SRC/ssytd2.f(3)            Library Functions Manual            SRC/ssytd2.f(3)

NAME
       SRC/ssytd2.f

SYNOPSIS
   Functions/Subroutines
       subroutine ssytd2 (uplo, n, a, lda, d, e, tau, info)
           SSYTD2 reduces a symmetric matrix to real symmetric tridiagonal
           form by an orthogonal similarity transformation (unblocked
           algorithm).

Function/Subroutine Documentation
   subroutine ssytd2 (character uplo, integer n, real, dimension( lda, * ) a,
       integer lda, real, dimension( * ) d, real, dimension( * ) e, real,
       dimension( * ) tau, integer info)
       SSYTD2 reduces a symmetric matrix to real symmetric tridiagonal form by
       an orthogonal similarity transformation (unblocked algorithm).

       Purpose:


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

       Parameters
           UPLO

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

           N

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

           A

           !>          A is 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

           !>          LDA is INTEGER
           !>          The leading dimension of the array A.  LDA >= max(1,N).
           !>

           D

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

           E

           !>          E is 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

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

           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


           Univ. of Colorado Denver


           NAG Ltd.

       Further Details:


           !>
           !>  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).
           !>

       Definition at line 172 of file ssytd2.f.

Author
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LAPACK                          Version 3.12.0                 SRC/ssytd2.f(3)