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zhbtrd.f -

# SYNOPSIS

## Functions/Subroutines

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

ZHBTRD

# Function/Subroutine Documentation

## subroutine zhbtrd (characterVECT, characterUPLO, integerN, integerKD, complex*16, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )D, double precision, dimension( * )E, complex*16, dimension( ldq, * )Q, integerLDQ, complex*16, dimension( * )WORK, integerINFO)

ZHBTRD
Purpose:
``` ZHBTRD 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*16 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 DOUBLE PRECISION array, dimension (N)
The diagonal elements of the tridiagonal matrix T.
```
E
```          E is DOUBLE PRECISION 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*16 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*16 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
NAG Ltd.
Date:
November 2011
Further Details:
```  Modified by Linda Kaufman, Bell Labs.
```
Definition at line 163 of file zhbtrd.f.

# Author

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