zhbgst.f man page

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

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 165 of file zhbgst.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

zhbgst(3) is an alias of zhbgst.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK