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sparse_solvers.cpp
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rSPECMICP SpecMiCP / ReactMiCP
sparse_solvers.cpp
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#include "catch.hpp"
#include "utils/sparse_solvers/sparse_solver.hpp"
#include <vector>
using
namespace
specmicp
;
constexpr
int
size
=
10
;
using
MatrixT
=
Eigen
::
SparseMatrix
<
scalar_t
>
;
// simple diffusion problem
// BC :
// left : fixed value
// right : no flow
void
fill_residuals
(
Vector
&
x
,
Vector
&
residuals
)
{
residuals
.
resize
(
size
);
for
(
int
i
=
0
;
i
<
size
-
1
;
++
i
)
{
residuals
(
i
)
=
(
-
2
*
x
(
i
+
1
)
+
x
(
i
)
+
x
(
i
+
2
));
}
residuals
(
9
)
=
x
(
9
)
-
x
(
10
);
}
void
update_solution
(
Vector
&
xp
,
const
Vector
&
x
,
const
Vector
solution
)
{
for
(
int
i
=
0
;
i
<
size
;
++
i
)
{
xp
(
i
+
1
)
=
x
(
i
+
1
)
+
solution
(
i
);
}
}
void
fill_jacobian
(
MatrixT
&
jacobian
)
{
using
Triplet
=
Eigen
::
Triplet
<
scalar_t
,
index_t
>
;
std
::
vector
<
Triplet
>
list_triplets
;
list_triplets
.
emplace_back
(
Triplet
(
0
,
0
,
-
2
));
list_triplets
.
emplace_back
(
Triplet
(
9
,
9
,
-
1
));
for
(
auto
i
=
1
;
i
<
size
-
1
;
++
i
)
{
list_triplets
.
emplace_back
(
Triplet
(
i
,
i
,
-
2
));
}
for
(
auto
i
=
0
;
i
<
size
-
1
;
++
i
)
{
list_triplets
.
emplace_back
(
Triplet
(
i
,
i
+
1
,
1
));
list_triplets
.
emplace_back
(
Triplet
(
i
+
1
,
i
,
1
));
}
jacobian
=
MatrixT
(
size
,
size
);
jacobian
.
setFromTriplets
(
list_triplets
.
begin
(),
list_triplets
.
end
());
}
TEST_CASE
(
"Sparse solvers"
,
"[Eigen],[Sparse],[Solver]"
)
{
Vector
x
(
size
+
1
);
x
<<
1
,
2
,
2
,
2
,
3
,
2
,
2
,
2
,
2
,
2
,
2
;
Vector
scaling
(
size
);
scaling
.
setConstant
(
1.0e3
);
SECTION
(
"LU solver"
,
"[LU]"
)
{
Vector
residuals
;
fill_residuals
(
x
,
residuals
);
MatrixT
jacobian
;
fill_jacobian
(
jacobian
);
auto
lu_solver
=
sparse_solvers
::
get_sparse_solver
<
MatrixT
,
Vector
,
Vector
>
(
sparse_solvers
::
SparseSolver
::
SparseLU
);
lu_solver
->
analyse_pattern
(
jacobian
);
auto
retcode
=
lu_solver
->
decompose
(
jacobian
);
REQUIRE
(
retcode
==
sparse_solvers
::
SparseSolverReturnCode
::
Success
);
Vector
solution
(
size
);
retcode
=
lu_solver
->
solve
(
residuals
,
solution
);
REQUIRE
(
retcode
==
sparse_solvers
::
SparseSolverReturnCode
::
Success
);
Vector
xp
(
size
+
1
);
xp
(
0
)
=
1
;
update_solution
(
xp
,
x
,
solution
);
fill_residuals
(
xp
,
residuals
);
REQUIRE
(
residuals
.
norm
()
<
1e-10
);
}
SECTION
(
"LU solver with scaling"
,
"[LU],[scaling]"
)
{
Vector
residuals
;
fill_residuals
(
x
,
residuals
);
MatrixT
jacobian
;
fill_jacobian
(
jacobian
);
jacobian
=
jacobian
*
scaling
.
asDiagonal
();
jacobian
.
