dsbgst(3)

NAME

DSBGST - reduce a real symmetric-definite banded general

ized eigenproblem A*x = lambda*B*x to standard form C*y = lamb

da*y,

SYNOPSIS

SUBROUTINE DSBGST( VECT, UPLO, N, KA, KB,  AB,  LDAB,  BB,
LDBB, X, LDX, WORK, INFO )
    CHARACTER      UPLO, VECT
    INTEGER        INFO, KA, KB, LDAB, LDBB, LDX, N
    DOUBLE         PRECISION AB( LDAB, * ), BB( LDBB, * ),
WORK( * ), X( LDX, * )

PURPOSE

DSBGST reduces a real symmetric-definite banded general

ized eigenproblem A*x = lambda*B*x to standard form C*y = lamb

da*y, such that C has the same bandwidth as A.

B must have been previously factorized as S**T*S by DPB

STF, 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) DOUBLE PRECISION 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 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) DOUBLE PRECISION array, dimension (LDBB,N)

The banded factor S from the split Cholesky fac

torization of B, as returned by DPBSTF, 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension

(2*N)

INFO (output) INTEGER

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

gal value.

LAPACK version 3.0 15 June 2000

DSBGST(3)