.TH "ssbgvd.f" 3 "Tue Nov 14 2017" "Version 3.8.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
ssbgvd.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBssbgvd\fP (JOBZ, UPLO, \fBN\fP, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO)"
.br
.RI "\fBSSBGVD\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine ssbgvd (character JOBZ, character UPLO, integer N, integer KA, integer KB, real, dimension( ldab, * ) AB, integer LDAB, real, dimension( ldbb, * ) BB, integer LDBB, real, dimension( * ) W, real, dimension( ldz, * ) Z, integer LDZ, real, dimension( * ) WORK, integer LWORK, integer, dimension( * ) IWORK, integer LIWORK, integer INFO)"

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

.PP
.nf
 SSBGVD 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.  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.
.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
\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
\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 (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK.
          If N <= 1,               LWORK >= 1.
          If JOBZ = 'N' and N > 1, LWORK >= 3*N.
          If JOBZ = 'V' and N > 1, LWORK >= 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.
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
          On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
.fi
.PP
.br
\fILIWORK\fP 
.PP
.nf
          LIWORK is INTEGER
          The dimension of the array IWORK.
          If JOBZ  = 'N' or N <= 1, LIWORK >= 1.
          If JOBZ  = 'V' and N > 1, LIWORK >= 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.
.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
          > 0:  if INFO = i, and i is:
             <= N:  the algorithm failed to converge:
                    i off-diagonal elements of an intermediate
                    tridiagonal form did not converge to zero;
             > N:   if INFO = N + i, for 1 <= i <= N, then SPBSTF
                    returned INFO = i: B is not positive definite.
                    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
.PP
\fBDate:\fP
.RS 4
June 2016 
.RE
.PP
\fBContributors: \fP
.RS 4
Mark Fahey, Department of Mathematics, Univ\&. of Kentucky, USA 
.RE
.PP

.PP
Definition at line 229 of file ssbgvd\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.
