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rTAMAAS tamaas
conic.hh
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/**
* @file
*
* @author Lucas Frérot <lucas.frerot@epfl.ch>
*
* @section LICENSE
*
* Copyright (©) 2017 EPFL (Ecole Polytechnique Fédérale de
* Lausanne) Laboratory (LSMS - Laboratoire de Simulation en Mécanique des
* Solides)
*
* Tamaas is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Tamaas 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 Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Tamaas. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#ifndef CONIC_HH
#define CONIC_HH
/* -------------------------------------------------------------------------- */
#include "static_types.hh"
#include <cmath>
/* -------------------------------------------------------------------------- */
namespace
tamaas
{
/// Conic algebra operations
namespace
conic
{
template
<
typename
DT
,
typename
ST
,
UInt
m
>
__device__
__host__
std
::
remove_cv_t
<
DT
>
det
(
const
StaticVector
<
DT
,
ST
,
m
>&
v
)
{
static_assert
(
m
>=
1
,
"degenerate cone"
);
VectorProxy
<
const
DT
,
m
-
1
>
tail
(
&
v
(
1
));
return
v
(
0
)
*
v
(
0
)
-
tail
.
l2squared
();
}
template
<
typename
DT
,
typename
ST
,
UInt
m
>
__device__
__host__
Matrix
<
std
::
remove_cv_t
<
DT
>
,
m
,
m
>
mat
(
const
StaticVector
<
DT
,
ST
,
m
>&
v
)
{
Matrix
<
std
::
remove_cv_t
<
DT
>
,
m
,
m
>
matrix
;
for
(
UInt
i
=
0
;
i
<
m
;
++
i
)
{
matrix
(
0
,
m
)
=
matrix
(
m
,
0
)
=
v
(
m
);
matrix
(
m
,
m
)
=
v
(
0
);
}
return
matrix
;
}
template
<
typename
DT
,
typename
ST
,
UInt
m
>
__device__
__host__
Vector
<
std
::
remove_cv_t
<
DT
>
,
m
>
hat
(
const
StaticVector
<
DT
,
ST
,
m
>&
v
)
{
Vector
<
std
::
remove_cv_t
<
DT
>
,
m
>
res
(
v
);
VectorProxy
<
std
::
remove_cv_t
<
DT
>
,
m
-
1
>
tail
(
&
res
(
1
));
tail
*=
-
1
;
return
res
;
}
/// theta in Nesterov-Todd scaling
template
<
typename
DT
,
typename
ST1
,
typename
ST2
,
UInt
m
>
__device__
__host__
std
::
remove_cv_t
<
DT
>
scaling_factor
(
const
StaticVector
<
DT
,
ST1
,
m
>&
x
,
const
StaticVector
<
DT
,
ST2
,
m
>&
s
)
{
return
std
::
pow
(
det
(
s
)
/
det
(
x
),
0.25
);
}
/// w in Nesterov-Todd scaling
template
<
typename
DT
,
typename
ST1
,
typename
ST2
,
UInt
m
>
__device__
__host__
std
::
remove_cv_t
<
DT
>
scaling_vector
(
const
StaticVector
<
DT
,
ST1
,
m
>&
x
,
const
StaticVector
<
DT
,
ST2
,
m
>&
s
)
{
auto
theta
=
scaling_factor
(
x
,
s
);
auto
res
=
(
1.
/
theta
)
*
s
+
theta
*
hat
(
x
);
auto
scal
=
x
.
dot
(
s
);
auto
z
=
std
::
sqrt
(
det
(
s
)
*
det
(
x
));
res
*=
1
/
std
::
sqrt
(
2
*
(
scal
+
z
));
return
res
;
}
/// F in Nesterov-Todd scaling
template
<
typename
DT
,
typename
ST1
,
typename
ST2
,
UInt
m
>
__device__
__host__
std
::
remove_cv_t
<
DT
>
scaling_matrix
(
const
StaticVector
<
DT
,
ST1
,
m
>&
x
,
const
StaticVector
<
DT
,
ST2
,
m
>&
s
)
{
auto
theta
=
scaling_factor
(
x
,
s
);
auto
w
=
scaling_vector
(
x
,
s
);
Matrix
<
std
::
remove_cv_t
<
DT
>
,
m
,
m
>
F
;
for
(
UInt
i
=
1
;
i
<
m
;
++
i
)
{
F
(
0
,
i
)
=
F
(
i
,
0
)
=
w
(
i
);
for
(
UInt
j
=
1
;
j
<
m
;
++
i
)
F
(
i
,
j
)
=
1
+
(
w
(
i
)
*
w
(
j
))
/
(
1
+
w
(
0
));
}
F
*=
theta
;
return
F
;
}
/// F² in Nesterov-Todd scaling
template
<
typename
DT
,
typename
ST1
,
typename
ST2
,
UInt
m
>
__device__
__host__
std
::
remove_cv_t
<
DT
>
scaling_matrix_squared
(
const
StaticVector
<
DT
,
ST1
,
m
>&
x
,
const
StaticVector
<
DT
,
ST2
,
m
>&
s
)
{
auto
theta
=
scaling_factor
(
x
,
s
);
auto
w
=
scaling_factor
(
x
,
s
);
Matrix
<
std
::
remove_cv_t
<
DT
>
,
m
,
m
>
F
;
for
(
UInt
i
=
0
;
i
<
m
;
++
i
)
for
(
UInt
j
=
0
;
j
<
m
;
++
j
)
F
(
i
,
j
)
=
(
i
==
j
)
+
2
*
w
(
i
)
*
w
(
j
);
F
(
0
,
0
)
-=
2
;
F
*=
theta
*
theta
;
return
F
;
}
}
// namespace conic
}
// namespace tamaas
#endif
// CONIC_HH
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