The R Project SVN – R – Diff – /trunk/src/modules/lapack/dlapack.f



*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2017
*
*> \ingroup doubleGEcomputational
*
*> \par Further Details:
*  =====================

*>
*  =====================================================================
      SUBROUTINE DGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,
     $                   INFO )
*
*  -- LAPACK computational routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2017
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, LWORK, M, N
*     ..
*     .. Array Arguments ..

      PARAMETER          ( ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY
      INTEGER            I, IINFO, J, LDWRKX, LDWRKY, LWKOPT, MINMN, NB,
     $                   NBMIN, NX, WS
 
*     ..
*     .. External Subroutines ..
      EXTERNAL           DGEBD2, DGEMM, DLABRD, XERBLA
*     ..
*     .. Intrinsic Functions ..

*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2017
*
*> \ingroup doubleGEauxiliary
*
*> \par Contributors:
*  ==================

*>     Umea University, S-901 87 Umea, Sweden.
*
*  =====================================================================
      SUBROUTINE DGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
*
*  -- LAPACK auxiliary routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2017
*
*     .. Scalar Arguments ..
      INTEGER            LDA, N
      DOUBLE PRECISION   SCALE
*     ..

*     .. Local Scalars ..
      INTEGER            I, J
      DOUBLE PRECISION   BIGNUM, EPS, SMLNUM, TEMP
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLASWP, DSCAL, DLABAD
*     ..
*     .. External Functions ..
      INTEGER            IDAMAX
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           IDAMAX, DLAMCH

*>     Umea University, S-901 87 Umea, Sweden.
*
*  =====================================================================
      SUBROUTINE DGETC2( N, A, LDA, IPIV, JPIV, INFO )
*
*  -- LAPACK auxiliary routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     June 2016
*
*     .. Scalar Arguments ..

*     .. Local Scalars ..
      INTEGER            I, IP, IPV, J, JP, JPV
      DOUBLE PRECISION   BIGNUM, EPS, SMIN, SMLNUM, XMAX
*     ..
*     .. External Subroutines ..
      EXTERNAL           DGER, DSWAP, DLABAD
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           DLAMCH
*     ..

*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2017
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
*  =====================

*
*  =====================================================================
      SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,
     $                   SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
*
*  -- LAPACK computational routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2017
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP
      DOUBLE PRECISION   EPS, SFMIN, TOL
      CHARACTER*1        JOBV

      INTEGER            IDAMAX
      LOGICAL            LSAME
      EXTERNAL           IDAMAX, LSAME, DDOT, DNRM2
*     ..
*     .. External Subroutines ..
      EXTERNAL           DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP,
     $                   XERBLA
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*

*
*  =====================================================================
      SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
     $                   EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
*
*  -- LAPACK computational routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     June 2016
*
*     .. Scalar Arguments ..

      INTEGER            IDAMAX
      LOGICAL            LSAME
      EXTERNAL           IDAMAX, LSAME, DDOT, DNRM2
*     ..
*     .. External Subroutines ..
      EXTERNAL           DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP,
     $                   XERBLA
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*

*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2017
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )
*
*  -- LAPACK auxiliary routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2017
*
*     .. Scalar Arguments ..
      INTEGER            INCX, N
      DOUBLE PRECISION   ALPHA, TAU
*     ..

   10       CONTINUE
            KNT = KNT + 1
            CALL DSCAL( N-1, RSAFMN, X, INCX )
            BETA = BETA*RSAFMN
            ALPHA = ALPHA*RSAFMN
            IF( (ABS( BETA ).LT.SAFMIN) .AND. (KNT .LT. 20) )
     $         GO TO 10
*
*           New BETA is at most 1, at least SAFMIN
*
            XNORM = DNRM2( N-1, X, INCX )

*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2017
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLARFGP( N, ALPHA, X, INCX, TAU )
*
*  -- LAPACK auxiliary routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2017
*
*     .. Scalar Arguments ..
      INTEGER            INCX, N
      DOUBLE PRECISION   ALPHA, TAU
*     ..

   10       CONTINUE
            KNT = KNT + 1
            CALL DSCAL( N-1, BIGNUM, X, INCX )
            BETA = BETA*BIGNUM
            ALPHA = ALPHA*BIGNUM
            IF( (ABS( BETA ).LT.SMLNUM) .AND. (KNT .LT. 20) )
     $         GO TO 10
*
*           New BETA is at most 1, at least SMLNUM
*
            XNORM = DNRM2( N-1, X, INCX )

      SUBROUTINE DLARRE( RANGE, N, VL, VU, IL, IU, D, E, E2,
     $                    RTOL1, RTOL2, SPLTOL, NSPLIT, ISPLIT, M,
     $                    W, WERR, WGAP, IBLOCK, INDEXW, GERS, PIVMIN,
     $                    WORK, IWORK, INFO )
*
*  -- LAPACK auxiliary routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     June 2016
*
*     .. Scalar Arguments ..

      EXTERNAL           DLAMCH, LSAME
 
*     ..
*     .. External Subroutines ..
      EXTERNAL           DCOPY, DLARNV, DLARRA, DLARRB, DLARRC, DLARRD,
     $                   DLASQ2, DLARRK
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, MAX, MIN
 
*     ..

*> \param[in] VU
*> \verbatim
*>          VU is DOUBLE PRECISION
*>          Upper bound of the interval that contains the desired
*>          eigenvalues. VL < VU. 
*>          Note: VU is currently not used by this implementation of DLARRV, VU is
*>          passed to DLARRV because it could be used compute gaps on the right end
*>          of the extremal eigenvalues. However, with not much initial accuracy in
*>          LAMBDA and VU, the formula can lead to an overestimation of the right gap
*>          and thus to inadequately early RQI 'convergence'. This is currently
*>          prevented this by forcing a small right gap. And so it turns out that VU

     $                   ISPLIT, M, DOL, DOU, MINRGP,
     $                   RTOL1, RTOL2, W, WERR, WGAP,
     $                   IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ,
     $                   WORK, IWORK, INFO )
*
*  -- LAPACK auxiliary routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     June 2016
*
*     .. Scalar Arguments ..

*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2017
*
*> \ingroup auxOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DLARTGS( X, Y, SIGMA, CS, SN )
*
*  -- LAPACK computational routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2017
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION        CS, SIGMA, SN, X, Y
*     ..
*

      PARAMETER          ( NEGONE = -1.0D0, ONE = 1.0D0, ZERO = 0.0D0 )
*     ..
*     .. Local Scalars ..
      DOUBLE PRECISION        R, S, THRESH, W, Z
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLARTGP
*     ..
*     .. External Functions ..
      DOUBLE PRECISION        DLAMCH
      EXTERNAL           DLAMCH
*     .. Executable Statements ..
*

*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2017
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DRSCL( N, SA, SX, INCX )
*
*  -- LAPACK auxiliary routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2017
*
*     .. Scalar Arguments ..
      INTEGER            INCX, N
      DOUBLE PRECISION   SA
*     ..

