dsbtrd(3P) Sun Performance Library dsbtrd(3P)NAMEdsbtrd - reduce a real symmetric band matrix A to symmetric tridiagonal
form T by an orthogonal similarity transformation
SYNOPSIS
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);
PURPOSEdsbtrd reduces a real symmetric band matrix A to symmetric tridiagonal
form T by an orthogonal similarity transformation: Q**T * A * Q = T.
ARGUMENTS
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 symmetric 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 elements of AB are
overwritten by the diagonal elements 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 during 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 illegal value
FURTHER DETAILS
Modified by Linda Kaufman, Bell Labs.
6 Mar 2009 dsbtrd(3P)
