New MEX for solving discrete Lyapunov equations with doubling algorithm

This is a Fortran 2008 rewrite of disclyap_fast.m.

Closes: #1737
parent 3f53a949
Pipeline #4088 passed with stages
in 97 minutes and 10 seconds
......@@ -86,7 +86,7 @@ function pruned_state_space = pruned_state_space_system(M, options, dr, indy, nl
% This function calls
% * allVL1.m
% * commutation.m
% * disclyap_fast.m
% * disclyap_fast (MEX)
% * duplication.m
% * lyapunov_symm.m
% * prodmom
......
mex_PROGRAMS = disclyap_fast
nodist_disclyap_fast_SOURCES = disclyap_fast.f08 matlab_mex.F08 blas_lapack.F08
BUILT_SOURCES = $(nodist_disclyap_fast_SOURCES)
CLEANFILES = $(nodist_disclyap_fast_SOURCES)
disclyap_fast.o : matlab_mex.mod lapack.mod
%.f08: $(top_srcdir)/../../sources/disclyap_fast/%.f08
$(LN_S) -f $< $@
ACLOCAL_AMFLAGS = -I ../../../m4
SUBDIRS = mjdgges kronecker bytecode block_kalman_filter sobol perfect_foresight_problem num_procs
SUBDIRS = mjdgges kronecker bytecode block_kalman_filter sobol perfect_foresight_problem num_procs disclyap_fast
# libdynare++ must come before gensylv, k_order_perturbation, dynare_simul_
if ENABLE_MEX_DYNAREPLUSPLUS
......
......@@ -172,6 +172,7 @@ AC_CONFIG_FILES([Makefile
sobol/Makefile
local_state_space_iterations/Makefile
perfect_foresight_problem/Makefile
num_procs/Makefile])
num_procs/Makefile
disclyap_fast/Makefile])
AC_OUTPUT
include ../mex.am
include ../../disclyap_fast.am
ACLOCAL_AMFLAGS = -I ../../../m4
SUBDIRS = mjdgges kronecker bytecode block_kalman_filter sobol perfect_foresight_problem num_procs
SUBDIRS = mjdgges kronecker bytecode block_kalman_filter sobol perfect_foresight_problem num_procs disclyap_fast
# libdynare++ must come before gensylv, k_order_perturbation, dynare_simul_
if ENABLE_MEX_DYNAREPLUSPLUS
......
......@@ -137,6 +137,7 @@ AC_CONFIG_FILES([Makefile
sobol/Makefile
local_state_space_iterations/Makefile
perfect_foresight_problem/Makefile
num_procs/Makefile])
num_procs/Makefile
disclyap_fast/Makefile])
AC_OUTPUT
EXEEXT = .mex
include ../mex.am
include ../../disclyap_fast.am
......@@ -18,7 +18,8 @@ EXTRA_DIST = \
gensylv \
dynare_simul_ \
perfect_foresight_problem \
num_procs
num_procs \
disclyap_fast
clean-local:
rm -rf `find mex/sources -name *.o`
......
! Solve the discrete Lyapunov Equation (X = G·X·Gᵀ + V) using the Doubling Algorithm
!
! Syntax:
! [X, error_flag] = disclyap_fast(G, V, tol, check_flag)
!
! Inputs:
! G [double] (n×n) first input matrix
! V [double] (n×n) second input matrix
! tol [double] scalar, tolerance criterion
! check_flag [boolean] if true: check positive-definiteness (optional)
! max_iter [integer] scalar, maximum number of iterations (optional)
!
! Outputs:
! X [double] solution matrix
! error_flag [boolean] true if solution is found, false otherwise (optional)
!
! If check_flag is true, then the code will check if the resulting X
! is positive definite and generate an error message if it is not.
!
! This is a Fortran translation of a code originally written by Joe Pearlman
! and Alejandro Justiniano.
! Copyright © 2020 Dynare Team
!
! This file is part of Dynare.
!
! Dynare is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! Dynare is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with Dynare. If not, see <http://www.gnu.org/licenses/>.
subroutine mexFunction(nlhs, plhs, nrhs, prhs) bind(c, name='mexFunction')
use iso_fortran_env
use ieee_arithmetic
use matlab_mex
use lapack
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(c_size_t) :: n
real(real64) :: tol, max_iter
logical :: check_flag
real(real64), dimension(:, :), allocatable :: P0, P1, A0, A1, Ptmp
real(real64) :: matd
integer :: iter
integer (blint) :: n_bl
real(real64), dimension(:, :), pointer :: X
if (nlhs < 1 .or. nlhs > 2 .or. nrhs < 3 .or. nrhs > 5) then
call mexErrMsgTxt("disclyap_fast: requires between 3 and 5 input arguments, and 1 or 2 output arguments")
return
end if
n = mxGetM(prhs(1))
if (.not. mxIsDouble(prhs(1)) .or. mxIsComplex(prhs(1)) &
.or. .not. mxIsDouble(prhs(2)) .or. mxIsComplex(prhs(2)) &
.or. mxGetN(prhs(1)) /= n .or. mxGetM(prhs(2)) /= n .or. mxGetN(prhs(2)) /= n) then
call mexErrMsgTxt("disclyap_fast: first two arguments should be real matrices of the same dimension")
return
end if
if (.not. (mxIsScalar(prhs(3)) .and. mxIsNumeric(prhs(3)))) then
call mexErrMsgTxt("disclyap_fast: third argument (tol) should be a numeric scalar")
return
end if
tol = mxGetScalar(prhs(3))
if (nrhs >= 4) then
if (.not. (mxIsLogicalScalar(prhs(4)))) then
call mexErrMsgTxt("disclyap_fast: fourth argument (check_flag) should be a logical scalar")
return
end if
check_flag = mxGetScalar(prhs(4)) == 1_c_double
else
check_flag = .false.
end if
if (nrhs >= 5) then
if (.not. (mxIsScalar(prhs(5)) .and. mxIsNumeric(prhs(5)))) then
call mexErrMsgTxt("disclyap_fast: fifth argument (max_iter) should be a numeric scalar")
return
end if
max_iter = int(mxGetScalar(prhs(5)))
else
max_iter = 2000
end if
! Allocate and initialize temporary variables
allocate(P0(n,n), P1(n,n), A0(n,n), A1(n,n), Ptmp(n,n))
associate (G => mxGetPr(prhs(1)), V => mxGetPr(prhs(2)))
P0 = reshape(V, [n, n])
A0 = reshape(G, [n, n])
end associate
iter = 1
n_bl = int(n, blint)
do
! We don't use matmul() for the time being because -fuse-external-blas does
! not work as expected under gfortran 8
! Ptmp = A0·P0
call dgemm("N", "N", n_bl, n_bl, n_bl, 1._real64, A0, n_bl, P0, n_bl, 0._real64, Ptmp, n_bl)
! P1 = P0+Ptmp·A0ᵀ
P1 = P0
call dgemm("N", "T", n_bl, n_bl, n_bl, 1._real64, Ptmp, n_bl, A0, n_bl, 1._real64, P1, n_bl)
! A1 = A0·A0
call dgemm("N", "N", n_bl, n_bl, n_bl, 1._real64, A0, n_bl, A0, n_bl, 0._real64, A1, n_bl)
matd = maxval(abs(P1-P0))
P0 = P1
A0 = A1
iter = iter + 1
if (matd <= tol .or. iter == max_iter) exit
end do
! Allocate and set outputs
plhs(1) = mxCreateDoubleMatrix(n, n, mxREAL)
X(1:n, 1:n) => mxGetPr(plhs(1))
if (nlhs > 1) plhs(2) = mxCreateLogicalScalar(.false._mxLogical)
if (iter == max_iter) then
X = ieee_value(X, ieee_quiet_nan)
if (nlhs > 1) then
call mxDestroyArray(plhs(2))
plhs(2) = mxCreateLogicalScalar(.true._mxLogical)
end if
return
end if
X = (P0+transpose(P0))/2._real64
! Check that X is positive definite
if (check_flag .and. nlhs > 1) then
block
real(real64), dimension(n, n) :: X2
integer(blint) :: info
! X2=chol(X)
X2 = X
call dpotrf("L", n_bl, X2, n_bl, info)
if (info /= 0) then
call mxDestroyArray(plhs(2))
plhs(2) = mxCreateLogicalScalar(.true._mxLogical)
end if
end block
end if
end subroutine mexFunction
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