Contents
dsbgst - reduce a real symmetric-definite banded generalized
eigenproblem A*x = lambda*B*x to standard form C*y =
lambda*y,
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);
dsbgst 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.
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 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)
The leading dimension of the array AB. LDAB >=
KA+1.
BB (input)
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)
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 ille-
gal value.