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

.in +1c
.ti -1c
.RI "subroutine \fBssbgst\fP (VECT, UPLO, \fBN\fP, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, INFO)"
.br
.RI "\fBSSBGST\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine ssbgst (character VECT, character UPLO, integer N, integer KA, integer KB, real, dimension( ldab, * ) AB, integer LDAB, real, dimension( ldbb, * ) BB, integer LDBB, real, dimension( ldx, * ) X, integer LDX, real, dimension( * ) WORK, integer INFO)"

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

.PP
.nf
 SSBGST reduces a real symmetric-definite banded generalized
 eigenproblem  A*x = lambda*B*x  to standard form  C*y = lambda*y,
 such that C has the same bandwidth as A.

 B must have been previously factorized as S**T*S by SPBSTF, using a
 split Cholesky factorization. A is overwritten by C = X**T*A*X, where
 X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the
 bandwidth of A.
.fi
.PP
 
.RE
.PP
\fBParameters:\fP
.RS 4
\fIVECT\fP 
.PP
.nf
          VECT is CHARACTER*1
          = 'N':  do not form the transformation matrix X;
          = 'V':  form X.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is 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'.  KA >= 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 transformed matrix X**T*A*X, stored in the same
          format as A.
.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)
          The banded factor S from the split Cholesky factorization of
          B, as returned by SPBSTF, stored in the first KB+1 rows of
          the array.
.fi
.PP
.br
\fILDBB\fP 
.PP
.nf
          LDBB is INTEGER
          The leading dimension of the array BB.  LDBB >= KB+1.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is REAL array, dimension (LDX,N)
          If VECT = 'V', the n-by-n matrix X.
          If VECT = 'N', the array X is not referenced.
.fi
.PP
.br
\fILDX\fP 
.PP
.nf
          LDX is INTEGER
          The leading dimension of the array X.
          LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (2*N)
.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.
.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
December 2016 
.RE
.PP

.PP
Definition at line 161 of file ssbgst\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.
