Contents
dsbtrd - reduce a real symmetric band matrix A to symmetric
tridiagonal form T by an orthogonal similarity transforma-
tion
SUBROUTINE DSBTRD(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK,
INFO)
CHARACTER * 1 VECT, UPLO
INTEGER N, KD, LDAB, LDQ, INFO
DOUBLE PRECISION AB(LDAB,*), D(*), E(*), Q(LDQ,*), WORK(*)
SUBROUTINE DSBTRD_64(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK,
INFO)
CHARACTER * 1 VECT, UPLO
INTEGER*8 N, KD, LDAB, LDQ, INFO
DOUBLE PRECISION AB(LDAB,*), D(*), E(*), Q(LDQ,*), WORK(*)
F95 INTERFACE
SUBROUTINE SBTRD(VECT, UPLO, [N], KD, AB, [LDAB], D, E, Q, [LDQ],
[WORK], [INFO])
CHARACTER(LEN=1) :: VECT, UPLO
INTEGER :: N, KD, LDAB, LDQ, INFO
REAL(8), DIMENSION(:) :: D, E, WORK
REAL(8), DIMENSION(:,:) :: AB, Q
SUBROUTINE SBTRD_64(VECT, UPLO, [N], KD, AB, [LDAB], D, E, Q, [LDQ],
[WORK], [INFO])
CHARACTER(LEN=1) :: VECT, UPLO
INTEGER(8) :: N, KD, LDAB, LDQ, INFO
REAL(8), DIMENSION(:) :: D, E, WORK
REAL(8), DIMENSION(:,:) :: AB, Q
C INTERFACE
#include <sunperf.h>
void dsbtrd(char vect, char uplo, int n, int kd, double *ab,
int ldab, double *d, double *e, double *q, int
ldq, int *info);
void dsbtrd_64(char vect, char uplo, long n, long kd, double
*ab, long ldab, double *d, double *e, double *q,
long ldq, long *info);
dsbtrd reduces a real symmetric band matrix A to symmetric
tridiagonal form T by an orthogonal similarity transforma-
tion: Q**T * A * Q = T.
VECT (input)
= 'N': do not form Q;
= 'V': form Q;
= 'U': update a matrix X, by forming X*Q.
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The order of the matrix A. N >= 0.
KD (input)
The number of superdiagonals of the matrix A if
UPLO = 'U', or the number of subdiagonals if UPLO
= 'L'. KD >= 0.
AB (input/output)
On entry, the upper or lower triangle of the sym-
metric band matrix A, stored in the first KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-
kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j)
for j<=i<=min(n,j+kd). On exit, the diagonal ele-
ments of AB are overwritten by the diagonal ele-
ments of the tridiagonal matrix T; if KD > 0, the
elements on the first superdiagonal (if UPLO =
'U') or the first subdiagonal (if UPLO = 'L') are
overwritten by the off-diagonal elements of T; the
rest of AB is overwritten by values generated dur-
ing the reduction.
LDAB (input)
The leading dimension of the array AB. LDAB >=
KD+1.
D (output)
The diagonal elements of the tridiagonal matrix T.
E (output)
The off-diagonal elements of the tridiagonal
matrix T: E(i) = T(i,i+1) if UPLO = 'U'; E(i) =
T(i+1,i) if UPLO = 'L'.
Q (input/output)
On entry, if VECT = 'U', then Q must contain an
N-by-N matrix X; if VECT = 'N' or 'V', then Q need
not be set.
On exit: if VECT = 'V', Q contains the N-by-N
orthogonal matrix Q; if VECT = 'U', Q contains the
product X*Q; if VECT = 'N', the array Q is not
referenced.
LDQ (input)
The leading dimension of the array Q. LDQ >= 1,
and LDQ >= N if VECT = 'V' or 'U'.
WORK (workspace)
dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value
Modified by Linda Kaufman, Bell Labs.