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aka_math.cc
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rAKA akantu
aka_math.cc
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/**
* @file aka_math.cc
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
* @author David Simon Kammer <david.kammer@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Leonardo Snozzi <leonardo.snozzi@epfl.ch>
* @author Peter Spijker <peter.spijker@epfl.ch>
* @author Marco Vocialta <marco.vocialta@epfl.ch>
*
* @date creation: Wed Aug 04 2010
* @date last modification: Tue Sep 29 2020
*
* @brief Implementation of the math toolbox
*
*
* @section LICENSE
*
* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* Akantu 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.
*
* Akantu 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 Akantu. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "aka_math.hh"
#include "aka_array.hh"
#include "aka_iterators.hh"
/* -------------------------------------------------------------------------- */
namespace
akantu
{
namespace
Math
{
/* --------------------------------------------------------------------------
*/
void
matrix_vector
(
UInt
m
,
UInt
n
,
const
Array
<
Real
>
&
A
,
const
Array
<
Real
>
&
x
,
Array
<
Real
>
&
y
,
Real
alpha
)
{
AKANTU_DEBUG_IN
();
AKANTU_DEBUG_ASSERT
(
A
.
size
()
==
x
.
size
(),
"The vector A("
<<
A
.
getID
()
<<
") and the vector x("
<<
x
.
getID
()
<<
") must have the same size"
);
AKANTU_DEBUG_ASSERT
(
A
.
getNbComponent
()
==
m
*
n
,
"The vector A("
<<
A
.
getID
()
<<
") has the good number of component."
);
AKANTU_DEBUG_ASSERT
(
x
.
getNbComponent
()
==
n
,
"The vector x("
<<
x
.
getID
()
<<
") do not the good number of component."
);
AKANTU_DEBUG_ASSERT
(
y
.
getNbComponent
()
==
n
,
"The vector y("
<<
y
.
getID
()
<<
") do not the good number of component."
);
UInt
nb_element
=
A
.
size
();
UInt
offset_A
=
A
.
getNbComponent
();
UInt
offset_x
=
x
.
getNbComponent
();
y
.
resize
(
nb_element
);
Real
*
A_val
=
A
.
storage
();
Real
*
x_val
=
x
.
storage
();
Real
*
y_val
=
y
.
storage
();
for
(
UInt
el
=
0
;
el
<
nb_element
;
++
el
)
{
matrix_vector
(
m
,
n
,
A_val
,
x_val
,
y_val
,
alpha
);
A_val
+=
offset_A
;
x_val
+=
offset_x
;
y_val
+=
offset_x
;
}
AKANTU_DEBUG_OUT
();
}
/* --------------------------------------------------------------------------
*/
void
matrix_matrix
(
UInt
m
,
UInt
n
,
UInt
k
,
const
Array
<
Real
>
&
A
,
const
Array
<
Real
>
&
B
,
Array
<
Real
>
&
C
,
Real
alpha
)
{
AKANTU_DEBUG_IN
();
AKANTU_DEBUG_ASSERT
(
A
.
size
()
==
B
.
size
(),
"The vector A("
<<
A
.
getID
()
<<
") and the vector B("
<<
B
.
getID
()
<<
") must have the same size"
);
AKANTU_DEBUG_ASSERT
(
A
.
getNbComponent
()
==
m
*
k
,
"The vector A("
<<
A
.
getID
()
<<
") has the good number of component."
);
AKANTU_DEBUG_ASSERT
(
B
.
getNbComponent
()
==
k
*
n
,
"The vector B("
<<
B
.
getID
()
<<
") do not the good number of component."
);
AKANTU_DEBUG_ASSERT
(
C
.
getNbComponent
()
==
m
*
n
,
"The vector C("
<<
C
.
getID
()
<<
") do not the good number of component."
);
UInt
nb_element
=
A
.
size
();
UInt
offset_A
=
A
.
getNbComponent
();
UInt
offset_B
=
B
.
getNbComponent
();
UInt
offset_C
=
C
.
getNbComponent
();
C
.
resize
(
nb_element
);
Real
*
A_val
=
A
.
storage
();
Real
*
B_val
=
B
.
storage
();
Real
*
C_val
=
C
.
storage
();
for
(
UInt
el
=
0
;
el
<
nb_element
;
++
el
)
{
matrix_matrix
(
m
,
n
,
k
,
A_val
,
B_val
,
C_val
,
alpha
);
A_val
+=
offset_A
;
B_val
+=
offset_B
;
C_val
+=
offset_C
;
}
AKANTU_DEBUG_OUT
();
}
/* --------------------------------------------------------------------------
*/
void
matrix_matrixt
(
UInt
m
,
UInt
n
,
UInt
k
,
const
Array
<
Real
>
&
A
,
const
Array
<
Real
>
&
B
,
Array
<
Real
>
&
C
,
Real
alpha
)
{
AKANTU_DEBUG_IN
();
AKANTU_DEBUG_ASSERT
(
A
.
size
()
==
B
.
size
(),
"The vector A("
<<
A
.
getID
()
<<
") and the vector B("
<<
B
.
getID
()
<<
") must have the same size"
);
AKANTU_DEBUG_ASSERT
(
A
.
getNbComponent
()
==
m
*
k
,
"The vector A("
<<
A
.
getID
()
<<
") has the good number of component."
