CHBEVD man page on IRIX

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CHBEVD(3F)							    CHBEVD(3F)

NAME
     CHBEVD - compute all the eigenvalues and, optionally, eigenvectors of a
     complex Hermitian band matrix A

SYNOPSIS
     SUBROUTINE CHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK,
			RWORK, LRWORK, IWORK, LIWORK, INFO )

	 CHARACTER	JOBZ, UPLO

	 INTEGER	INFO, KD, LDAB, LDZ, LIWORK, LRWORK, LWORK, N

	 INTEGER	IWORK( * )

	 REAL		RWORK( * ), W( * )

	 COMPLEX	AB( LDAB, * ), WORK( * ), Z( LDZ, * )

PURPOSE
     CHBEVD computes all the eigenvalues and, optionally, eigenvectors of a
     complex Hermitian band matrix A.  If eigenvectors are desired, it uses a
     divide and conquer algorithm.

     The divide and conquer algorithm makes very mild assumptions about
     floating point arithmetic. It will work on machines with a guard digit in
     add/subtract, or on those binary machines without guard digits which
     subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
     conceivably fail on hexadecimal or decimal machines without guard digits,
     but we know of none.

ARGUMENTS
     JOBZ    (input) CHARACTER*1
	     = 'N':  Compute eigenvalues only;
	     = 'V':  Compute eigenvalues and eigenvectors.

     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 matrix A.	 N >= 0.

     KD	     (input) INTEGER
	     The number of superdiagonals of the matrix A if UPLO = 'U', or
	     the number of subdiagonals if UPLO = 'L'.	KD >= 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 KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-

									Page 1

CHBEVD(3F)							    CHBEVD(3F)

	     kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for
	     j<=i<=min(n,j+kd).

	     On exit, AB is overwritten by values generated during the
	     reduction to tridiagonal form.  If UPLO = 'U', the first
	     superdiagonal and the diagonal of the tridiagonal matrix T are
	     returned in rows KD and KD+1 of AB, and if UPLO = 'L', the
	     diagonal and first subdiagonal of T are returned in the first two
	     rows of AB.

     LDAB    (input) INTEGER
	     The leading dimension of the array AB.  LDAB >= KD + 1.

     W	     (output) REAL array, dimension (N)
	     If INFO = 0, the eigenvalues in ascending order.

     Z	     (output) COMPLEX array, dimension (LDZ, N)
	     If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
	     eigenvectors of the matrix A, with the i-th column of Z holding
	     the eigenvector associated with W(i).  If JOBZ = 'N', then Z is
	     not referenced.

     LDZ     (input) INTEGER
	     The leading dimension of the array Z.  LDZ >= 1, and if JOBZ =
	     'V', LDZ >= max(1,N).

     WORK    (workspace/output) COMPLEX array, dimension (LWORK)
	     On exit, if LWORK > 0, WORK(1) returns the optimal LWORK.

     LWORK   (input) INTEGER
	     The dimension of the array WORK.  If N <= 1,		LWORK
	     must be at least 1.  If JOBZ = 'N' and N > 1, LWORK must be at
	     least N.  If JOBZ = 'V' and N > 1, LWORK must be at least 2*N**2.

     RWORK   (workspace/output) REAL array,
	     dimension (LRWORK) On exit, if LRWORK > 0, RWORK(1) returns the
	     optimal LRWORK.

     LRWORK  (input) INTEGER
	     The dimension of array RWORK.  If N <= 1,		     LRWORK
	     must be at least 1.  If JOBZ = 'N' and N > 1, LRWORK must be at
	     least N.  If JOBZ = 'V' and N > 1, LRWORK must be at least 1 +
	     4*N + 2*N*lg N + 3*N**2 , where lg( N ) = smallest integer k such
	     that 2**k >= N .

     IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
	     On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.

     LIWORK  (input) INTEGER
	     The dimension of array IWORK.  If JOBZ = 'N' or N <= 1, LIWORK
	     must be at least 1.  If JOBZ = 'V' and N > 1, LIWORK must be at
	     least 2 + 5*N .

									Page 2

CHBEVD(3F)							    CHBEVD(3F)

     INFO    (output) INTEGER
	     = 0:  successful exit.
	     < 0:  if INFO = -i, the i-th argument had an illegal value.
	     > 0:  if INFO = i, the algorithm failed to converge; i off-
	     diagonal elements of an intermediate tridiagonal form did not
	     converge to zero.

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