--- rpl/lapack/lapack/dlaed6.f 2011/07/22 07:40:26 1.8
+++ rpl/lapack/lapack/dlaed6.f 2017/06/17 10:53:53 1.18
@@ -1,9 +1,149 @@
+*> \brief \b DLAED6 used by sstedc. Computes one Newton step in solution of the secular equation.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLAED6 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO )
+*
+* .. Scalar Arguments ..
+* LOGICAL ORGATI
+* INTEGER INFO, KNITER
+* DOUBLE PRECISION FINIT, RHO, TAU
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION D( 3 ), Z( 3 )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLAED6 computes the positive or negative root (closest to the origin)
+*> of
+*> z(1) z(2) z(3)
+*> f(x) = rho + --------- + ---------- + ---------
+*> d(1)-x d(2)-x d(3)-x
+*>
+*> It is assumed that
+*>
+*> if ORGATI = .true. the root is between d(2) and d(3);
+*> otherwise it is between d(1) and d(2)
+*>
+*> This routine will be called by DLAED4 when necessary. In most cases,
+*> the root sought is the smallest in magnitude, though it might not be
+*> in some extremely rare situations.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] KNITER
+*> \verbatim
+*> KNITER is INTEGER
+*> Refer to DLAED4 for its significance.
+*> \endverbatim
+*>
+*> \param[in] ORGATI
+*> \verbatim
+*> ORGATI is LOGICAL
+*> If ORGATI is true, the needed root is between d(2) and
+*> d(3); otherwise it is between d(1) and d(2). See
+*> DLAED4 for further details.
+*> \endverbatim
+*>
+*> \param[in] RHO
+*> \verbatim
+*> RHO is DOUBLE PRECISION
+*> Refer to the equation f(x) above.
+*> \endverbatim
+*>
+*> \param[in] D
+*> \verbatim
+*> D is DOUBLE PRECISION array, dimension (3)
+*> D satisfies d(1) < d(2) < d(3).
+*> \endverbatim
+*>
+*> \param[in] Z
+*> \verbatim
+*> Z is DOUBLE PRECISION array, dimension (3)
+*> Each of the elements in z must be positive.
+*> \endverbatim
+*>
+*> \param[in] FINIT
+*> \verbatim
+*> FINIT is DOUBLE PRECISION
+*> The value of f at 0. It is more accurate than the one
+*> evaluated inside this routine (if someone wants to do
+*> so).
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*> TAU is DOUBLE PRECISION
+*> The root of the equation f(x).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> > 0: if INFO = 1, failure to converge
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date December 2016
+*
+*> \ingroup auxOTHERcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> 10/02/03: This version has a few statements commented out for thread
+*> safety (machine parameters are computed on each entry). SJH.
+*>
+*> 05/10/06: Modified from a new version of Ren-Cang Li, use
+*> Gragg-Thornton-Warner cubic convergent scheme for better stability.
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> Ren-Cang Li, Computer Science Division, University of California
+*> at Berkeley, USA
+*>
+* =====================================================================
SUBROUTINE DLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO )
*
-* -- LAPACK routine (version 3.2) --
+* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* February 2007
+* December 2016
*
* .. Scalar Arguments ..
LOGICAL ORGATI
@@ -14,69 +154,6 @@
DOUBLE PRECISION D( 3 ), Z( 3 )
* ..
*
-* Purpose
-* =======
-*
-* DLAED6 computes the positive or negative root (closest to the origin)
-* of
-* z(1) z(2) z(3)
-* f(x) = rho + --------- + ---------- + ---------
-* d(1)-x d(2)-x d(3)-x
-*
-* It is assumed that
-*
-* if ORGATI = .true. the root is between d(2) and d(3);
-* otherwise it is between d(1) and d(2)
-*
-* This routine will be called by DLAED4 when necessary. In most cases,
-* the root sought is the smallest in magnitude, though it might not be
-* in some extremely rare situations.
-*
-* Arguments
-* =========
-*
-* KNITER (input) INTEGER
-* Refer to DLAED4 for its significance.
