.TH "SRC/ssbgvx.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/ssbgvx.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBssbgvx\fP (jobz, range, uplo, n, ka, kb, ab, ldab, bb, ldbb, q, ldq, vl, vu, il, iu, abstol, m, w, z, ldz, work, iwork, ifail, info)"
.br
.RI "\fBSSBGVX\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine ssbgvx (character jobz, character range, character uplo, integer n, integer ka, integer kb, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldbb, * ) bb, integer ldbb, real, dimension( ldq, * ) q, integer ldq, real vl, real vu, integer il, integer iu, real abstol, integer m, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)"

.PP
\fBSSBGVX\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SSBGVX computes selected eigenvalues, and optionally, 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\&.  Eigenvalues and
!> eigenvectors can be selected by specifying either all eigenvalues,
!> a range of values or a range of indices for the desired eigenvalues\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBZ\fP 
.PP
.nf
!>          JOBZ is CHARACTER*1
!>          = 'N':  Compute eigenvalues only;
!>          = 'V':  Compute eigenvalues and eigenvectors\&.
!> 
.fi
.PP
.br
\fIRANGE\fP 
.PP
.nf
!>          RANGE is CHARACTER*1
!>          = 'A': all eigenvalues will be found\&.
!>          = 'V': all eigenvalues in the half-open interval (VL,VU]
!>                 will be found\&.
!>          = 'I': the IL-th through IU-th eigenvalues will be found\&.
!> 
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangles of A and B are stored;
!>          = 'L':  Lower triangles of A and B are stored\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrices A and B\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIKA\fP 
.PP
.nf
!>          KA is INTEGER
!>          The number of superdiagonals of the matrix A if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'\&.  KA >= 0\&.
!> 
.fi
.PP
.br
\fIKB\fP 
.PP
.nf
!>          KB is INTEGER
!>          The number of superdiagonals of the matrix B if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'\&.  KB >= 0\&.
!> 
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
!>          AB is REAL 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\&.
!> 
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
!>          LDAB is INTEGER
!>          The leading dimension of the array AB\&.  LDAB >= KA+1\&.
!> 
.fi
.PP
.br
\fIBB\fP 
.PP
.nf
!>          BB is REAL 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(ka+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 SPBSTF\&.
!> 
.fi
.PP
.br
\fILDBB\fP 
.PP
.nf
!>          LDBB is INTEGER
!>          The leading dimension of the array BB\&.  LDBB >= KB+1\&.
!> 
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
!>          Q is REAL array, dimension (LDQ, N)
!>          If JOBZ = 'V', the n-by-n matrix used in the reduction of
!>          A*x = (lambda)*B*x to standard form, i\&.e\&. C*x = (lambda)*x,
!>          and consequently C to tridiagonal form\&.
!>          If JOBZ = 'N', the array Q is not referenced\&.
!> 
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
!>          LDQ is INTEGER
!>          The leading dimension of the array Q\&.  If JOBZ = 'N',
!>          LDQ >= 1\&. If JOBZ = 'V', LDQ >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIVL\fP 
.PP
.nf
!>          VL is REAL
!>
!>          If RANGE='V', the lower bound of the interval to
!>          be searched for eigenvalues\&. VL < VU\&.
!>          Not referenced if RANGE = 'A' or 'I'\&.
!> 
.fi
.PP
.br
\fIVU\fP 
.PP
.nf
!>          VU is REAL
!>
!>          If RANGE='V', the upper bound of the interval to
!>          be searched for eigenvalues\&. VL < VU\&.
!>          Not referenced if RANGE = 'A' or 'I'\&.
!> 
.fi
.PP
.br
\fIIL\fP 
.PP
.nf
!>          IL is INTEGER
!>
!>          If RANGE='I', the index of the
!>          smallest eigenvalue to be returned\&.
!>          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0\&.
!>          Not referenced if RANGE = 'A' or 'V'\&.
!> 
.fi
.PP
.br
\fIIU\fP 
.PP
.nf
!>          IU is INTEGER
!>
!>          If RANGE='I', the index of the
!>          largest eigenvalue to be returned\&.
!>          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0\&.
!>          Not referenced if RANGE = 'A' or 'V'\&.
!> 
.fi
.PP
.br
\fIABSTOL\fP 
.PP
.nf
!>          ABSTOL is REAL
!>          The absolute error tolerance for the eigenvalues\&.
!>          An approximate eigenvalue is accepted as converged
!>          when it is determined to lie in an interval [a,b]
!>          of width less than or equal to
!>
!>                  ABSTOL + EPS *   max( |a|,|b| ) ,
!>
!>          where EPS is the machine precision\&.  If ABSTOL is less than
!>          or equal to zero, then  EPS*|T|  will be used in its place,
!>          where |T| is the 1-norm of the tridiagonal matrix obtained
!>          by reducing A to tridiagonal form\&.
!>
!>          Eigenvalues will be computed most accurately when ABSTOL is
!>          set to twice the underflow threshold 2*SLAMCH('S'), not zero\&.
!>          If this routine returns with INFO>0, indicating that some
!>          eigenvectors did not converge, try setting ABSTOL to
!>          2*SLAMCH('S')\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The total number of eigenvalues found\&.  0 <= M <= N\&.
!>          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1\&.
!> 
.fi
.PP
.br
\fIW\fP 
.PP
.nf
!>          W is REAL array, dimension (N)
!>          If INFO = 0, the eigenvalues in ascending order\&.
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          Z is REAL 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 Z**T*B*Z = I\&.
!>          If JOBZ = 'N', then Z is not referenced\&.
!> 
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
!>          LDZ is INTEGER
!>          The leading dimension of the array Z\&.  LDZ >= 1, and if
!>          JOBZ = 'V', LDZ >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (7*N)
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (5*N)
!> 
.fi
.PP
.br
\fIIFAIL\fP 
.PP
.nf
!>          IFAIL is INTEGER array, dimension (M)
!>          If JOBZ = 'V', then if INFO = 0, the first M elements of
!>          IFAIL are zero\&.  If INFO > 0, then IFAIL contains the
!>          indices of the eigenvalues that failed to converge\&.
!>          If JOBZ = 'N', then IFAIL is not referenced\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          <= N: if INFO = i, then i eigenvectors failed to converge\&.
!>                  Their indices are stored in IFAIL\&.
!>          > N:  SPBSTF returned an error code; i\&.e\&.,
!>                if INFO = N + i, for 1 <= i <= N, then the leading
!>                principal minor of order i of B is not positive\&.
!>                The factorization of B could not be completed and
!>                no eigenvalues or eigenvectors were computed\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
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\fBContributors:\fP
.RS 4
Mark Fahey, Department of Mathematics, Univ\&. of Kentucky, USA 
.RE
.PP

.PP
Definition at line \fB291\fP of file \fBssbgvx\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.