*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           DLAMCH
*     ..
*     .. External Subroutines ..
      EXTERNAL           DSCAL, DLABAD
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS
*     ..
*     .. Executable Statements ..

*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2017
*
*> \ingroup doubleSYcomputational
*
*> \par References:
*  ================

*>  Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679
*>
*  =====================================================================
      SUBROUTINE DSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2017
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, N
      DOUBLE PRECISION   AMAX, SCOND
      CHARACTER          UPLO

      DOUBLE PRECISION   DLAMCH
      LOGICAL            LSAME
      EXTERNAL           DLAMCH, LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLASSQ, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, INT, LOG, MAX, MIN, SQRT
*     ..
*     .. Executable Statements ..

*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2017
*
*> \ingroup doubleSYcomputational
*
*  =====================================================================
      SUBROUTINE DSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
*  -- LAPACK computational routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2017
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, LWORK, N
*     ..

      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           LSAME, ILAENV
*     ..
*     .. External Subroutines ..
      EXTERNAL           DSYTRI, DSYTRI2X, XERBLA
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*

*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2017
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
*  =====================

*>
*  =====================================================================
      SUBROUTINE DTPMQRT( SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT,
     $                    A, LDA, B, LDB, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2017
*
*     .. Scalar Arguments ..
      CHARACTER SIDE, TRANS
      INTEGER   INFO, K, LDV, LDA, LDB, M, N, L, NB, LDT
*     ..

*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           DTPRFB, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN
*     ..
*     .. Executable Statements ..

*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2017
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
*  =====================

*>
*  =====================================================================
      SUBROUTINE DTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
     $                   LDVR, MM, M, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2017
*
*     .. Scalar Arguments ..
      CHARACTER          HOWMNY, SIDE
      INTEGER            INFO, LDT, LDVL, LDVR, M, MM, N
*     ..

      INTEGER            IDAMAX
      DOUBLE PRECISION   DDOT, DLAMCH
      EXTERNAL           LSAME, IDAMAX, DDOT, DLAMCH
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLABAD, DAXPY, DCOPY, DGEMV, DLALN2, DSCAL,
     $                   XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, MAX, SQRT
*     ..
*     .. Local Arrays ..

*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2017
*
*  @precisions fortran d -> s
*
*> \ingroup doubleOTHERcomputational
*

*  =====================================================================
      SUBROUTINE DTREVC3( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL,
     $                    VR, LDVR, MM, M, WORK, LWORK, INFO )
      IMPLICIT NONE
*
*  -- LAPACK computational routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2017
*
*     .. Scalar Arguments ..
      CHARACTER          HOWMNY, SIDE
      INTEGER            INFO, LDT, LDVL, LDVR, LWORK, M, MM, N
*     ..

      DOUBLE PRECISION   DDOT, DLAMCH
      EXTERNAL           LSAME, IDAMAX, ILAENV, DDOT, DLAMCH
*     ..
*     .. External Subroutines ..
      EXTERNAL           DAXPY, DCOPY, DGEMV, DLALN2, DSCAL, XERBLA,
     $                   DGEMM, DLASET, DLABAD, DLACPY
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, MAX, SQRT
*     ..
*     .. Local Arrays ..

*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2017
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
*  =====================

*  =====================================================================
      SUBROUTINE DTRSNA( JOB, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
     $                   LDVR, S, SEP, MM, M, WORK, LDWORK, IWORK,
     $                   INFO )
*
*  -- LAPACK computational routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2017
*
*     .. Scalar Arguments ..
      CHARACTER          HOWMNY, JOB
      INTEGER            INFO, LDT, LDVL, LDVR, LDWORK, M, MM, N
*     ..

      LOGICAL            LSAME
      DOUBLE PRECISION   DDOT, DLAMCH, DLAPY2, DNRM2
      EXTERNAL           LSAME, DDOT, DLAMCH, DLAPY2, DNRM2
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLABAD, DLACN2, DLACPY, DLAQTR, DTREXC, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, MAX, SQRT
*     ..
*     .. Executable Statements ..

*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2017
*
*> \ingroup OTHERauxiliary
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3, N4 )
*
*  -- LAPACK auxiliary routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2017
*
*     .. Scalar Arguments ..
      CHARACTER*( * )    NAME, OPTS
      INTEGER            ISPEC, N1, N2, N3, N4
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      INTEGER            I, IC, IZ, NB, NBMIN, NX
      LOGICAL            CNAME, SNAME, TWOSTAGE
      CHARACTER          C1*1, C2*2, C4*2, C3*3, SUBNAM*16
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          CHAR, ICHAR, INT, MIN, REAL
*     ..
*     .. External Functions ..

      EXTERNAL           IEEECK, IPARMQ, IPARAM2STAGE
*     ..
*     .. Executable Statements ..
*
      GO TO ( 10, 10, 10, 80, 90, 100, 110, 120,
     $        130, 140, 150, 160, 160, 160, 160, 160)ISPEC
 
*
*     Invalid value for ISPEC
*
      ILAENV = -1
      RETURN

      IF( .NOT.( CNAME .OR. SNAME ) )
     $   RETURN
      C2 = SUBNAM( 2: 3 )
      C3 = SUBNAM( 4: 6 )
      C4 = C3( 2: 3 )
      TWOSTAGE = LEN( SUBNAM ).GE.11
     $           .AND. SUBNAM( 11: 11 ).EQ.'2'
*
      GO TO ( 50, 60, 70 )ISPEC
*
   50 CONTINUE
*

            END IF
         END IF
      ELSE IF( C2.EQ.'SY' ) THEN
         IF( C3.EQ.'TRF' ) THEN
            IF( SNAME ) THEN
               IF( TWOSTAGE ) THEN
                  NB = 192
               ELSE
                  NB = 64
               END IF
            ELSE
               IF( TWOSTAGE ) THEN
                  NB = 192
               ELSE
                  NB = 64
               END IF
            END IF
         ELSE IF( SNAME .AND. C3.EQ.'TRD' ) THEN
            NB = 32
         ELSE IF( SNAME .AND. C3.EQ.'GST' ) THEN
            NB = 64
         END IF
      ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN
         IF( C3.EQ.'TRF' ) THEN
            IF( TWOSTAGE ) THEN
               NB = 192
            ELSE
               NB = 64
            END IF
         ELSE IF( C3.EQ.'TRD' ) THEN
            NB = 32
         ELSE IF( C3.EQ.'GST' ) THEN
            NB = 64
         END IF

