# chbgst(3) [centos man page]

```chbgst.f(3)							      LAPACK							       chbgst.f(3)

NAME
chbgst.f -

SYNOPSIS
Functions/Subroutines
subroutine chbgst (VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO)
CHBGST

Function/Subroutine Documentation
subroutine chbgst (characterVECT, characterUPLO, integerN, integerKA, integerKB, complex, dimension( ldab, * )AB, integerLDAB, complex,
dimension( ldbb, * )BB, integerLDBB, complex, dimension( ldx, * )X, integerLDX, complex, dimension( * )WORK, real, dimension( * )RWORK,
integerINFO)
CHBGST

Purpose:

CHBGST 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 CPBSTF, 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 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 array, dimension (LDBB,N)
The banded factor S from the split Cholesky factorization of
B, as returned by CPBSTF, 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 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 array, dimension (N)

RWORK

RWORK is REAL 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

Definition at line 165 of file chbgst.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       chbgst.f(3)```

## Check Out this Related Man Page

```CHBGST(l)								 )								 CHBGST(l)

NAME
CHBGST - reduce a complex Hermitian-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,

SYNOPSIS
SUBROUTINE CHBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO )

CHARACTER	  UPLO, VECT

INTEGER	  INFO, KA, KB, LDAB, LDBB, LDX, N

REAL 	  RWORK( * )

COMPLEX	  AB( LDAB, * ), BB( LDBB, * ), WORK( * ), X( LDX, * )

PURPOSE
CHBGST  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 CPBSTF, 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.

ARGUMENTS
VECT    (input) CHARACTER*1
= 'N':  do not form the transformation matrix X;
= 'V':  form X.

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

N       (input) INTEGER
The order of the matrices A and B.  N >= 0.

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

KB      (input) INTEGER
The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'.  KA >= KB >= 0.

AB      (input/output) COMPLEX 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    (input) INTEGER
The leading dimension of the array AB.  LDAB >= KA+1.

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

LDBB    (input) INTEGER
The leading dimension of the array BB.  LDBB >= KB+1.

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

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

WORK    (workspace) COMPLEX array, dimension (N)

RWORK   (workspace) REAL array, dimension (N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value.

LAPACK version 3.0						   15 June 2000 							 CHBGST(l)```
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