zhbgst (3)

Functions/Subroutines

subroutine zhbgst (VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO)

ZHBGST

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.

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