dsbevd man page on Scientific

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DSBEVD(1)	      LAPACK driver routine (version 3.2)	     DSBEVD(1)

NAME
       DSBEVD  - computes all the eigenvalues and, optionally, eigenvectors of
       a real symmetric band matrix A

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

	   CHARACTER	  JOBZ, UPLO

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

	   INTEGER	  IWORK( * )

	   DOUBLE	  PRECISION  AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ,
			  * )

PURPOSE
       DSBEVD computes all the eigenvalues and, optionally, eigenvectors of  a
       real  symmetric	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  dig‐
       its, 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) DOUBLE PRECISION array, dimension (LDAB, N)
	       On entry, the upper or lower triangle  of  the  symmetric  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-
	       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 gener‐
	       ated 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) DOUBLE PRECISION array, dimension (N)
	       If INFO = 0, the eigenvalues in ascending order.

       Z       (output) DOUBLE PRECISION 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) DOUBLE PRECISION array,
	       dimension (LWORK) On exit, if INFO =  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 > 2, LWORK must
	       be  at  least  2*N.  If JOBZ  = 'V' and N > 2, LWORK must be at
	       least ( 1 + 5*N + 2*N**2 ).  If LWORK = -1,  then  a  workspace
	       query is assumed; the routine only calculates the optimal sizes
	       of the WORK and IWORK arrays, returns these values as the first
	       entries	of  the	 WORK  and  IWORK arrays, and no error message
	       related to LWORK or LIWORK is issued by XERBLA.

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

       LIWORK  (input) INTEGER
	       The dimension of the array LIWORK.  If JOBZ  = 'N' or N	<=  1,
	       LIWORK  must  be	 at least 1.  If JOBZ  = 'V' and N > 2, LIWORK
	       must be at least 3 + 5*N.  If LIWORK =  -1,  then  a  workspace
	       query is assumed; the routine only calculates the optimal sizes
	       of the WORK and IWORK arrays, returns these values as the first
	       entries	of  the	 WORK  and  IWORK arrays, and no error message
	       related to LWORK or LIWORK is issued by XERBLA.

       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.

 LAPACK driver routine (version 3November 2008			     DSBEVD(1)
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