td3%yhat1(j, is)
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td3%y3(im,is) = td3%y3(im,is) + td3%ghx(j,im)*td3%yhat3(j,is) +&
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&0.5*td3%ghxss(j,im)*td3%yhat1(j,is) +&
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&td3%ghxx(j,im)*td3%yhat1(1, is)*td3%yhat2(j, is)+&
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&(1./6.)*td3%ghxxx(j,im)*td3%yhat1(1, is)*&
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&td3%yhat1(1, is)*td3%yhat1(j,is)
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! y2 += + ghxu·ŷ1⊗ε
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! y3 += + ghxu·ŷ1⊗ε + ghxu·ŷ2⊗ε
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! + first n*q folded indices of (3/6)·ghxxu·ŷ1⊗ŷ1⊗ε
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do k=1,td3%q
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td3%y2(im,is) = td3%y2(im,is)+&
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&td3%ghxu(td3%q*(j-1)+k,im)*&
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&td3%yhat1(j, is)*td3%e(k, is)
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td3%y3(im,is) = td3%y3(im,is)+&
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&td3%ghxu(td3%q*(j-1)+k,im)*&
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&(td3%yhat1(j, is)+td3%yhat2(j, is))*td3%e(k, is)+&
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&0.5*td3%ghxxu(td3%q*(j-1)+k,im)*td3%yhat1(1, is)*&
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&td3%yhat1(j, is)*td3%e(k, is)
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end do
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end do
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! y1 += +ghu·ε
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! y2 += +ghu·ε + first q folded indices for ½ghuu·ε⊗ε
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! y3 += +ghu·ε + first q folded indices for ghuu·ε⊗ε
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! + first n*q folded indices of (3/6)·ghxuu·ŷ1⊗ε⊗ε
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! + first n folded indices of (1/6)·ghuuu·ε⊗ε⊗ε
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do j=1,td3%q
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x = td3%ghu(j,im)*td3%e(j,is)
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y = td3%ghuu(j,im)*td3%e(1, is)*td3%e(j, is)
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td3%y1(im,is) = td3%y1(im,is) + x
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td3%y2(im,is) = td3%y2(im,is) + x + 0.5*y
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td3%y3(im,is) = td3%y3(im,is) + x + y +&
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&td3%ghuss(j,im)*td3%e(j,is)+&
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&(1./6.)*td3%ghuuu(j,im)*td3%e(1, is)*td3%e(1, is)*&
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&td3%e(j, is)
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do k=1,td3%n
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td3%y3(im,is) = td3%y3(im,is) + &
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&0.5*td3%ghxuu(td3%uu_size*(k-1)+j,im)*&
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&td3%yhat1(k, is)*td3%e(1, is)*td3%e(j, is)
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end do
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end do
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! y2 += remaining ½ghxx·ŷ1⊗ŷ1 terms
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! y3 += remaining ghxx·ŷ1⊗ŷ2 terms
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! + the next terms starting from n+1 up to xx_size
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! of (1/6)ghxxx·ŷ1⊗ŷ1⊗ŷ1
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! + remaining terms of (3/6)·ghxxu·ŷ1⊗ŷ1⊗ε
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do j=td3%n+1,td3%xx_size
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td3%y2(im,is) = td3%y2(im,is) + &
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&0.5*td3%ghxx(j,im)*&
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&td3%yhat1(td3%xx_idcs(j)%coor(1), is)*&
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&td3%yhat1(td3%xx_idcs(j)%coor(2), is)
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td3%y3(im,is) = td3%y3(im,is) + &
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&td3%ghxx(j,im)*&
|
|||
|
|
&td3%yhat1(td3%xx_idcs(j)%coor(1), is)*&
|
|||
|
|
&td3%yhat2(td3%xx_idcs(j)%coor(2), is)+&
|
|||
|
|
&(1./6.)*td3%ghxxx(j,im)*td3%yhat1(1, is)*&
|
|||
|
|
&td3%yhat1(td3%xx_idcs(j)%coor(1), is)*&
|
|||
|
|
&td3%yhat1(td3%xx_idcs(j)%coor(2), is)
|
|||
|
|
do k=1,td3%n
|
|||
|
|
td3%y3(im,is) = td3%y3(im,is) + &
|
|||
|
|
&0.5*td3%ghxxu(td3%q*(j-1)+k,im)*&
|
|||
|
|
&td3%yhat1(td3%xx_idcs(j)%coor(1), is)*&
|
|||
|
|
&td3%yhat1(td3%xx_idcs(j)%coor(2), is)*&
|
|||
|
|
&td3%e(k, is)
|
|||
|
|
end do
|
|||
|
|
end do
|
|||
|
|
! y2 += remaining ½ghuu·ε⊗ε terms
|
|||
|
|
! y3 += remaining ghuu·ε⊗ε terms
|
|||
|
|
! + remaining terms of (3/6)·ghxuu·ŷ⊗ε⊗ε
|
|||
|
|
! + the next uu_size terms starting from q+1
|
|||
|
|
! of (1/6)·ghuuu·ε⊗ε⊗ε
|
|||
|
|
do j=td3%q+1,td3%uu_size
|
|||
|
|
x = td3%ghuu(j,im)*&
|
|||
|
|
&td3%e(td3%uu_idcs(j)%coor(1), is)*&
|
|||
|
|
&td3%e(td3%uu_idcs(j)%coor(2), is)
|
|||
|
|
td3%y2(im,is) = td3%y2(im,is)+0.5*x
|
|||
|
|
td3%y3(im,is) = td3%y3(im,is)+x+&
|
|||
|
|
&(1./6.)*td3%ghuuu(j,im)*td3%e(1, is)*&
|
|||
|
|
&td3%e(td3%uu_idcs(j)%coor(1), is)*&
|
|||
|
|
&td3%e(td3%uu_idcs(j)%coor(2), is)
|
|||
|
|
do k=1,td3%n
|
|||
|
|
td3%y3(im,is) = td3%y3(im,is) + &
|
|||
|
|
&0.5*td3%ghxuu(td3%uu_size*(k-1)+j,im)*&
|
|||
|
|
&td3%yhat1(k, is)*&
|
|||
|
|
&td3%e(td3%uu_idcs(j)%coor(1), is)*&
|
|||
|
|
&td3%e(td3%uu_idcs(j)%coor(2), is)
|
|||
|
|
end do
|
|||
|
|
end do
|
|||
|
|
! y3 += remaining (1/6)·ghxxx·ŷ⊗ŷ⊗ŷ terms
|
|||
|
|
do j=td3%xx_size+1,td3%xxx_size
|
|||
|
|
td3%y3(im,is) = td3%y3(im,is)+&
|
|||
|
|
&(1./6.)*td3%ghxxx(j,im)*&
|
|||
|
|
&td3%yhat1(td3%xxx_idcs(j)%coor(1), is)*&
|
|||
|
|
&td3%yhat1(td3%xxx_idcs(j)%coor(2), is)*&
|
|||
|
|
&td3%yhat1(td3%xxx_idcs(j)%coor(3), is)
|
|||
|
|
end do
|
|||
|
|
! y3 += remaining (1/6)ghuuu·ε⊗ε⊗ε terms
|
|||
|
|
do j=td3%uu_size+1,td3%uuu_size
|
|||
|
|
td3%y3(im,is) = td3%y3(im,is) + &
|
|||
|
|
&(1./6.)*td3%ghuuu(j,im)*&
|
|||
|
|
&td3%e(td3%uuu_idcs(j)%coor(1), is)*&
|
|||
|
|
&td3%e(td3%uuu_idcs(j)%coor(2), is)*&
|
|||
|
|
&td3%e(td3%uuu_idcs(j)%coor(3), is)
|
|||
|
|
end do
|
|||
|
|
end do
|
|||
|
|
end do
|
|||
|
|
|
|||
|
|
end subroutine thread_eval_3_pruning
|
|||
|
|
|
|||
|
|
end module pparticle_3
|
|||
|
|
|
|||
|
|
! The code of the local_state_space_iteration_3 routine
|
|||
|
|
! Input:
|
|||
|
|
! prhs[1] yhat3 [double] n×s array, time t particles.
|
|||
|
|
! prhs[2] e [double] q×s array, time t innovations.
|
|||
|
|
! prhs[3] ghx [double] m×n array, first order reduced form.
|
|||
|
|
! prhs[4] ghu [double] m×q array, first order reduced form.
|
|||
|
|
! prhs[5] constant [double] m×1 array, deterministic steady state +
|
|||
|
|
! third order correction for the union of
|
|||
|
|
! the states and observed variables.
|
|||
|
|
! prhs[6] ghxx [double] m×n² array, second order reduced form.
|
|||
|
|
! prhs[7] ghuu [double] m×q² array, second order reduced form.
|
|||
|
|
! prhs[8] ghxu [double] m×nq array, second order reduced form.
|
|||
|
|
! prhs[9] ghxxx [double] m×n array, third order reduced form.
|
|||
|
|
! prhs[10] ghuuu [double] m×q array, third order reduced form.
|
|||
|
|
! prhs[11] ghxxu [double] m×n²q array, third order reduced form.
|
|||
|
|
! prhs[12] ghxuu [double] m×nq² array, third order reduced form.
|
|||
|
|
! prhs[13] ghxss [double] m×n array, third order reduced form.
|
|||
|
|
! prhs[14] ghuss [double] m×q array, third order reduced form.
|
|||
|
|
! prhs[15] yhat2 [double] [OPTIONAL] 2n×s array, time t particles up to 2nd order pruning additional latent variables. The first n rows concern the pruning first-order latent variables, while the last n rows concern the pruning 2nd-order latent variables
|
|||
|
|
! prhs[16] ss [double] [OPTIONAL] m×1 array, steady state for the union of the states and the observed variables (needed for the pruning mode).
|
|||
|
|
! prhs[15 or 17] [double] num of threads
|
|||
|
|
!
|
|||
|
|
! Output:
|
|||
|
|
! plhs[1] y3 [double] m×s array, time t+1 particles.
|
|||
|
|
! plhs[2] y2 [double] 2m×s array, time t+1 particles for the pruning latent variables up to 2nd order. The first m rows concern the pruning first-order latent variables, while the last m rows concern the pruning 2nd-order latent variables
|
|||
|
|
subroutine mexFunction(nlhs, plhs, nrhs, prhs) bind(c, name='mexFunction')
|
|||
|
|
use iso_c_binding
|
|||
|
|
use matlab_mex
|
|||
|
|
use pascal
|
|||
|
|
use partitions
|
|||
|
|
use pthread
|
|||
|
|
use pparticle_3
|
|||
|
|
implicit none
|
|||
|
|
|
|||
|
|
type(c_ptr), dimension(*), intent(in), target :: prhs
|
|||
|
|
type(c_ptr), dimension(*), intent(out) :: plhs
|
|||
|
|
integer(c_int), intent(in), value :: nlhs, nrhs
|
|||
|
|
integer :: n, m, s, q, numthreads
|
|||
|
|
real(real64), pointer, contiguous :: ghx(:,:), ghu(:,:), ghxx(:,:), &
|
|||
|
|
&ghuu(:,:), ghxu(:,:), ghxxx(:,:), ghuuu(:,:), ghxxu(:,:), &
|
|||
|
|
&ghxuu(:,:), ghxss(:,:), ghuss(:,:), yhatlat(:,:), ylat(:,:)
|
|||
|
|
integer :: i, j, k, xx_size, uu_size, xxx_size, uuu_size, rc
|
|||
|
|
character(kind=c_char, len=10) :: arg_nber
|
|||
|
|
type(pascal_triangle) :: p
|
|||
|
|
integer, allocatable :: xx_nbeq(:), xxx_nbeq(:), &
|
|||
|
|
&uu_nbeq(:), uuu_nbeq(:), xx_off(:), uu_off(:), &
|
|||
|
|
&xxx_off(:), uuu_off(:)
|
|||
|
|
type(c_pthread_t), allocatable :: threads(:)
|
|||
|
|
integer, allocatable, target :: routines(:)
|
|||
|
|
|
|||
|
|
! 0. Checking the consistency and validity of input arguments
|
|||
|
|
if (nrhs /= 15 .and. nrhs /= 17) then
|
|||
|
|
call mexErrMsgTxt("Must have exactly 15 inputs or 18 inputs")
|
|||
|
|
end if
|
|||
|
|
|
|||
|
|
if (nlhs > 2) then
|
|||
|
|
call mexErrMsgTxt("Too many output arguments.")
|
|||
|
|
end if
|
|||
|
|
|
|||
|
|
do i=1, max(14, nrhs-1)
|
|||
|
|
if (.not. (c_associated(prhs(i)) .and. mxIsDouble(prhs(i)) .and. &
|
|||
|
|
(.not. mxIsComplex(prhs(i))) .and. (.not. mxIsSparse(prhs(i))))) then
|
|||
|
|
write (arg_nber,"(i2)") i
|
|||
|
|
call mexErrMsgTxt("Argument " // trim(arg_nber) // " should be a real dense matrix")
|
|||
|
|
end if
|
|||
|
|
end do
|
|||
|
|
|
|||
|
|
i = max(15,nrhs)
|
|||
|
|
if (.not. (c_associated(prhs(i)) .and. mxIsScalar(prhs(i)) .and. &
|
|||
|
|
mxIsNumeric(prhs(i)))) then
|
|||
|
|
write (arg_nber,"(i2)") i
|
|||
|
|
call mexErrMsgTxt("Argument " // trim(arg_nber) // " should be a numeric scalar")
|
|||
|
|
end if
|
|||
|
|
numthreads = int(mxGetScalar(prhs(i)))
|
|||
|
|
if (numthreads <= 0) then
|
|||
|
|
write (arg_nber,"(i2)") i
|
|||
|
|
call mexErrMsgTxt("Argument " // trim(arg_nber) // " should be a positive integer")
|
|||
|
|
end if
|
|||
|
|
td3%numthreads = numthreads
|
|||
|
|
|
|||
|
|
n = int(mxGetM(prhs(1))) ! Number of states.
|
|||
|
|
s = int(mxGetN(prhs(1))) ! Number of particles.
|
|||
|
|
q = int(mxGetM(prhs(2))) ! Number of innovations.
|
|||
|
|
m = int(mxGetM(prhs(3))) ! Number of elements in the union of states and observed variables.
|
|||
|
|
td3%n = n
|
|||
|
|
td3%s = s
|
|||
|
|
td3%q = q
|
|||
|
|
td3%m = m
|
|||
|
|
|
|||
|
|
if ((s /= mxGetN(prhs(2))) & ! Number of columns for epsilon
|
|||
|
|
&.or. (n /= mxGetN(prhs(3))) & ! Number of columns for ghx
|
|||
|
|
&.or. (m /= mxGetM(prhs(4))) & ! Number of rows for ghu
|
|||
|
|
&.or. (q /= mxGetN(prhs(4))) & ! Number of columns for ghu
|
|||
|
|
&.or. (m /= mxGetM(prhs(5))) & ! Number of rows for 2nd order constant correction + deterministic steady state
|
|||
|
|
&.or. (m /= mxGetM(prhs(6))) & ! Number of rows for ghxx
|
|||
|
|
&.or. (n*n /= mxGetN(prhs(6))) & ! Number of columns for ghxx
|
|||
|
|
&.or. (m /= mxGetM(prhs(7))) & ! Number of rows for ghuu
|
|||
|
|
&.or. (q*q /= mxGetN(prhs(7))) & ! Number of columns for ghuu
|
|||
|
|
&.or. (m /= mxGetM(prhs(8))) & ! Number of rows for ghxu
|
|||
|
|
&.or. (n*q /= mxGetN(prhs(8))) & ! Number of columns for ghxu
|
|||
|
|
&.or. (m /= mxGetM(prhs(9))) & ! Number of rows for ghxxx
|
|||
|
|
&.or. (n*n*n /= mxGetN(prhs(9))) & ! Number of columns for ghxxx
|
|||
|
|
&.or. (m /= mxGetM(prhs(10))) & ! Number of rows for ghuuu
|
|||
|
|
&.or. (q*q*q /= mxGetN(prhs(10))) & ! Number of columns for ghuuu
