.TH "laqr1" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
laqr1 \- laqr1: step in hseqr
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclaqr1\fP (n, h, ldh, s1, s2, v)"
.br
.RI "\fBCLAQR1\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\&. "
.ti -1c
.RI "subroutine \fBdlaqr1\fP (n, h, ldh, sr1, si1, sr2, si2, v)"
.br
.RI "\fBDLAQR1\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\&. "
.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\&. "
.ti -1c
.RI "subroutine \fBzlaqr1\fP (n, h, ldh, s1, s2, v)"
.br
.RI "\fBZLAQR1\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 "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine claqr1 (integer n, complex, dimension( ldh, * ) h, integer ldh, complex s1, complex s2, complex, dimension( * ) v)"

.PP
\fBCLAQR1\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, CLAQR1 sets v to a
!>      scalar multiple of the first column of the product
!>
!>      (*)  K = (H - s1*I)*(H - s2*I)
!>
!>      scaling to avoid overflows and most underflows\&.
!>
!>      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 COMPLEX 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
\fIS1\fP 
.PP
.nf
!>          S1 is COMPLEX
!> 
.fi
.PP
.br
\fIS2\fP 
.PP
.nf
!>          S2 is COMPLEX
!>
!>          S1 and S2 are the shifts defining K in (*) above\&.
!> 
.fi
.PP
.br
\fIV\fP 
.PP
.nf
!>          V is COMPLEX 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 \fB106\fP of file \fBclaqr1\&.f\fP\&.
.SS "subroutine dlaqr1 (integer n, double precision, dimension( ldh, * ) h, integer ldh, double precision sr1, double precision si1, double precision sr2, double precision si2, double precision, dimension( * ) v)"

.PP
\fBDLAQR1\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, DLAQR1 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 DOUBLE PRECISION 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 DOUBLE PRECISION
!> 
.fi
.PP
.br
\fISI1\fP 
.PP
.nf
!>          SI1 is DOUBLE PRECISION
!> 
.fi
.PP
.br
\fISR2\fP 
.PP
.nf
!>          SR2 is DOUBLE PRECISION
!> 
.fi
.PP
.br
\fISI2\fP 
.PP
.nf
!>          SI2 is DOUBLE PRECISION
!>              The shifts in (*)\&.
!> 
.fi
.PP
.br
\fIV\fP 
.PP
.nf
!>          V is DOUBLE PRECISION 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 \fBdlaqr1\&.f\fP\&.
.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\&.
.SS "subroutine zlaqr1 (integer n, complex*16, dimension( ldh, * ) h, integer ldh, complex*16 s1, complex*16 s2, complex*16, dimension( * ) v)"

.PP
\fBZLAQR1\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, ZLAQR1 sets v to a
!>      scalar multiple of the first column of the product
!>
!>      (*)  K = (H - s1*I)*(H - s2*I)
!>
!>      scaling to avoid overflows and most underflows\&.
!>
!>      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 COMPLEX*16 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
\fIS1\fP 
.PP
.nf
!>          S1 is COMPLEX*16
!> 
.fi
.PP
.br
\fIS2\fP 
.PP
.nf
!>          S2 is COMPLEX*16
!>
!>          S1 and S2 are the shifts defining K in (*) above\&.
!> 
.fi
.PP
.br
\fIV\fP 
.PP
.nf
!>          V is COMPLEX*16 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 \fB106\fP of file \fBzlaqr1\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.