.TH "lartgs" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lartgs \- lartgs: generate plane rotation for bidiag SVD
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBdlartgs\fP (x, y, sigma, cs, sn)"
.br
.RI "\fBDLARTGS\fP generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem\&. "
.ti -1c
.RI "subroutine \fBslartgs\fP (x, y, sigma, cs, sn)"
.br
.RI "\fBSLARTGS\fP generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine dlartgs (double precision x, double precision y, double precision sigma, double precision cs, double precision sn)"

.PP
\fBDLARTGS\fP generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLARTGS generates a plane rotation designed to introduce a bulge in
 Golub-Reinsch-style implicit QR iteration for the bidiagonal SVD
 problem\&. X and Y are the top-row entries, and SIGMA is the shift\&.
 The computed CS and SN define a plane rotation satisfying

    [  CS  SN  ]  \&.  [ X^2 - SIGMA ]  =  [ R ],
    [ -SN  CS  ]     [    X * Y    ]     [ 0 ]

 with R nonnegative\&.  If X^2 - SIGMA and X * Y are 0, then the
 rotation is by PI/2\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIX\fP 
.PP
.nf
          X is DOUBLE PRECISION
          The (1,1) entry of an upper bidiagonal matrix\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          Y is DOUBLE PRECISION
          The (1,2) entry of an upper bidiagonal matrix\&.
.fi
.PP
.br
\fISIGMA\fP 
.PP
.nf
          SIGMA is DOUBLE PRECISION
          The shift\&.
.fi
.PP
.br
\fICS\fP 
.PP
.nf
          CS is DOUBLE PRECISION
          The cosine of the rotation\&.
.fi
.PP
.br
\fISN\fP 
.PP
.nf
          SN is DOUBLE PRECISION
          The sine of the rotation\&.
.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

.SS "subroutine slartgs (real x, real y, real sigma, real cs, real sn)"

.PP
\fBSLARTGS\fP generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SLARTGS generates a plane rotation designed to introduce a bulge in
 Golub-Reinsch-style implicit QR iteration for the bidiagonal SVD
 problem\&. X and Y are the top-row entries, and SIGMA is the shift\&.
 The computed CS and SN define a plane rotation satisfying

    [  CS  SN  ]  \&.  [ X^2 - SIGMA ]  =  [ R ],
    [ -SN  CS  ]     [    X * Y    ]     [ 0 ]

 with R nonnegative\&.  If X^2 - SIGMA and X * Y are 0, then the
 rotation is by PI/2\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIX\fP 
.PP
.nf
          X is REAL
          The (1,1) entry of an upper bidiagonal matrix\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          Y is REAL
          The (1,2) entry of an upper bidiagonal matrix\&.
.fi
.PP
.br
\fISIGMA\fP 
.PP
.nf
          SIGMA is REAL
          The shift\&.
.fi
.PP
.br
\fICS\fP 
.PP
.nf
          CS is REAL
          The cosine of the rotation\&.
.fi
.PP
.br
\fISN\fP 
.PP
.nf
          SN is REAL
          The sine of the rotation\&.
.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

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.