LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ dlasq6()

 subroutine dlasq6 ( integer i0, integer n0, double precision, dimension( * ) z, integer pp, double precision dmin, double precision dmin1, double precision dmin2, double precision dn, double precision dnm1, double precision dnm2 )

DLASQ6 computes one dqd transform in ping-pong form. Used by sbdsqr and sstegr.

Purpose:
``` DLASQ6 computes one dqd (shift equal to zero) transform in
ping-pong form, with protection against underflow and overflow.```
Parameters
 [in] I0 ``` I0 is INTEGER First index.``` [in] N0 ``` N0 is INTEGER Last index.``` [in] Z ``` Z is DOUBLE PRECISION array, dimension ( 4*N ) Z holds the qd array. EMIN is stored in Z(4*N0) to avoid an extra argument.``` [in] PP ``` PP is INTEGER PP=0 for ping, PP=1 for pong.``` [out] DMIN ``` DMIN is DOUBLE PRECISION Minimum value of d.``` [out] DMIN1 ``` DMIN1 is DOUBLE PRECISION Minimum value of d, excluding D( N0 ).``` [out] DMIN2 ``` DMIN2 is DOUBLE PRECISION Minimum value of d, excluding D( N0 ) and D( N0-1 ).``` [out] DN ``` DN is DOUBLE PRECISION d(N0), the last value of d.``` [out] DNM1 ``` DNM1 is DOUBLE PRECISION d(N0-1).``` [out] DNM2 ``` DNM2 is DOUBLE PRECISION d(N0-2).```

Definition at line 117 of file dlasq6.f.

119*
120* -- LAPACK computational routine --
121* -- LAPACK is a software package provided by Univ. of Tennessee, --
122* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
123*
124* .. Scalar Arguments ..
125 INTEGER I0, N0, PP
126 DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2
127* ..
128* .. Array Arguments ..
129 DOUBLE PRECISION Z( * )
130* ..
131*
132* =====================================================================
133*
134* .. Parameter ..
135 DOUBLE PRECISION ZERO
136 parameter( zero = 0.0d0 )
137* ..
138* .. Local Scalars ..
139 INTEGER J4, J4P2
140 DOUBLE PRECISION D, EMIN, SAFMIN, TEMP
141* ..
142* .. External Function ..
143 DOUBLE PRECISION DLAMCH
144 EXTERNAL dlamch
145* ..
146* .. Intrinsic Functions ..
147 INTRINSIC min
148* ..
149* .. Executable Statements ..
150*
151 IF( ( n0-i0-1 ).LE.0 )
152 \$ RETURN
153*
154 safmin = dlamch( 'Safe minimum' )
155 j4 = 4*i0 + pp - 3
156 emin = z( j4+4 )
157 d = z( j4 )
158 dmin = d
159*
160 IF( pp.EQ.0 ) THEN
161 DO 10 j4 = 4*i0, 4*( n0-3 ), 4
162 z( j4-2 ) = d + z( j4-1 )
163 IF( z( j4-2 ).EQ.zero ) THEN
164 z( j4 ) = zero
165 d = z( j4+1 )
166 dmin = d
167 emin = zero
168 ELSE IF( safmin*z( j4+1 ).LT.z( j4-2 ) .AND.
169 \$ safmin*z( j4-2 ).LT.z( j4+1 ) ) THEN
170 temp = z( j4+1 ) / z( j4-2 )
171 z( j4 ) = z( j4-1 )*temp
172 d = d*temp
173 ELSE
174 z( j4 ) = z( j4+1 )*( z( j4-1 ) / z( j4-2 ) )
175 d = z( j4+1 )*( d / z( j4-2 ) )
176 END IF
177 dmin = min( dmin, d )
178 emin = min( emin, z( j4 ) )
179 10 CONTINUE
180 ELSE
181 DO 20 j4 = 4*i0, 4*( n0-3 ), 4
182 z( j4-3 ) = d + z( j4 )
183 IF( z( j4-3 ).EQ.zero ) THEN
184 z( j4-1 ) = zero
185 d = z( j4+2 )
186 dmin = d
187 emin = zero
188 ELSE IF( safmin*z( j4+2 ).LT.z( j4-3 ) .AND.
189 \$ safmin*z( j4-3 ).LT.z( j4+2 ) ) THEN
190 temp = z( j4+2 ) / z( j4-3 )
191 z( j4-1 ) = z( j4 )*temp
192 d = d*temp
193 ELSE
194 z( j4-1 ) = z( j4+2 )*( z( j4 ) / z( j4-3 ) )
195 d = z( j4+2 )*( d / z( j4-3 ) )
196 END IF
197 dmin = min( dmin, d )
198 emin = min( emin, z( j4-1 ) )
199 20 CONTINUE
200 END IF
201*
202* Unroll last two steps.
203*
204 dnm2 = d
205 dmin2 = dmin
206 j4 = 4*( n0-2 ) - pp
207 j4p2 = j4 + 2*pp - 1
208 z( j4-2 ) = dnm2 + z( j4p2 )
209 IF( z( j4-2 ).EQ.zero ) THEN
210 z( j4 ) = zero
211 dnm1 = z( j4p2+2 )
212 dmin = dnm1
213 emin = zero
214 ELSE IF( safmin*z( j4p2+2 ).LT.z( j4-2 ) .AND.
215 \$ safmin*z( j4-2 ).LT.z( j4p2+2 ) ) THEN
216 temp = z( j4p2+2 ) / z( j4-2 )
217 z( j4 ) = z( j4p2 )*temp
218 dnm1 = dnm2*temp
219 ELSE
220 z( j4 ) = z( j4p2+2 )*( z( j4p2 ) / z( j4-2 ) )
221 dnm1 = z( j4p2+2 )*( dnm2 / z( j4-2 ) )
222 END IF
223 dmin = min( dmin, dnm1 )
224*
225 dmin1 = dmin
226 j4 = j4 + 4
227 j4p2 = j4 + 2*pp - 1
228 z( j4-2 ) = dnm1 + z( j4p2 )
229 IF( z( j4-2 ).EQ.zero ) THEN
230 z( j4 ) = zero
231 dn = z( j4p2+2 )
232 dmin = dn
233 emin = zero
234 ELSE IF( safmin*z( j4p2+2 ).LT.z( j4-2 ) .AND.
235 \$ safmin*z( j4-2 ).LT.z( j4p2+2 ) ) THEN
236 temp = z( j4p2+2 ) / z( j4-2 )
237 z( j4 ) = z( j4p2 )*temp
238 dn = dnm1*temp
239 ELSE
240 z( j4 ) = z( j4p2+2 )*( z( j4p2 ) / z( j4-2 ) )
241 dn = z( j4p2+2 )*( dnm1 / z( j4-2 ) )
242 END IF
243 dmin = min( dmin, dn )
244*
245 z( j4+2 ) = dn
246 z( 4*n0-pp ) = emin
247 RETURN
248*
249* End of DLASQ6
250*
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
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