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---
:name: dlartgs
:md5sum: bf0292e885c671bdbb8046966e02a27e
:category: :subroutine
:arguments:
- x:
:type: doublereal
:intent: input
- y:
:type: doublereal
:intent: input
- sigma:
:type: doublereal
:intent: input
- cs:
:type: doublereal
:intent: output
- sn:
:type: doublereal
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DLARTGS( X, Y, SIGMA, CS, SN )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLARTGS generates a plane rotation designed to introduce a bulge in\n\
* Golub-Reinsch-style implicit QR iteration for the bidiagonal SVD\n\
* problem. X and Y are the top-row entries, and SIGMA is the shift.\n\
* The computed CS and SN define a plane rotation satisfying\n\
*\n\
* [ CS SN ] . [ X^2 - SIGMA ] = [ R ],\n\
* [ -SN CS ] [ X * Y ] [ 0 ]\n\
*\n\
* with R nonnegative. If X^2 - SIGMA and X * Y are 0, then the\n\
* rotation is by PI/2.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* X (input) DOUBLE PRECISION\n\
* The (1,1) entry of an upper bidiagonal matrix.\n\
*\n\
* Y (input) DOUBLE PRECISION\n\
* The (1,2) entry of an upper bidiagonal matrix.\n\
*\n\
* SIGMA (input) DOUBLE PRECISION\n\
* The shift.\n\
*\n\
* CS (output) DOUBLE PRECISION\n\
* The cosine of the rotation.\n\
*\n\
* SN (output) DOUBLE PRECISION\n\
* The sine of the rotation.\n\
*\n\n\
* ===================================================================\n\
*\n"
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