-*
-* ORGATI (input) LOGICAL
-* If ORGATI is true, the needed root is between d(2) and
-* d(3); otherwise it is between d(1) and d(2). See
-* DLAED4 for further details.
-*
-* RHO (input) DOUBLE PRECISION
-* Refer to the equation f(x) above.
-*
-* D (input) DOUBLE PRECISION array, dimension (3)
-* D satisfies d(1) < d(2) < d(3).
-*
-* Z (input) DOUBLE PRECISION array, dimension (3)
-* Each of the elements in z must be positive.
-*
-* FINIT (input) DOUBLE PRECISION
-* The value of f at 0. It is more accurate than the one
-* evaluated inside this routine (if someone wants to do
-* so).
-*
-* TAU (output) DOUBLE PRECISION
-* The root of the equation f(x).
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* > 0: if INFO = 1, failure to converge
-*
-* Further Details
-* ===============
-*
-* 30/06/99: Based on contributions by
-* Ren-Cang Li, Computer Science Division, University of California
-* at Berkeley, USA
-*
-* 10/02/03: This version has a few statements commented out for thread
-* safety (machine parameters are computed on each entry). SJH.
-*
-* 05/10/06: Modified from a new version of Ren-Cang Li, use
-* Gragg-Thornton-Warner cubic convergent scheme for better stability.
-*
* =====================================================================
*
* .. Parameters ..
@@ -98,7 +175,7 @@
INTEGER I, ITER, NITER
DOUBLE PRECISION A, B, BASE, C, DDF, DF, EPS, ERRETM, ETA, F,
$ FC, SCLFAC, SCLINV, SMALL1, SMALL2, SMINV1,
- $ SMINV2, TEMP, TEMP1, TEMP2, TEMP3, TEMP4,
+ $ SMINV2, TEMP, TEMP1, TEMP2, TEMP3, TEMP4,
$ LBD, UBD
* ..
* .. Intrinsic Functions ..
@@ -118,7 +195,7 @@
IF( FINIT .LT. ZERO )THEN
LBD = ZERO
ELSE
- UBD = ZERO
+ UBD = ZERO
END IF
*
NITER = 1
@@ -286,27 +363,32 @@
*
TAU = TAU + ETA
IF( TAU .LT. LBD .OR. TAU .GT. UBD )
- $ TAU = ( LBD + UBD )/TWO
+ $ TAU = ( LBD + UBD )/TWO
*
FC = ZERO
ERRETM = ZERO
DF = ZERO
DDF = ZERO
DO 40 I = 1, 3
- TEMP = ONE / ( DSCALE( I )-TAU )
- TEMP1 = ZSCALE( I )*TEMP
- TEMP2 = TEMP1*TEMP
- TEMP3 = TEMP2*TEMP
- TEMP4 = TEMP1 / DSCALE( I )
- FC = FC + TEMP4
- ERRETM = ERRETM + ABS( TEMP4 )
- DF = DF + TEMP2
- DDF = DDF + TEMP3
+ IF ( ( DSCALE( I )-TAU ).NE.ZERO ) THEN
+ TEMP = ONE / ( DSCALE( I )-TAU )
+ TEMP1 = ZSCALE( I )*TEMP
+ TEMP2 = TEMP1*TEMP
+ TEMP3 = TEMP2*TEMP
+ TEMP4 = TEMP1 / DSCALE( I )
+ FC = FC + TEMP4
+ ERRETM = ERRETM + ABS( TEMP4 )
+ DF = DF + TEMP2
+ DDF = DDF + TEMP3
+ ELSE
+ GO TO 60
+ END IF
40 CONTINUE
F = FINIT + TAU*FC
ERRETM = EIGHT*( ABS( FINIT )+ABS( TAU )*ERRETM ) +
$ ABS( TAU )*DF
- IF( ABS( F ).LE.EPS*ERRETM )
+ IF( ( ABS( F ).LE.FOUR*EPS*ERRETM ) .OR.
+ $ ( (UBD-LBD).LE.FOUR*EPS*ABS(TAU) ) )
$ GO TO 60
IF( F .LE. ZERO )THEN
LBD = TAU