SYNOPSIS
 SUBROUTINE DSBTRD(
 VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO )
 CHARACTER UPLO, VECT
 INTEGER INFO, KD, LDAB, LDQ, N
 DOUBLE PRECISION AB( LDAB, * ), D( * ), E( * ), Q( LDQ, * ), WORK( * )
PURPOSE
DSBTRD 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 subdiagonals if UPLO = 'L'. KD >= 0.
 AB (input/output) DOUBLE PRECISION 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 column 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 offdiagonal 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) DOUBLE PRECISION array, dimension (N)
 The diagonal elements of the tridiagonal matrix T.
 E (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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.