LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ dlas2()

subroutine dlas2 ( double precision  F,
double precision  G,
double precision  H,
double precision  SSMIN,
double precision  SSMAX 
)

DLAS2 computes singular values of a 2-by-2 triangular matrix.

Download DLAS2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DLAS2  computes the singular values of the 2-by-2 matrix
    [  F   G  ]
    [  0   H  ].
 On return, SSMIN is the smaller singular value and SSMAX is the
 larger singular value.
Parameters
[in]F
          F is DOUBLE PRECISION
          The (1,1) element of the 2-by-2 matrix.
[in]G
          G is DOUBLE PRECISION
          The (1,2) element of the 2-by-2 matrix.
[in]H
          H is DOUBLE PRECISION
          The (2,2) element of the 2-by-2 matrix.
[out]SSMIN
          SSMIN is DOUBLE PRECISION
          The smaller singular value.
[out]SSMAX
          SSMAX is DOUBLE PRECISION
          The larger singular value.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
  Barring over/underflow, all output quantities are correct to within
  a few units in the last place (ulps), even in the absence of a guard
  digit in addition/subtraction.

  In IEEE arithmetic, the code works correctly if one matrix element is
  infinite.

  Overflow will not occur unless the largest singular value itself
  overflows, or is within a few ulps of overflow. (On machines with
  partial overflow, like the Cray, overflow may occur if the largest
  singular value is within a factor of 2 of overflow.)

  Underflow is harmless if underflow is gradual. Otherwise, results
  may correspond to a matrix modified by perturbations of size near
  the underflow threshold.

Definition at line 106 of file dlas2.f.

107 *
108 * -- LAPACK auxiliary routine --
109 * -- LAPACK is a software package provided by Univ. of Tennessee, --
110 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
111 *
112 * .. Scalar Arguments ..
113  DOUBLE PRECISION F, G, H, SSMAX, SSMIN
114 * ..
115 *
116 * ====================================================================
117 *
118 * .. Parameters ..
119  DOUBLE PRECISION ZERO
120  parameter( zero = 0.0d0 )
121  DOUBLE PRECISION ONE
122  parameter( one = 1.0d0 )
123  DOUBLE PRECISION TWO
124  parameter( two = 2.0d0 )
125 * ..
126 * .. Local Scalars ..
127  DOUBLE PRECISION AS, AT, AU, C, FA, FHMN, FHMX, GA, HA
128 * ..
129 * .. Intrinsic Functions ..
130  INTRINSIC abs, max, min, sqrt
131 * ..
132 * .. Executable Statements ..
133 *
134  fa = abs( f )
135  ga = abs( g )
136  ha = abs( h )
137  fhmn = min( fa, ha )
138  fhmx = max( fa, ha )
139  IF( fhmn.EQ.zero ) THEN
140  ssmin = zero
141  IF( fhmx.EQ.zero ) THEN
142  ssmax = ga
143  ELSE
144  ssmax = max( fhmx, ga )*sqrt( one+
145  $ ( min( fhmx, ga ) / max( fhmx, ga ) )**2 )
146  END IF
147  ELSE
148  IF( ga.LT.fhmx ) THEN
149  as = one + fhmn / fhmx
150  at = ( fhmx-fhmn ) / fhmx
151  au = ( ga / fhmx )**2
152  c = two / ( sqrt( as*as+au )+sqrt( at*at+au ) )
153  ssmin = fhmn*c
154  ssmax = fhmx / c
155  ELSE
156  au = fhmx / ga
157  IF( au.EQ.zero ) THEN
158 *
159 * Avoid possible harmful underflow if exponent range
160 * asymmetric (true SSMIN may not underflow even if
161 * AU underflows)
162 *
163  ssmin = ( fhmn*fhmx ) / ga
164  ssmax = ga
165  ELSE
166  as = one + fhmn / fhmx
167  at = ( fhmx-fhmn ) / fhmx
168  c = one / ( sqrt( one+( as*au )**2 )+
169  $ sqrt( one+( at*au )**2 ) )
170  ssmin = ( fhmn*c )*au
171  ssmin = ssmin + ssmin
172  ssmax = ga / ( c+c )
173  END IF
174  END IF
175  END IF
176  RETURN
177 *
178 * End of DLAS2
179 *
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