SYNOPSIS

SUBROUTINE SSBGST(

VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, INFO )

    

CHARACTER UPLO, VECT

    

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

    

REAL AB( LDAB, * ), BB( LDBB, * ), WORK( * ), X( LDX, * )

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.

ARGUMENTS

VECT (input) CHARACTER*1

= 'N': do not form the transformation matrix X;
= 'V': form X.

UPLO (input) CHARACTER*1

= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is 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'. KA >= KB >= 0.

AB (input/output) 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 (input) INTEGER

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

BB (input) 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 (input) INTEGER

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

X (output) REAL array, dimension (LDX,N)

If VECT = 'V', the n-by-n matrix X. If VECT = 'N', the array X is not referenced.

LDX (input) INTEGER

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

WORK (workspace) REAL array, dimension (2*N)

INFO (output) INTEGER

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