
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
nbyn 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 nbyn 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 (N1)
If UPLO = 'U', E(nnb:n1) 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 (N1)
The scalar factors of the elementary reflectors, stored in
TAU(nnb:n1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'.
See Further Details.
W
W is COMPLEX array, dimension (LDW,NB)
The nbynb 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
Univ. of Colorado Denver
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(n1) . . . H(nnb+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(i1) = 1; v(1:i1) is stored on exit in A(1:i1,i),
and tau in TAU(i1).
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 nbynb matrix V
which is needed, with W, to apply the transformation to the unreduced
part of the matrix, using a Hermitian rank2k 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) 