);
AKANTU_DEBUG_ASSERT
(
B
.
getNbComponent
()
==
k
*
n
,
"The vector B("
<<
B
.
getID
()
<<
") do not the good number of component."
);
AKANTU_DEBUG_ASSERT
(
C
.
getNbComponent
()
==
m
*
n
,
"The vector C("
<<
C
.
getID
()
<<
") do not the good number of component."
);
UInt
nb_element
=
A
.
size
();
UInt
offset_A
=
A
.
getNbComponent
();
UInt
offset_B
=
B
.
getNbComponent
();
UInt
offset_C
=
C
.
getNbComponent
();
C
.
resize
(
nb_element
);
Real
*
A_val
=
A
.
storage
();
Real
*
B_val
=
B
.
storage
();
Real
*
C_val
=
C
.
storage
();
for
(
UInt
el
=
0
;
el
<
nb_element
;
++
el
)
{
matrix_matrixt
(
m
,
n
,
k
,
A_val
,
B_val
,
C_val
,
alpha
);
A_val
+=
offset_A
;
B_val
+=
offset_B
;
C_val
+=
offset_C
;
}
AKANTU_DEBUG_OUT
();
}
/* --------------------------------------------------------------------------
*/
void
compute_tangents
(
const
Array
<
Real
>
&
normals
,
Array
<
Real
>
&
tangents
)
{
AKANTU_DEBUG_IN
();
if
(
normals
.
empty
())
{
return
;
}
auto
spatial_dimension
=
normals
.
getNbComponent
();
auto
tangent_components
=
spatial_dimension
*
(
spatial_dimension
-
1
);
if
(
tangent_components
==
0
)
{
return
;
}
AKANTU_DEBUG_ASSERT
(
tangent_components
==
tangents
.
getNbComponent
(),
"Cannot compute the tangents, the storage array for tangents"
<<
" does not have the good amount of components."
);
auto
nb_normals
=
normals
.
size
();
tangents
.
resize
(
nb_normals
);
tangents
.
zero
();
/// compute first tangent
for
(
auto
&&
data
:
zip
(
make_view
(
normals
,
spatial_dimension
),
make_view
(
tangents
,
tangent_components
)))
{
const
auto
&
normal
=
std
::
get
<
0
>
(
data
);
auto
&
tangent
=
std
::
get
<
1
>
(
data
);
if
(
are_float_equal
(
norm2
(
normal
.
storage
()),
0.
))
{
tangent
(
0
)
=
1.
;
}
else
{
normal2
(
normal
.
storage
(),
tangent
.
storage
());
}
}
/// compute second tangent (3D case)
if
(
spatial_dimension
==
3
)
{
for
(
auto
&&
data
:
zip
(
make_view
(
normals
,
spatial_dimension
),
make_view
(
tangents
,
tangent_components
)))
{
const
auto
&
normal
=
std
::
get
<
0
>
(
data
);
auto
&
tangent
=
std
::
get
<
1
>
(
data
);
normal3
(
normal
.
storage
(),
tangent
.
storage
(),
tangent
.
storage
()
+
spatial_dimension
);
}
}
AKANTU_DEBUG_OUT
();
}
// namespace akantu
/* --------------------------------------------------------------------------
*/
Real
reduce
(
Array
<
Real
>
&
array
)
{
UInt
nb_values
=
array
.
size
();
if
(
nb_values
==
0
)
{
return
0.
;
}
UInt
nb_values_to_sum
=
nb_values
>>
1
;
std
::
sort
(
array
.
begin
(),
array
.
end
());
// as long as the half is not empty
while
(
nb_values_to_sum
!=
0U
)
{
UInt
remaining
=
(
nb_values
-
2
*
nb_values_to_sum
);
if
(
remaining
!=
0U
)
{
array
(
nb_values
-
2
)
+=
array
(
nb_values
-
1
);
}
// sum to consecutive values and store the sum in the first half
for
(
UInt
i
=
0
;
i
<
nb_values_to_sum
;
++
i
)
{
array
(
i
)
=
array
(
2
*
i
)
+
array
(
2
*
i
+
1
);
}
nb_values
=
nb_values_to_sum
;
nb_values_to_sum
>>=
1
;
}
return
array
(
0
);
}
}
// namespace Math
}
// namespace akantu
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