gtsam
3rdparty
Eigen
unsupported
Eigen
src
NonLinearOptimization
dogleg.h
Go to the documentation of this file.
1
namespace
Eigen
{
2
3
namespace
internal
{
4
5
template
<
typename
Scalar>
6
void
dogleg
(
7
const
Matrix< Scalar, Dynamic, Dynamic >
&qrfac,
8
const
Matrix< Scalar, Dynamic, 1 >
&
diag
,
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const
Matrix< Scalar, Dynamic, 1 >
&qtb,
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Scalar
delta
,
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Matrix< Scalar, Dynamic, 1 >
&
x
)
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{
13
using
std::abs
;
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using
std::sqrt
;
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16
typedef
DenseIndex
Index
;
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/* Local variables */
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Index
i
,
j
;
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Scalar
sum, temp,
alpha
, bnorm;
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Scalar
gnorm, qnorm;
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Scalar
sgnorm;
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/* Function Body */
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const
Scalar
epsmch =
NumTraits<Scalar>::epsilon
();
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const
Index
n
= qrfac.
cols
();
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eigen_assert
(
n
==qtb.size());
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eigen_assert
(
n
==
x
.
size
());
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eigen_assert
(
n
==
diag
.size());
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Matrix< Scalar, Dynamic, 1 >
wa1(
n
), wa2(
n
);
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/* first, calculate the gauss-newton direction. */
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for
(
j
=
n
-1;
j
>=0; --
j
) {
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temp = qrfac(
j
,
j
);
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if
(temp == 0.) {
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temp = epsmch * qrfac.col(
j
).head(
j
+1).maxCoeff();
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if
(temp == 0.)
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temp = epsmch;
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}
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if
(
j
==
n
-1)
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x
[
j
] = qtb[
j
] / temp;
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else
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x
[
j
] = (qtb[
j
] - qrfac.row(
j
).tail(
n
-
j
-1).dot(
x
.tail(
n
-
j
-1))) / temp;
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}
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/* test whether the gauss-newton direction is acceptable. */
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qnorm =
diag
.cwiseProduct(
x
).stableNorm();
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if
(qnorm <=
delta
)
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return
;
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// TODO : this path is not tested by Eigen unit tests
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/* the gauss-newton direction is not acceptable. */
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/* next, calculate the scaled gradient direction. */
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wa1.fill(0.);
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for
(
j
= 0;
j
<
n
; ++
j
) {
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wa1.tail(
n
-
j
) += qrfac.row(
j
).tail(
n
-
j
) * qtb[
j
];
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wa1[
j
] /=
diag
[
j
];
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}
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/* calculate the norm of the scaled gradient and test for */
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/* the special case in which the scaled gradient is zero. */
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gnorm = wa1.stableNorm();
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sgnorm = 0.;
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alpha
=
delta
/ qnorm;
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if
(gnorm == 0.)
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goto
algo_end;
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/* calculate the point along the scaled gradient */
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/* at which the quadratic is minimized. */
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wa1.array() /= (
diag
*gnorm).
array
();
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// TODO : once unit tests cover this part,:
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// wa2 = qrfac.template triangularView<Upper>() * wa1;
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for
(
j
= 0;
j
<
n
; ++
j
) {
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sum = 0.;
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for
(
i
=
j
;
i
<
n
; ++
i
) {
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sum += qrfac(
j
,
i
) * wa1[
i
];
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}
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wa2[
j
] = sum;
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}
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temp = wa2.stableNorm();
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sgnorm = gnorm / temp / temp;
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/* test whether the scaled gradient direction is acceptable. */
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alpha
= 0.;
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if
(sgnorm >=
delta
)
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goto
algo_end;
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/* the scaled gradient direction is not acceptable. */
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/* finally, calculate the point along the dogleg */
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/* at which the quadratic is minimized. */
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bnorm = qtb.stableNorm();
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temp = bnorm / gnorm * (bnorm / qnorm) * (sgnorm /
delta
);
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temp = temp -
delta
/ qnorm *
numext::abs2
(sgnorm /
delta
) +
sqrt
(
numext::abs2
(temp -
delta
/ qnorm) + (1.-
numext::abs2
(
delta
/ qnorm)) * (1.-
numext::abs2
(sgnorm /
delta
)));
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alpha
=
delta
/ qnorm * (1. -
numext::abs2
(sgnorm /
delta
)) / temp;
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algo_end:
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/* form appropriate convex combination of the gauss-newton */
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/* direction and the scaled gradient direction. */
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temp = (1.-
alpha
) * (
std::min
)(sgnorm,
delta
);
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x
= temp * wa1 +
alpha
*
x
;
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}
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105
}
// end namespace internal
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107
}
// end namespace Eigen
Eigen
Namespace containing all symbols from the Eigen library.
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Eigen::internal::dogleg
void dogleg(const Matrix< Scalar, Dynamic, Dynamic > &qrfac, const Matrix< Scalar, Dynamic, 1 > &diag, const Matrix< Scalar, Dynamic, 1 > &qtb, Scalar delta, Matrix< Scalar, Dynamic, 1 > &x)
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gtsam
Author(s):
autogenerated on Sat Nov 16 2024 04:02:13