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## man page of LAPACK-3

### LAPACK-3: reduces a complex Hermitian-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,

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LAPACK-3 - reduces a complex Hermitian-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,## SYNOPSIS

SUBROUTINE ZHBGST( 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 DOUBLE PRECISION RWORK( * ) COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ), X( LDX, * )## 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.## 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*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 (input) INTEGER The leading dimension of the array AB. LDAB >= KA+1. BB (input) 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 (input) INTEGER The leading dimension of the array BB. LDBB >= KB+1. X (output) 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 (input) INTEGER The leading dimension of the array X. LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise. WORK (workspace) COMPLEX*16 array, dimension (N) RWORK (workspace) DOUBLE PRECISION array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. LAPACK routine (version 3.2.2) March 2011 LAPACK-3(3)

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