|
|||
|
|
&.or. (m /= mxGetM(prhs(11))) & ! Number of rows for ghxxu
|
|||
|
|
&.or. (n*n*q /= mxGetN(prhs(11))) & ! Number of columns for ghxxu
|
|||
|
|
&.or. (m /= mxGetM(prhs(12))) & ! Number of rows for ghxuu
|
|||
|
|
&.or. (n*q*q /= mxGetN(prhs(12))) & ! Number of columns for ghxuu
|
|||
|
|
&.or. (m /= mxGetM(prhs(13))) & ! Number of rows for ghxss
|
|||
|
|
&.or. (n /= mxGetN(prhs(13))) & ! Number of columns for ghxss
|
|||
|
|
&.or. (m /= mxGetM(prhs(14))) & ! Number of rows for ghuss
|
|||
|
|
&.or. (q /= mxGetN(prhs(14))) & ! Number of columns for ghuss
|
|||
|
|
&.or. ((nrhs == 17) & ! With pruning optional inputs
|
|||
|
|
&.and. ((2*n /= mxGetM(prhs(15))) & ! Number of rows for yhat2
|
|||
|
|
&.or. (s /= mxGetN(prhs(15))) & ! Number of columns for yhat2
|
|||
|
|
&.or. (m /= mxGetM(prhs(16)))))) then ! Number of rows for ss
|
|||
|
|
! &) then
|
|||
|
|
call mexErrMsgTxt("Input dimension mismatch")
|
|||
|
|
end if
|
|||
|
|
|
|||
|
|
! 1. Getting relevant information to take advantage of symmetries
|
|||
|
|
! There are symmetries in the ghxx, ghuu, ghxxx, ghuuu, ghxxu and ghxuu terms
|
|||
|
|
! that we may exploit to avoid unnecessarily repeating operations in matrix-vector
|
|||
|
|
! multiplications, e.g in ghxx·ŷ⊗ŷ.
|
|||
|
|
! In matrix-vector multiplications such as ghxx·ŷ⊗ŷ, we loop through all the folded offsets
|
|||
|
|
! and thus need for each one of them :
|
|||
|
|
! (i) the corresponding folded index, e.g (α₁,α₂), α₁≤α₂ for ghxx
|
|||
|
|
! (i) the corresponding offset in the unfolded matrix
|
|||
|
|
! (ii) the corresponding number of equivalent unfolded indices (1 if α₁=α₂, 2 otherwise)
|
|||
|
|
! It is better to compute these beforehand as it avoids repeating the calculation for
|
|||
|
|
! each particle. The `folded_offset_loop` routine carries out this operation.
|
|||
|
|
|
|||
|
|
p = pascal_triangle(max(n,q)+3-1)
|
|||
|
|
xx_size = get(2,n+2-1,p)
|
|||
|
|
uu_size = get(2,q+2-1,p)
|
|||
|
|
xxx_size = get(3,n+3-1,p)
|
|||
|
|
uuu_size = get(3,q+3-1,p)
|
|||
|
|
|
|||
|
|
td3%xx_size = xx_size
|
|||
|
|
td3%uu_size = uu_size
|
|||
|
|
td3%xxx_size = xxx_size
|
|||
|
|
td3%uuu_size = uuu_size
|
|||
|
|
|
|||
|
|
allocate(td3%xx_idcs(xx_size), td3%uu_idcs(uu_size), &
|
|||
|
|
&td3%xxx_idcs(xxx_size), td3%uuu_idcs(uuu_size), &
|
|||
|
|
&xx_off(xx_size), uu_off(uu_size), &
|
|||
|
|
