
SSBTRD(l) ) SSBTRD(l)
NAME
SSBTRD  reduce a real symmetric band matrix A to symmetric tridiagonal form T by an
orthogonal similarity transformation
SYNOPSIS
SUBROUTINE SSBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO )
CHARACTER UPLO, VECT
INTEGER INFO, KD, LDAB, LDQ, N
REAL AB( LDAB, * ), D( * ), E( * ), Q( LDQ, * ), WORK( * )
PURPOSE
SSBTRD 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) CHARACTER*1
= 'N': do not form Q;
= 'V': form Q;
= 'U': update a matrix X, by forming X*Q.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
KD (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U', or the number of sub
diagonals if UPLO = 'L'. KD >= 0.
AB (input/output) REAL array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric band matrix A, stored in
the first KD+1 rows of the array. The jth column of A is stored in the jth col
umn of the array AB as follows: if UPLO = 'U', AB(kd+1+ij,j) = A(i,j) for
max(1,jkd)<=i<=j; if UPLO = 'L', AB(1+ij,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) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
D (output) REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T.
E (output) REAL array, dimension (N1)
The offdiagonal 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) REAL array, dimension (LDQ,N)
On entry, if VECT = 'U', then Q must contain an NbyN matrix X; if VECT = 'N' or
'V', then Q need not be set.
On exit: if VECT = 'V', Q contains the NbyN orthogonal matrix Q; if VECT = 'U',
Q contains the product X*Q; if VECT = 'N', the array Q is not referenced.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= 1, and LDQ >= N if VECT = 'V' or
'U'.
WORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
FURTHER DETAILS
Modified by Linda Kaufman, Bell Labs.
LAPACK version 3.0 15 June 2000 SSBTRD(l) 
