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integration.hh
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rEXPOLIT expolit
integration.hh
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/**
* @file
*
* @author Lucas Frérot <lucas.frerot@epfl.ch>
*
* @section LICENSE
*
* Copyright (©) 2018 EPFL (Ecole Polytechnique Fédérale de
* Lausanne) Laboratory (LSMS - Laboratoire de Simulation en Mécanique des
* Solides)
*
* Expolit 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 INTEGRATION_HH
#define INTEGRATION_HH
#include "differentiation.hh"
#include "exponential.hh"
#include "polynomial.hh"
#include "types.hh"
namespace
expolit
{
template
<
typename
T
,
UInt
order
,
typename
CT
>
auto
integrate
(
const
Polynomial
<
T
,
order
,
CT
>&
p
)
{
Polynomial
<
T
,
order
+
1
,
CT
>
ip
;
for
(
UInt
i
=
1
;
i
<
ip
.
terms
;
++
i
)
ip
.
coeffs
[
i
]
=
p
.
coeffs
[
i
-
1
]
/
static_cast
<
Real
>
(
i
);
return
ip
;
}
template
<
typename
T
,
typename
CT
,
typename
Derived
>
auto
integrate
(
const
Product
<
Constant
<
T
,
CT
>
,
Derived
>&
p
)
{
return
p
.
operands
.
first
*
integrate
(
p
.
operands
.
second
);
}
template
<
typename
T
,
typename
CT
,
typename
Derived
>
auto
integrate
(
const
Product
<
Derived
,
Constant
<
T
,
CT
>>&
p
)
{
return
p
.
operands
.
second
*
integrate
(
p
.
operands
.
first
);
}
template
<
typename
T
,
typename
CT
>
auto
integrate
(
const
Exponential
<
Polynomial
<
T
,
1
,
CT
>>&
e
)
{
return
Constant
<
T
,
CT
>
({
1
/
e
.
expression
.
coeffs
.
back
()})
*
e
;
}
template
<
typename
Derived
,
typename
T2
,
typename
CT2
,
UInt
order
>
auto
integrate
(
const
Product
<
Derived
,
Polynomial
<
T2
,
order
,
CT2
>>&
p
)
{
auto
u
=
integrate
(
p
.
operands
.
first
);
return
u
*
p
.
operands
.
second
-
integrate
(
u
*
differentiate
(
p
.
operands
.
second
));
}
}
// namespace expolit
#endif
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