# zhbgst.f - Man Page

SRC/zhbgst.f

## Synopsis

### Functions/Subroutines

subroutine zhbgst (vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx, work, rwork, info)
ZHBGST

## Function/Subroutine Documentation

### subroutine zhbgst (character vect, character uplo, integer n, integer ka, integer kb, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldbb, * ) bb, integer ldbb, complex*16, dimension( ldx, * ) x, integer ldx, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)

ZHBGST

Purpose:

``` ZHBGST reduces a complex Hermitian-definite banded generalized
eigenproblem  A*x = lambda*B*x  to standard form  C*y = lambda*y,
such that C has the same bandwidth as A.

B must have been previously factorized as S**H*S by ZPBSTF, using a
split Cholesky factorization. A is overwritten by C = X**H*A*X, where
X = S**(-1)*Q and Q is a unitary matrix chosen to preserve the
bandwidth of A.```
Parameters

VECT

```          VECT is CHARACTER*1
= 'N':  do not form the transformation matrix X;
= 'V':  form X.```

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 matrices A and B.  N >= 0.```

KA

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

KB

```          KB is INTEGER
The number of superdiagonals of the matrix B if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'.  KA >= KB >= 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 ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).

On exit, the transformed matrix X**H*A*X, stored in the same
format as A.```

LDAB

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

BB

```          BB is COMPLEX*16 array, dimension (LDBB,N)
The banded factor S from the split Cholesky factorization of
B, as returned by ZPBSTF, stored in the first kb+1 rows of
the array.```

LDBB

```          LDBB is INTEGER
The leading dimension of the array BB.  LDBB >= KB+1.```

X

```          X is COMPLEX*16 array, dimension (LDX,N)
If VECT = 'V', the n-by-n matrix X.
If VECT = 'N', the array X is not referenced.```

LDX

```          LDX is INTEGER
The leading dimension of the array X.
LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.```

WORK

`          WORK is COMPLEX*16 array, dimension (N)`

RWORK

`          RWORK is DOUBLE PRECISION 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.

Definition at line 163 of file zhbgst.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zhbgst(3) is an alias of zhbgst.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK