diff --git a/matlab/cycle_reduction.m b/matlab/missing/mex/cycle_reduction/cycle_reduction.m
similarity index 90%
rename from matlab/cycle_reduction.m
rename to matlab/missing/mex/cycle_reduction/cycle_reduction.m
index a1c0197e1f41afeb497661842e0616d1027b8e4f..18ba3637f47cba994e6571f32edbf961cb8a0ca3 100644
--- a/matlab/cycle_reduction.m
+++ b/matlab/missing/mex/cycle_reduction/cycle_reduction.m
@@ -88,14 +88,13 @@ while cont
if norm(A2,1) < cvg_tol
cont = 0;
end
- elseif isnan(crit) || it == max_it
- if crit < cvg_tol
- info(1) = 4;
- info(2) = log(norm(A2,1));
- else
- info(1) = 3;
- info(2) = log(norm(A1,1));
- end
+ elseif it == max_it
+ info(1) = 401;
+ info(2) = log(norm(A1,1));
+ return
+ elseif isnan(crit)
+ info(1) = 402;
+ info(2) = log(norm(A1,1))
return
end
it = it + 1;
@@ -105,9 +104,11 @@ X = -Ahat1\A0_0;
if (nargin == 5 && ~isempty(ch) )
%check the solution
- res = A0_0 + A1_0 * X + A2_0 * X * X;
- if (sum(sum(abs(res))) > cvg_tol)
- disp(['the norm residual of the residu ' num2str(res) ' compare to the tolerance criterion ' num2str(cvg_tol)]);
+ res = norm(A0_0 + A1_0 * X + A2_0 * X * X, 1);
+ if (res > cvg_tol)
+ info(1) = 403
+ info(2) = log(res)
+ error(['The norm of the residual is ' num2str(res) ' whereas the tolerance criterion is ' num2str(cvg_tol)]);
end
end
diff --git a/mex/build/cycle_reduction.am b/mex/build/cycle_reduction.am
new file mode 100644
index 0000000000000000000000000000000000000000..a5aa334c9f1c403aeb8d29519adde4d4a3e203e6
--- /dev/null
+++ b/mex/build/cycle_reduction.am
@@ -0,0 +1,17 @@
+mex_PROGRAMS = cycle_reduction
+
+nodist_cycle_reduction_SOURCES = \
+ mexFunction.f08 \
+ matlab_mex.F08 \
+ blas_lapack.F08
+
+BUILT_SOURCES = $(nodist_cycle_reduction_SOURCES)
+CLEANFILES = $(nodist_cycle_reduction_SOURCES)
+
+mexFunction.o: matlab_mex.mod blas.mod lapack.mod
+
+%.f08: $(top_srcdir)/../../sources/cycle_reduction/%.f08
+ $(LN_S) -f $< $@
+
+%.F08: $(top_srcdir)/../../sources/cycle_reduction/%.F08
+ $(LN_S) -f $< $@
diff --git a/mex/build/matlab/Makefile.am b/mex/build/matlab/Makefile.am
index 091eec8a1be72668f56e58eb52402b2762bb880a..e6617b39c2acbc56b2aaf519abbda9233ef2b5cb 100644
--- a/mex/build/matlab/Makefile.am
+++ b/mex/build/matlab/Makefile.am
@@ -1,6 +1,6 @@
ACLOCAL_AMFLAGS = -I ../../../m4
-SUBDIRS = mjdgges kronecker bytecode block_kalman_filter sobol perfect_foresight_problem num_procs block_trust_region disclyap_fast libkordersim local_state_space_iterations folded_to_unfolded_dr k_order_simul k_order_mean
+SUBDIRS = mjdgges kronecker bytecode block_kalman_filter sobol perfect_foresight_problem num_procs block_trust_region disclyap_fast libkordersim local_state_space_iterations folded_to_unfolded_dr k_order_simul k_order_mean cycle_reduction
# libdynare++ must come before gensylv and k_order_perturbation
if ENABLE_MEX_DYNAREPLUSPLUS
diff --git a/mex/build/matlab/configure.ac b/mex/build/matlab/configure.ac
index 7e275f8f32f5b36866a9dc58e6b37e9e10431bbc..97f5f336815786ebc4b70215aa06fdc8c9a5bb7d 100644
--- a/mex/build/matlab/configure.ac
+++ b/mex/build/matlab/configure.ac
@@ -169,6 +169,7 @@ AC_CONFIG_FILES([Makefile
perfect_foresight_problem/Makefile
num_procs/Makefile
block_trust_region/Makefile
- disclyap_fast/Makefile])
+ disclyap_fast/Makefile
+ cycle_reduction/Makefile])
AC_OUTPUT
diff --git a/mex/build/matlab/cycle_reduction/Makefile.am b/mex/build/matlab/cycle_reduction/Makefile.am
new file mode 100644
index 0000000000000000000000000000000000000000..f05308c1f470bfeb94c1cd51a500d029c1f6fe48
--- /dev/null
+++ b/mex/build/matlab/cycle_reduction/Makefile.am
@@ -0,0 +1,2 @@
+include ../mex.am
+include ../../cycle_reduction.am
diff --git a/mex/build/octave/Makefile.am b/mex/build/octave/Makefile.am
index 495d73e7278c574e578195f87aed02bbd28991a6..7057795ede177336796323ef7a76ea5fc69c43b0 100644
--- a/mex/build/octave/Makefile.am
+++ b/mex/build/octave/Makefile.am
@@ -1,6 +1,6 @@
ACLOCAL_AMFLAGS = -I ../../../m4
-SUBDIRS = mjdgges kronecker bytecode block_kalman_filter sobol perfect_foresight_problem num_procs block_trust_region disclyap_fast libkordersim local_state_space_iterations folded_to_unfolded_dr k_order_simul k_order_mean
+SUBDIRS = mjdgges kronecker bytecode block_kalman_filter sobol perfect_foresight_problem num_procs block_trust_region disclyap_fast libkordersim local_state_space_iterations folded_to_unfolded_dr k_order_simul k_order_mean cycle_reduction
# libdynare++ must come before gensylv and k_order_perturbation
if ENABLE_MEX_DYNAREPLUSPLUS
diff --git a/mex/build/octave/configure.ac b/mex/build/octave/configure.ac
index 32c0c97551d11de27a9d53912f043dde8da36142..9806965a31aa0267b9004ab6585c44b9f6841431 100644
--- a/mex/build/octave/configure.ac
+++ b/mex/build/octave/configure.ac
@@ -172,6 +172,7 @@ AC_CONFIG_FILES([Makefile
perfect_foresight_problem/Makefile
num_procs/Makefile
block_trust_region/Makefile
- disclyap_fast/Makefile])
+ disclyap_fast/Makefile
+ cycle_reduction/Makefile])
AC_OUTPUT
diff --git a/mex/build/octave/cycle_reduction/Makefile.am b/mex/build/octave/cycle_reduction/Makefile.am
new file mode 100644
index 0000000000000000000000000000000000000000..f8ae0acd3f852975e6a4c92bcf51814d7b6b5cc6
--- /dev/null
+++ b/mex/build/octave/cycle_reduction/Makefile.am
@@ -0,0 +1,3 @@
+EXEEXT = .mex
+include ../mex.am
+include ../../cycle_reduction.am
diff --git a/mex/sources/Makefile.am b/mex/sources/Makefile.am
index c1e6727b952d5782ac46a517ade6d27bd837942b..9ebd3edf8181f7aa088669e66fcf5710be680a2e 100644
--- a/mex/sources/Makefile.am
+++ b/mex/sources/Makefile.am
@@ -25,7 +25,8 @@ EXTRA_DIST = \
perfect_foresight_problem \
num_procs \
block_trust_region \
- disclyap_fast
+ disclyap_fast \
+ cycle_reduction
clean-local:
rm -rf `find mex/sources -name *.o`
diff --git a/mex/sources/blas_lapack.F08 b/mex/sources/blas_lapack.F08
index 8df746a17734744deab6fc495044168483a9706f..a597ca5006aecde7ac075c8cbb7c8a0b2b9016f6 100644
--- a/mex/sources/blas_lapack.F08
+++ b/mex/sources/blas_lapack.F08
@@ -93,4 +93,16 @@ module lapack
integer(blint), intent(out) :: info
end subroutine dpotrf
end interface
+
+ interface
+ function dlange(norm, m, n, a, lda, work)
+ import :: blint, real64
+ character, intent(in) :: norm
+ integer(blint), intent(in) :: m, n, lda
+ real(real64), dimension(*), intent(in) :: a
+ real(real64), dimension(*), intent(out) :: work
+ real(real64) :: dlange
+ end function dlange
+ end interface
+
end module lapack
diff --git a/mex/sources/cycle_reduction/mexFunction.f08 b/mex/sources/cycle_reduction/mexFunction.f08
new file mode 100644
index 0000000000000000000000000000000000000000..e0e5fe8a3c463ff81eb3669ed6282b3aaf1c59b7
--- /dev/null
+++ b/mex/sources/cycle_reduction/mexFunction.f08
@@ -0,0 +1,233 @@
+! Copyright © 2022 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 <https://www.gnu.org/licenses/>.
+
+! Implements the cyclic reduction algorithm described in
+! D.A. Bini, G. Latouche, B. Meini (2002), "Solving matrix polynomial equations arising in queueing problems", Linear Algebra and its Applications 340, pp. 222-244
+! D.A. Bini, B. Meini (1996), "On the solution of a nonlinear matrix equation arising in queueing problems", SIAM J. Matrix Anal. Appl. 17, pp. 906-926.
+
+module reduction
+ use matlab_mex
+ use lapack
+ use blas
+ implicit none
+
+contains
+ ! Matlab-like norm function calling lapack DLANGE routine
+ real(real64) function norm(A, c)
+ real(real64), dimension(:,:), intent(in) :: A
+ character, intent(in) :: c
+ real(real64), dimension(:), allocatable :: work
+ integer(blint) :: nrow
+ nrow = int(size(A,1),blint)
+ norm = dlange(c, nrow, int(size(A,2), blint), &
+ &A, nrow, work)
+ end function norm
+
+ ! Updating a matrix using blas DGEMM
+ ! C <- alpha*A*B + beta*C
+ subroutine updatemat(alpha, A, B, beta, C)
+ real(real64), dimension(:,:), intent(in) :: A, B
+ real(real64), dimension(:,:), intent(inout) :: C
+ real(real64), intent(in) :: alpha, beta
+ integer(blint) :: m, n, k
+ m = int(size(A,1), blint)
+ n = int(size(B,2), blint)
+ k = int(size(A,2), blint)
+ call dgemm("N", "N", m, n, k, alpha, A, m, B, &
+ k, beta, C, m)
+ end subroutine
+
+ ! Computing inv(A)*B using lapack DGESV
+ ! B <- inv(A)*B
+ subroutine invA_B(A, B, ipiv, info)
+ real(real64), dimension(:,:), intent(inout) :: A
+ real(real64), dimension(:,:), intent(inout) :: B
+ integer(blint), dimension(:), intent(inout) :: ipiv
+ integer(blint), intent(inout) :: info
+ integer(blint) :: m, n
+ m = int(size(A,1), blint)
+ n = int(size(B,2), blint)
+ call dgesv(m, n, A, m, ipiv, B, m, info)
+ end subroutine invA_B
+
+ ! Cycle reduction algorithm
+ subroutine cycle_reduction(A0, A1, A2, X, cvg_tol, check, info)
+ real(real64), dimension(:,:), intent(in) :: A0, A1, A2
+ real(real64), dimension(:,:), intent(inout) :: X
+ real(real64), intent(in) :: cvg_tol
+ logical, intent(in) :: check
+ real(c_double), dimension(2), intent(inout) :: info
+
+ real(real64), dimension(:,:), allocatable :: A02, &
+ Q0, Q2, Ahat, invA1_A02, A1i, A0_tmp, A1_tmp
+ integer :: it, n, dn, max_it
+ integer(blint) :: info_inv
+ integer(blint), dimension(:), allocatable :: ipiv
+ real(real64) :: residual, crit
+ character(kind=c_char, len=10) :: cvg_tol_str, residual_str
+
+ Ahat = A1
+ A1i = A1
+ n = size(A0,1)
+ dn = 2*n
+ allocate(A02(n,dn), ipiv(n), invA1_A02(n,dn), Q0(n,dn), Q2(n,dn))
+ A02(:,1:n) = A0
+ A02(:,n+1:dn) = A2
+ it = 0
+ max_it = 300
+loop: do
+ ! Computing [A0;A2]*(A1\[A0 A2])
+ A1_tmp = A1i
+ invA1_A02 = A02
+ call invA_B(A1_tmp, invA1_A02, ipiv, info_inv)
+ call updatemat(1._real64, A02(:,1:n), invA1_A02, 0._real64, Q0)
+ call updatemat(1._real64, A02(:,n+1:dn), invA1_A02, 0._real64, Q2)
+ ! Updating A02, A1 and Ahat
+ A1i = A1i - Q0(:,n+1:dn) - Q2(:,1:n)
+ A02(:,1:n) = -Q0(:,1:n)
+ A02(:,n+1:dn) = -Q2(:,n+1:dn)
+ Ahat = Ahat-Q2(:,1:n)
+ crit = norm(A02(:,1:n),"1")
+ ! Checking for stopping conditions
+ if (crit < cvg_tol) then
+ if (norm(A02(:,n+1:dn), "1") < cvg_tol) then
+ exit loop
+ end if
+ elseif (it == max_it) then
+ info(1) = 401._c_double
+ info(2) = real(log(norm(A1i,"1")), c_double)
+ exit loop
+ elseif (isnan(crit) .or. (info_inv /= 0_blint)) then
+ info(1) = 402._c_double
+ info(2) = real(log(norm(A1i,"1")), c_double)
+ exit loop
+ end if
+ it = it + 1
+ end do loop
+
+ ! Computing X = -Ahat\A0
+ X = -A0
+ call invA_B(Ahat, X, ipiv, info_inv)
+
+ ! Checking residuals if necessary
+ if (check) then
+ ! A1_tmp <- A2*X + A1
+ A1_tmp = A1
+ call updatemat(1._real64, A2, X, 1._real64, A1_tmp)
+ ! A0_tmp <- A1_tmp*X + A0
+ A0_tmp = A0
+ call updatemat(1._real64, A1_tmp, X, 1._real64, A0_tmp)
+ residual = norm(A0_tmp, "1")
+ if (residual>cvg_tol) then
+ info(1) = 403._c_double
+ info(2) = log(residual)
+ write (cvg_tol_str,"(es8.2)") cvg_tol
+ write (residual_str,"(es8.2)") residual
+ call mexErrMsgTxt("The norm of the residual is "&
+ &// trim(residual_str) // &
+ &", whereas the tolerance criterion is " &
+ // trim(cvg_tol_str) // "." )
+ end if
+ end if
+ end subroutine cycle_reduction
+
+end module reduction
+
+subroutine mexFunction(nlhs, plhs, nrhs, prhs) bind(c, name='mexFunction')
+ use reduction
+ use matlab_mex
+ 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 :: i, n
+ character(kind=c_char, len=2) :: num2str
+ real(real64) :: cvg_tol
+ real(real64), dimension(:,:), pointer, contiguous :: A0, A1, A2, X
+ real(real64), dimension(2) :: info
+ logical :: check
+
+ ! 0. Checking the consistency and validity of input arguments
+ if (nrhs < 4) then
+ call mexErrMsgTxt("Must have at least 4 inputs")
+ end if
+ if (nrhs > 5) then
+ call mexErrMsgTxt("Too many input arguments")
+ end if
+ if (nlhs > 2) then
+ call mexErrMsgTxt("Too many output arguments")
+ end if
+
+ do i=1,3
+ if (.not. (c_associated(prhs(i)) .and. mxIsDouble(prhs(i)) .and. &
+ (.not. mxIsComplex(prhs(i))) .and. (.not. mxIsSparse(prhs(i))))) then
+ write (num2str,"(i2)") i
+ call mexErrMsgTxt("Argument" // trim(num2str) // " should be a real dense matrix")
+ end if
+ end do
+ if (.not. (c_associated(prhs(4)) .and. mxIsScalar(prhs(4)) .and. &
+ mxIsNumeric(prhs(4)))) then
+ call mexErrMsgTxt("Argument 4 should be a numeric scalar")
+ end if
+
+ check = .false.
+ if (nrhs == 5) then
+ if (.not. (c_associated(prhs(5)))) then
+ call mexErrMsgTxt("Argument 5 should be a Matlab object")
+ else
+ if (.not. (mxIsEmpty(prhs(5)))) then
+ check = .true.
+ end if
+ end if
+ end if
+
+ n = int(mxGetM(prhs(1))) ! Order of the considered matrices
+ if ((n /= mxGetN(prhs(1))) & ! Number of columns of A0
+ &.or. (n /= mxGetM(prhs(2))) & ! Number of lines of A1
+ &.or. (n /= mxGetN(prhs(2))) & ! Number of columns of A1
+ &.or. (n /= mxGetM(prhs(3))) & ! Number of lines of A2
+ &.or. (n /= mxGetN(prhs(3))) & ! Number of columns of A2
+ ) then
+ call mexErrMsgTxt("Input dimension mismatch")
+ end if
+
+ ! 1. Storing the relevant information in Fortran format
+ A0(1:n,1:n) => mxGetPr(prhs(1))
+ A1(1:n,1:n) => mxGetPr(prhs(2))
+ A2(1:n,1:n) => mxGetPr(prhs(3))
+ cvg_tol = mxGetScalar(prhs(4))
+ info = [0._c_double,0._c_double]
+
+ plhs(1) = mxCreateDoubleMatrix(int(n, mwSize), int(n, mwSize), mxREAL)
+ X(1:n,1:n) => mxGetPr(plhs(1))
+
+ ! 2. Calling the Cycle Reduction algorithm
+ call cycle_reduction(A0, A1, A2, X, cvg_tol, check, info)
+
+ ! 3. Editing the information output if necessary
+ if (nlhs == 2) then
+ if (info(1) == 0.) then
+ plhs(2) = mxCreateDoubleScalar(0._c_double)
+ else
+ plhs(2) = mxCreateDoubleMatrix(1_mwSize, 2_mwSize, mxREAL)
+ mxGetPr(plhs(2)) = info
+ end if
+ end if
+
+end subroutine mexFunction
\ No newline at end of file
diff --git a/mex/sources/matlab_mex.F08 b/mex/sources/matlab_mex.F08
index 31619ccfcd39c27fcb263ed2e9c1c67cfdef6727..601b78e59f2e7b6f9c3850a788dd9b67a58c34d4 100644
--- a/mex/sources/matlab_mex.F08
+++ b/mex/sources/matlab_mex.F08
@@ -105,6 +105,11 @@ module matlab_mat
type(c_ptr), intent(in), value :: pm
end function mxGetN
+ logical(c_bool) function mxIsEmpty(pm) bind(c, name="mxIsEmpty"//API_VER)
+ use iso_c_binding
+ type(c_ptr), intent(in), value :: pm
+ end function mxIsEmpty
+
!! Create, Query, and Access Data Types
! Numeric types
diff --git a/tests/Makefile.am b/tests/Makefile.am
index 27d0f76ee4acafb923b499f1b97befb6b9197001..81f3ec588ecc0324a379d0534d92a44fa539c707 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -1223,7 +1223,8 @@ M_TRS_FILES += run_block_byte_tests_matlab.m.trs \
test_aggregate_routine_1_2.m.trs \
test_aggregate_routine_1_2_3.m.trs \
run_kronecker_tests.m.trs \
- nonlinearsolvers.m.trs
+ nonlinearsolvers.m.trs \
+ cyclereduction.m.trs
M_XFAIL_TRS_FILES = $(patsubst %.mod, %.m.trs, $(XFAIL_MODFILES))
@@ -1235,7 +1236,8 @@ O_TRS_FILES += run_block_byte_tests_octave.o.trs \
run_all_unitary_tests.o.trs \
histval_initval_file_unit_tests.o.trs \
run_kronecker_tests.o.trs \
- nonlinearsolvers.o.trs
+ nonlinearsolvers.o.trs \
+ cyclereduction.o.trs
O_XFAIL_TRS_FILES = $(patsubst %.mod, %.o.trs, $(XFAIL_MODFILES))
diff --git a/tests/cyclereduction.m b/tests/cyclereduction.m
new file mode 100644
index 0000000000000000000000000000000000000000..211e591cccd258cfd760815dd1d17a1fb9816fa9
--- /dev/null
+++ b/tests/cyclereduction.m
@@ -0,0 +1,140 @@
+debug = false;
+
+if debug
+ [top_test_dir, ~, ~] = fileparts(mfilename('fullpath'));
+else
+ top_test_dir = getenv('TOP_TEST_DIR');
+end
+
+addpath([top_test_dir filesep '..' filesep 'matlab']);
+
+if ~debug
+ % Test Dynare Version
+ if ~strcmp(dynare_version(), getenv('DYNARE_VERSION'))
+ error('Incorrect version of Dynare is being tested')
+ end
+end
+
+dynare_config;
+
+NumberOfTests = 0;
+testFailed = 0;
+
+if ~debug
+ skipline()
+ disp('*** TESTING: cyclereduction.m ***');
+end
+
+matlab_cr_path = [top_test_dir filesep '..' filesep 'matlab' filesep 'missing' filesep 'mex' filesep 'cycle_reduction'];
+addpath(matlab_cr_path);
+cycle_reduction_matlab = @cycle_reduction;
+rmpath(matlab_cr_path);
+
+if isoctave
+ addpath([top_test_dir filesep '..' filesep 'mex' filesep 'octave']);
+else
+ addpath([top_test_dir filesep '..' filesep 'mex' filesep 'matlab']);
+end
+
+t0 = clock;
+
+% Set the dimension of the problem to be solved.
