CLATRD man page on Oracle

```clatrd.f(3)			    LAPACK			   clatrd.f(3)

NAME
clatrd.f -

SYNOPSIS
Functions/Subroutines
subroutine clatrd (UPLO, N, NB, A, LDA, E, TAU, W, LDW)
CLATRD reduces the first nb rows and columns of a
symmetric/Hermitian matrix A to real tridiagonal form by an unitary
similarity transformation.

Function/Subroutine Documentation
subroutine clatrd (characterUPLO, integerN, integerNB, complex, dimension(
lda, * )A, integerLDA, real, dimension( * )E, complex, dimension( *
)TAU, complex, dimension( ldw, * )W, integerLDW)
CLATRD reduces the first nb rows and columns of a symmetric/Hermitian
matrix A to real tridiagonal form by an unitary similarity
transformation.

Purpose:

CLATRD reduces NB rows and columns of a complex Hermitian matrix A to
Hermitian tridiagonal form by a unitary similarity
transformation Q**H * A * Q, and returns the matrices V and W which are
needed to apply the transformation to the unreduced part of A.

If UPLO = 'U', CLATRD reduces the last NB rows and columns of a
matrix, of which the upper triangle is supplied;
if UPLO = 'L', CLATRD reduces the first NB rows and columns of a
matrix, of which the lower triangle is supplied.

This is an auxiliary routine called by CHETRD.

Parameters:
UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular

N

N is INTEGER
The order of the matrix A.

NB

NB is INTEGER
The number of rows and columns to be reduced.

A

A is COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A.	If UPLO = 'U', the leading
n-by-n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced.  If UPLO = 'L', the
leading n-by-n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit:
if UPLO = 'U', the last NB columns have been reduced to
tridiagonal form, with the diagonal elements overwriting
the diagonal elements of A; the elements above the diagonal
with the array TAU, represent the unitary matrix Q as a
product of elementary reflectors;
if UPLO = 'L', the first NB columns have been reduced to
tridiagonal form, with the diagonal elements overwriting
the diagonal elements of A; the elements below the diagonal
with the array TAU, represent the  unitary matrix Q as a
product of elementary reflectors.
See Further Details.

LDA

LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,N).

E

E is REAL array, dimension (N-1)
If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal
elements of the last NB columns of the reduced matrix;
if UPLO = 'L', E(1:nb) contains the subdiagonal elements of
the first NB columns of the reduced matrix.

TAU

TAU is COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors, stored in
TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'.
See Further Details.

W

W is COMPLEX array, dimension (LDW,NB)
The n-by-nb matrix W required to update the unreduced part
of A.

LDW

LDW is INTEGER
The leading dimension of the array W. LDW >= max(1,N).

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
September 2012

Further Details:

If UPLO = 'U', the matrix Q is represented as a product of elementary
reflectors

Q = H(n) H(n-1) . . . H(n-nb+1).

Each H(i) has the form

H(i) = I - tau * v * v**H

where tau is a complex scalar, and v is a complex vector with
v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
and tau in TAU(i-1).

If UPLO = 'L', the matrix Q is represented as a product of elementary
reflectors

Q = H(1) H(2) . . . H(nb).

Each H(i) has the form

H(i) = I - tau * v * v**H

where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
and tau in TAU(i).

The elements of the vectors v together form the n-by-nb matrix V
which is needed, with W, to apply the transformation to the unreduced
part of the matrix, using a Hermitian rank-2k update of the form:
A := A - V*W**H - W*V**H.

The contents of A on exit are illustrated by the following examples
with n = 5 and nb = 2:

if UPLO = 'U':			  if UPLO = 'L':

(  a   a	  a   v4  v5 )		    (  d		  )
(      a	  a   v4  v5 )		    (  1   d		  )
(	  a   1	  v5 )		    (  v1  1   a	  )
(	      d	  1  )		    (  v1  v2  a   a	  )
(		  d  )		    (  v1  v2  a   a   a  )

where d denotes a diagonal element of the reduced matrix, a denotes
an element of the original matrix that is unchanged, and vi denotes
an element of the vector defining H(i).

Definition at line 200 of file clatrd.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2			Tue Sep 25 2012			   clatrd.f(3)
```
[top]

List of man pages available for Oracle

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

Polarhome, production since 1999.
Member of Polarhome portal.