table of contents
| 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 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 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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |