lartgs - Man Page

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.

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.

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.