.TH "SRC/slaqr1.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/slaqr1.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBslaqr1\fP (n, 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

.PP
.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 
.PP
.nf
          H is REAL array, dimension (LDH,N)
              The 2-by-2 or 3-by-3 matrix H in (*)\&.
.fi
.PP
.br
\fILDH\fP 
.PP
.nf
          LDH is INTEGER
              The leading dimension of H as declared in
              the calling procedure\&.  LDH >= N
.fi
.PP
.br
\fISR1\fP 
.PP
.nf
          SR1 is REAL
.fi
.PP
.br
\fISI1\fP 
.PP
.nf
          SI1 is REAL
.fi
.PP
.br
\fISR2\fP 
.PP
.nf
          SR2 is REAL
.fi
.PP
.br
\fISI2\fP 
.PP
.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 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBContributors:\fP
.RS 4
Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA 
.RE
.PP

.PP
Definition at line \fB120\fP of file \fBslaqr1\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.