&xxx_off(xxx_size), uuu_off(uuu_size), &
|
|||
|
|
&xx_nbeq(xx_size), uu_nbeq(uu_size), &
|
|||
|
|
&xxx_nbeq(xxx_size), uuu_nbeq(uuu_size))
|
|||
|
|
|
|||
|
|
call folded_offset_loop(td3%xx_idcs, xx_nbeq, &
|
|||
|
|
&xx_off, n, 2, p)
|
|||
|
|
call folded_offset_loop(td3%uu_idcs, uu_nbeq, &
|
|||
|
|
&uu_off, q, 2, p)
|
|||
|
|
call folded_offset_loop(td3%xxx_idcs, xxx_nbeq, &
|
|||
|
|
&xxx_off, n, 3, p)
|
|||
|
|
call folded_offset_loop(td3%uuu_idcs, uuu_nbeq, &
|
|||
|
|
&uuu_off, q, 3, p)
|
|||
|
|
|
|||
|
|
! 1. Storing the relevant input variables in Fortran
|
|||
|
|
td3%yhat3(1:n,1:s) => mxGetPr(prhs(1))
|
|||
|
|
td3%e(1:q,1:s) => mxGetPr(prhs(2))
|
|||
|
|
ghx(1:m,1:n) => mxGetPr(prhs(3))
|
|||
|
|
ghu(1:m,1:q) => mxGetPr(prhs(4))
|
|||
|
|
td3%constant => mxGetPr(prhs(5))
|
|||
|
|
ghxx(1:m,1:n*n) => mxGetPr(prhs(6))
|
|||
|
|
ghuu(1:m,1:q*q) => mxGetPr(prhs(7))
|
|||
|
|
ghxu(1:m,1:n*q) => mxGetPr(prhs(8))
|
|||
|
|
ghxxx(1:m,1:n*n*n) => mxGetPr(prhs(9))
|
|||
|
|
ghuuu(1:m,1:q*q*q) => mxGetPr(prhs(10))
|
|||
|
|
ghxxu(1:m,1:n*n*q) => mxGetPr(prhs(11))
|
|||
|
|
ghxuu(1:m,1:n*q*q) => mxGetPr(prhs(12))
|
|||
|
|
ghxss(1:m,1:n) => mxGetPr(prhs(13))
|
|||
|
|
ghuss(1:m,1:q) => mxGetPr(prhs(14))
|
|||
|
|
if (nrhs == 17) then
|
|||
|
|
yhatlat(1:2*n,1:s) => mxGetPr(prhs(15))
|
|||
|
|
td3%yhat1 => yhatlat(1:n,1:s)
|
|||
|
|
td3%yhat2 => yhatlat(n+1:2*n,1:s)
|
|||
|
|
td3%ss => mxGetPr(prhs(16))
|
|||
|
|
end if
|
|||
|
|
|
|||
|
|
! Getting a transposed folded copy of the unfolded tensors
|
|||
|
|
! for future loops to be more efficient
|
|||
|
|
allocate(td3%ghx(n,m), td3%ghu(q,m),&
|
|||
|
|
&td3%ghuu(uu_size,m), td3%ghxu(n*q,m), &
|
|||
|
|
&td3%ghxx(xx_size,m), &
|
|||
|
|
&td3%ghxxx(xxx_size,m), td3%ghuuu(uuu_size,m), &
|
|||
|
|
&td3%ghxxu(xx_size*q,m), td3%ghxuu(n*uu_size,m), &
|
|||
|
|
&td3%ghxss(n,m), td3%ghuss(q,m))
|
|||
|
|
do i=1,m
|
|||
|
|
do j=1,n
|
|||
|
|
td3%ghx(j,i) = ghx(i,j)
|
|||
|
|
td3%ghxss(j,i) = ghxss(i,j)
|
|||
|
|
td3%ghxx(j,i) = xx_nbeq(j)*ghxx(i,xx_off(j))
|
|||
|
|
td3%ghxxx(j,i) = xxx_nbeq(j)*ghxxx(i,xxx_off(j))
|
|||
|
|
do k=1,q
|
|||
|
|
td3%ghxu(q*(j-1)+k,i) = ghxu(i,q*(j-1)+k)
|
|||
|
|
td3%ghxxu(q*(j-1)+k,i) = xx_nbeq(j)*ghxxu(i,q*(xx_off(j)-1)+k)
|
|||
|
|
end do
|
|||
|
|
end do
|
|||
|
|
do j=n+1,xx_size
|
|||
|
|
td3%ghxx(j,i) = xx_nbeq(j)*ghxx(i,xx_off(j))
|
|||
|
|
td3%ghxxx(j,i) = xxx_nbeq(j)*ghxxx(i,xxx_off(j))
|
|||
|
|
do k=1,q
|
|||
|
|
td3%ghxxu(q*(j-1)+k,i) = xx_nbeq(j)*ghxxu(i,q*(xx_off(j)-1)+k)
|
|||
|
|
end do
|
|||
|
|
end do
|
|||
|
|
do j=xx_size+1,xxx_size
|
|||
|
|
td3%ghxxx(j,i) = xxx_nbeq(j)*ghxxx(i,xxx_off(j))
|
|||
|
|
end do
|
|||
|
|
do j=1,q
|
|||
|
|
td3%ghu(j,i) = ghu(i,j)
|
|||
|
|
td3%ghuss(j,i) = ghuss(i,j)
|
|||
|
|
td3%ghuu(j,i) = uu_nbeq(j)*ghuu(i,uu_off(j))
|
|||
|
|
td3%ghuuu(j,i) = uuu_nbeq(j)*ghuuu(i,uuu_off(j))
|
|||
|
|
do k=1,n
|
|||
|
|
td3%ghxuu(uu_size*(k-1)+j,i) = uu_nbeq(j)*ghxuu(i,q*q*(k-1)+uu_off(j))
|
|||
|
|
end do
|
|||
|
|
end do
|
|||
|
|
do j=q+1,uu_size
|
|||
|
|
td3%ghuu(j,i) = uu_nbeq(j)*ghuu(i,uu_off(j))
|
|||
|
|
td3%ghuuu(j,i) = uuu_nbeq(j)*ghuuu(i,uuu_off(j))
|
|||
|
|
do k=1,n
|
|||
|
|
td3%ghxuu(uu_size*(k-1)+j,i) = uu_nbeq(j)*ghxuu(i,q*q*(k-1)+uu_off(j))
|
|||
|
|
end do
|
|||
|
|
end do
|
|||
|
|
do j=uu_size+1,uuu_size
|
|||
|
|
td3%ghuuu(j,i) = uuu_nbeq(j)*ghuuu(i,uuu_off(j))
|
|||
|
|
end do
|
|||
|
|
end do
|
|||
|
|
|
|||
|
|
! 3. Implementing the calculations:
|
|||
|
|
|
|||
|
|
plhs(1) = mxCreateDoubleMatrix(int(m, mwSize), int(s, mwSize), mxREAL)
|
|||
|
|
td3%y3(1:m,1:s) => mxGetPr(plhs(1))
|
|||
|
|
if (nrhs == 17) then
|
|||
|
|
plhs(2) = mxCreateDoubleMatrix(int(2*m, mwSize), int(s, mwSize), mxREAL)
|
|||
|
|
ylat(1:2*m,1:s) => mxGetPr(plhs(2))
|
|||
|
|
td3%y1 => ylat(1:m,1:s)
|
|||
|
|
td3%y2 => ylat(m+1:2*m,1:s)
|
|||
|
|
end if
|
|||
|
|
|
|||
|
|
allocate(threads(numthreads), routines(numthreads))
|
|||
|
|
routines = [ (i, i = 1, numthreads) ]
|
|||
|
|
|
|||
|
|
if (numthreads == 1) then
|
|||
|
|
if (nrhs == 17) then
|
|||
|
|
call thread_eval_3_pruning(c_loc(routines(1)))
|
|||
|
|
else
|
|||
|
|
call thread_eval_3(c_loc(routines(1)))
|
|||
|
|
end if
|
|||
|
|
else
|
|||
|
|
! Creating the threads
|
|||
|
|
if (nrhs == 17) then
|
|||
|
|
do i = 1, numthreads
|
|||
|
|
rc = c_pthread_create(threads(i), c_null_ptr, c_funloc(thread_eval_3_pruning), c_loc(routines(i)))
|
|||
|
|
end do
|
|||
|
|
else
|
|||
|
|
do i = 1, numthreads
|
|||
|
|
rc = c_pthread_create(threads(i), c_null_ptr, c_funloc(thread_eval_3), c_loc(routines(i)))
|
|||
|
|
end do
|
|||
|
|
end if
|
|||
|
|
|
|||
|
|
! Joining the threads
|
|||
|
|
do i = 1, numthreads
|
|||
|
|
rc = c_pthread_join(threads(i), c_loc(routines(i)))
|
|||
|
|
end do
|
|||
|
|
end if
|
|||
|
|
|
|||
|
|
end subroutine mexFunction
|