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# dsbtrd

```
NAME
DSBTRD - reduce a real symmetric band matrix A to symmetric
tridiagonal form T by an orthogonal similarity transforma-
tion

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 transforma-
tion: Q**T * A * Q = T.

ARGUMENTS
VECT    (input) CHARACTER*1
= 'N':  do not form Q;
= 'V':  form 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 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 elements
of A 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 A is

overwritten by values generated during the reduc-
tion.

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 (N-1)
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       (output) DOUBLE PRECISION array, dimension (LDQ,N)
If VECT = 'V', the N-by-N orthogonal matrix Q.  If
VECT = 'N', the array Q is not referenced.

LDQ     (input) INTEGER
The leading dimension of the array Q.  LDQ >=
max(1,N) if VECT = 'V'.

WORK    (workspace) DOUBLE PRECISION array, dimension (N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal
value
```