dsbgst(3P) Sun Performance Library dsbgst(3P)NAMEdsbgst - reduce a real symmetric-definite banded generalized eigenprob‐
lem A*x = lambda*B*x to standard form C*y = lambda*y,
SYNOPSIS
SUBROUTINE DSBGST(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX,
WORK, INFO)
CHARACTER * 1 VECT, UPLO
INTEGER N, KA, KB, LDAB, LDBB, LDX, INFO
DOUBLE PRECISION AB(LDAB,*), BB(LDBB,*), X(LDX,*), WORK(*)
SUBROUTINE DSBGST_64(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X,
LDX, WORK, INFO)
CHARACTER * 1 VECT, UPLO
INTEGER*8 N, KA, KB, LDAB, LDBB, LDX, INFO
DOUBLE PRECISION AB(LDAB,*), BB(LDBB,*), X(LDX,*), WORK(*)
F95 INTERFACE
SUBROUTINE SBGST(VECT, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB], X,
[LDX], [WORK], [INFO])
CHARACTER(LEN=1) :: VECT, UPLO
INTEGER :: N, KA, KB, LDAB, LDBB, LDX, INFO
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: AB, BB, X
SUBROUTINE SBGST_64(VECT, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB],
X, [LDX], [WORK], [INFO])
CHARACTER(LEN=1) :: VECT, UPLO
INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDX, INFO
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: AB, BB, X
C INTERFACE
#include <sunperf.h>
void dsbgst(char vect, char uplo, int n, int ka, int kb, double *ab,
int ldab, double *bb, int ldbb, double *x, int ldx, int
*info);
void dsbgst_64(char vect, char uplo, long n, long ka, long kb, double
*ab, long ldab, double *bb, long ldbb, double *x, long ldx,
long *info);
PURPOSEdsbgst reduces a real symmetric-definite banded generalized eigenprob‐
lem 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 band‐
width of A.
ARGUMENTS
VECT (input)
= 'N': do not form the transformation matrix X;
= 'V': form X.
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The order of the matrices A and B. N >= 0.
KA (input)
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KA >= 0.
KB (input)
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)
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)
The leading dimension of the array AB. LDAB >= KA+1.
BB (input)
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)
The leading dimension of the array BB. LDBB >= KB+1.
X (output)
If VECT = 'V', the n-by-n matrix X. If VECT = 'N', the array
X is not referenced.
LDX (input)
The leading dimension of the array X. LDX >= max(1,N) if
VECT = 'V'; LDX >= 1 otherwise.
WORK (workspace)
dimension(2*N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
6 Mar 2009 dsbgst(3P)