*     12 <= ISPEC <= 16: xHSEQR or related subroutines.
*
      ILAENV = IPARMQ( ISPEC, NAME, OPTS, N1, N2, N3, N4 )
      RETURN
*
 
 
 
 
 
 
 
*     End of ILAENV
*
      END
*> \brief \b ILAPREC
*

*  =====================================================================
*
      INTEGER VERS_MAJOR, VERS_MINOR, VERS_PATCH
*  =====================================================================
      VERS_MAJOR = 3
      VERS_MINOR = 8
      VERS_PATCH = 0
*  =====================================================================
*
      RETURN
      END
# 1 "SRC/iparam2stage.F"
# 1 "<built-in>" 1
# 1 "<built-in>" 3
# 330 "<built-in>" 3
# 1 "<command line>" 1
# 1 "<built-in>" 2
# 1 "SRC/iparam2stage.F" 2
*> \brief \b IPARAM2STAGE
*

*>
*>      This program sets problem and machine dependent parameters
*>      useful for xHETRD_2STAGE, xHETRD_H@2HB, xHETRD_HB2ST,
*>      xGEBRD_2STAGE, xGEBRD_GE2GB, xGEBRD_GB2BD 
*>      and related subroutines for eigenvalue problems. 
*>      It is called whenever ILAENV is called with 17 <= ISPEC <= 21.
*>      It is called whenever ILAENV2STAGE is called with 1 <= ISPEC <= 5
*>      with a direct conversion ISPEC + 16.
*> \endverbatim
*
*  Arguments:
*  ==========
*

 
 
 
      IMPLICIT NONE
*
*  -- LAPACK auxiliary routine (version 3.8.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     June 2016
*
*     .. Scalar Arguments ..