+n = 500;
+% Set the equation to be solved
+A = eye(n);
+B = diag(30*ones(n,1)); B(1,1) = 20; B(end,end) = 20; B = B - diag(10*ones(n-1,1),-1); B = B - diag(10*ones(n-1,1),1);
+C = diag(15*ones(n,1)); C = C - diag(5*ones(n-1,1),-1); C = C - diag(5*ones(n-1,1),1);
+cvg_tol = 1e-12;
+X1 = zeros(n,n);
+X2 = zeros(n,n);
+
+% 1. Solve the equation with the Matlab cycle reduction algorithm
+NumberOfTests = NumberOfTests+1;
+tElapsed1 = 0.;
+try
+ tic; [X1,info] = cycle_reduction_matlab(C,B,A,cvg_tol,[0.]); tElapsed1 = toc;
+ disp(['Elapsed time for the Matlab cycle reduction algorithm is: ' num2str(tElapsed1) ' (n=' int2str(n) ').'])
+ R = C+B*X1+A*X1*X1;
+ if (max(abs(R(:))) > cvg_tol)
+ testFailed = testFailed+1;
+ if debug
+ dprintf('Matlab cycle_reduction solution is wrong')
+ end
+ end
+catch
+ testFailed = testFailed+1;
+ if debug
+ dprintf('Matlab cycle_reduction failed')
+ end
+end
+
+% 2. Solve the equation with the Fortran cycle reduction algorithm
+NumberOfTests = NumberOfTests+1;
+tElapsed2 = 0.;
+try
+ tic; [X2,info] = cycle_reduction(C,B,A,cvg_tol,[0.]); tElapsed2 = toc;
+ disp(['Elapsed time for the Fortran cycle reduction algorithm is: ' num2str(tElapsed2) ' (n=' int2str(n) ').'])
+ R = C+B*X2+A*X2*X2;
+ if (max(abs(R(:))) > cvg_tol)
+ testFailed = testFailed+1;
+ if debug
+ dprintf('Fortran cycle_reduction solution is wrong')
+ end
+ end
+catch
+ testFailed = testFailed+1;
+ if debug
+ dprintf('Fortran cycle_reduction failed')
+ end
+end
+
+% 3. Compare solutions of the Fortran and Matlab routines
+NumberOfTests = NumberOfTests+1;
+if (max(abs(X1(:) - X2(:))) > cvg_tol)
+ testFailed = testFailed+1;
+ if debug
+ dprintf('Fortran and Matlab cycle reduction solutions differ');
+ end
+end
+
+% Compare the Fortran and Matlab execution time
+if debug
+ if tElapsed1<tElapsed2
+ skipline()
+ dprintf('Matlab cyclic reduction is %5.2f times faster than its Fortran counterpart.', tElapsed2/tElapsed1)
+ skipline()
+ else
+ skipline()
+ dprintf('Fortran cyclic reduction is %5.2f times faster than its Matlab counterpart.', tElapsed1/tElapsed2)
+ skipline()
+ end
+end
+
+t1 = clock;
+
+if ~debug
+ cd(getenv('TOP_TEST_DIR'));
+else
+ dprintf('FAILED tests: %i', testFailed)
+end
+
+if isoctave
+ fid = fopen('cyclereduction.o.trs', 'w+');
+else
+ fid = fopen('cyclereduction.m.trs', 'w+');
+end
+if testFailed
+ fprintf(fid,':test-result: FAIL\n');
+else
+ fprintf(fid,':test-result: PASS\n');
+end
+fprintf(fid,':number-tests: %i\n', NumberOfTests);
+fprintf(fid,':number-failed-tests: %i\n', testFailed);
+fprintf(fid,':list-of-passed-tests: cyclereduction.m\n');
+fprintf(fid,':elapsed-time: %f\n', etime(t1, t0));
+fclose(fid);
+
+if ~debug
+ exit;
+end
+