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Tridiagonalization.h
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_TRIDIAGONALIZATION_H
#define EIGEN_TRIDIAGONALIZATION_H
namespace
Eigen
{
namespace
internal
{
template
<
typename
MatrixType
>
struct
TridiagonalizationMatrixTReturnType
;
template
<
typename
MatrixType
>
struct
traits
<
TridiagonalizationMatrixTReturnType
<
MatrixType
>
>
{
typedef
typename
MatrixType
::
PlainObject
ReturnType
;
};
template
<
typename
MatrixType
,
typename
CoeffVectorType
>
void
tridiagonalization_inplace
(
MatrixType
&
matA
,
CoeffVectorType
&
hCoeffs
);
}
/** \eigenvalues_module \ingroup Eigenvalues_Module
*
*
* \class Tridiagonalization
*
* \brief Tridiagonal decomposition of a selfadjoint matrix
*
* \tparam _MatrixType the type of the matrix of which we are computing the
* tridiagonal decomposition; this is expected to be an instantiation of the
* Matrix class template.
*
* This class performs a tridiagonal decomposition of a selfadjoint matrix \f$ A \f$ such that:
* \f$ A = Q T Q^* \f$ where \f$ Q \f$ is unitary and \f$ T \f$ a real symmetric tridiagonal matrix.
*
* A tridiagonal matrix is a matrix which has nonzero elements only on the
* main diagonal and the first diagonal below and above it. The Hessenberg
* decomposition of a selfadjoint matrix is in fact a tridiagonal
* decomposition. This class is used in SelfAdjointEigenSolver to compute the
* eigenvalues and eigenvectors of a selfadjoint matrix.
*
* Call the function compute() to compute the tridiagonal decomposition of a
* given matrix. Alternatively, you can use the Tridiagonalization(const MatrixType&)
* constructor which computes the tridiagonal Schur decomposition at
* construction time. Once the decomposition is computed, you can use the
* matrixQ() and matrixT() functions to retrieve the matrices Q and T in the
* decomposition.
*
* The documentation of Tridiagonalization(const MatrixType&) contains an
* example of the typical use of this class.
*
* \sa class HessenbergDecomposition, class SelfAdjointEigenSolver
*/
template
<
typename
_MatrixType
>
class
Tridiagonalization
{
public:
/** \brief Synonym for the template parameter \p _MatrixType. */
typedef
_MatrixType
MatrixType
;
typedef
typename
MatrixType
::
Scalar
Scalar
;
typedef
typename
NumTraits
<
Scalar
>::
Real
RealScalar
;
typedef
typename
MatrixType
::
Index
Index
;
enum
{
Size
=
MatrixType
::
RowsAtCompileTime
,
SizeMinusOne
=
Size
==
Dynamic
?
Dynamic
:
(
Size
>
1
?
Size
-
1
:
1
),
Options
=
MatrixType
::
Options
,
MaxSize
=
MatrixType
::
MaxRowsAtCompileTime
,
MaxSizeMinusOne
=
MaxSize
==
Dynamic
?
Dynamic
:
(
MaxSize
>
1
?
MaxSize
-
1
:
1
)
};
typedef
Matrix
<
Scalar
,
SizeMinusOne
,
1
,
Options
&
~
RowMajor
,
MaxSizeMinusOne
,
1
>
CoeffVectorType
;
typedef
typename
internal
::
plain_col_type
<
MatrixType
,
RealScalar
>::
type
DiagonalType
;
typedef
Matrix
<
RealScalar
,
SizeMinusOne
,
1
,
Options
&
~
RowMajor
,
MaxSizeMinusOne
,
1
>
SubDiagonalType
;
typedef
typename
internal
::
remove_all
<
typename
MatrixType
::
RealReturnType
>::
type
MatrixTypeRealView
;
typedef
internal
::
TridiagonalizationMatrixTReturnType
<
MatrixTypeRealView
>
MatrixTReturnType
;
typedef
typename
internal
::
conditional
<
NumTraits
<
Scalar
>::
IsComplex
,
typename
internal
::
add_const_on_value_type
<
typename
Diagonal
<
const
MatrixType
>::
RealReturnType
>::
type
,
const
Diagonal
<
const
MatrixType
>
>::
type
DiagonalReturnType
;
typedef
typename
internal
::
conditional
<
NumTraits
<
Scalar
>::
IsComplex
,
typename
internal
::
add_const_on_value_type
<
typename
Diagonal
<
Block
<
const
MatrixType
,
SizeMinusOne
,
SizeMinusOne
>
>::
RealReturnType
>::
type
,
const
Diagonal
<
Block
<
const
MatrixType
,
SizeMinusOne
,
SizeMinusOne
>
>
>::
type
SubDiagonalReturnType
;
/** \brief Return type of matrixQ() */
typedef
HouseholderSequence
<
MatrixType
,
typename
internal
::
remove_all
<
typename
CoeffVectorType
::
ConjugateReturnType
>::
type
>
HouseholderSequenceType
;
/** \brief Default constructor.
