# ssbgst.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine ssbgst (VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, INFO)
SSBGST

## Function/Subroutine Documentation

### 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)

SSBGST

Purpose:

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.
Parameters:

VECT

VECT is CHARACTER*1
= 'N':  do not form the transformation matrix X;
= 'V':  form X.

UPLO

UPLO is CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N

N is INTEGER
The order of the matrices A and B.  N >= 0.

KA

KA is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'.  KA >= 0.

KB

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.

AB

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.

LDAB

LDAB is INTEGER
The leading dimension of the array AB.  LDAB >= KA+1.

BB

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.

LDBB

LDBB is INTEGER
The leading dimension of the array BB.  LDBB >= KB+1.

X

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.

LDX

LDX is INTEGER
The leading dimension of the array X.
LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.

WORK

WORK is REAL array, dimension (2*N)

INFO

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value.
Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

December 2016

Definition at line 161 of file ssbgst.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page ssbgst(3) is an alias of ssbgst.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK