SGEHRD (3) - Linux Manuals

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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