# dlatrd.f(3) [centos man page]

```dlatrd.f(3)							      LAPACK							       dlatrd.f(3)

NAME
dlatrd.f -

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

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

Purpose:

DLATRD reduces NB rows and columns of a real symmetric matrix A to
symmetric tridiagonal form by an orthogonal similarity
transformation Q**T * 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', DLATRD reduces the last NB rows and columns of a
matrix, of which the upper triangle is supplied;
if UPLO = 'L', DLATRD reduces the first NB rows and columns of a
matrix, of which the lower triangle is supplied.

This is an auxiliary routine called by DSYTRD.

Parameters:
UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric 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 DOUBLE PRECISION array, dimension (LDA,N)
On entry, the symmetric 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 orthogonal 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  orthogonal matrix Q as a
product of elementary reflectors.
See Further Details.

LDA

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

E

E is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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**T

where tau is a real scalar, and v is a real 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**T

where tau is a real scalar, and v is a real 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 symmetric rank-2k update of the form:
A := A - V*W**T - W*V**T.

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 199 of file dlatrd.f.

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

Version 3.4.2							  Tue Sep 25 2012						       dlatrd.f(3)```
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