--- rpl/lapack/lapack/dlasq2.f 2010/12/21 13:53:33 1.7
+++ rpl/lapack/lapack/dlasq2.f 2011/11/21 20:42:59 1.8
@@ -1,14 +1,121 @@
- SUBROUTINE DLASQ2( N, Z, INFO )
+*> \brief \b DLASQ2
*
-* -- LAPACK routine (version 3.2) --
+* =========== DOCUMENTATION ===========
*
-* -- Contributed by Osni Marques of the Lawrence Berkeley National --
-* -- Laboratory and Beresford Parlett of the Univ. of California at --
-* -- Berkeley --
-* -- November 2008 --
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
*
+*> \htmlonly
+*> Download DLASQ2 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLASQ2( N, Z, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER INFO, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION Z( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLASQ2 computes all the eigenvalues of the symmetric positive
+*> definite tridiagonal matrix associated with the qd array Z to high
+*> relative accuracy are computed to high relative accuracy, in the
+*> absence of denormalization, underflow and overflow.
+*>
+*> To see the relation of Z to the tridiagonal matrix, let L be a
+*> unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and
+*> let U be an upper bidiagonal matrix with 1's above and diagonal
+*> Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the
+*> symmetric tridiagonal to which it is similar.
+*>
+*> Note : DLASQ2 defines a logical variable, IEEE, which is true
+*> on machines which follow ieee-754 floating-point standard in their
+*> handling of infinities and NaNs, and false otherwise. This variable
+*> is passed to DLASQ3.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of rows and columns in the matrix. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] Z
+*> \verbatim
+*> Z is DOUBLE PRECISION array, dimension ( 4*N )
+*> On entry Z holds the qd array. On exit, entries 1 to N hold
+*> the eigenvalues in decreasing order, Z( 2*N+1 ) holds the
+*> trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If
+*> N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 )
+*> holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of
+*> shifts that failed.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if the i-th argument is a scalar and had an illegal
+*> value, then INFO = -i, if the i-th argument is an
+*> array and the j-entry had an illegal value, then
+*> INFO = -(i*100+j)
+*> > 0: the algorithm failed
+*> = 1, a split was marked by a positive value in E
+*> = 2, current block of Z not diagonalized after 100*N
+*> iterations (in inner while loop). On exit Z holds
+*> a qd array with the same eigenvalues as the given Z.
+*> = 3, termination criterion of outer while loop not met
+*> (program created more than N unreduced blocks)
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> Local Variables: I0:N0 defines a current unreduced segment of Z.
+*> The shifts are accumulated in SIGMA. Iteration count is in ITER.
+*> Ping-pong is controlled by PP (alternates between 0 and 1).
+*> \endverbatim
+*>
+* =====================================================================
+ SUBROUTINE DLASQ2( N, Z, INFO )
+*
+* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2011
*
* .. Scalar Arguments ..
INTEGER INFO, N
@@ -17,58 +124,6 @@
DOUBLE PRECISION Z( * )
* ..
*
-* Purpose
-* =======
-*
-* DLASQ2 computes all the eigenvalues of the symmetric positive
-* definite tridiagonal matrix associated with the qd array Z to high
-* relative accuracy are computed to high relative accuracy, in the
-* absence of denormalization, underflow and overflow.
-*
-* To see the relation of Z to the tridiagonal matrix, let L be a
-* unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and
-* let U be an upper bidiagonal matrix with 1's above and diagonal
-* Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the
-* symmetric tridiagonal to which it is similar.
-*
-* Note : DLASQ2 defines a logical variable, IEEE, which is true
-* on machines which follow ieee-754 floating-point standard in their
-* handling of infinities and NaNs, and false otherwise. This variable
-* is passed to DLASQ3.
-*
-* Arguments
-* =========
-*
-* N (input) INTEGER
-* The number of rows and columns in the matrix. N >= 0.