Rev 72877	Rev 73873
Line 7760...	Line 7760...
7760	`*> \author Univ. of Tennessee`	7760	`*> \author Univ. of Tennessee`
7761	`*> \author Univ. of California Berkeley`	7761	`*> \author Univ. of California Berkeley`
7762	`*> \author Univ. of Colorado Denver`	7762	`*> \author Univ. of Colorado Denver`
7763	`*> \author NAG Ltd.`	7763	`*> \author NAG Ltd.`
7764	`*`	7764	`*`
7765	`*> \date June 2017`	7765	`*> \date November 2017`
7766	`*`	7766	`*`
7767	`*> \ingroup doubleGEcomputational`	7767	`*> \ingroup doubleGEcomputational`
7768	`*`	7768	`*`
7769	`*> \par Further Details:`	7769	`*> \par Further Details:`
7770	`* =====================`	7770	`* =====================`
Line 7818...	Line 7818...
7818	`*>`	7818	`*>`
7819	`* =====================================================================`	7819	`* =====================================================================`
7820	`SUBROUTINE DGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,`	7820	`SUBROUTINE DGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,`
7821	`$ INFO )`	7821	`$ INFO )`
7822	`*`	7822	`*`
7823	`* -- LAPACK computational routine (version 3.7.1) --`	7823	`* -- LAPACK computational routine (version 3.8.0) --`
7824	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	7824	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
7825	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	7825	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
7826	`* June 2017`	7826	`* November 2017`
7827	`*`	7827	`*`
7828	`* .. Scalar Arguments ..`	7828	`* .. Scalar Arguments ..`
7829	`INTEGER INFO, LDA, LWORK, M, N`	7829	`INTEGER INFO, LDA, LWORK, M, N`
7830	`* ..`	7830	`* ..`
7831	`* .. Array Arguments ..`	7831	`* .. Array Arguments ..`
Line 7840...	Line 7840...
7840	`PARAMETER ( ONE = 1.0D+0 )`	7840	`PARAMETER ( ONE = 1.0D+0 )`
7841	`* ..`	7841	`* ..`
7842	`* .. Local Scalars ..`	7842	`* .. Local Scalars ..`
7843	`LOGICAL LQUERY`	7843	`LOGICAL LQUERY`
7844	`INTEGER I, IINFO, J, LDWRKX, LDWRKY, LWKOPT, MINMN, NB,`	7844	`INTEGER I, IINFO, J, LDWRKX, LDWRKY, LWKOPT, MINMN, NB,`
7845	`$ NBMIN, NX`	7845	`$ NBMIN, NX, WS`
7846	`DOUBLE PRECISION WS`	-
7847	`* ..`	7846	`* ..`
7848	`* .. External Subroutines ..`	7847	`* .. External Subroutines ..`
7849	`EXTERNAL DGEBD2, DGEMM, DLABRD, XERBLA`	7848	`EXTERNAL DGEBD2, DGEMM, DLABRD, XERBLA`
7850	`* ..`	7849	`* ..`
7851	`* .. Intrinsic Functions ..`	7850	`* .. Intrinsic Functions ..`
Line 22277...	Line 22276...
22277	`*> \author Univ. of Tennessee`	22276	`*> \author Univ. of Tennessee`
22278	`*> \author Univ. of California Berkeley`	22277	`*> \author Univ. of California Berkeley`
22279	`*> \author Univ. of Colorado Denver`	22278	`*> \author Univ. of Colorado Denver`
22280	`*> \author NAG Ltd.`	22279	`*> \author NAG Ltd.`
22281	`*`	22280	`*`
22282	`*> \date December 2016`	22281	`*> \date November 2017`
22283	`*`	22282	`*`
22284	`*> \ingroup doubleGEauxiliary`	22283	`*> \ingroup doubleGEauxiliary`
22285	`*`	22284	`*`
22286	`*> \par Contributors:`	22285	`*> \par Contributors:`
22287	`* ==================`	22286	`* ==================`
Line 22290...	Line 22289...
22290	`*> Umea University, S-901 87 Umea, Sweden.`	22289	`*> Umea University, S-901 87 Umea, Sweden.`
22291	`*`	22290	`*`
22292	`* =====================================================================`	22291	`* =====================================================================`
22293	`SUBROUTINE DGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )`	22292	`SUBROUTINE DGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )`
22294	`*`	22293	`*`
22295	`* -- LAPACK auxiliary routine (version 3.7.0) --`	22294	`* -- LAPACK auxiliary routine (version 3.8.0) --`
22296	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	22295	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
22297	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	22296	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
22298	`* December 2016`	22297	`* November 2017`
22299	`*`	22298	`*`
22300	`* .. Scalar Arguments ..`	22299	`* .. Scalar Arguments ..`
22301	`INTEGER LDA, N`	22300	`INTEGER LDA, N`
22302	`DOUBLE PRECISION SCALE`	22301	`DOUBLE PRECISION SCALE`
22303	`* ..`	22302	`* ..`
Line 22315...	Line 22314...
22315	`* .. Local Scalars ..`	22314	`* .. Local Scalars ..`
22316	`INTEGER I, J`	22315	`INTEGER I, J`
22317	`DOUBLE PRECISION BIGNUM, EPS, SMLNUM, TEMP`	22316	`DOUBLE PRECISION BIGNUM, EPS, SMLNUM, TEMP`
22318	`* ..`	22317	`* ..`
22319	`* .. External Subroutines ..`	22318	`* .. External Subroutines ..`
22320	`EXTERNAL DLASWP, DSCAL`	22319	`EXTERNAL DLASWP, DSCAL, DLABAD`
22321	`* ..`	22320	`* ..`
22322	`* .. External Functions ..`	22321	`* .. External Functions ..`
22323	`INTEGER IDAMAX`	22322	`INTEGER IDAMAX`
22324	`DOUBLE PRECISION DLAMCH`	22323	`DOUBLE PRECISION DLAMCH`
22325	`EXTERNAL IDAMAX, DLAMCH`	22324	`EXTERNAL IDAMAX, DLAMCH`
Line 29936...	Line 29935...
29936	`*> Umea University, S-901 87 Umea, Sweden.`	29935	`*> Umea University, S-901 87 Umea, Sweden.`
29937	`*`	29936	`*`
29938	`* =====================================================================`	29937	`* =====================================================================`
29939	`SUBROUTINE DGETC2( N, A, LDA, IPIV, JPIV, INFO )`	29938	`SUBROUTINE DGETC2( N, A, LDA, IPIV, JPIV, INFO )`
29940	`*`	29939	`*`
29941	`* -- LAPACK auxiliary routine (version 3.7.0) --`	29940	`* -- LAPACK auxiliary routine (version 3.8.0) --`
29942	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	29941	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
29943	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	29942	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
29944	`* June 2016`	29943	`* June 2016`
29945	`*`	29944	`*`
29946	`* .. Scalar Arguments ..`	29945	`* .. Scalar Arguments ..`
Line 29960...	Line 29959...
29960	`* .. Local Scalars ..`	29959	`* .. Local Scalars ..`
29961	`INTEGER I, IP, IPV, J, JP, JPV`	29960	`INTEGER I, IP, IPV, J, JP, JPV`
29962	`DOUBLE PRECISION BIGNUM, EPS, SMIN, SMLNUM, XMAX`	29961	`DOUBLE PRECISION BIGNUM, EPS, SMIN, SMLNUM, XMAX`
29963	`* ..`	29962	`* ..`
29964	`* .. External Subroutines ..`	29963	`* .. External Subroutines ..`
29965	`EXTERNAL DGER, DSWAP`	29964	`EXTERNAL DGER, DSWAP, DLABAD`
29966	`* ..`	29965	`* ..`
29967	`* .. External Functions ..`	29966	`* .. External Functions ..`
29968	`DOUBLE PRECISION DLAMCH`	29967	`DOUBLE PRECISION DLAMCH`
29969	`EXTERNAL DLAMCH`	29968	`EXTERNAL DLAMCH`
29970	`* ..`	29969	`* ..`
Line 37922...	Line 37921...
37922	`*> \author Univ. of Tennessee`	37921	`*> \author Univ. of Tennessee`
