NAME

       lartgs - lartgs: generate plane rotation for bidiag SVD

SYNOPSIS

   Functions
       subroutine dlartgs (x, y, sigma, cs, sn)
           DLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the
           bidiagonal SVD problem.
       subroutine slartgs (x, y, sigma, cs, sn)
           SLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the
           bidiagonal SVD problem.

Detailed Description

Function Documentation

   subroutine dlartgs (double precision x, double precision y, double precision sigma, double precision cs,
       double precision sn)
       DLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the
       bidiagonal SVD problem.

       Purpose:

            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.

       Parameters
           X

                     X is DOUBLE PRECISION
                     The (1,1) entry of an upper bidiagonal matrix.

           Y

                     Y is DOUBLE PRECISION
                     The (1,2) entry of an upper bidiagonal matrix.

           SIGMA

                     SIGMA is DOUBLE PRECISION
                     The shift.

           CS

                     CS is DOUBLE PRECISION
                     The cosine of the rotation.

           SN

                     SN is DOUBLE PRECISION
                     The sine of the rotation.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

   subroutine slartgs (real x, real y, real sigma, real cs, real sn)
       SLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the
       bidiagonal SVD problem.

       Purpose:

            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.

       Parameters
           X

                     X is REAL
                     The (1,1) entry of an upper bidiagonal matrix.

           Y

                     Y is REAL
                     The (1,2) entry of an upper bidiagonal matrix.

           SIGMA

                     SIGMA is REAL
                     The shift.

           CS

                     CS is REAL
                     The cosine of the rotation.

           SN

                     SN is REAL
                     The sine of the rotation.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

Author

       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.12.0                               Fri Aug 9 2024 02:33:22                                   lartgs(3)