.TH "slaqr1.f" 3 "Tue Nov 14 2017" "Version 3.8.0" "LAPACK" \" -*- nroff -*-
.ad l
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.SH NAME
slaqr1.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBslaqr1\fP (\fBN\fP, H, LDH, SR1, SI1, SR2, SI2, V)"
.br
.RI "\fBSLAQR1\fP sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine slaqr1 (integer N, real, dimension( ldh, * ) H, integer LDH, real SR1, real SI1, real SR2, real SI2, real, dimension( * ) V)"

.PP
\fBSLAQR1\fP sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts\&.  
.PP
\fBPurpose: \fP
.RS 4

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.nf
      Given a 2-by-2 or 3-by-3 matrix H, SLAQR1 sets v to a
      scalar multiple of the first column of the product

      (*)  K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)

      scaling to avoid overflows and most underflows. It
      is assumed that either

              1) sr1 = sr2 and si1 = -si2
          or
              2) si1 = si2 = 0.

      This is useful for starting double implicit shift bulges
      in the QR algorithm.
.fi
.PP
 
.RE
.PP
\fBParameters:\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
              Order of the matrix H. N must be either 2 or 3.
.fi
.PP
.br
\fIH\fP 
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          H is REAL array, dimension (LDH,N)
              The 2-by-2 or 3-by-3 matrix H in (*).
.fi
.PP
.br
\fILDH\fP 
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.nf
          LDH is INTEGER
              The leading dimension of H as declared in
              the calling procedure.  LDH.GE.N
.fi
.PP
.br
\fISR1\fP 
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.nf
          SR1 is REAL
.fi
.PP
.br
\fISI1\fP 
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.nf
          SI1 is REAL
.fi
.PP
.br
\fISR2\fP 
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.nf
          SR2 is REAL
.fi
.PP
.br
\fISI2\fP 
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.nf
          SI2 is REAL
              The shifts in (*).
.fi
.PP
.br
\fIV\fP 
.PP
.nf
          V is REAL array, dimension (N)
              A scalar multiple of the first column of the
              matrix K in (*).
.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
June 2017 
.RE
.PP
\fBContributors: \fP
.RS 4
Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA 
.RE
.PP

.PP
Definition at line 123 of file slaqr1\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.