37923	`*> \author Univ. of California Berkeley`	37922	`*> \author Univ. of California Berkeley`
37924	`*> \author Univ. of Colorado Denver`	37923	`*> \author Univ. of Colorado Denver`
37925	`*> \author NAG Ltd.`	37924	`*> \author NAG Ltd.`
37926	`*`	37925	`*`
37927	`*> \date December 2016`	37926	`*> \date November 2017`
37928	`*`	37927	`*`
37929	`*> \ingroup doubleOTHERcomputational`	37928	`*> \ingroup doubleOTHERcomputational`
37930	`*`	37929	`*`
37931	`*> \par Further Details:`	37930	`*> \par Further Details:`
37932	`* =====================`	37931	`* =====================`
Line 37947...	Line 37946...
37947	`*`	37946	`*`
37948	`* =====================================================================`	37947	`* =====================================================================`
37949	`SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,`	37948	`SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,`
37950	`$ SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )`	37949	`$ SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )`
37951	`*`	37950	`*`
37952	`* -- LAPACK computational routine (version 3.7.0) --`	37951	`* -- LAPACK computational routine (version 3.8.0) --`
37953	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	37952	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
37954	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	37953	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
37955	`* December 2016`	37954	`* November 2017`
37956	`*`	37955	`*`
37957	`* .. Scalar Arguments ..`	37956	`* .. Scalar Arguments ..`
37958	`INTEGER INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP`	37957	`INTEGER INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP`
37959	`DOUBLE PRECISION EPS, SFMIN, TOL`	37958	`DOUBLE PRECISION EPS, SFMIN, TOL`
37960	`CHARACTER*1 JOBV`	37959	`CHARACTER*1 JOBV`
Line 37991...	Line 37990...
37991	`INTEGER IDAMAX`	37990	`INTEGER IDAMAX`
37992	`LOGICAL LSAME`	37991	`LOGICAL LSAME`
37993	`EXTERNAL IDAMAX, LSAME, DDOT, DNRM2`	37992	`EXTERNAL IDAMAX, LSAME, DDOT, DNRM2`
37994	`* ..`	37993	`* ..`
37995	`* .. External Subroutines ..`	37994	`* .. External Subroutines ..`
37996	`EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP`	37995	`EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP,`
-		37996	`$ XERBLA`
37997	`* ..`	37997	`* ..`
37998	`* .. Executable Statements ..`	37998	`* .. Executable Statements ..`
37999	`*`	37999	`*`
38000	`* Test the input parameters.`	38000	`* Test the input parameters.`
38001	`*`	38001	`*`
Line 39043...	Line 39043...
39043	`*`	39043	`*`
39044	`* =====================================================================`	39044	`* =====================================================================`
39045	`SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,`	39045	`SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,`
39046	`$ EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )`	39046	`$ EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )`
39047	`*`	39047	`*`
39048	`* -- LAPACK computational routine (version 3.7.0) --`	39048	`* -- LAPACK computational routine (version 3.8.0) --`
39049	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	39049	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
39050	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	39050	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
39051	`* June 2016`	39051	`* June 2016`
39052	`*`	39052	`*`
39053	`* .. Scalar Arguments ..`	39053	`* .. Scalar Arguments ..`
Line 39087...	Line 39087...
39087	`INTEGER IDAMAX`	39087	`INTEGER IDAMAX`
39088	`LOGICAL LSAME`	39088	`LOGICAL LSAME`
39089	`EXTERNAL IDAMAX, LSAME, DDOT, DNRM2`	39089	`EXTERNAL IDAMAX, LSAME, DDOT, DNRM2`
39090	`* ..`	39090	`* ..`
39091	`* .. External Subroutines ..`	39091	`* .. External Subroutines ..`
39092	`EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP`	39092	`EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP,`
-		39093	`$ XERBLA`
39093	`* ..`	39094	`* ..`
39094	`* .. Executable Statements ..`	39095	`* .. Executable Statements ..`
39095	`*`	39096	`*`
39096	`* Test the input parameters.`	39097	`* Test the input parameters.`
39097	`*`	39098	`*`
Line 71862...	Line 71863...
71862	`*> \author Univ. of Tennessee`	71863	`*> \author Univ. of Tennessee`
71863	`*> \author Univ. of California Berkeley`	71864	`*> \author Univ. of California Berkeley`
71864	`*> \author Univ. of Colorado Denver`	71865	`*> \author Univ. of Colorado Denver`
71865	`*> \author NAG Ltd.`	71866	`*> \author NAG Ltd.`
71866	`*`	71867	`*`
71867	`*> \date December 2016`	71868	`*> \date November 2017`
71868	`*`	71869	`*`
71869	`*> \ingroup doubleOTHERauxiliary`	71870	`*> \ingroup doubleOTHERauxiliary`
71870	`*`	71871	`*`
71871	`* =====================================================================`	71872	`* =====================================================================`
71872	`SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )`	71873	`SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )`
71873	`*`	71874	`*`
71874	`* -- LAPACK auxiliary routine (version 3.7.0) --`	71875	`* -- LAPACK auxiliary routine (version 3.8.0) --`
71875	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	71876	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
71876	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	71877	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
71877	`* December 2016`	71878	`* November 2017`
71878	`*`	71879	`*`
71879	`* .. Scalar Arguments ..`	71880	`* .. Scalar Arguments ..`
71880	`INTEGER INCX, N`	71881	`INTEGER INCX, N`
71881	`DOUBLE PRECISION ALPHA, TAU`	71882	`DOUBLE PRECISION ALPHA, TAU`
71882	`* ..`	71883	`* ..`
Line 71933...	Line 71934...
71933	`10 CONTINUE`	71934	`10 CONTINUE`
71934	`KNT = KNT + 1`	71935	`KNT = KNT + 1`
71935	`CALL DSCAL( N-1, RSAFMN, X, INCX )`	71936	`CALL DSCAL( N-1, RSAFMN, X, INCX )`
71936	`BETA = BETA*RSAFMN`	71937	`BETA = BETA*RSAFMN`
71937	`ALPHA = ALPHA*RSAFMN`	71938	`ALPHA = ALPHA*RSAFMN`
71938	`IF( ABS( BETA ).LT.SAFMIN )`	71939	`IF( (ABS( BETA ).LT.SAFMIN) .AND. (KNT .LT. 20) )`
71939	`$ GO TO 10`	71940	`$ GO TO 10`
71940	`*`	71941	`*`
71941	`* New BETA is at most 1, at least SAFMIN`	71942	`* New BETA is at most 1, at least SAFMIN`
71942	`*`	71943	`*`
71943	`XNORM = DNRM2( N-1, X, INCX )`	71944	`XNORM = DNRM2( N-1, X, INCX )`
Line 72056...	Line 72057...
72056	`*> \author Univ. of Tennessee`	72057	`*> \author Univ. of Tennessee`
72057	`*> \author Univ. of California Berkeley`	72058	`*> \author Univ. of California Berkeley`
