Provided by: liblapack-doc_3.3.1-1_all NAME

LAPACK-3  -  reduces  a  real  symmetric  matrix  A  to symmetric tridiagonal form T by an
orthogonal similarity transformation

SYNOPSIS

SUBROUTINE SSYTD2( UPLO, N, A, LDA, D, E, TAU, INFO )

CHARACTER      UPLO

INTEGER        INFO, LDA, N

REAL           A( LDA, * ), D( * ), E( * ), TAU( * )

PURPOSE

SSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal form T by an  orthogonal
similarity transformation: Q**T * A * Q = T.

ARGUMENTS

UPLO    (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U':  Upper triangular
= 'L':  Lower triangular

N       (input) INTEGER
The order of the matrix A.  N >= 0.

A       (input/output) REAL array, dimension (LDA,N)
On entry, the symmetric matrix A.  If UPLO = 'U', the leading
n-by-n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced.  If UPLO = 'L', the
leading n-by-n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if UPLO = 'U', the diagonal and first superdiagonal
of A are overwritten by the corresponding elements of the
tridiagonal matrix T, and the elements above the first
superdiagonal, with the array TAU, represent the orthogonal
matrix Q as a product of elementary reflectors; if UPLO
= 'L', the diagonal and first subdiagonal of A are over-
written by the corresponding elements of the tridiagonal
matrix T, and the elements below the first subdiagonal, with
the array TAU, represent the orthogonal matrix Q as a product
of elementary reflectors. See Further Details.
LDA     (input) INTEGER
The leading dimension of the array A.  LDA >= max(1,N).

D       (output) REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).

E       (output) REAL array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.

TAU     (output) REAL array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).

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

FURTHERDETAILS

If UPLO = 'U', the matrix Q is represented as a product of elementary
reflectors
Q = H(n-1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I - tau * v * v**T
where tau is a real scalar, and v is a real vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau in TAU(i).
If UPLO = 'L', the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(n-1).
Each H(i) has the form
H(i) = I - tau * v * v**T
where tau is a real scalar, and v is a real vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
and tau in TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = 'U':                       if UPLO = 'L':
(  d   e   v2  v3  v4 )              (  d                  )
(      d   e   v3  v4 )              (  e   d              )
(          d   e   v4 )              (  v1  e   d          )
(              d   e  )              (  v1  v2  e   d      )
(                  d  )              (  v1  v2  v3  e   d  )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).

LAPACK routine (version 3.3.1)             April 2011                            SSYTD2(3lapack)