# CentOS 7.0 - man page for ssbtrd (centos section 3)

```ssbtrd.f(3)							      LAPACK							       ssbtrd.f(3)

NAME
ssbtrd.f -

SYNOPSIS
Functions/Subroutines
subroutine ssbtrd (VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
SSBTRD

Function/Subroutine Documentation
subroutine ssbtrd (characterVECT, characterUPLO, integerN, integerKD, real, dimension( ldab, * )AB, integerLDAB, real, dimension( * )D, real,
dimension( * )E, real, dimension( ldq, * )Q, integerLDQ, real, dimension( * )WORK, integerINFO)
SSBTRD

Purpose:

SSBTRD reduces a real symmetric band matrix A to symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**T * A * Q = T.

Parameters:
VECT

VECT is CHARACTER*1
= 'N':  do not form Q;
= 'V':  form Q;
= 'U':  update a matrix X, by forming X*Q.

UPLO

UPLO is CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A.  N >= 0.

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

AB

AB is 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
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

LDAB is INTEGER
The leading dimension of the array AB.  LDAB >= KD+1.

D

D is REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T.

E

E is REAL 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

Q is REAL array, dimension (LDQ,N)
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

LDQ is INTEGER
The leading dimension of the array Q.
LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.

WORK

WORK is REAL array, dimension (N)

INFO

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
November 2011

Further Details:

Modified by Linda Kaufman, Bell Labs.

Definition at line 163 of file ssbtrd.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       ssbtrd.f(3)```