72058	`*> \author Univ. of Colorado Denver`	72059	`*> \author Univ. of Colorado Denver`
72059	`*> \author NAG Ltd.`	72060	`*> \author NAG Ltd.`
72060	`*`	72061	`*`
72061	`*> \date December 2016`	72062	`*> \date November 2017`
72062	`*`	72063	`*`
72063	`*> \ingroup doubleOTHERauxiliary`	72064	`*> \ingroup doubleOTHERauxiliary`
72064	`*`	72065	`*`
72065	`* =====================================================================`	72066	`* =====================================================================`
72066	`SUBROUTINE DLARFGP( N, ALPHA, X, INCX, TAU )`	72067	`SUBROUTINE DLARFGP( N, ALPHA, X, INCX, TAU )`
72067	`*`	72068	`*`
72068	`* -- LAPACK auxiliary routine (version 3.7.0) --`	72069	`* -- LAPACK auxiliary routine (version 3.8.0) --`
72069	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	72070	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
72070	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	72071	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
72071	`* December 2016`	72072	`* November 2017`
72072	`*`	72073	`*`
72073	`* .. Scalar Arguments ..`	72074	`* .. Scalar Arguments ..`
72074	`INTEGER INCX, N`	72075	`INTEGER INCX, N`
72075	`DOUBLE PRECISION ALPHA, TAU`	72076	`DOUBLE PRECISION ALPHA, TAU`
72076	`* ..`	72077	`* ..`
Line 72140...	Line 72141...
72140	`10 CONTINUE`	72141	`10 CONTINUE`
72141	`KNT = KNT + 1`	72142	`KNT = KNT + 1`
72142	`CALL DSCAL( N-1, BIGNUM, X, INCX )`	72143	`CALL DSCAL( N-1, BIGNUM, X, INCX )`
72143	`BETA = BETA*BIGNUM`	72144	`BETA = BETA*BIGNUM`
72144	`ALPHA = ALPHA*BIGNUM`	72145	`ALPHA = ALPHA*BIGNUM`
72145	`IF( ABS( BETA ).LT.SMLNUM )`	72146	`IF( (ABS( BETA ).LT.SMLNUM) .AND. (KNT .LT. 20) )`
72146	`$ GO TO 10`	72147	`$ GO TO 10`
72147	`*`	72148	`*`
72148	`* New BETA is at most 1, at least SMLNUM`	72149	`* New BETA is at most 1, at least SMLNUM`
72149	`*`	72150	`*`
72150	`XNORM = DNRM2( N-1, X, INCX )`	72151	`XNORM = DNRM2( N-1, X, INCX )`
Line 75611...	Line 75612...
75611	`SUBROUTINE DLARRE( RANGE, N, VL, VU, IL, IU, D, E, E2,`	75612	`SUBROUTINE DLARRE( RANGE, N, VL, VU, IL, IU, D, E, E2,`
75612	`$ RTOL1, RTOL2, SPLTOL, NSPLIT, ISPLIT, M,`	75613	`$ RTOL1, RTOL2, SPLTOL, NSPLIT, ISPLIT, M,`
75613	`$ W, WERR, WGAP, IBLOCK, INDEXW, GERS, PIVMIN,`	75614	`$ W, WERR, WGAP, IBLOCK, INDEXW, GERS, PIVMIN,`
75614	`$ WORK, IWORK, INFO )`	75615	`$ WORK, IWORK, INFO )`
75615	`*`	75616	`*`
75616	`* -- LAPACK auxiliary routine (version 3.7.1) --`	75617	`* -- LAPACK auxiliary routine (version 3.8.0) --`
75617	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	75618	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
75618	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	75619	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
75619	`* June 2016`	75620	`* June 2016`
75620	`*`	75621	`*`
75621	`* .. Scalar Arguments ..`	75622	`* .. Scalar Arguments ..`
Line 75666...	Line 75667...
75666	`EXTERNAL DLAMCH, LSAME`	75667	`EXTERNAL DLAMCH, LSAME`
75667		75668
75668	`* ..`	75669	`* ..`
75669	`* .. External Subroutines ..`	75670	`* .. External Subroutines ..`
75670	`EXTERNAL DCOPY, DLARNV, DLARRA, DLARRB, DLARRC, DLARRD,`	75671	`EXTERNAL DCOPY, DLARNV, DLARRA, DLARRB, DLARRC, DLARRD,`
75671	`$ DLASQ2`	75672	`$ DLASQ2, DLARRK`
75672	`* ..`	75673	`* ..`
75673	`* .. Intrinsic Functions ..`	75674	`* .. Intrinsic Functions ..`
75674	`INTRINSIC ABS, MAX, MIN`	75675	`INTRINSIC ABS, MAX, MIN`
75675		75676
75676	`* ..`	75677	`* ..`
Line 77620...	Line 77621...
77620	`*> \param[in] VU`	77621	`*> \param[in] VU`
77621	`*> \verbatim`	77622	`*> \verbatim`
77622	`*> VU is DOUBLE PRECISION`	77623	`*> VU is DOUBLE PRECISION`
77623	`*> Upper bound of the interval that contains the desired`	77624	`*> Upper bound of the interval that contains the desired`
77624	`*> eigenvalues. VL < VU.`	77625	`*> eigenvalues. VL < VU.`
77625	`*> Note: VU is currently not used by this implmentation of DLARRV, VU is`	77626	`*> Note: VU is currently not used by this implementation of DLARRV, VU is`
77626	`*> passed to DLARRV because it could be used compute gaps on the right end`	77627	`*> passed to DLARRV because it could be used compute gaps on the right end`
77627	`*> of the extremal eigenvalues. However, with not much initial accuracy in`	77628	`*> of the extremal eigenvalues. However, with not much initial accuracy in`
77628	`*> LAMBDA and VU, the formula can lead to an overestimation of the right gap`	77629	`*> LAMBDA and VU, the formula can lead to an overestimation of the right gap`
77629	`*> and thus to inadequately early RQI 'convergence'. This is currently`	77630	`*> and thus to inadequately early RQI 'convergence'. This is currently`
77630	`*> prevented this by forcing a small right gap. And so it turns out that VU`	77631	`*> prevented this by forcing a small right gap. And so it turns out that VU`
Line 77843...	Line 77844...
77843	`$ ISPLIT, M, DOL, DOU, MINRGP,`	77844	`$ ISPLIT, M, DOL, DOU, MINRGP,`
77844	`$ RTOL1, RTOL2, W, WERR, WGAP,`	77845	`$ RTOL1, RTOL2, W, WERR, WGAP,`
77845	`$ IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ,`	77846	`$ IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ,`
77846	`$ WORK, IWORK, INFO )`	77847	`$ WORK, IWORK, INFO )`
77847	`*`	77848	`*`
77848	`* -- LAPACK auxiliary routine (version 3.7.1) --`	77849	`* -- LAPACK auxiliary routine (version 3.8.0) --`
77849	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	77850	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
77850	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	77851	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
77851	`* June 2016`	77852	`* June 2016`
77852	`*`	77853	`*`
77853	`* .. Scalar Arguments ..`	77854	`* .. Scalar Arguments ..`
Line 79204...	Line 79205...
79204	`*> \author Univ. of Tennessee`	79205	`*> \author Univ. of Tennessee`
79205	`*> \author Univ. of California Berkeley`	79206	`*> \author Univ. of California Berkeley`
79206	`*> \author Univ. of Colorado Denver`	79207	`*> \author Univ. of Colorado Denver`
79207	`*> \author NAG Ltd.`	79208	`*> \author NAG Ltd.`
79208	`*`	79209	`*`
79209	`*> \date December 2016`	79210	`*> \date November 2017`
79210	`*`	79211	`*`
79211	`*> \ingroup auxOTHERcomputational`	79212	`*> \ingroup auxOTHERcomputational`
79212	`*`	79213	`*`
79213	`* =====================================================================`	79214	`* =====================================================================`
79214	`SUBROUTINE DLARTGS( X, Y, SIGMA, CS, SN )`	79215	`SUBROUTINE DLARTGS( X, Y, SIGMA, CS, SN )`
79215	`*`	79216	`*`
79216	`* -- LAPACK computational routine (version 3.7.0) --`	79217	`* -- LAPACK computational routine (version 3.8.0) --`
