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Kirill Terekhov
INMOST
Commits
7b6e4ef8
Commit
7b6e4ef8
authored
Feb 09, 2016
by
Kirill Terekhov
Browse files
Synchronize
Algorithms for removing rows and columns in dense matrices. Update for MFD example.
parent
217fbf88
Changes
2
Hide whitespace changes
Inline
Side-by-side
Examples/ADMFD/main.cpp
View file @
7b6e4ef8
...
...
@@ -177,12 +177,12 @@ int main(int argc,char ** argv)
//K0.SVD(U,S,V);
//for(int k = 0; k < 3; ++k) S(k,k) = sqrt(S(k,k));
//rMatrix K = U*S*V;
rMatrix
nKGRAD
(
NF
,
NF
),
NK
(
NF
,
3
),
R
(
NF
,
3
);
//big gradient matrix, co-normals, directions
rMatrix
nKGRAD
(
NF
,
NF
),
NK
(
NF
,
3
),
R
(
NF
,
3
)
,
D
(
NF
,
NF
),
U
(
NF
,
NF
),
Areas
(
NF
,
1
)
;
//big gradient matrix, co-normals, directions
for
(
int
k
=
0
;
k
<
NF
;
++
k
)
//loop over faces
{
aF
=
faces
[
k
]
->
Area
();
faces
[
k
]
->
Centroid
(
yF
);
faces
[
k
]
->
OrientedUnitNormal
(
cell
->
self
(),
nF
);
aF
=
faces
[
k
]
.
Area
();
faces
[
k
]
.
Centroid
(
yF
);
faces
[
k
]
.
OrientedUnitNormal
(
cell
->
self
(),
nF
);
// assemble matrix of directions
R
(
k
,
0
)
=
(
yF
[
0
]
-
xP
[
0
])
*
aF
;
R
(
k
,
1
)
=
(
yF
[
1
]
-
xP
[
1
])
*
aF
;
...
...
@@ -193,10 +193,125 @@ int main(int argc,char ** argv)
NK
(
k
,
1
)
=
nK
(
0
,
1
);
NK
(
k
,
2
)
=
nK
(
0
,
2
);
}
//end of loop over faces
rMatrix
SU
,
SS
,
SV
;
nKGRAD
=
NK
*
(
NK
.
Transpose
()
*
R
).
Invert
(
true
).
first
*
NK
.
Transpose
();
//stability part
nKGRAD
+=
(
rMatrix
::
Unit
(
NF
)
-
R
*
(
R
.
Transpose
()
*
R
).
Invert
(
true
).
first
*
R
.
Transpose
())
*
(
2.0
/
(
static_cast
<
real
>
(
NF
)
*
vP
)
*
(
NK
*
K
.
Invert
(
true
).
first
*
NK
.
Transpose
()).
Trace
());
//nKGRAD += (rMatrix::Unit(NF) - R*(R.Transpose()*R).Invert().first*R.Transpose())*(2.0/(static_cast<real>(NF))*nKGRAD.Trace());
real_array
W
=
cell
->
RealArrayDV
(
tag_W
);
//access data structure for gradient matrix in mesh
/*
std::cout << "W" << std::endl;
nKGRAD.Print();
nKGRAD.SVD(SU,SS,SV);
std::cout << "U" << std::endl;
SU.Print();
std::cout << "S" << std::endl;
SS.Print();
std::cout << "V" << std::endl;
SV.Print();
std::cout << "Check " << (nKGRAD - SU*SS*SV.Transpose()).FrobeniusNorm() << std::endl;
*/
int
rank
=
0
;
//size of matrix U
{
//Retrive orthogonal to R matrix D
//Symmetric orthogonal matrix
rMatrix
DUD
=
(
rMatrix
::
Unit
(
NF
)
-
R
*
(
R
.
Transpose
()
*
R
).
Invert
(
true
).
first
*
R
.
Transpose
());
//perfrom singular value decomposition
//S should be unity matrix with rank NF-3
rMatrix
DUD_U
,
DUD_S
,
DUD_V
;
DUD
.
SVD
(
DUD_U
,
DUD_S
,
DUD_V
);
//compute the rank
for
(
int
q
=
0
;
q
<
NF
;
++
q
)
if
(
DUD_S
(
q
,
q
)
>
1.0e-2
)
rank
++
;
rank
=
NF
-
3
;
if
(
rank
!=
NF
-
3
)
{
std
::
cout
<<
"rank: "
<<
rank
<<
" expected "
<<
NF
-
3
<<
std
::
endl
;
DUD_S
.
Print
();
}
//chop matrix to the full rank
DUD_S
.
