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ae74f3e3
Commit
ae74f3e3
authored
2 years ago
by
Emmanuel Labourasse
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Add tests for TaylorPolynomial
parent
74b23a60
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tests/test_TaylorPolynomial.cpp
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ae74f3e3
#include
<Kokkos_Core.hpp>
#include
<algebra/TinyMatrix.hpp>
#include
<analysis/GaussQuadratureDescriptor.hpp>
#include
<analysis/QuadratureManager.hpp>
#include
<analysis/SquareGaussQuadrature.hpp>
#include
<analysis/TaylorPolynomial.hpp>
#include
<catch2/catch_approx.hpp>
#include
<catch2/catch_test_macros.hpp>
#include
<utils/PugsAssert.hpp>
#include
<utils/Types.hpp>
// Instantiate to ensure full coverage is performed
template
class
TaylorPolynomial
<
0
,
2
>;
template
class
TaylorPolynomial
<
1
,
2
>;
template
class
TaylorPolynomial
<
2
,
2
>;
template
class
TaylorPolynomial
<
3
,
2
>;
// clazy:excludeall=non-pod-global-static
TinyVector
<
2
>
x0
{
1
,
-
1
};
TinyVector
<
3
>
x1
{
1
,
-
1
,
1
};
TEST_CASE
(
"TaylorPolynomial"
,
"[analysis]"
)
{
SECTION
(
"construction"
)
{
TinyVector
<
6
>
coef
(
1
,
2
,
3
,
4
,
5
,
6
);
REQUIRE_NOTHROW
(
TaylorPolynomial
<
2
,
2
>
(
coef
,
x0
));
}
SECTION
(
"degree"
)
{
TinyVector
<
3
>
coef
(
1
,
2
,
3
);
TaylorPolynomial
<
1
,
2
>
P
(
coef
,
x0
);
REQUIRE
(
P
.
degree
()
==
1
);
REQUIRE
(
P
.
dim
()
==
2
);
}
SECTION
(
"equality"
)
{
TinyVector
<
6
>
coef
(
1
,
2
,
3
,
4
,
5
,
6
);
TinyVector
<
3
>
coef2
(
1
,
2
,
3
);
TinyVector
<
6
>
coef3
(
1
,
2
,
3
,
3
,
3
,
3
);
TaylorPolynomial
<
2
,
2
>
P
(
coef
,
x0
);
TaylorPolynomial
<
2
,
2
>
Q
(
coef
,
x0
);
TaylorPolynomial
<
2
,
2
>
R
(
coef3
,
x0
);
REQUIRE
(
P
==
Q
);
REQUIRE
(
P
!=
R
);
}
SECTION
(
"addition"
)
{
TinyVector
<
6
>
coef
(
1
,
2
,
3
,
4
,
5
,
6
);
TinyVector
<
6
>
coef2
(
1
,
2
,
3
,
-
2
,
-
1
,
-
3
);
TinyVector
<
6
>
coef3
(
2
,
4
,
6
,
2
,
4
,
3
);
TaylorPolynomial
<
2
,
2
>
P
(
coef
,
x0
);
TaylorPolynomial
<
2
,
2
>
Q
(
coef2
,
x0
);
TaylorPolynomial
<
2
,
2
>
R
(
coef3
,
x0
);
REQUIRE
(
R
==
(
P
+
Q
));
REQUIRE
((
P
+
Q
)
==
R
);
}
SECTION
(
"opposed"
)
{
TinyVector
<
6
>
coef
(
1
,
2
,
3
,
4
,
5
,
6
);
TinyVector
<
6
>
coef2
(
-
1
,
-
2
,
-
3
,
-
4
,
-
5
,
-
6
);
TaylorPolynomial
<
2
,
2
>
P
(
coef
,
x0
);
REQUIRE
(
-
P
==
TaylorPolynomial
<
2
,
2
>
(
coef2
,
x0
));
}
SECTION
(
"difference"
)
{
TinyVector
<
6
>
coef
(
1
,
2
,
3
,
4
,
5
,
6
);
TinyVector
<
6
>
coef2
(
1
,
2
,
3
,
-
2
,
-
1
,
-
3
);
TinyVector
<
6
>
coef3
(
0
,
0
,
0
,
6
,
6
,
9
);
TaylorPolynomial
<
2
,
2
>
P
(
coef
,
x0
);
TaylorPolynomial
<
2
,
2
>
Q
(
coef2
,
x0
);
TaylorPolynomial
<
2
,
2
>
R
(
coef3
,
x0
);
R
=
P
-
Q
;
REQUIRE
(
R
==
TaylorPolynomial
<
2
,
2
>
(
coef3
,
x0
));
}
SECTION
(
"product_by_scalar"
)
{
TinyVector
<
6
>
coef
(
1
,
2
,
3
,
4
,
5
,
6
);
TinyVector
<
6
>
coef2
(
2
,
4
,
6
,
8
,
10
,
12
);
TaylorPolynomial
<
2
,
2
>
P
(
coef
,
x0
);
TaylorPolynomial
<
2
,
2
>
Q
(
coef2
,
x0
);
REQUIRE
(
Q
==
(
P
*
2
));
REQUIRE
(
Q
==
(
2
*
P
));
}
SECTION
(
"access_coef"
)
{
TinyVector
<
6
>
coef
(
1
,
-
2
,
10
,
7
,
2
,
9
);
TinyVector
<
10
>
coef2
(
2
,
-
4
,
-
1
,
-
3
,
3
,
-
5
,
-
6
,
0
,
1
,
7
);
TinyVector
<
10
>
coef3
(
2
,
-
4
,
-
1
,
-
3
,
3
,
-
5
,
-
6
,
0
,
1
,
7
);
TinyVector
<
20
>
coef4
(
2
,
-
4
,
-
1
,
-
3
,
3
,
-
5
,
-
6
,
-
2
,
1
,
7
,
3
,
-
2
,
1
,
2.5
,
6
,
-
9
,
0.5
,
4
,
-
5
,
-
8
);
TaylorPolynomial
<
2
,
2
>
P
(
coef
,
x0
);
TaylorPolynomial
<
3
,
2
>
Q
(
coef2
,
x0
);
TaylorPolynomial
<
2
,
3
>
R
(
coef3
,
x1
);
TaylorPolynomial
<
3
,
3
>
S
(
coef4
,
x1
);
TinyVector
<
2
,
size_t
>
relative_coef
(
1
,
1
);
TinyVector
<
2
,
size_t
>
relative_coef2
(
1
,
2
);
TinyVector
<
3
,
size_t
>
relative_coef3
(
1
,
0
,
1
);
TinyVector
<
3
,
size_t
>
relative_coef3b
(
0
,
0
,
2
);
TinyVector
<
3
,
size_t
>
relative_coef4
(
1
,
1
,
1
);
TinyVector
<
3
,
size_t
>
relative_coef5
(
0
,
2
,
1
);
REQUIRE
(
P
[
relative_coef
]
==
2
);
REQUIRE
(
Q
[
relative_coef2
]
==
1
);
REQUIRE
(
Q
[
relative_coef
]
==
3
);
REQUIRE
(
R
[
relative_coef3
]
==
-
6
);
REQUIRE
(
R
[
relative_coef3b
]
==
7
);
REQUIRE
(
S
[
relative_coef4
]
==
6
);
REQUIRE
(
S
[
relative_coef5
]
==
4
);
}
SECTION
(
"evaluation"
)
{
TinyVector
<
6
>
coef
(
1
,
-
2
,
10
,
7
,
2
,
9
);
TinyVector
<
10
>
coef2
(
2
,
-
4
,
-
1
,
-
3
,
3
,
-
5
,
-
6
,
0
,
1
,
7
);
TaylorPolynomial
<
2
,
2
>
P
(
coef
,
x0
