.TH "sgehd2.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*-
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.SH NAME
sgehd2.f \- 
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBsgehd2\fP (N, ILO, IHI, A, LDA, TAU, WORK, INFO)"
.br
.RI "\fI\fBSGEHD2\fP reduces a general square matrix to upper Hessenberg form using an unblocked algorithm\&. \fP"
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine sgehd2 (integerN, integerILO, integerIHI, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( * )WORK, integerINFO)"

.PP
\fBSGEHD2\fP reduces a general square matrix to upper Hessenberg form using an unblocked algorithm\&.  
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\fBPurpose: \fP
.RS 4

.PP
.nf
 SGEHD2 reduces a real general matrix A to upper Hessenberg form H by
 an orthogonal similarity transformation:  Q**T * A * Q = H .
.fi
.PP
 
.RE
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\fBParameters:\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A.  N >= 0.
.fi
.PP
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\fIILO\fP 
.PP
.nf
          ILO is INTEGER
.fi
.PP
.br
\fIIHI\fP 
.PP
.nf
          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 <= max(1,N).
.fi
.PP
.br
\fIA\fP 
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.nf
          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.
.fi
.PP
.br
\fILDA\fP 
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.nf
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
.fi
.PP
.br
\fITAU\fP 
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.nf
          TAU is REAL array, dimension (N-1)
          The scalar factors of the elementary reflectors (see Further
          Details).
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (N)
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
.fi
.PP
 
.RE
.PP
\fBAuthor:\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
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Univ\&. of Colorado Denver 
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NAG Ltd\&. 
.RE
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\fBDate:\fP
.RS 4
September 2012 
.RE
.PP
\fBFurther Details: \fP
.RS 4

.PP
.nf
  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).
.fi
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.RE
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.PP
Definition at line 150 of file sgehd2\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.