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lartgs(3) LAPACK 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.

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

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Tue Jan 14 2025 16:19:47 Version 3.12.0