Contents
chbgst - reduce a complex Hermitian-definite banded general-
ized eigenproblem A*x = lambda*B*x to standard form C*y =
lambda*y,
SUBROUTINE CHBGST(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX,
WORK, RWORK, INFO)
CHARACTER * 1 VECT, UPLO
COMPLEX AB(LDAB,*), BB(LDBB,*), X(LDX,*), WORK(*)
INTEGER N, KA, KB, LDAB, LDBB, LDX, INFO
REAL RWORK(*)
SUBROUTINE CHBGST_64(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X,
LDX, WORK, RWORK, INFO)
CHARACTER * 1 VECT, UPLO
COMPLEX AB(LDAB,*), BB(LDBB,*), X(LDX,*), WORK(*)
INTEGER*8 N, KA, KB, LDAB, LDBB, LDX, INFO
REAL RWORK(*)
F95 INTERFACE
SUBROUTINE HBGST(VECT, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB], X,
[LDX], [WORK], [RWORK], [INFO])
CHARACTER(LEN=1) :: VECT, UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: AB, BB, X
INTEGER :: N, KA, KB, LDAB, LDBB, LDX, INFO
REAL, DIMENSION(:) :: RWORK
SUBROUTINE HBGST_64(VECT, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB],
X, [LDX], [WORK], [RWORK], [INFO])
CHARACTER(LEN=1) :: VECT, UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: AB, BB, X
INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDX, INFO
REAL, DIMENSION(:) :: RWORK
C INTERFACE
#include <sunperf.h>
void chbgst(char vect, char uplo, int n, int ka, int kb,
complex *ab, int ldab, complex *bb, int ldbb, com-
plex *x, int ldx, int *info);
void chbgst_64(char vect, char uplo, long n, long ka, long
kb, complex *ab, long ldab, complex *bb, long
ldbb, complex *x, long ldx, long *info);
chbgst reduces a complex Hermitian-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**H*S by CPBSTF,
using a split Cholesky factorization. A is overwritten by C
= X**H*A*X, where X = S**(-1)*Q and Q is a unitary 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 Her-
mitian 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**H*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 CPBSTF, 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(N)
RWORK (workspace)
dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value.