lartgs(3)                  Library Functions Manual                  lartgs(3)

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.

       Definition at line 89 of file dlartgs.f.

   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.

       Definition at line 89 of file slartgs.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                       lartgs(3)