# zhbgst (3) - Linux Manuals

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 (characterVECT, characterUPLO, integerN, integerKA, integerKB, complex*16, dimension( ldab, * )AB, integerLDAB, complex*16, dimension( ldbb, * )BB, integerLDBB, complex*16, dimension( ldx, * )X, integerLDX, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)

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