79217	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	79218	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
79218	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	79219	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
79219	`* December 2016`	79220	`* November 2017`
79220	`*`	79221	`*`
79221	`* .. Scalar Arguments ..`	79222	`* .. Scalar Arguments ..`
79222	`DOUBLE PRECISION CS, SIGMA, SN, X, Y`	79223	`DOUBLE PRECISION CS, SIGMA, SN, X, Y`
79223	`* ..`	79224	`* ..`
79224	`*`	79225	`*`
Line 79229...	Line 79230...
79229	`PARAMETER ( NEGONE = -1.0D0, ONE = 1.0D0, ZERO = 0.0D0 )`	79230	`PARAMETER ( NEGONE = -1.0D0, ONE = 1.0D0, ZERO = 0.0D0 )`
79230	`* ..`	79231	`* ..`
79231	`* .. Local Scalars ..`	79232	`* .. Local Scalars ..`
79232	`DOUBLE PRECISION R, S, THRESH, W, Z`	79233	`DOUBLE PRECISION R, S, THRESH, W, Z`
79233	`* ..`	79234	`* ..`
-		79235	`* .. External Subroutines ..`
-		79236	`EXTERNAL DLARTGP`
-		79237	`* ..`
79234	`* .. External Functions ..`	79238	`* .. External Functions ..`
79235	`DOUBLE PRECISION DLAMCH`	79239	`DOUBLE PRECISION DLAMCH`
79236	`EXTERNAL DLAMCH`	79240	`EXTERNAL DLAMCH`
79237	`* .. Executable Statements ..`	79241	`* .. Executable Statements ..`
79238	`*`	79242	`*`
Line 116873...	Line 116877...
116873	`*> \author Univ. of Tennessee`	116877	`*> \author Univ. of Tennessee`
116874	`*> \author Univ. of California Berkeley`	116878	`*> \author Univ. of California Berkeley`
116875	`*> \author Univ. of Colorado Denver`	116879	`*> \author Univ. of Colorado Denver`
116876	`*> \author NAG Ltd.`	116880	`*> \author NAG Ltd.`
116877	`*`	116881	`*`
116878	`*> \date December 2016`	116882	`*> \date November 2017`
116879	`*`	116883	`*`
116880	`*> \ingroup doubleOTHERauxiliary`	116884	`*> \ingroup doubleOTHERauxiliary`
116881	`*`	116885	`*`
116882	`* =====================================================================`	116886	`* =====================================================================`
116883	`SUBROUTINE DRSCL( N, SA, SX, INCX )`	116887	`SUBROUTINE DRSCL( N, SA, SX, INCX )`
116884	`*`	116888	`*`
116885	`* -- LAPACK auxiliary routine (version 3.7.0) --`	116889	`* -- LAPACK auxiliary routine (version 3.8.0) --`
116886	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	116890	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
116887	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	116891	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
116888	`* December 2016`	116892	`* November 2017`
116889	`*`	116893	`*`
116890	`* .. Scalar Arguments ..`	116894	`* .. Scalar Arguments ..`
116891	`INTEGER INCX, N`	116895	`INTEGER INCX, N`
116892	`DOUBLE PRECISION SA`	116896	`DOUBLE PRECISION SA`
116893	`* ..`	116897	`* ..`
Line 116908...	Line 116912...
116908	`* .. External Functions ..`	116912	`* .. External Functions ..`
116909	`DOUBLE PRECISION DLAMCH`	116913	`DOUBLE PRECISION DLAMCH`
116910	`EXTERNAL DLAMCH`	116914	`EXTERNAL DLAMCH`
116911	`* ..`	116915	`* ..`
116912	`* .. External Subroutines ..`	116916	`* .. External Subroutines ..`
116913	`EXTERNAL DSCAL`	116917	`EXTERNAL DSCAL, DLABAD`
116914	`* ..`	116918	`* ..`
116915	`* .. Intrinsic Functions ..`	116919	`* .. Intrinsic Functions ..`
116916	`INTRINSIC ABS`	116920	`INTRINSIC ABS`
116917	`* ..`	116921	`* ..`
116918	`* .. Executable Statements ..`	116922	`* .. Executable Statements ..`
Line 133519...	Line 133523...
133519	`*> \author Univ. of Tennessee`	133523	`*> \author Univ. of Tennessee`
133520	`*> \author Univ. of California Berkeley`	133524	`*> \author Univ. of California Berkeley`
133521	`*> \author Univ. of Colorado Denver`	133525	`*> \author Univ. of Colorado Denver`
133522	`*> \author NAG Ltd.`	133526	`*> \author NAG Ltd.`
133523	`*`	133527	`*`
133524	`*> \date December 2016`	133528	`*> \date November 2017`
133525	`*`	133529	`*`
133526	`*> \ingroup doubleSYcomputational`	133530	`*> \ingroup doubleSYcomputational`
133527	`*`	133531	`*`
133528	`*> \par References:`	133532	`*> \par References:`
133529	`* ================`	133533	`* ================`
Line 133534...	Line 133538...
133534	`*> Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679`	133538	`*> Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679`
133535	`*>`	133539	`*>`
133536	`* =====================================================================`	133540	`* =====================================================================`
133537	`SUBROUTINE DSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )`	133541	`SUBROUTINE DSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )`
133538	`*`	133542	`*`
133539	`* -- LAPACK computational routine (version 3.7.0) --`	133543	`* -- LAPACK computational routine (version 3.8.0) --`
133540	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	133544	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
133541	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	133545	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
133542	`* December 2016`	133546	`* November 2017`
133543	`*`	133547	`*`
133544	`* .. Scalar Arguments ..`	133548	`* .. Scalar Arguments ..`
133545	`INTEGER INFO, LDA, N`	133549	`INTEGER INFO, LDA, N`
133546	`DOUBLE PRECISION AMAX, SCOND`	133550	`DOUBLE PRECISION AMAX, SCOND`
133547	`CHARACTER UPLO`	133551	`CHARACTER UPLO`
Line 133568...	Line 133572...
133568	`DOUBLE PRECISION DLAMCH`	133572	`DOUBLE PRECISION DLAMCH`
133569	`LOGICAL LSAME`	133573	`LOGICAL LSAME`
133570	`EXTERNAL DLAMCH, LSAME`	133574	`EXTERNAL DLAMCH, LSAME`
133571	`* ..`	133575	`* ..`
133572	`* .. External Subroutines ..`	133576	`* .. External Subroutines ..`
133573	`EXTERNAL DLASSQ`	133577	`EXTERNAL DLASSQ, XERBLA`
133574	`* ..`	133578	`* ..`
133575	`* .. Intrinsic Functions ..`	133579	`* .. Intrinsic Functions ..`
133576	`INTRINSIC ABS, INT, LOG, MAX, MIN, SQRT`	133580	`INTRINSIC ABS, INT, LOG, MAX, MIN, SQRT`
133577	`* ..`	133581	`* ..`
133578	`* .. Executable Statements ..`	133582	`* .. Executable Statements ..`
Line 140872...	Line 140876...
140872	`*> \author Univ. of Tennessee`	140876	`*> \author Univ. of Tennessee`
140873	`*> \author Univ. of California Berkeley`	140877	`*> \author Univ. of California Berkeley`
140874	`*> \author Univ. of Colorado Denver`	140878	`*> \author Univ. of Colorado Denver`
140875	`*> \author NAG Ltd.`	140879	`*> \author NAG Ltd.`
140876	`*`	140880	`*`
140877	`*> \date December 2016`	140881	`*> \date November 2017`
140878	`*`	140882	`*`
140879	`*> \ingroup doubleSYcomputational`	140883	`*> \ingroup doubleSYcomputational`
140880	`*`	140884	`*`