makeCompressed
();
auto
lu_solver
=
sparse_solvers
::
get_sparse_solver
<
MatrixT
,
Vector
,
Vector
>
(
sparse_solvers
::
SparseSolver
::
SparseLU
);
lu_solver
->
analyse_pattern
(
jacobian
);
auto
retcode
=
lu_solver
->
decompose
(
jacobian
);
REQUIRE
(
retcode
==
sparse_solvers
::
SparseSolverReturnCode
::
Success
);
Vector
solution
(
size
);
retcode
=
lu_solver
->
solve_scaling
(
residuals
,
scaling
,
solution
);
REQUIRE
(
retcode
==
sparse_solvers
::
SparseSolverReturnCode
::
Success
);
Vector
xp
(
size
+
1
);
xp
(
0
)
=
1
;
update_solution
(
xp
,
x
,
solution
);
fill_residuals
(
xp
,
residuals
);
REQUIRE
(
residuals
.
norm
()
<
1e-10
);
}
SECTION
(
"QR solver"
,
"[QR]"
)
{
Vector
residuals
;
fill_residuals
(
x
,
residuals
);
MatrixT
jacobian
;
fill_jacobian
(
jacobian
);
auto
qr_solver
=
sparse_solvers
::
get_sparse_solver
<
MatrixT
,
Vector
,
Vector
>
(
sparse_solvers
::
SparseSolver
::
SparseQR
);
qr_solver
->
analyse_pattern
(
jacobian
);
auto
retcode
=
qr_solver
->
decompose
(
jacobian
);
REQUIRE
(
retcode
==
sparse_solvers
::
SparseSolverReturnCode
::
Success
);
Vector
solution
(
size
);
retcode
=
qr_solver
->
solve
(
residuals
,
solution
);
REQUIRE
(
retcode
==
sparse_solvers
::
SparseSolverReturnCode
::
Success
);
Vector
xp
(
size
+
1
);
xp
(
0
)
=
1
;
update_solution
(
xp
,
x
,
solution
);
fill_residuals
(
xp
,
residuals
);
REQUIRE
(
residuals
.
norm
()
<
1e-10
);
}
SECTION
(
"QR solver with scaling"
,
"[QR],[scaling]"
)
{
Vector
residuals
;
fill_residuals
(
x
,
residuals
);
MatrixT
jacobian
;
fill_jacobian
(
jacobian
);
jacobian
=
jacobian
*
scaling
.
asDiagonal
();
jacobian
.
makeCompressed
();
auto
qr_solver
=
sparse_solvers
::
get_sparse_solver
<
MatrixT
,
Vector
,
Vector
>
(
sparse_solvers
::
SparseSolver
::
SparseQR
);
qr_solver
->
analyse_pattern
(
jacobian
);
auto
retcode
=
qr_solver
->
decompose
(
jacobian
);
REQUIRE
(
retcode
==
sparse_solvers
::
SparseSolverReturnCode
::
Success
);
Vector
solution
(
size
);
retcode
=
qr_solver
->
solve_scaling
(
residuals
,
scaling
,
solution
);
REQUIRE
(
retcode
==
sparse_solvers
::
SparseSolverReturnCode
::
Success
);
Vector
xp
(
size
+
1
);
xp
(
0
)
=
1
;
update_solution
(
xp
,
x
,
solution
);
fill_residuals
(
xp
,
residuals
);
REQUIRE
(
residuals
.
norm
()
<
1e-10
);
}
SECTION
(
"BiCGSTAB solver"
,
"[BiCGSTAB]"
)
{
Vector
residuals
;
fill_residuals
(
x
,
residuals
);
MatrixT
jacobian
;
fill_jacobian
(
jacobian
);
auto
bicgstab_solver
=
sparse_solvers
::
get_sparse_solver
<
MatrixT
,
Vector
,
Vector
>
(
sparse_solvers
::
SparseSolver
::
BiCGSTAB
);
bicgstab_solver
->
analyse_pattern
(
jacobian
);
auto
retcode
=
bicgstab_solver
->
decompose
(
jacobian
);
REQUIRE
(
retcode
==
sparse_solvers
::
SparseSolverReturnCode
::
Success
);
Vector
solution
(
size
);
retcode
=
bicgstab_solver
->
solve
(
residuals
,
solution
);
REQUIRE
(
retcode
==
sparse_solvers
::
SparseSolverReturnCode
::
Success
);
Vector
xp
(
size
+
1
);
xp
(
0
)
=
1
;
update_solution
(
xp
,
x
,
solution
);
fill_residuals
(
xp
,
residuals
);
REQUIRE
(
residuals
.
norm
()
<
1e-10
);
}
SECTION
(
"BiCGSTAB solver with scaling"
,
"[BiCGSTAB], [scaling]"
)
{
Vector
residuals
;
fill_residuals
(
x
,
residuals
);
MatrixT
jacobian
;
fill_jacobian
(
jacobian
);
jacobian
=
jacobian
*
scaling
.
asDiagonal
();
jacobian
.
makeCompressed
();
auto
bicgstab_solver
=
sparse_solvers
::
get_sparse_solver
<
MatrixT
,
Vector
,
Vector
>
(
sparse_solvers
::
SparseSolver
::
BiCGSTAB
);
bicgstab_solver
->
analyse_pattern
(
jacobian
);
auto
retcode
=
bicgstab_solver
->
decompose
(
jacobian
);
REQUIRE
(
retcode
==
sparse_solvers
::
SparseSolverReturnCode
::
Success
);
Vector
solution
(
size
);
retcode
=
bicgstab_solver
->
solve_scaling
(
residuals
,
scaling
,
solution
);
REQUIRE
(
retcode
==
sparse_solvers
::
SparseSolverReturnCode
::
Success
);
Vector
xp
(
size
+
1
);
xp
(
0
)
=
1
;
update_solution
(
xp
,
x
,
solution
);
fill_residuals
(
xp
,
residuals
);
REQUIRE
(
residuals
.
norm
()
<
1e-10
);
}
#ifdef EIGEN_UNSUPPORTED_FOUND
SECTION
(
"GMRES solver"
,
"[GMRES]"
)
{
Vector
residuals
;
fill_residuals
(
x
,
residuals
);
MatrixT
jacobian
;
fill_jacobian
(
jacobian
);
auto
gmres_solver
=
sparse_solvers
::
get_sparse_solver
<
MatrixT
,
Vector
,
Vector
>
(
sparse_solvers
::
SparseSolver
::
GMRES
);
gmres_solver
->
analyse_pattern
(
jacobian
);
auto
retcode
=
gmres_solver
->
decompose
(
jacobian
);
REQUIRE
(
retcode
==
sparse_solvers
::
SparseSolverReturnCode
::
Success
);
Vector
solution
(
size
);
retcode
=
gmres_solver
->
solve
(
residuals
,
solution
);
REQUIRE
(
retcode
==
sparse_solvers
::
SparseSolverReturnCode
::
Success
);
Vector
xp
(
size
+
1
);
xp
(
0
)
=
1
;
update_solution
(
xp
,
x
,
solution
);
fill_residuals
(
xp
,
residuals
);
REQUIRE
(
residuals
.
norm
()
<
1e-10
);
}
SECTION
(
"GMRES solver with scaling"
,
"[GMRES],[scaling]"
)
{
Vector
residuals
;
fill_residuals
(
x
,
residuals
);
MatrixT
jacobian
;
fill_jacobian
(
jacobian
);
jacobian
=
jacobian
*
scaling
.
asDiagonal
();
jacobian
.
makeCompressed
();
auto
gmres_solver
=
sparse_solvers
::
get_sparse_solver
<
MatrixT
,
Vector
,
Vector
>
(
sparse_solvers
::
SparseSolver
::
GMRES
);
gmres_solver
->
analyse_pattern
(
jacobian
);
auto
retcode
=
gmres_solver
->
decompose
(
jacobian
);
REQUIRE
(
retcode
==
sparse_solvers
::
SparseSolverReturnCode
::
Success
);
Vector
solution
(
size
);
retcode
=
gmres_solver
->
solve_scaling
(
residuals
,
scaling
,
solution
);
REQUIRE
(
retcode
==
sparse_solvers
::
SparseSolverReturnCode
::
Success
);
Vector
xp
(
size
+
1
);
xp
(
0
)
=
1
;
update_solution
(
xp
,
x
,
solution
);
fill_residuals
(
xp
,
residuals
);
REQUIRE
(
residuals
.
norm
()
<
1e-10
);
}
#endif
}
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