-*
-* Z (input/output) DOUBLE PRECISION array, dimension ( 4*N )
-* On entry Z holds the qd array. On exit, entries 1 to N hold
-* the eigenvalues in decreasing order, Z( 2*N+1 ) holds the
-* trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If
-* N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 )
-* holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of
-* shifts that failed.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if the i-th argument is a scalar and had an illegal
-* value, then INFO = -i, if the i-th argument is an
-* array and the j-entry had an illegal value, then
-* INFO = -(i*100+j)
-* > 0: the algorithm failed
-* = 1, a split was marked by a positive value in E
-* = 2, current block of Z not diagonalized after 30*N
-* iterations (in inner while loop)
-* = 3, termination criterion of outer while loop not met
-* (program created more than N unreduced blocks)
-*
-* Further Details
-* ===============
-* Local Variables: I0:N0 defines a current unreduced segment of Z.
-* The shifts are accumulated in SIGMA. Iteration count is in ITER.
-* Ping-pong is controlled by PP (alternates between 0 and 1).
-*
* =====================================================================
*
* .. Parameters ..
@@ -80,12 +135,13 @@
* ..
* .. Local Scalars ..
LOGICAL IEEE
- INTEGER I0, I4, IINFO, IPN4, ITER, IWHILA, IWHILB, K,
- $ KMIN, N0, NBIG, NDIV, NFAIL, PP, SPLT, TTYPE
+ INTEGER I0, I1, I4, IINFO, IPN4, ITER, IWHILA, IWHILB,
+ $ K, KMIN, N0, N1, NBIG, NDIV, NFAIL, PP, SPLT,
+ $ TTYPE
DOUBLE PRECISION D, DEE, DEEMIN, DESIG, DMIN, DMIN1, DMIN2, DN,
$ DN1, DN2, E, EMAX, EMIN, EPS, G, OLDEMN, QMAX,
$ QMIN, S, SAFMIN, SIGMA, T, TAU, TEMP, TOL,
- $ TOL2, TRACE, ZMAX
+ $ TOL2, TRACE, ZMAX, TEMPE, TEMPQ
* ..
* .. External Subroutines ..
EXTERNAL DLASQ3, DLASRT, XERBLA
@@ -396,7 +452,7 @@
* and that the tests for deflation upon entry in DLASQ3
* should not be performed.
*
- NBIG = 30*( N0-I0+1 )
+ NBIG = 100*( N0-I0+1 )
DO 140 IWHILB = 1, NBIG
IF( I0.GT.N0 )
$ GO TO 150
@@ -441,6 +497,47 @@
140 CONTINUE
*
INFO = 2
+*
+* Maximum number of iterations exceeded, restore the shift
+* SIGMA and place the new d's and e's in a qd array.
+* This might need to be done for several blocks
+*
+ I1 = I0
+ N1 = N0
+ 145 CONTINUE
+ TEMPQ = Z( 4*I0-3 )
+ Z( 4*I0-3 ) = Z( 4*I0-3 ) + SIGMA
+ DO K = I0+1, N0
+ TEMPE = Z( 4*K-5 )
+ Z( 4*K-5 ) = Z( 4*K-5 ) * (TEMPQ / Z( 4*K-7 ))
+ TEMPQ = Z( 4*K-3 )
+ Z( 4*K-3 ) = Z( 4*K-3 ) + SIGMA + TEMPE - Z( 4*K-5 )
+ END DO
+*
+* Prepare to do this on the previous block if there is one
+*
+ IF( I1.GT.1 ) THEN
+ N1 = I1-1
+ DO WHILE( ( I1.GE.2 ) .AND. ( Z(4*I1-5).GE.ZERO ) )
+ I1 = I1 - 1
+ END DO
+ SIGMA = -Z(4*N1-1)
+ GO TO 145
+ END IF
+
+ DO K = 1, N
+ Z( 2*K-1 ) = Z( 4*K-3 )
+*
+* Only the block 1..N0 is unfinished. The rest of the e's
+* must be essentially zero, although sometimes other data
+* has been stored in them.
+*
+ IF( K.LT.N0 ) THEN
+ Z( 2*K ) = Z( 4*K-1 )
+ ELSE
+ Z( 2*K ) = 0
+ END IF
+ END DO
RETURN
*
* end IWHILB