RemoveSubset
(
rank
,
NF
,
rank
,
NF
);
DUD_V
.
RemoveColumns
(
rank
,
NF
);
//assign the matrix
D
=
DUD_V
;
U
=
DUD_S
;
}
//std::cout << "D" << std::endl;
//D.Print();
//std::cout << "U" << std::endl;
//U.Print();
//std::cout << "DtR" << std::endl;
//(D.Transpose()*R).Print();
U
*=
(
2.0
/
(
static_cast
<
real
>
(
NF
)
*
vP
)
*
(
NK
*
K
.
Invert
(
true
).
first
*
NK
.
Transpose
()).
Trace
());
{
//Make W a Z-matrix
vMatrix
vU
(
rank
,
rank
),
vW
(
NF
,
NF
);
int
unk
=
0
;
for
(
int
i
=
0
;
i
<
rank
;
++
i
)
vU
(
i
,
i
)
=
unknown
(
U
(
i
,
i
),
unk
++
);
for
(
int
i
=
0
;
i
<
rank
;
++
i
)
for
(
int
j
=
i
+
1
;
j
<
rank
;
++
j
)
{
vU
(
i
,
j
)
=
unknown
(
0.0
,
unk
);
vU
(
j
,
i
)
=
unknown
(
0.0
,
unk
);
unk
++
;
}
//std::cout << "unknowns: " << unk << std::endl;
variable
phi
,
s
;
int
iter
=
0
;
do
{
//Optimize U matrix
vW
=
nKGRAD
+
D
*
vU
*
D
.
Transpose
();
//construct minimization functional phi(W)
phi
=
0.0
;
for
(
int
i
=
0
;
i
<
NF
;
++
i
)
{
phi
+=
1.0
/
(
vW
(
i
,
i
)
*
vW
(
i
,
i
));
s
=
vW
(
i
,
i
)
*
faces
[
i
].
Area
();
for
(
int
j
=
0
;
j
<
NF
;
++
j
)
if
(
i
!=
j
)
{
s
+=
vW
(
i
,
j
)
*
faces
[
j
].
Area
();
phi
+=
(
vW
(
i
,
j
)
+
abs
(
vW
(
i
,
j
)))
*
(
vW
(
i
,
j
)
+
abs
(
vW
(
i
,
j
)));
}
phi
+=
(
s
-
abs
(
s
))
*
(
s
-
abs
(
s
));
}
//std::cout << "[" << iter << "] phi: " << get_value(phi) << "\r" << std::endl;
Sparse
::
Row
&
der
=
phi
.
GetRow
();
//row of derivatives
//std::sort(der.Begin(),der.End());
//for(int i = 0; i < der.Size(); ++i)
// std::cout << "(" << der.GetIndex(i) << "," << der.GetValue(i) << ") ";
//std::cout<<std::endl;
int
q
=
0
;
real
a
=
0.05
;
for
(
int
i
=
0
;
i
<
rank
;
++
i
)
vU
(
i
,
i
)
-=
a
*
der
[
q
++
];
for
(
int
i
=
0
;
i
<
rank
;
++
i
)
for
(
int
j
=
i
+
1
;
j
<
rank
;
++
j
)
{
real
d
=
a
*
der
[
q
++
];
vU
(
i
,
j
)
-=
d
;
vU
(
j
,
i
)
-=
d
;
}
iter
++
;
}
while
(
iter
<
6
&&
phi
>
1.0e-3
);
for
(
int
i
=
0
;
i
<
rank
;
++
i
)
for
(
int
j
=
0
;
j
<
rank
;
++
j
)
U
(
i
,
j
)
=
get_value
(
vU
(
i
,
j
));
//std::cout << "U: " << std::endl;
//U.Print();
}
//std::cout << "UDtR" << std::endl;
//(U*D.Transpose()*R).Print();
nKGRAD
+=
D
*
U
*
D
.
Transpose
();
//std::cout << "W: " << std::endl;
//nKGRAD.Print();
real_array
W
=
cell
->
RealArrayDV
(
tag_W
);
//access data structure for gradient matrix in mesh
W
.
resize
(
NF
*
NF
);
//resize the structure
std
::
copy
(
nKGRAD
.
data
(),
nKGRAD
.
data
()
+
NF
*
NF
,
W
.
data
());
//write down the gradient matrix
}
//end of loop over cells
...
...
@@ -301,11 +416,11 @@ int main(int argc,char ** argv)
if
(
R
.
Norm
()
<
1.0e-4
)
break
;
Solver
S
(
Solver
::
INNER_
MPT
ILU
C
);
Solver
S
(
Solver
::
INNER_ILU
2
);
S
.
SetMatrix
(
R
.
GetJacobian
());
S
.
SetParameterReal
(
"relative_tolerance"
,
1.0e-14
);
S
.
SetParameterReal
(
"absolute_tolerance"
,
1.0e-12
);
S
.
SetParameterReal
(
"drop_tolerance"
,
1.0e-
2
);
S
.
SetParameterReal
(
"drop_tolerance"
,
1.0e-
3
);
S
.
SetParameterReal
(
"reuse_tolerance"
,
1.0e-4
);
//std::fill(Update.Begin(),Update.End(),0.0);
if
(
S
.
Solve
(
R
.
GetResidual
(),
Update
)
)
...
...
Source/Headers/inmost_dense.h
View file @
7b6e4ef8
...
...
@@ -63,17 +63,63 @@ namespace INMOST
space
.
resize
((
n
-
1
)
*
m
);
--
n
;
}
void
RemoveRows
(
enumerator
first
,
enumerator
last
)
{
enumerator
shift
=
last
-
first
;
for
(
enumerator
k
=
last
+
1
;
k
<
n
;
++
k
)
{
for
(
enumerator
l
=
0
;
l
<
m
;
++
l
)
(
*
this
)(
k
-
shift
-
1
,
l
)
=
(
*
this
)(
k
,
l
);
}
space
.
resize
((
n
-
shift
)
*
m
);
n
-=
shift
;
}
void
RemoveColumn
(
enumerator
col
)
{
array
<
Var
>
tmp
(
n
*
(
m
-
1
)
)
;
Matrix
<
Var
>
tmp
(
n
,
m
-
1
);
for
(
enumerator
k
=
0
;
k
<
n
;
++
k
)
{
for
(
enumerator
l
=
0
;
l
<
col
;
++
l
)
tmp
(
k
,
l
)
=
(
*
this
)(
k
,
l
);
for
(
enumerator
l
=
col
+
1
;
l
<
m
;
++
l
)
(
*
this
)
(
k
,
l
-
1
)
=
(
*
this
)(
k
,
l
);
tmp
(
k
,
l
-
1
)
=
(
*
this
)(
k
,
l
);
}
space
.
swap
(
tmp
);
--
m
;
this
->
Swap
(
tmp
);
}
void
RemoveColumns
(
enumerator
first
,
enumerator
last
)
{
enumerator
shift
=
last
-
first
;
Matrix
<
Var
>
tmp
(
n
,
m
-
shift
);
for
(
enumerator
k
=
0
;
k
<
n
;
++
k
)
{
for
(
enumerator
l
=
0
;
l
<
first
;
++
l
)
tmp
(
k
,
l
)
=
(
*
this
)(
k
,
l
);
for
(
enumerator
l
=
last
+
1
;
l
<
m
;
++
l
)
tmp
(
k
,
l
-
shift
-
1
)
=
(
*
this
)(
k
,
l
);
}
this
->
Swap
(
tmp
);
}
void
RemoveSubset
(
enumerator
firstrow
,
enumerator
lastrow
,
enumerator
firstcol
,
enumerator
lastcol
)
{
enumerator
shiftrow
=
lastrow
-
firstrow
;
enumerator
shiftcol
=
lastcol
-
firstcol
;
Matrix
<
Var
>
tmp
(
n
-
shiftrow
,
m
-
shiftcol
);
for
(
enumerator
k
=
0
;
k
<
firstrow
;
++
k
)
{
for
(
enumerator
l
=
0
;
l
<
firstcol
;
++
l
)
tmp
(
k
,
l
)
=
(
*
this
)(
k
,
l
);
for
(
enumerator
l
=
lastcol
+
1
;
l
<
m
;
++
l
)
tmp
(
k
,
l
-
shiftcol
-
1
)
=
(
*
this
)(
k
,
l
);
}
for
(
enumerator
k
=
lastrow
+
1
;
k
<
n
;
++
k
)
{
for
(
enumerator
l
=
0
;
l
<
firstcol
;
++
l
)
tmp
(
k
-
shiftrow
-
1
,
l
)
=
(
*
this
)(
k
,
l
);
for
(
enumerator
l
=
lastcol
+
1
;
l
<
m
;
++
l
)
tmp
(
k
-
shiftrow
-
1
,
l
-
shiftcol
-
1
)
=
(
*
this
)(
k
,
l
);
}
this
->
Swap
(
tmp
);
}
void
Swap
(
Matrix
&
b
)
{
space
.
swap
(
b
.
space
);
...
...
