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.

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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2011