sgehrd.f(3)

NAME
sgehrd.f -

SYNOPSIS

  Functions/Subroutines

subroutine sgehrd (N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO)
SGEHRD

Function/Subroutine Documentation

  subroutine sgehrd (integerN, integerILO, integerIHI, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( * )WORK, integerLWORK, integerINFO)

SGEHRD

Purpose:

     SGEHRD reduces a real general matrix A to upper Hessenberg form H by
     an orthogonal similarity transformation:  Q**T * A * Q = H .

Parameters:
    N

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

    ILO

              ILO is INTEGER

    IHI

              IHI is INTEGER

              It is assumed that A is already upper triangular in rows
              and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
              set by a previous call to SGEBAL; otherwise they should be
              set to 1 and N respectively. See Further Details.
              1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

    A

              A is REAL array, dimension (LDA,N)
              On entry, the N-by-N general matrix to be reduced.
              On exit, the upper triangle and the first subdiagonal of A
              are overwritten with the upper Hessenberg matrix H, 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).

    TAU

              TAU is REAL array, dimension (N-1)
              The scalar factors of the elementary reflectors (see Further
              Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
              zero.

    WORK

              WORK is REAL array, dimension (LWORK)
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The length of the array WORK.  LWORK >= max(1,N).
              For optimum performance LWORK >= N*NB, where NB is the
              optimal blocksize.

              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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.

Date:
    November 2011

Further Details:

      The matrix Q is represented as a product of (ihi-ilo) elementary
      reflectors

         Q = H(ilo) H(ilo+1) . . . H(ihi-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, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
      exit in A(i+2:ihi,i), and tau in TAU(i).

      The contents of A are illustrated by the following example, with
      n = 7, ilo = 2 and ihi = 6:

      on entry,                        on exit,

      ( a   a   a   a   a   a   a )    (  a   a   h   h   h   h   a )
      (     a   a   a   a   a   a )    (      a   h   h   h   h   a )
      (     a   a   a   a   a   a )    (      h   h   h   h   h   h )
      (     a   a   a   a   a   a )    (      v2  h   h   h   h   h )
      (     a   a   a   a   a   a )    (      v2  v3  h   h   h   h )
      (     a   a   a   a   a   a )    (      v2  v3  v4  h   h   h )
      (                         a )    (                          a )

      where a denotes an element of the original matrix A, h denotes a
      modified element of the upper Hessenberg matrix H, and vi denotes an
      element of the vector defining H(i).

      This file is a slight modification of LAPACK-3.0's DGEHRD
      subroutine incorporating improvements proposed by Quintana-Orti and
      Van de Geijn (2006). (See DLAHR2.)

Definition at line 169 of file sgehrd.f.

Author

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