--- rpl/lapack/lapack/dlasq2.f 2012/12/14 14:22:36 1.12
+++ rpl/lapack/lapack/dlasq2.f 2017/06/17 11:06:27 1.16
@@ -2,38 +2,38 @@
*
* =========== DOCUMENTATION ===========
*
-* Online html documentation available at
-* http://www.netlib.org/lapack/explore-html/
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
-*> Download DLASQ2 + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download DLASQ2 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \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
+*> 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.
@@ -83,19 +83,19 @@
*> = 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
+*> = 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.
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
-*> \date September 2012
+*> \date December 2016
*
*> \ingroup auxOTHERcomputational
*
@@ -112,10 +112,10 @@
* =====================================================================
SUBROUTINE DLASQ2( N, Z, INFO )
*
-* -- LAPACK computational routine (version 3.4.2) --
+* -- 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..--
-* September 2012
+* December 2016
*
* .. Scalar Arguments ..
INTEGER INFO, N
@@ -136,7 +136,7 @@
* .. Local Scalars ..
LOGICAL IEEE
INTEGER I0, I1, I4, IINFO, IPN4, ITER, IWHILA, IWHILB,
- $ K, KMIN, N0, N1, NBIG, NDIV, NFAIL, PP, SPLT,
+ $ 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,
@@ -155,7 +155,7 @@
INTRINSIC ABS, DBLE, MAX, MIN, SQRT
* ..
* .. Executable Statements ..
-*
+*
* Test the input arguments.
* (in case DLASQ2 is not called by DLASQ1)
*
@@ -195,7 +195,7 @@
END IF
Z( 5 ) = Z( 1 ) + Z( 2 ) + Z( 3 )
IF( Z( 2 ).GT.Z( 3 )*TOL2 ) THEN
- T = HALF*( ( Z( 1 )-Z( 3 ) )+Z( 2 ) )
+ T = HALF*( ( Z( 1 )-Z( 3 ) )+Z( 2 ) )
S = Z( 3 )*( Z( 2 ) / T )
IF( S.LE.T ) THEN
S = Z( 3 )*( Z( 2 ) / ( T*( ONE+SQRT( ONE+S / T ) ) ) )
@@ -264,19 +264,19 @@
Z( 2*N-1 ) = ZERO
RETURN
END IF
-*
+*
* Check whether the machine is IEEE conformable.
-*
+*
IEEE = ILAENV( 10, 'DLASQ2', 'N', 1, 2, 3, 4 ).EQ.1 .AND.
- $ ILAENV( 11, 'DLASQ2', 'N', 1, 2, 3, 4 ).EQ.1
-*
+ $ ILAENV( 11, 'DLASQ2', 'N', 1, 2, 3, 4 ).EQ.1
+*
* Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...).
*
DO 30 K = 2*N, 2, -2
- Z( 2*K ) = ZERO
- Z( 2*K-1 ) = Z( K )
- Z( 2*K-2 ) = ZERO
- Z( 2*K-3 ) = Z( K-1 )
+ Z( 2*K ) = ZERO
+ Z( 2*K-1 ) = Z( K )
+ Z( 2*K-2 ) = ZERO
+ Z( 2*K-3 ) = Z( K-1 )
30 CONTINUE
*
I0 = 1
@@ -333,7 +333,7 @@
D = Z( I4+1 )*( D / Z( I4-2*PP-2 ) )
END IF
EMIN = MIN( EMIN, Z( I4-2*PP ) )
- 60 CONTINUE
+ 60 CONTINUE
Z( 4*N0-PP-2 ) = D
*
* Now find qmax.
@@ -364,14 +364,14 @@
NDIV = 2*( N0-I0 )
*
DO 160 IWHILA = 1, N + 1
- IF( N0.LT.1 )
+ IF( N0.LT.1 )
$ GO TO 170
*
-* While array unfinished do
+* While array unfinished do
*
* E(N0) holds the value of SIGMA when submatrix in I0:N0
* splits from the rest of the array, but is negated.
-*
+*
DESIG = ZERO
IF( N0.EQ.N ) THEN
SIGMA = ZERO
@@ -386,7 +386,7 @@
* Find last unreduced submatrix's top index I0, find QMAX and
* EMIN. Find Gershgorin-type bound if Q's much greater than E's.
*
- EMAX = ZERO
+ EMAX = ZERO
IF( N0.GT.I0 ) THEN
EMIN = ABS( Z( 4*N0-5 ) )
ELSE
@@ -404,7 +404,7 @@
QMAX = MAX( QMAX, Z( I4-7 )+Z( I4-5 ) )
EMIN = MIN( EMIN, Z( I4-5 ) )
90 CONTINUE
- I4 = 4
+ I4 = 4
*
100 CONTINUE
I0 = I4 / 4
@@ -421,7 +421,7 @@
KMIN = ( I4+3 )/4
END IF
110 CONTINUE
- IF( (KMIN-I0)*2.LT.N0-KMIN .AND.
+ IF( (KMIN-I0)*2.LT.N0-KMIN .AND.
$ DEEMIN.LE.HALF*Z(4*N0-3) ) THEN
IPN4 = 4*( I0+N0 )
PP = 2
@@ -446,15 +446,15 @@
*
DMIN = -MAX( ZERO, QMIN-TWO*SQRT( QMIN )*SQRT( EMAX ) )
*
-* Now I0:N0 is unreduced.
+* Now I0:N0 is unreduced.
* PP = 0 for ping, PP = 1 for pong.
* PP = 2 indicates that flipping was applied to the Z array and
-* and that the tests for deflation upon entry in DLASQ3
+* and that the tests for deflation upon entry in DLASQ3
* should not be performed.
*
NBIG = 100*( N0-I0+1 )
DO 140 IWHILB = 1, NBIG
- IF( I0.GT.N0 )
+ IF( I0.GT.N0 )
$ GO TO 150
*
* While submatrix unfinished take a good dqds step.
@@ -497,8 +497,8 @@
140 CONTINUE
*
INFO = 2
-*
-* Maximum number of iterations exceeded, restore the shift
+*
+* 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
*
@@ -549,16 +549,16 @@
INFO = 3
RETURN
*
-* end IWHILA
+* end IWHILA
*
170 CONTINUE
-*
+*
* Move q's to the front.
-*
+*
DO 180 K = 2, N
Z( K ) = Z( 4*K-3 )
180 CONTINUE
-*
+*
* Sort and compute sum of eigenvalues.
*
CALL DLASRT( 'D', N, Z, IINFO )
@@ -570,7 +570,7 @@
*
* Store trace, sum(eigenvalues) and information on performance.
*
- Z( 2*N+1 ) = TRACE
+ Z( 2*N+1 ) = TRACE
Z( 2*N+2 ) = E
Z( 2*N+3 ) = DBLE( ITER )
Z( 2*N+4 ) = DBLE( NDIV ) / DBLE( N**2 )