140881	`* =====================================================================`	140885	`* =====================================================================`
140882	`SUBROUTINE DSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )`	140886	`SUBROUTINE DSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )`
140883	`*`	140887	`*`
140884	`* -- LAPACK computational routine (version 3.7.0) --`	140888	`* -- LAPACK computational routine (version 3.8.0) --`
140885	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	140889	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
140886	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	140890	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
140887	`* December 2016`	140891	`* November 2017`
140888	`*`	140892	`*`
140889	`* .. Scalar Arguments ..`	140893	`* .. Scalar Arguments ..`
140890	`CHARACTER UPLO`	140894	`CHARACTER UPLO`
140891	`INTEGER INFO, LDA, LWORK, N`	140895	`INTEGER INFO, LDA, LWORK, N`
140892	`* ..`	140896	`* ..`
Line 140905...	Line 140909...
140905	`LOGICAL LSAME`	140909	`LOGICAL LSAME`
140906	`INTEGER ILAENV`	140910	`INTEGER ILAENV`
140907	`EXTERNAL LSAME, ILAENV`	140911	`EXTERNAL LSAME, ILAENV`
140908	`* ..`	140912	`* ..`
140909	`* .. External Subroutines ..`	140913	`* .. External Subroutines ..`
140910	`EXTERNAL DSYTRI, DSYTRI2X`	140914	`EXTERNAL DSYTRI, DSYTRI2X, XERBLA`
140911	`* ..`	140915	`* ..`
140912	`* .. Executable Statements ..`	140916	`* .. Executable Statements ..`
140913	`*`	140917	`*`
140914	`* Test the input parameters.`	140918	`* Test the input parameters.`
140915	`*`	140919	`*`
Line 152728...	Line 152732...
152728	`*> \author Univ. of Tennessee`	152732	`*> \author Univ. of Tennessee`
152729	`*> \author Univ. of California Berkeley`	152733	`*> \author Univ. of California Berkeley`
152730	`*> \author Univ. of Colorado Denver`	152734	`*> \author Univ. of Colorado Denver`
152731	`*> \author NAG Ltd.`	152735	`*> \author NAG Ltd.`
152732	`*`	152736	`*`
152733	`*> \date December 2016`	152737	`*> \date November 2017`
152734	`*`	152738	`*`
152735	`*> \ingroup doubleOTHERcomputational`	152739	`*> \ingroup doubleOTHERcomputational`
152736	`*`	152740	`*`
152737	`*> \par Further Details:`	152741	`*> \par Further Details:`
152738	`* =====================`	152742	`* =====================`
Line 152769...	Line 152773...
152769	`*>`	152773	`*>`
152770	`* =====================================================================`	152774	`* =====================================================================`
152771	`SUBROUTINE DTPMQRT( SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT,`	152775	`SUBROUTINE DTPMQRT( SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT,`
152772	`$ A, LDA, B, LDB, WORK, INFO )`	152776	`$ A, LDA, B, LDB, WORK, INFO )`
152773	`*`	152777	`*`
152774	`* -- LAPACK computational routine (version 3.7.0) --`	152778	`* -- LAPACK computational routine (version 3.8.0) --`
152775	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	152779	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
152776	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	152780	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
152777	`* December 2016`	152781	`* November 2017`
152778	`*`	152782	`*`
152779	`* .. Scalar Arguments ..`	152783	`* .. Scalar Arguments ..`
152780	`CHARACTER SIDE, TRANS`	152784	`CHARACTER SIDE, TRANS`
152781	`INTEGER INFO, K, LDV, LDA, LDB, M, N, L, NB, LDT`	152785	`INTEGER INFO, K, LDV, LDA, LDB, M, N, L, NB, LDT`
152782	`* ..`	152786	`* ..`
Line 152795...	Line 152799...
152795	`* .. External Functions ..`	152799	`* .. External Functions ..`
152796	`LOGICAL LSAME`	152800	`LOGICAL LSAME`
152797	`EXTERNAL LSAME`	152801	`EXTERNAL LSAME`
152798	`* ..`	152802	`* ..`
152799	`* .. External Subroutines ..`	152803	`* .. External Subroutines ..`
152800	`EXTERNAL XERBLA`	152804	`EXTERNAL DTPRFB, XERBLA`
152801	`* ..`	152805	`* ..`
152802	`* .. Intrinsic Functions ..`	152806	`* .. Intrinsic Functions ..`
152803	`INTRINSIC MAX, MIN`	152807	`INTRINSIC MAX, MIN`
152804	`* ..`	152808	`* ..`
152805	`* .. Executable Statements ..`	152809	`* .. Executable Statements ..`
Line 156400...	Line 156404...
156400	`*> \author Univ. of Tennessee`	156404	`*> \author Univ. of Tennessee`
156401	`*> \author Univ. of California Berkeley`	156405	`*> \author Univ. of California Berkeley`
156402	`*> \author Univ. of Colorado Denver`	156406	`*> \author Univ. of Colorado Denver`
156403	`*> \author NAG Ltd.`	156407	`*> \author NAG Ltd.`
156404	`*`	156408	`*`
156405	`*> \date December 2016`	156409	`*> \date November 2017`
156406	`*`	156410	`*`
156407	`*> \ingroup doubleOTHERcomputational`	156411	`*> \ingroup doubleOTHERcomputational`
156408	`*`	156412	`*`
156409	`*> \par Further Details:`	156413	`*> \par Further Details:`
156410	`* =====================`	156414	`* =====================`
Line 156422...	Line 156426...
156422	`*>`	156426	`*>`
156423	`* =====================================================================`	156427	`* =====================================================================`
156424	`SUBROUTINE DTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,`	156428	`SUBROUTINE DTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,`
156425	`$ LDVR, MM, M, WORK, INFO )`	156429	`$ LDVR, MM, M, WORK, INFO )`
156426	`*`	156430	`*`
156427	`* -- LAPACK computational routine (version 3.7.0) --`	156431	`* -- LAPACK computational routine (version 3.8.0) --`
156428	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	156432	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
156429	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	156433	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
156430	`* December 2016`	156434	`* November 2017`
156431	`*`	156435	`*`
156432	`* .. Scalar Arguments ..`	156436	`* .. Scalar Arguments ..`
156433	`CHARACTER HOWMNY, SIDE`	156437	`CHARACTER HOWMNY, SIDE`
156434	`INTEGER INFO, LDT, LDVL, LDVR, M, MM, N`	156438	`INTEGER INFO, LDT, LDVL, LDVR, M, MM, N`
156435	`* ..`	156439	`* ..`
Line 156457...	Line 156461...
156457	`INTEGER IDAMAX`	156461	`INTEGER IDAMAX`
156458	`DOUBLE PRECISION DDOT, DLAMCH`	156462	`DOUBLE PRECISION DDOT, DLAMCH`
156459	`EXTERNAL LSAME, IDAMAX, DDOT, DLAMCH`	156463	`EXTERNAL LSAME, IDAMAX, DDOT, DLAMCH`
156460	`* ..`	156464	`* ..`
156461	`* .. External Subroutines ..`	156465	`* .. External Subroutines ..`
156462	`EXTERNAL DAXPY, DCOPY, DGEMV, DLALN2, DSCAL, XERBLA`	156466	`EXTERNAL DLABAD, DAXPY, DCOPY, DGEMV, DLALN2, DSCAL,`

The R Project SVN R

(root)/trunk/src/modules/lapack/dlapack.f – Rev 72877 → 73873