dsbgv man page on Scientific

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

NAME
       DSBGV  - computes all the eigenvalues, and optionally, the eigenvectors
       of a real generalized symmetric-definite banded	eigenproblem,  of  the
       form A*x=(lambda)*B*x

SYNOPSIS
       SUBROUTINE DSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ,
			 WORK, INFO )

	   CHARACTER	 JOBZ, UPLO

	   INTEGER	 INFO, KA, KB, LDAB, LDBB, LDZ, N

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

PURPOSE
       DSBGV computes all the eigenvalues, and optionally, the eigenvectors of
       a real generalized symmetric-definite banded eigenproblem, of the  form
       A*x=(lambda)*B*x.  Here A and B are assumed to be symmetric and banded,
       and B is also positive definite.

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

       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangles of A and B are stored;
	       = 'L':  Lower triangles of A and B are 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'. KB >= 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 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 contents of AB are destroyed.

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

       BB      (input/output) DOUBLE PRECISION array, dimension (LDBB, N)
	       On  entry,  the	upper  or lower triangle of the symmetric band
	       matrix B, stored in the first kb+1 rows of the array.  The j-th
	       column  of  B  is  stored in the j-th column of the array BB as
	       follows: if UPLO = 'U', BB(kb+1+i-j,j) =	 B(i,j)	 for  max(1,j-
	       kb)<=i<=j;   if	 UPLO  =  'L',	BB(1+i-j,j)	=  B(i,j)  for
	       j<=i<=min(n,j+kb).  On  exit,  the  factor  S  from  the	 split
	       Cholesky factorization B = S**T*S, as returned by DPBSTF.

       LDBB    (input) INTEGER
	       The leading dimension of the array BB.  LDBB >= KB+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 matrix Z of
	       eigenvectors, with the i-th column of Z holding the eigenvector
	       associated  with	 W(i). The eigenvectors are normalized so that
	       Z**T*B*Z = 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 >= N.

       WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value
	       > 0:  if INFO = i, and i is:
	       <=  N:	the  algorithm failed to converge: i off-diagonal ele‐
	       ments of an intermediate tridiagonal form did not  converge  to
	       zero; > N:   if INFO = N + i, for 1 <= i <= N, then DPBSTF
	       returned	 INFO = i: B is not positive definite.	The factoriza‐
	       tion of B could not be completed and no eigenvalues  or	eigen‐
	       vectors were computed.

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