*
* \param [in] size Positive integer, size of the matrix whose tridiagonal
* decomposition will be computed.
*
* The default constructor is useful in cases in which the user intends to
* perform decompositions via compute(). The \p size parameter is only
* used as a hint. It is not an error to give a wrong \p size, but it may
* impair performance.
*
* \sa compute() for an example.
*/
Tridiagonalization
(
Index
size
=
Size
==
Dynamic
?
2
:
Size
)
:
m_matrix
(
size
,
size
),
m_hCoeffs
(
size
>
1
?
size
-
1
:
1
),
m_isInitialized
(
false
)
{}
/** \brief Constructor; computes tridiagonal decomposition of given matrix.
*
* \param[in] matrix Selfadjoint matrix whose tridiagonal decomposition
* is to be computed.
*
* This constructor calls compute() to compute the tridiagonal decomposition.
*
* Example: \include Tridiagonalization_Tridiagonalization_MatrixType.cpp
* Output: \verbinclude Tridiagonalization_Tridiagonalization_MatrixType.out
*/
Tridiagonalization
(
const
MatrixType
&
matrix
)
:
m_matrix
(
matrix
),
m_hCoeffs
(
matrix
.
cols
()
>
1
?
matrix
.
cols
()
-
1
:
1
),
m_isInitialized
(
false
)
{
internal
::
tridiagonalization_inplace
(
m_matrix
,
m_hCoeffs
);
m_isInitialized
=
true
;
}
/** \brief Computes tridiagonal decomposition of given matrix.
*
* \param[in] matrix Selfadjoint matrix whose tridiagonal decomposition
* is to be computed.
* \returns Reference to \c *this
*
* The tridiagonal decomposition is computed by bringing the columns of
* the matrix successively in the required form using Householder
* reflections. The cost is \f$ 4n^3/3 \f$ flops, where \f$ n \f$ denotes
* the size of the given matrix.
*
* This method reuses of the allocated data in the Tridiagonalization
* object, if the size of the matrix does not change.
*
* Example: \include Tridiagonalization_compute.cpp
* Output: \verbinclude Tridiagonalization_compute.out
*/
Tridiagonalization
&
compute
(
const
MatrixType
&
matrix
)
{
m_matrix
=
matrix
;
m_hCoeffs
.
resize
(
matrix
.
rows
()
-
1
,
1
);
internal
::
tridiagonalization_inplace
(
m_matrix
,
m_hCoeffs
);
m_isInitialized
=
true
;
return
*
this
;
}
/** \brief Returns the Householder coefficients.
*
* \returns a const reference to the vector of Householder coefficients
*
* \pre Either the constructor Tridiagonalization(const MatrixType&) or
* the member function compute(const MatrixType&) has been called before
* to compute the tridiagonal decomposition of a matrix.
*
* The Householder coefficients allow the reconstruction of the matrix
* \f$ Q \f$ in the tridiagonal decomposition from the packed data.
*
* Example: \include Tridiagonalization_householderCoefficients.cpp
* Output: \verbinclude Tridiagonalization_householderCoefficients.out
*
* \sa packedMatrix(), \ref Householder_Module "Householder module"
*/
inline
CoeffVectorType
householderCoefficients
()
const
{
eigen_assert
(
m_isInitialized
&&
"Tridiagonalization is not initialized."
);
return
m_hCoeffs
;
}
/** \brief Returns the internal representation of the decomposition
*
* \returns a const reference to a matrix with the internal representation
* of the decomposition.
*
* \pre Either the constructor Tridiagonalization(const MatrixType&) or
* the member function compute(const MatrixType&) has been called before
* to compute the tridiagonal decomposition of a matrix.