);
TaylorPolynomial
<
3
,
2
>
Q
(
coef2
,
x0
);
TinyVector
<
6
>
coefx
(
1
,
-
2
,
0
,
7
,
0
,
0
);
TinyVector
<
6
>
coefy
(
2
,
0
,
-
2
,
0
,
0
,
7
);
TinyVector
<
2
>
pos
(
1
,
-
1
);
TinyVector
<
2
>
pos2
(
-
1
,
2
);
TaylorPolynomial
<
2
,
2
>
Px
(
coefx
,
x0
);
TaylorPolynomial
<
2
,
2
>
Py
(
coefy
,
x0
);
REQUIRE
(
Px
(
pos
)
==
1
);
REQUIRE
(
Py
(
pos
)
==
2
);
REQUIRE
(
Px
(
pos2
)
==
33
);
REQUIRE
(
P
(
pos2
)
==
132
);
REQUIRE
(
Q
(
pos
)
==
2
);
}
SECTION
(
"derivation"
)
{
TinyVector
<
6
>
coef
(
1
,
-
2
,
10
,
7
,
2
,
9
);
TinyVector
<
6
>
coef2
(
-
2
,
14
,
2
,
0
,
0
,
0
);
TinyVector
<
6
>
coef3
(
10
,
2
,
18
,
0
,
0
,
0
);
TinyVector
<
10
>
coef4
(
2
,
-
4
,
-
1
,
-
3
,
3
,
-
5
,
-
6
,
1
,
1
,
7
);
TinyVector
<
10
>
coef5
(
-
1
,
-
5
,
2
,
1
,
0
,
0
,
0
,
0
,
0
,
0
);
TaylorPolynomial
<
2
,
2
>
P
(
coef
,
x0
);
TaylorPolynomial
<
2
,
2
>
Q
(
coef2
,
x0
);
TaylorPolynomial
<
2
,
2
>
R
(
coef3
,
x0
);
TaylorPolynomial
<
2
,
3
>
S
(
coef4
,
x1
);
TaylorPolynomial
<
2
,
3
>
T
(
coef5
,
x1
);
REQUIRE
(
Q
==
P
.
derivative
(
0
));
REQUIRE
(
R
==
P
.
derivative
(
1
));
REQUIRE
(
T
==
S
.
derivative
(
1
));
}
SECTION
(
"integrate"
)
{
TinyVector
<
6
>
coef
(
1
,
-
2
,
10
,
7
,
2
,
9
);
std
::
array
<
TinyVector
<
2
>
,
4
>
positions
;
std
::
array
<
TinyVector
<
2
>
,
3
>
positions2
;
std
::
array
<
TinyVector
<
2
>
,
4
>
positions3
;
std
::
array
<
TinyVector
<
2
>
,
2
>
positions4
;
positions
[
0
]
=
TinyVector
<
2
>
{
0
,
0
};
positions
[
1
]
=
TinyVector
<
2
>
{
0
,
0.5
};
positions
[
2
]
=
TinyVector
<
2
>
{
0.3
,
0.7
};
positions
[
3
]
=
TinyVector
<
2
>
{
0.4
,
0.1
};
positions2
[
0
]
=
TinyVector
<
2
>
{
0
,
0
};
positions2
[
1
]
=
TinyVector
<
2
>
{
0
,
0.5
};
positions2
[
2
]
=
TinyVector
<
2
>
{
0.3
,
0.7
};
positions3
[
0
]
=
TinyVector
<
2
>
{
0
,
0
};
positions3
[
1
]
=
TinyVector
<
2
>
{
1
,
0
};
positions3
[
2
]
=
TinyVector
<
2
>
{
1
,
1
};
positions3
[
3
]
=
TinyVector
<
2
>
{
0
,
1
};
positions4
[
0
]
=
TinyVector
<
2
>
{
0
,
0.5
};
positions4
[
1
]
=
TinyVector
<
2
>
{
0.3
,
0.7
};
TaylorPolynomial
<
2
,
2
>
P
(
coef
,
x0
);
auto
p1
=
[](
const
TinyVector
<
2
>&
X
)
{
const
double
x
=
X
[
0
];
const
double
y
=
X
[
1
];
return
1
-
2.