@@ -392,7 +438,7 @@ namespace INMOST
}
Matrix
&
operator
=
(
Matrix
const
&
other
)
{
space
.
resize
(
other
.
n
*
other
.
m
);
if
(
n
*
m
!=
other
.
n
*
other
.
m
)
space
.
resize
(
other
.
n
*
other
.
m
);
for
(
enumerator
i
=
0
;
i
<
other
.
n
*
other
.
m
;
++
i
)
space
[
i
]
=
other
.
space
[
i
];
n
=
other
.
n
;
...
...
@@ -427,7 +473,9 @@ namespace INMOST
assert
(
Rows
()
==
other
.
Rows
());
assert
(
Cols
()
==
other
.
Cols
());
Matrix
<
typename
Promote
<
Var
,
typeB
>::
type
>
ret
(
n
,
m
);
//check RVO
for
(
enumerator
k
=
0
;
k
<
n
*
m
;
++
k
)
ret
.
space
[
k
]
=
space
[
k
]
-
other
.
space
[
k
];
for
(
enumerator
i
=
0
;
i
<
Rows
();
++
i
)
for
(
enumerator
j
=
0
;
j
<
Cols
();
++
j
)
ret
(
i
,
j
)
=
(
*
this
)(
i
,
j
)
-
other
(
i
,
j
);
return
ret
;
}
Matrix
&
operator
-=
(
const
Matrix
&
other
)
...
...
@@ -443,7 +491,9 @@ namespace INMOST
assert
(
Rows
()
==
other
.
Rows
());
assert
(
Cols
()
==
other
.
Cols
());
Matrix
<
typename
Promote
<
Var
,
typeB
>::
type
>
ret
(
n
,
m
);
//check RVO
for
(
enumerator
k
=
0
;
k
<
n
*
m
;
++
k
)
ret
.
space
[
k
]
=
space
[
k
]
+
other
.
space
[
k
];
for
(
enumerator
i
=
0
;
i
<
Rows
();
++
i
)
for
(
enumerator
j
=
0
;
j
<
Cols
();
++
j
)
ret
(
i
,
j
)
=
(
*
this
)(
i
,
j
)
+
other
(
i
,
j
);
return
ret
;
}
Matrix
&
operator
+=
(
const
Matrix
&
other
)
...
...
@@ -457,7 +507,8 @@ namespace INMOST
Matrix
<
typename
Promote
<
Var
,
typeB
>::
type
>
operator
*
(
typeB
coef
)
const
{
Matrix
<
typename
Promote
<
Var
,
typeB
>::
type
>
ret
(
n
,
m
);
//check RVO
for
(
enumerator
k
=
0
;
k
<
n
*
m
;
++
k
)
ret
.
space
[
k
]
=
space
[
k
]
*
coef
;
for
(
enumerator
i
=
0
;
i
<
Rows
();
++
i
)
for
(
enumerator
j
=
0
;
j
<
Cols
();
++
j
)
ret
(
i
,
j
)
=
(
*
this
)(
i
,
j
)
*
coef
;
return
ret
;
}
Matrix
&
operator
*=
(
Var
coef
)
...
...
@@ -469,7 +520,8 @@ namespace INMOST
Matrix
<
typename
Promote
<
Var
,
typeB
>::
type
>
operator
/
(
typeB
coef
)
const
{
Matrix
<
typename
Promote
<
Var
,
typeB
>::
type
>
ret
(
n
,
m
);
//check RVO
for
(
enumerator
k
=
0
;
k
<
n
*
m
;
++
k
)
ret
.
space
[
k
]
=
space
[
k
]
/
coef
;
for
(
enumerator
i
=
0
;
i
<
Rows
();
++
i
)
for
(
enumerator
j
=
0
;
j
<
Cols
();
++
j
)
ret
(
i
,
j
)
=
(
*
this
)(
i
,
j
)
/
coef
;
return
ret
;
}
Matrix
&
operator
/=
(
Var
coef
)
...
...
@@ -661,8 +713,12 @@ namespace INMOST
for
(
enumerator
l
=
0
;
l
<
m
;
++
l
)
{
if
(
fabs
(
get_value
((
*
this
)(
k
,
l
)))
>
threshold
)
#if defined(USE_AUTODIFF)
std
::
cout
<<
std
::
setw
(
10
)
<<
get_value
((
*
this
)(
k
,
l
));
else
#else
std
::
cout
<<
std
::
setw
(
10
)
<<
(
*
this
)(
k
,
l
);
#endif
else
std
::
cout
<<
std
::
setw
(
10
)
<<
0
;
std
::
cout
<<
" "
;
}
...
...
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