ssbtrd(3)

NAME

SSBTRD - reduce a real symmetric band matrix A to symmet

ric 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 subdiagonals if UPLO = 'L'. KD >=

0.

AB (input/output) REAL 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 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 (N-1)

The off-diagonal elements of the tridiagonal ma

trix 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 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 or

thogonal 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 i-th argument had an ille

gal value

FURTHER DETAILS

Modified by Linda Kaufman, Bell Labs.

LAPACK version 3.0 15 June 2000

SSBTRD(3)