LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ slartgs()

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.

Download SLARTGS + dependencies [TGZ] [ZIP] [TXT]

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
[in]X
          X is REAL
          The (1,1) entry of an upper bidiagonal matrix.
[in]Y
          Y is REAL
          The (1,2) entry of an upper bidiagonal matrix.
[in]SIGMA
          SIGMA is REAL
          The shift.
[out]CS
          CS is REAL
          The cosine of the rotation.
[out]SN
          SN is REAL
          The sine of the rotation.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2017

Definition at line 92 of file slartgs.f.

92 *
93 * -- LAPACK computational routine (version 3.8.0) --
94 * -- LAPACK is a software package provided by Univ. of Tennessee, --
95 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
96 * November 2017
97 *
98 * .. Scalar Arguments ..
99  REAL cs, sigma, sn, x, y
100 * ..
101 *
102 * ===================================================================
103 *
104 * .. Parameters ..
105  REAL negone, one, zero
106  parameter( negone = -1.0e0, one = 1.0e0, zero = 0.0e0 )
107 * ..
108 * .. Local Scalars ..
109  REAL r, s, thresh, w, z
110 * ..
111 * .. External Subroutines ..
112  EXTERNAL slartgp
113 * ..
114 * .. External Functions ..
115  REAL slamch
116  EXTERNAL slamch
117 * .. Executable Statements ..
118 *
119  thresh = slamch('E')
120 *
121 * Compute the first column of B**T*B - SIGMA^2*I, up to a scale
122 * factor.
123 *
124  IF( (sigma .EQ. zero .AND. abs(x) .LT. thresh) .OR.
125  $ (abs(x) .EQ. sigma .AND. y .EQ. zero) ) THEN
126  z = zero
127  w = zero
128  ELSE IF( sigma .EQ. zero ) THEN
129  IF( x .GE. zero ) THEN
130  z = x
131  w = y
132  ELSE
133  z = -x
134  w = -y
135  END IF
136  ELSE IF( abs(x) .LT. thresh ) THEN
137  z = -sigma*sigma
138  w = zero
139  ELSE
140  IF( x .GE. zero ) THEN
141  s = one
142  ELSE
143  s = negone
144  END IF
145  z = s * (abs(x)-sigma) * (s+sigma/x)
146  w = s * y
147  END IF
148 *
149 * Generate the rotation.
150 * CALL SLARTGP( Z, W, CS, SN, R ) might seem more natural;
151 * reordering the arguments ensures that if Z = 0 then the rotation
152 * is by PI/2.
153 *
154  CALL slartgp( w, z, sn, cs, r )
155 *
156  RETURN
157 *
158 * End SLARTGS
159 *
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine slartgp(F, G, CS, SN, R)
SLARTGP generates a plane rotation so that the diagonal is nonnegative.
Definition: slartgp.f:97
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