.TH "SRC/slaqz1.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/slaqz1.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBslaqz1\fP (a, lda, b, ldb, sr1, sr2, si, beta1, beta2, v)"
.br
.RI "\fBSLAQZ1\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine slaqz1 (real, dimension( lda, * ), intent(in) a, integer, intent(in) lda, real, dimension( ldb, * ), intent(in) b, integer, intent(in) ldb, real, intent(in) sr1, real, intent(in) sr2, real, intent(in) si, real, intent(in) beta1, real, intent(in) beta2, real, dimension( * ), intent(out) v)"

.PP
\fBSLAQZ1\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
      Given a 3-by-3 matrix pencil (A,B), SLAQZ1 sets v to a
      scalar multiple of the first column of the product

      (*)  K = (A - (beta2*sr2 - i*si)*B)*B^(-1)*(beta1*A - (sr2 + i*si2)*B)*B^(-1)\&.

      It is assumed that either

              1) sr1 = sr2
          or
              2) si = 0\&.

      This is useful for starting double implicit shift bulges
      in the QZ algorithm\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIA\fP 
.PP
.nf
          A is REAL array, dimension (LDA,N)
              The 3-by-3 matrix A in (*)\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
              The leading dimension of A as declared in
              the calling procedure\&.
.fi
.PP
 
.br
\fIB\fP 
.PP
.nf
          B is REAL array, dimension (LDB,N)
              The 3-by-3 matrix B in (*)\&.
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
              The leading dimension of B as declared in
              the calling procedure\&.
.fi
.PP
.br
\fISR1\fP 
.PP
.nf
          SR1 is REAL
.fi
.PP
.br
\fISR2\fP 
.PP
.nf
          SR2 is REAL
.fi
.PP
.br
\fISI\fP 
.PP
.nf
          SI is REAL
.fi
.PP
.br
\fIBETA1\fP 
.PP
.nf
          BETA1 is REAL
.fi
.PP
.br
\fIBETA2\fP 
.PP
.nf
          BETA2 is REAL
.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
Thijs Steel, KU Leuven 
.RE
.PP
\fBDate\fP
.RS 4
May 2020 
.RE
.PP

.PP
Definition at line \fB125\fP of file \fBslaqz1\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.