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Elementary reflector - Definition and Overview |
| Related Words: Aboriginal, Acid, Alkali, Antenatal, Autochthonous, Bare, Basal, Basic, Beginning, Biochemical, Budding, Central, Chemical, Clear, Component, Constituent, Constitutive |
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An "Elementrary Reflector" is a vector that implements reflection (mathematics).
It is also referred to as a triangular factor, and is a triangular matrix and they are used in the Householder transformation
The routines in LAPACK "*LARZ" apply an "elementary reflector" H to a M-by-N Matrix, from either the left or the right.
The elementary reflector is expressed as
H = I - tau * v * v'
where tau is a scalar and v is a vector.
H is a product of k elementary reflectors.
A block reflector is formed out of k elementary reflectors by the routines "*LARZT", which forms the triangular factor T of a block reflector H of order > n.
LAPACK ROUTINES
- "*larf" applies an elementary reflector to a general rectangular matrix.
- "*larfc" applies the conjugate transpose of an "elementary reflector" to a general matrix.
- "*larfg" generates an elementary reflector Householder matrix.
- "*larzc" applies (multiplies by) the conjugate transpose of an elementary reflector as returned by "*tzrzf" to a general matrix.
- "*larz" applies an elementary reflector as returned by "*tzrzf" to a general matrix.
- "*tzrzf" reduces the upper trapezoidal matrix A to upper triangular matrix.
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