SSBGST - reduce a real symmetric-definite banded general
ized eigenproblem A*x = lambda*B*x to standard form C*y =
lambda*y,
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 general
ized 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 SPB
STF, using a split Cholesky factorization. A is overwrit
ten 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 sym
metric 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
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 fac
torization 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 ille
gal value.
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