 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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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