Preload (cardiology): Difference between revisions

Revision as of 23:51, 4 January 2014

"A block reflector is an orthogonal, symmetric matrix that reverses a subspace whose dimension may be greater than one."

see abstract here http://locus.siam.org/SINUM/volume-25/art_0725014.html

It is built out of many elementary reflectors.

It is also referred to as a triangular factor, and is a triangular matrix and they are used in the Householder transformation.

A reflector $Q$ belonging to ${\mathcal {M}}_{n}(\mathbb {R} )$ can be written in the form : $Q=I-auu^{T}$ where $I$ is the identity matrix for ${\mathcal {M}}_{n}(\mathbb {R} )$ , $a$ is a scalar and $u$ belongs to ${\mathcal {\mathbb {R} }}^{n}$ .

LAPACK routines

Here are some of the LAPACK routines that apply to block reflectors

"*larft" forms the triangular vector T of a block reflector H=I-VTVH.
"*larzb" applies a block reflector or its transpose/conjugate transpose as returned by "*tzrzf" to a general matrix.
"*larzt" forms the triangular vector T of a block reflector H=I-VTVH as returned by "*tzrzf".
"*larfb" applies a block reflector or its transpose/conjugate transpose to a general rectangular matrix.

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+"A '''block reflector''' is an orthogonal, symmetric [[matrix (mathematics)|matrix]] that reverses a subspace whose dimension may be greater than one."
+* see abstract here http://locus.siam.org/SINUM/volume-25/art_0725014.html
+It is built out of many [[elementary reflector]]s.
+It is also referred to as a [[triangular factor]], and is a [[triangular matrix]] and they are used in the [[Householder transformation]].
+A reflector <math> Q </math> belonging to <math>\mathcal M_n(\R) </math> can be written in the form :
+<math> Q = I -auu^T  </math> where <math>I</math> is the [[identity matrix]] for <math>\mathcal M_n(\R) </math> , <math>a</math> is a [[Scalar (mathematics)|scalar]] and <math>u</math> belongs to <math>\mathcal \R^n </math> .
+==LAPACK routines==
+Here are some of the [[LAPACK]] routines that apply to block reflectors
+* "*larft" forms the triangular vector T of a block reflector H=I-VTVH.
+* "*larzb" applies a block reflector or its [[transpose]]/[[conjugate transpose]] as returned by "*tzrzf" to a general [[matrix (mathematics)|matrix]].
+* "*larzt" forms the triangular vector T of a block reflector H=I-VTVH as returned by "*tzrzf".
+* "*larfb" applies a block reflector or its [[transpose]]/[[conjugate transpose]] to a general rectangular matrix.
+==See also==
+* [[Reflection (mathematics)]]
+* [[Householder transformation]]
+* [[Unitary matrix]]
+* [[Triangular matrix]]
+[[Category:Matrices]]
+{{Linear-algebra-stub}}
+{{compu-prog-stub}}

Preload (cardiology): Difference between revisions

Revision as of 23:51, 4 January 2014

LAPACK routines

See also

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