*
(
x
-
1.
)
+
10
*
(
y
+
1
)
+
7
*
(
x
-
1.
)
*
(
x
-
1
)
+
2
*
(
x
-
1
)
*
(
y
+
1
)
+
9
*
(
y
+
1
)
*
(
y
+
1
);
};
const
QuadratureFormula
<
2
>&
l3
=
QuadratureManager
::
instance
().
getSquareFormula
(
GaussQuadratureDescriptor
(
3
));
auto
point_list
=
l3
.
pointList
();
auto
weight_list
=
l3
.
weightList
();
SquareTransformation
<
2
>
s
{
positions
[
0
],
positions
[
1
],
positions
[
2
],
positions
[
3
]};
auto
value
=
weight_list
[
0
]
*
s
.
jacobianDeterminant
(
point_list
[
0
])
*
p1
(
s
(
point_list
[
0
]));
for
(
size_t
i
=
1
;
i
<
weight_list
.
size
();
++
i
)
{
value
+=
weight_list
[
i
]
*
s
.
jacobianDeterminant
(
point_list
[
i
])
*
p1
(
s
(
point_list
[
i
]));
}
SquareTransformation
<
2
>
s3
{
positions3
[
0
],
positions3
[
1
],
positions3
[
2
],
positions3
[
3
]};
auto
value3
=
weight_list
[
0
]
*
s3
.
jacobianDeterminant
(
point_list
[
0
])
*
p1
(
s3
(
point_list
[
0
]));
for
(
size_t
i
=
1
;
i
<
weight_list
.
size
();
++
i
)
{
value3
+=
weight_list
[
i
]
*
s3
.
jacobianDeterminant
(
point_list
[
i
])
*
p1
(
s3
(
point_list
[
i
]));
}
const
QuadratureFormula
<
2
>&
t3
=
QuadratureManager
::
instance
().
getTriangleFormula
(
GaussQuadratureDescriptor
(
3
));
auto
point_list2
=
t3
.
pointList
();
auto
weight_list2
=
t3
.
weightList
();
TriangleTransformation
<
2
>
t
{
positions2
[
0
],
positions2
[
1
],
positions2
[
2
]};
auto
value2
=
weight_list2
[
0
]
*
p1
(
t
(
point_list2
[
0
]));
for
(
size_t
i
=
1
;
i
<
weight_list2
.
size
();
++
i
)
{
value2
+=
weight_list2
[
i
]
*
p1
(
t
(
point_list2
[
i
]));
}
const
QuadratureFormula
<
1
>&
l1
=
QuadratureManager
::
instance
().
getLineFormula
(
GaussQuadratureDescriptor
(
2
));
const
LineTransformation
<
2
>
u
{
positions4
[
0
],
positions4
[
1
]};
double
value4
=
0.
;
for
(
size_t
i
=
0
;
i
<
l1
.
numberOfPoints
();
++
i
)
{
value4
+=
l1
.
weight
(
i
)
*
u
.
velocityNorm
()
*
p1
(
u
(
l1
.
point
(
i
)));
}
REQUIRE
(
value
==
Catch
::
Approx
(
integrate
(
P
,
positions
)));
REQUIRE
(
value2
==
Catch
::
Approx
(
integrate
(
P
,
positions2
)));
REQUIRE
(
value3
==
Catch
::
Approx
(
integrate
(
P
,
positions3
)));
REQUIRE
(
value4
==
Catch
::
Approx
(
integrate
(
P
,
positions4
)));
}
// // SECTION("product")
// {
// Polynomial<2> P(2, 3, 4);
// Polynomial<3> Q(1, 2, -1, 1);
// Polynomial<4 > R;
// Polynomial<5> S;
// R = P;
// S = P;
// S *= Q;
// REQUIRE(Polynomial<5>(2, 7, 8, 7, -1, 4) == (P * Q));
// REQUIRE(Polynomial<5>(2, 7, 8, 7, -1, 4) == S);
// // REQUIRE_THROWS_AS(R *= Q, AssertError);
// }
// SECTION("divide")
// {
// Polynomial<2> P(1, 0, 1);
// Polynomial<1> Q(0, 1);
// Polynomial<1> Q1(0, 1);
// Polynomial<2> R;
// Polynomial<2> S;
// REQUIRE(P.realDegree() == 2);
// REQUIRE(Q.realDegree() == 1);
// REQUIRE(Q1.realDegree() == 1);
// divide(P, Q1, R, S);
// REQUIRE(Polynomial<2>{1, 0, 0} == S);
// REQUIRE(Polynomial<2>{0, 1, 0} == R);
// }
// SECTION("primitive")
// {
// Polynomial<2> P(2, -3, 4);
// TinyVector<4> coefs = zero;
// Polynomial<3> Q(coefs);
// Q = primitive(P);
// Polynomial<3> R(0, 2, -3. / 2, 4. / 3);
// REQUIRE(Q == R);
// }
// SECTION("integrate")
// {
// Polynomial<2> P(2, -3, 3);
// double xinf = -1;
// double xsup = 1;
// double result = integrate(P, xinf, xsup);
// REQUIRE(result == 6);
// result = symmetricIntegrate(P, 2);
// REQUIRE(result == 24);
// }
// SECTION("derivative")
// {
// Polynomial<2> P(2, -3, 3);
// Polynomial<1> Q = derivative(P);
// REQUIRE(Q == Polynomial<1>(-3, 6));
// Polynomial<0> P2(3);
// Polynomial<0> R(0);
// REQUIRE(derivative(P2) == R);
// }
// SECTION("affectation")
// {
// Polynomial<2> Q(2, -3, 3);
// Polynomial<4> R(2, -3, 3, 0, 0);
// Polynomial<4> P(0, 1, 2, 3, 3);
// P = Q;
// REQUIRE(P == R);
// }
// SECTION("affectation addition")
// {
// Polynomial<2> Q(2, -3, 3);
// Polynomial<4> R(2, -2, 5, 3, 3);
// Polynomial<4> P(0, 1, 2, 3, 3);
// P += Q;
// REQUIRE(P == R);
// }
// SECTION("power")
// {
// Polynomial<2> P(2, -3, 3);
// Polynomial<4> R(4, -12, 21, -18, 9);
// Polynomial<1> Q(0, 2);
// Polynomial<2> S = Q.pow<2>(2);
// REQUIRE(P.pow<2>(2) == R);
// REQUIRE(S == Polynomial<2>(0, 0, 4));
// }
// SECTION("composition")
// {
// Polynomial<2> P(2, -3, 3);
// Polynomial<1> Q(0, 2);
// Polynomial<2> R(2, -1, 3);
// Polynomial<2> S(1, 2, 2);
// REQUIRE(P.compose(Q) == Polynomial<2>(2, -6, 12));
// REQUIRE(P.compose2(Q) == Polynomial<2>(2, -6, 12));
// REQUIRE(R(S) == Polynomial<4>(4, 10, 22, 24, 12));
// }
// SECTION("Lagrange polynomial")
// {
// Polynomial<1> S(0.5, -0.5);
// Polynomial<1> Q;
// Q = lagrangePolynomial<1>(TinyVector<2>{-1, 1}, 0);
// REQUIRE(S == Q);
// Polynomial<2> P(0, -0.5, 0.5);
// Polynomial<2> R;
// R = lagrangePolynomial<2>(TinyVector<3>{-1, 0, 1}, 0);
// REQUIRE(R == P);
// const std::array<Polynomial<2>, 3> basis = lagrangeBasis(TinyVector<3>{-1, 0, 1});
// REQUIRE(lagrangeToCanonical(TinyVector<3>{1, 0, 1}, basis) == Polynomial<2>(TinyVector<3>{0, 0, 1}));
// }
}
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