LAPACK  3.9.0
LAPACK: Linear Algebra PACKage

◆ sget53()

subroutine sget53 ( real, dimension( lda, * )  A,
integer  LDA,
real, dimension( ldb, * )  B,
integer  LDB,
real  SCALE,
real  WR,
real  WI,
real  RESULT,
integer  INFO 
)

SGET53

Purpose:
 SGET53  checks the generalized eigenvalues computed by SLAG2.

 The basic test for an eigenvalue is:

                              | det( s A - w B ) |
     RESULT =  ---------------------------------------------------
               ulp max( s norm(A), |w| norm(B) )*norm( s A - w B )

 Two "safety checks" are performed:

 (1)  ulp*max( s*norm(A), |w|*norm(B) )  must be at least
      safe_minimum.  This insures that the test performed is
      not essentially  det(0*A + 0*B)=0.

 (2)  s*norm(A) + |w|*norm(B) must be less than 1/safe_minimum.
      This insures that  s*A - w*B  will not overflow.

 If these tests are not passed, then  s  and  w  are scaled and
 tested anyway, if this is possible.
Parameters
[in]A
          A is REAL array, dimension (LDA, 2)
          The 2x2 matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of A.  It must be at least 2.
[in]B
          B is REAL array, dimension (LDB, N)
          The 2x2 upper-triangular matrix B.
[in]LDB
          LDB is INTEGER
          The leading dimension of B.  It must be at least 2.
[in]SCALE
          SCALE is REAL
          The "scale factor" s in the formula  s A - w B .  It is
          assumed to be non-negative.
[in]WR
          WR is REAL
          The real part of the eigenvalue  w  in the formula
          s A - w B .
[in]WI
          WI is REAL
          The imaginary part of the eigenvalue  w  in the formula
          s A - w B .
[out]RESULT
          RESULT is REAL
          If INFO is 2 or less, the value computed by the test
             described above.
          If INFO=3, this will just be 1/ulp.
[out]INFO
          INFO is INTEGER
          =0:  The input data pass the "safety checks".
          =1:  s*norm(A) + |w|*norm(B) > 1/safe_minimum.
          =2:  ulp*max( s*norm(A), |w|*norm(B) ) < safe_minimum
          =3:  same as INFO=2, but  s  and  w  could not be scaled so
               as to compute the test.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 128 of file sget53.f.

128 *
129 * -- LAPACK test routine (version 3.7.0) --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 * December 2016
133 *
134 * .. Scalar Arguments ..
135  INTEGER INFO, LDA, LDB
136  REAL RESULT, SCALE, WI, WR
137 * ..
138 * .. Array Arguments ..
139  REAL A( LDA, * ), B( LDB, * )
140 * ..
141 *
142 * =====================================================================
143 *
144 * .. Parameters ..
145  REAL ZERO, ONE
146  parameter( zero = 0.0, one = 1.0 )
147 * ..
148 * .. Local Scalars ..
149  REAL ABSW, ANORM, BNORM, CI11, CI12, CI22, CNORM,
150  $ CR11, CR12, CR21, CR22, CSCALE, DETI, DETR, S1,
151  $ SAFMIN, SCALES, SIGMIN, TEMP, ULP, WIS, WRS
152 * ..
153 * .. External Functions ..
154  REAL SLAMCH
155  EXTERNAL slamch
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC abs, max, sqrt
159 * ..
160 * .. Executable Statements ..
161 *
162 * Initialize
163 *
164  info = 0
165  result = zero
166  scales = scale
167  wrs = wr
168  wis = wi
169 *
170 * Machine constants and norms
171 *
172  safmin = slamch( 'Safe minimum' )
173  ulp = slamch( 'Epsilon' )*slamch( 'Base' )
174  absw = abs( wrs ) + abs( wis )
175  anorm = max( abs( a( 1, 1 ) )+abs( a( 2, 1 ) ),
176  $ abs( a( 1, 2 ) )+abs( a( 2, 2 ) ), safmin )
177  bnorm = max( abs( b( 1, 1 ) ), abs( b( 1, 2 ) )+abs( b( 2, 2 ) ),
178  $ safmin )
179 *
180 * Check for possible overflow.
181 *
182  temp = ( safmin*bnorm )*absw + ( safmin*anorm )*scales
183  IF( temp.GE.one ) THEN
184 *
185 * Scale down to avoid overflow
186 *
187  info = 1
188  temp = one / temp
189  scales = scales*temp
190  wrs = wrs*temp
191  wis = wis*temp
192  absw = abs( wrs ) + abs( wis )
193  END IF
194  s1 = max( ulp*max( scales*anorm, absw*bnorm ),
195  $ safmin*max( scales, absw ) )
196 *
197 * Check for W and SCALE essentially zero.
198 *
199  IF( s1.LT.safmin ) THEN
200  info = 2
201  IF( scales.LT.safmin .AND. absw.LT.safmin ) THEN
202  info = 3
203  result = one / ulp
204  RETURN
205  END IF
206 *
207 * Scale up to avoid underflow
208 *
209  temp = one / max( scales*anorm+absw*bnorm, safmin )
210  scales = scales*temp
211  wrs = wrs*temp
212  wis = wis*temp
213  absw = abs( wrs ) + abs( wis )
214  s1 = max( ulp*max( scales*anorm, absw*bnorm ),
215  $ safmin*max( scales, absw ) )
216  IF( s1.LT.safmin ) THEN
217  info = 3
218  result = one / ulp
219  RETURN
220  END IF
221  END IF
222 *
223 * Compute C = s A - w B
224 *
225  cr11 = scales*a( 1, 1 ) - wrs*b( 1, 1 )
226  ci11 = -wis*b( 1, 1 )
227  cr21 = scales*a( 2, 1 )
228  cr12 = scales*a( 1, 2 ) - wrs*b( 1, 2 )
229  ci12 = -wis*b( 1, 2 )
230  cr22 = scales*a( 2, 2 ) - wrs*b( 2, 2 )
231  ci22 = -wis*b( 2, 2 )
232 *
233 * Compute the smallest singular value of s A - w B:
234 *
235 * |det( s A - w B )|
236 * sigma_min = ------------------
237 * norm( s A - w B )
238 *
239  cnorm = max( abs( cr11 )+abs( ci11 )+abs( cr21 ),
240  $ abs( cr12 )+abs( ci12 )+abs( cr22 )+abs( ci22 ), safmin )
241  cscale = one / sqrt( cnorm )
242  detr = ( cscale*cr11 )*( cscale*cr22 ) -
243  $ ( cscale*ci11 )*( cscale*ci22 ) -
244  $ ( cscale*cr12 )*( cscale*cr21 )
245  deti = ( cscale*cr11 )*( cscale*ci22 ) +
246  $ ( cscale*ci11 )*( cscale*cr22 ) -
247  $ ( cscale*ci12 )*( cscale*cr21 )
248  sigmin = abs( detr ) + abs( deti )
249  result = sigmin / s1
250  RETURN
251 *
252 * End of SGET53
253 *
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slamch
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:70