*
* The returned matrix contains the following information:
* - the strict upper triangular part is equal to the input matrix A.
* - the diagonal and lower sub-diagonal represent the real tridiagonal
* symmetric matrix T.
* - the rest of the lower part contains the Householder vectors that,
* combined with Householder coefficients returned by
* householderCoefficients(), allows to reconstruct the matrix Q as
* \f$ Q = H_{N-1} \ldots H_1 H_0 \f$.
* Here, the matrices \f$ H_i \f$ are the Householder transformations
* \f$ H_i = (I - h_i v_i v_i^T) \f$
* where \f$ h_i \f$ is the \f$ i \f$th Householder coefficient and
* \f$ v_i \f$ is the Householder vector defined by
* \f$ v_i = [ 0, \ldots, 0, 1, M(i+2,i), \ldots, M(N-1,i) ]^T \f$
* with M the matrix returned by this function.
*
* See LAPACK for further details on this packed storage.
*
* Example: \include Tridiagonalization_packedMatrix.cpp
* Output: \verbinclude Tridiagonalization_packedMatrix.out
*
* \sa householderCoefficients()
*/
inline
const
MatrixType
&
packedMatrix
()
const
{
eigen_assert
(
m_isInitialized
&&
"Tridiagonalization is not initialized."
);
return
m_matrix
;
}
/** \brief Returns the unitary matrix Q in the decomposition
*
* \returns object representing the matrix Q
*
* \pre Either the constructor Tridiagonalization(const MatrixType&) or
* the member function compute(const MatrixType&) has been called before
* to compute the tridiagonal decomposition of a matrix.
*
* This function returns a light-weight object of template class
* HouseholderSequence. You can either apply it directly to a matrix or
* you can convert it to a matrix of type #MatrixType.
*
* \sa Tridiagonalization(const MatrixType&) for an example,
* matrixT(), class HouseholderSequence
*/
HouseholderSequenceType
matrixQ
()
const
{
eigen_assert
(
m_isInitialized
&&
"Tridiagonalization is not initialized."
);
return
HouseholderSequenceType
(
m_matrix
,
m_hCoeffs
.
conjugate
())
.
setLength
(
m_matrix
.
rows
()
-
1
)
.
setShift
(
1
);
}
/** \brief Returns an expression of the tridiagonal matrix T in the decomposition
*
* \returns expression object representing the matrix T
*
* \pre Either the constructor Tridiagonalization(const MatrixType&) or
* the member function compute(const MatrixType&) has been called before
* to compute the tridiagonal decomposition of a matrix.
*
* Currently, this function can be used to extract the matrix T from internal
* data and copy it to a dense matrix object. In most cases, it may be
* sufficient to directly use the packed matrix or the vector expressions
* returned by diagonal() and subDiagonal() instead of creating a new
* dense copy matrix with this function.
*
* \sa Tridiagonalization(const MatrixType&) for an example,
* matrixQ(), packedMatrix(), diagonal(), subDiagonal()
*/
MatrixTReturnType
matrixT
()
const
{
eigen_assert
(
m_isInitialized
&&
"Tridiagonalization is not initialized."
);
return
MatrixTReturnType
(
m_matrix
.
real
());
}
/** \brief Returns the diagonal of the tridiagonal matrix T in the decomposition.
*
* \returns expression representing the diagonal of T
*
* \pre Either the constructor Tridiagonalization(const MatrixType&) or
* the member function compute(const MatrixType&) has been called before
* to compute the tridiagonal decomposition of a matrix.
*
* Example: \include Tridiagonalization_diagonal.cpp
* Output: \verbinclude Tridiagonalization_diagonal.out
*
* \sa matrixT(), subDiagonal()
*/
DiagonalReturnType
diagonal
()
const
;
/** \brief Returns the subdiagonal of the tridiagonal matrix T in the decomposition.
*
* \returns expression representing the subdiagonal of T
*
* \pre Either the constructor Tridiagonalization(const MatrixType&) or
* the member function compute(const MatrixType&) has been called before
* to compute the tridiagonal decomposition of a matrix.
*
* \sa diagonal() for an example, matrixT()
*/
SubDiagonalReturnType
subDiagonal
()
const
;
protected:
MatrixType
m_matrix
;
CoeffVectorType
m_hCoeffs
;
bool
m_isInitialized
;
};
template
<
typename
MatrixType
>
typename
Tridiagonalization
<
MatrixType
>::
DiagonalReturnType
Tridiagonalization
<
MatrixType
>::
diagonal
()
const
{
eigen_assert
(
m_isInitialized
&&
"Tridiagonalization is not initialized."
);
return
m_matrix
.
diagonal
();
}
template
<
typename
MatrixType
>
typename
Tridiagonalization
<
MatrixType
>::
SubDiagonalReturnType
Tridiagonalization
<
MatrixType
>::
subDiagonal
()
const
{
eigen_assert
(
m_isInitialized
&&
"Tridiagonalization is not initialized."
);
Index
n
=
m_matrix
.
rows
();
return
Block
<
const
MatrixType
,
SizeMinusOne
,
SizeMinusOne
>
(
m_matrix
,
1
,
0
,
n
-
1
,
n
-
1
).
diagonal
();
}
namespace
internal
{
/** \internal
* Performs a tridiagonal decomposition of the selfadjoint matrix \a matA in-place.
*
* \param[in,out] matA On input the selfadjoint matrix. Only the \b lower triangular part is referenced.
* On output, the strict upper part is left unchanged, and the lower triangular part
* represents the T and Q matrices in packed format has detailed below.
* \param[out] hCoeffs returned Householder coefficients (see below)
*
* On output, the tridiagonal selfadjoint matrix T is stored in the diagonal
* and lower sub-diagonal of the matrix \a matA.
* The unitary matrix Q is represented in a compact way as a product of
* Householder reflectors \f$ H_i \f$ such that:
* \f$ Q = H_{N-1} \ldots H_1 H_0 \f$.
* The Householder reflectors are defined as
* \f$ H_i = (I - h_i v_i v_i^T) \f$
* where \f$ h_i = hCoeffs[i]\f$ is the \f$ i \f$th Householder coefficient and
* \f$ v_i \f$ is the Householder vector defined by
* \f$ v_i = [ 0, \ldots, 0, 1, matA(i+2,i), \ldots, matA(N-1,i) ]^T \f$.
*
* Implemented from Golub's "Matrix Computations", algorithm 8.3.1.
*
* \sa Tridiagonalization::packedMatrix()
*/
template
<
typename
MatrixType
,
typename
CoeffVectorType
>
void
tridiagonalization_inplace
(
MatrixType
&
matA
,
CoeffVectorType
&
hCoeffs
)
{
using
numext
::
conj
;
typedef
typename
MatrixType
::
Index
Index
;
typedef
typename
MatrixType
::
Scalar
Scalar
;
typedef
typename
MatrixType
::
RealScalar
RealScalar
;
Index
n
=
matA
.
rows
();
eigen_assert
(
n
==
matA
.
cols
());
eigen_assert
(
n
==
hCoeffs
.
size
()
+
1
||
n
==
1
);
for
(
Index
i
=
0
;
i
<
n
-
1
;
++
i
)
{
Index
remainingSize
=
n
-
i
-
1
;
RealScalar
beta
;
Scalar
h
;
matA
.
col
(
i
).
tail
(
remainingSize
).
makeHouseholderInPlace
(
h
,
beta
);
// Apply similarity transformation to remaining columns,
// i.e., A = H A H' where H = I - h v v' and v = matA.col(i).tail(n-i-1)
matA
.
col
(
i
).
coeffRef
(
i
+
1
)
=
1
;
hCoeffs
.
tail
(
n
-
i
-
1
).
noalias
()
=
(
matA
.
bottomRightCorner
(
remainingSize
,
remainingSize
).
template
selfadjointView
<
Lower
>
()
*
(
conj
(
h
)
*
matA
.
col
(
i
).
tail
(
remainingSize
)));
hCoeffs
.
tail
(
n
-
i
-
1
)
+=
(
conj
(
h
)
*
Scalar
(
-
0.5
)
*
(
hCoeffs
.
tail
(
remainingSize
).
dot
(
matA
.
col
(
i
).
tail
(
remainingSize
))))
*
matA
.
col
(
i
).
tail
(
n
-
i
-
1
);
matA
.
bottomRightCorner
(
remainingSize
,
remainingSize
).
template
selfadjointView
<
Lower
>
()
.
rankUpdate
(
matA
.
col
(
i
).
tail
(
remainingSize
),
hCoeffs
.
tail
(
remainingSize
),
-
1
);
matA
.
col
(
i
).
coeffRef
(
i
+
1
)
=
beta
;
hCoeffs
.
coeffRef
(
i
)
=
h
;
}
}
// forward declaration, implementation at the end of this file
template
<
typename
MatrixType
,
int
Size
=
MatrixType
::
ColsAtCompileTime
,
bool
IsComplex
=
NumTraits
<
typename
MatrixType
::
Scalar
>::
IsComplex
>
struct
tridiagonalization_inplace_selector
;
/** \brief Performs a full tridiagonalization in place
*
* \param[in,out] mat On input, the selfadjoint matrix whose tridiagonal
* decomposition is to be computed. Only the lower triangular part referenced.
* The rest is left unchanged. On output, the orthogonal matrix Q
* in the decomposition if \p extractQ is true.
* \param[out] diag The diagonal of the tridiagonal matrix T in the
* decomposition.
* \param[out] subdiag The subdiagonal of the tridiagonal matrix T in
* the decomposition.
* \param[in] extractQ If true, the orthogonal matrix Q in the
* decomposition is computed and stored in \p mat.
*
* Computes the tridiagonal decomposition of the selfadjoint matrix \p mat in place
* such that \f$ mat = Q T Q^* \f$ where \f$ Q \f$ is unitary and \f$ T \f$ a real
* symmetric tridiagonal matrix.
*
* The tridiagonal matrix T is passed to the output parameters \p diag and \p subdiag. If
* \p extractQ is true, then the orthogonal matrix Q is passed to \p mat. Otherwise the lower
* part of the matrix \p mat is destroyed.
*
* The vectors \p diag and \p subdiag are not resized. The function
* assumes that they are already of the correct size. The length of the
* vector \p diag should equal the number of rows in \p mat, and the
* length of the vector \p subdiag should be one left.
*
* This implementation contains an optimized path for 3-by-3 matrices
* which is especially useful for plane fitting.
*
* \note Currently, it requires two temporary vectors to hold the intermediate
* Householder coefficients, and to reconstruct the matrix Q from the Householder
* reflectors.
*
* Example (this uses the same matrix as the example in
* Tridiagonalization::Tridiagonalization(const MatrixType&)):
* \include Tridiagonalization_decomposeInPlace.cpp
* Output: \verbinclude Tridiagonalization_decomposeInPlace.out
*
* \sa class Tridiagonalization
*/
template
<
typename
MatrixType
,
typename
DiagonalType
,
typename
SubDiagonalType
>
void
tridiagonalization_inplace
(
MatrixType
&
mat
,
DiagonalType
&
diag
,
SubDiagonalType
&
subdiag
,
bool
extractQ
)
{
eigen_assert
(
mat
.
cols
()
==
mat
.
rows
()
&&
diag
.
size
()
==
mat
.
rows
()
&&
subdiag
.
size
()
==
mat
.
rows
()
-
1
);
tridiagonalization_inplace_selector
<
MatrixType
>::
run
(
mat
,
diag
,
subdiag
,
extractQ
);
}
/** \internal
* General full tridiagonalization
*/
template
<
typename
MatrixType
,
int
Size
,
bool
IsComplex
>
struct
tridiagonalization_inplace_selector
{
typedef
typename
Tridiagonalization
<
MatrixType
>::
CoeffVectorType
CoeffVectorType
;
typedef
typename
Tridiagonalization
<
MatrixType
>::
HouseholderSequenceType
HouseholderSequenceType
;
typedef
typename
MatrixType
::
Index
Index
;
template
<
typename
DiagonalType
,
typename
SubDiagonalType
>
static
void
run
(
MatrixType
&
mat
,
DiagonalType
&
diag
,
SubDiagonalType
&
subdiag
,
bool
extractQ
)
{
CoeffVectorType
hCoeffs
(
mat
.
cols
()
-
1
);
tridiagonalization_inplace
(
mat
,
hCoeffs
);
diag
=
mat
.
diagonal
().
real
();
subdiag
=
mat
.
template
diagonal
<-
1
>
().
real
();
if
(
extractQ
)
mat
=
HouseholderSequenceType
(
mat
,
hCoeffs
.
conjugate
())
.
setLength
(
mat
.
rows
()
-
1
)
.
setShift
(
1
);
}
};
/** \internal
* Specialization for 3x3 real matrices.
* Especially useful for plane fitting.
