 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dlartgs()

 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
 [in] X ``` X is DOUBLE PRECISION The (1,1) entry of an upper bidiagonal matrix.``` [in] Y ``` Y is DOUBLE PRECISION The (1,2) entry of an upper bidiagonal matrix.``` [in] SIGMA ``` SIGMA is DOUBLE PRECISION The shift.``` [out] CS ``` CS is DOUBLE PRECISION The cosine of the rotation.``` [out] SN ``` SN is DOUBLE PRECISION The sine of the rotation.```

Definition at line 89 of file dlartgs.f.

90*
91* -- LAPACK computational routine --
92* -- LAPACK is a software package provided by Univ. of Tennessee, --
93* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
94*
95* .. Scalar Arguments ..
96 DOUBLE PRECISION CS, SIGMA, SN, X, Y
97* ..
98*
99* ===================================================================
100*
101* .. Parameters ..
102 DOUBLE PRECISION NEGONE, ONE, ZERO
103 parameter( negone = -1.0d0, one = 1.0d0, zero = 0.0d0 )
104* ..
105* .. Local Scalars ..
106 DOUBLE PRECISION R, S, THRESH, W, Z
107* ..
108* .. External Subroutines ..
109 EXTERNAL dlartgp
110* ..
111* .. External Functions ..
112 DOUBLE PRECISION DLAMCH
113 EXTERNAL dlamch
114* .. Executable Statements ..
115*
116 thresh = dlamch('E')
117*
118* Compute the first column of B**T*B - SIGMA^2*I, up to a scale
119* factor.
120*
121 IF( (sigma .EQ. zero .AND. abs(x) .LT. thresh) .OR.
122 \$ (abs(x) .EQ. sigma .AND. y .EQ. zero) ) THEN
123 z = zero
124 w = zero
125 ELSE IF( sigma .EQ. zero ) THEN
126 IF( x .GE. zero ) THEN
127 z = x
128 w = y
129 ELSE
130 z = -x
131 w = -y
132 END IF
133 ELSE IF( abs(x) .LT. thresh ) THEN
134 z = -sigma*sigma
135 w = zero
136 ELSE
137 IF( x .GE. zero ) THEN
138 s = one
139 ELSE
140 s = negone
141 END IF
142 z = s * (abs(x)-sigma) * (s+sigma/x)
143 w = s * y
144 END IF
145*
146* Generate the rotation.
147* CALL DLARTGP( Z, W, CS, SN, R ) might seem more natural;
148* reordering the arguments ensures that if Z = 0 then the rotation
149* is by PI/2.
150*
151 CALL dlartgp( w, z, sn, cs, r )
152*
153 RETURN
154*
155* End DLARTGS
156*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine dlartgp(F, G, CS, SN, R)
DLARTGP generates a plane rotation so that the diagonal is nonnegative.
Definition: dlartgp.f:95
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