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ac5c82fd
Commit
ac5c82fd
authored
4 years ago
by
Emmanuel Labourasse
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construction of Lagrange polynomial
parent
be1a785f
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2 changed files
src/analysis/Polynomial.hpp
+36
-1
36 additions, 1 deletion
src/analysis/Polynomial.hpp
tests/test_Polynomial.cpp
+19
-0
19 additions, 0 deletions
tests/test_Polynomial.cpp
with
55 additions
and
1 deletion
src/analysis/Polynomial.hpp
+
36
−
1
View file @
ac5c82fd
...
...
@@ -122,6 +122,24 @@ class Polynomial
return
P
;
}
template
<
size_t
M
>
PUGS_INLINE
constexpr
Polynomial
<
N
>&
operator
*=
(
const
Polynomial
<
M
>&
Q
)
{
static_assert
(
N
>=
M
,
"Degree to small in affectation product"
);
for
(
size_t
i
=
N
-
M
+
1
;
i
<=
N
;
++
i
)
{
Assert
(
coefficients
()[
i
]
==
0
,
"Degree of affectation product greater than the degree of input polynomial"
);
}
Polynomial
<
N
>
P
(
zero
);
for
(
size_t
i
=
0
;
i
<=
N
-
M
;
++
i
)
{
for
(
size_t
j
=
0
;
j
<=
M
;
++
j
)
{
P
.
coefficients
()[
i
+
j
]
+=
coefficients
()[
i
]
*
Q
.
coefficients
()[
j
];
}
}
coefficients
()
=
P
.
coefficients
();
return
*
this
;
}
PUGS_INLINE
constexpr
Polynomial
<
N
>
operator
*
(
const
double
&
lambda
)
const
{
...
...
@@ -306,6 +324,24 @@ class Polynomial
return
os
;
}
PUGS_INLINE
constexpr
friend
void
lagrangePolynomial
(
const
TinyVector
<
N
+
1
>
zeros
,
const
size_t
k
,
Polynomial
<
N
>&
lk
)
{
for
(
size_t
i
=
0
;
i
<
N
;
++
i
)
{
Assert
(
zeros
[
i
]
<
zeros
[
i
+
1
],
"Interpolation values must be strictly increasing in Lagrange polynomials"
);
}
lk
.
coefficients
()
=
zero
;
lk
.
coefficients
()[
0
]
=
1
;
for
(
size_t
i
=
0
;
i
<
N
+
1
;
++
i
)
{
if
(
k
==
i
)
continue
;
double
factor
=
1.
/
(
zeros
[
k
]
-
zeros
[
i
]);
Polynomial
<
1
>
P
({
-
zeros
[
i
]
*
factor
,
factor
});
lk
*=
P
;
}
}
PUGS_INLINE
constexpr
Polynomial
(
const
TinyVector
<
N
+
1
>&
coefficients
)
noexcept
:
m_coefficients
{
coefficients
}
{}
PUGS_INLINE
...
...
@@ -315,5 +351,4 @@ class Polynomial
constexpr
Polynomial
()
noexcept
=
default
;
~
Polynomial
()
=
default
;
};
#endif // POLYNOMIAL_HPP
This diff is collapsed.
Click to expand it.
tests/test_Polynomial.cpp
+
19
−
0
View file @
ac5c82fd
...
...
@@ -64,7 +64,14 @@ TEST_CASE("Polynomial", "[analysis]")
{
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
(
"evaluation"
)
{
...
...
@@ -140,4 +147,16 @@ TEST_CASE("Polynomial", "[analysis]")
REQUIRE
(
P
.
compose
(
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
;
lagrangePolynomial
({
-
1
,
1
},
0
,
Q
);
REQUIRE
(
S
==
Q
);
Polynomial
<
2
>
P
({
0
,
-
0.5
,
0.5
});
Polynomial
<
2
>
R
;
lagrangePolynomial
({
-
1
,
0
,
1
},
0
,
R
);
REQUIRE
(
R
==
P
);
}
}
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