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chbtrd.f(3) LAPACK chbtrd.f(3)

NAME

chbtrd.f -

SYNOPSIS

Functions/Subroutines


subroutine chbtrd (VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
CHBTRD

Function/Subroutine Documentation

subroutine chbtrd (characterVECT, characterUPLO, integerN, integerKD, complex, dimension( ldab, * )AB, integerLDAB, real, dimension( * )D, real, dimension( * )E, complex, dimension( ldq, * )Q, integerLDQ, complex, dimension( * )WORK, integerINFO)

CHBTRD

Purpose:


CHBTRD reduces a complex Hermitian band matrix A to real symmetric
tridiagonal form T by a unitary similarity transformation:
Q**H * A * Q = T.

Parameters:

VECT


VECT is CHARACTER*1
= 'N': do not form Q;
= 'V': form Q;
= 'U': update a matrix X, by forming X*Q.

UPLO


UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

N


N is INTEGER
The order of the matrix A. N >= 0.

KD


KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD >= 0.

AB


AB is COMPLEX array, dimension (LDAB,N)
On entry, the upper or lower triangle of the Hermitian band
matrix A, stored in the first KD+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
On exit, the diagonal elements of AB are overwritten by the
diagonal elements of the tridiagonal matrix T; if KD > 0, the
elements on the first superdiagonal (if UPLO = 'U') or the
first subdiagonal (if UPLO = 'L') are overwritten by the
off-diagonal elements of T; the rest of AB is overwritten by
values generated during the reduction.

LDAB


LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

D


D is REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T.

E


E is REAL array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.

Q


Q is COMPLEX array, dimension (LDQ,N)
On entry, if VECT = 'U', then Q must contain an N-by-N
matrix X; if VECT = 'N' or 'V', then Q need not be set.
On exit:
if VECT = 'V', Q contains the N-by-N unitary matrix Q;
if VECT = 'U', Q contains the product X*Q;
if VECT = 'N', the array Q is not referenced.

LDQ


LDQ is INTEGER
The leading dimension of the array Q.
LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.

WORK


WORK is COMPLEX array, dimension (N)

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details:


Modified by Linda Kaufman, Bell Labs.

Definition at line 163 of file chbtrd.f.

Author

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Tue Sep 25 2012 Version 3.4.2