*/
template
<
typename
MatrixType
>
struct
tridiagonalization_inplace_selector
<
MatrixType
,
3
,
false
>
{
typedef
typename
MatrixType
::
Scalar
Scalar
;
typedef
typename
MatrixType
::
RealScalar
RealScalar
;
template
<
typename
DiagonalType
,
typename
SubDiagonalType
>
static
void
run
(
MatrixType
&
mat
,
DiagonalType
&
diag
,
SubDiagonalType
&
subdiag
,
bool
extractQ
)
{
using
std
::
sqrt
;
diag
[
0
]
=
mat
(
0
,
0
);
RealScalar
v1norm2
=
numext
::
abs2
(
mat
(
2
,
0
));
if
(
v1norm2
==
RealScalar
(
0
))
{
diag
[
1
]
=
mat
(
1
,
1
);
diag
[
2
]
=
mat
(
2
,
2
);
subdiag
[
0
]
=
mat
(
1
,
0
);
subdiag
[
1
]
=
mat
(
2
,
1
);
if
(
extractQ
)
mat
.
setIdentity
();
}
else
{
RealScalar
beta
=
sqrt
(
numext
::
abs2
(
mat
(
1
,
0
))
+
v1norm2
);
RealScalar
invBeta
=
RealScalar
(
1
)
/
beta
;
Scalar
m01
=
mat
(
1
,
0
)
*
invBeta
;
Scalar
m02
=
mat
(
2
,
0
)
*
invBeta
;
Scalar
q
=
RealScalar
(
2
)
*
m01
*
mat
(
2
,
1
)
+
m02
*
(
mat
(
2
,
2
)
-
mat
(
1
,
1
));
diag
[
1
]
=
mat
(
1
,
1
)
+
m02
*
q
;
diag
[
2
]
=
mat
(
2
,
2
)
-
m02
*
q
;
subdiag
[
0
]
=
beta
;
subdiag
[
1
]
=
mat
(
2
,
1
)
-
m01
*
q
;
if
(
extractQ
)
{
mat
<<
1
,
0
,
0
,
0
,
m01
,
m02
,
0
,
m02
,
-
m01
;
}
}
}
};
/** \internal
* Trivial specialization for 1x1 matrices
*/
template
<
typename
MatrixType
,
bool
IsComplex
>
struct
tridiagonalization_inplace_selector
<
MatrixType
,
1
,
IsComplex
>
{
typedef
typename
MatrixType
::
Scalar
Scalar
;
template
<
typename
DiagonalType
,
typename
SubDiagonalType
>
static
void
run
(
MatrixType
&
mat
,
DiagonalType
&
diag
,
SubDiagonalType
&
,
bool
extractQ
)
{
diag
(
0
,
0
)
=
numext
::
real
(
mat
(
0
,
0
));
if
(
extractQ
)
mat
(
0
,
0
)
=
Scalar
(
1
);
}
};
/** \internal
* \eigenvalues_module \ingroup Eigenvalues_Module
*
* \brief Expression type for return value of Tridiagonalization::matrixT()
*
* \tparam MatrixType type of underlying dense matrix
*/
template
<
typename
MatrixType
>
struct
TridiagonalizationMatrixTReturnType
:
public
ReturnByValue
<
TridiagonalizationMatrixTReturnType
<
MatrixType
>
>
{
typedef
typename
MatrixType
::
Index
Index
;
public:
/** \brief Constructor.
*
* \param[in] mat The underlying dense matrix
*/
TridiagonalizationMatrixTReturnType
(
const
MatrixType
&
mat
)
:
m_matrix
(
mat
)
{
}
template
<
typename
ResultType
>
inline
void
evalTo
(
ResultType
&
result
)
const
{
result
.
setZero
();
result
.
template
diagonal
<
1
>
()
=
m_matrix
.
template
diagonal
<-
1
>
().
conjugate
();
result
.
diagonal
()
=
m_matrix
.
diagonal
();
result
.
template
diagonal
<-
1
>
()
=
m_matrix
.
template
diagonal
<-
1
>
();
}
Index
rows
()
const
{
return
m_matrix
.
rows
();
}
Index
cols
()
const
{
return
m_matrix
.
cols
();
}
protected:
typename
MatrixType
::
Nested
m_matrix
;
};
}
// end namespace internal
}
// end namespace Eigen
#endif
// EIGEN_TRIDIAGONALIZATION_H
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