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



      RETURN
*
*     End of DGBSVX
*
      END
*> \brief \b DGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGBcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, KL, KU, LDAB, M, N
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DGEBAL
*
      END
*> \brief \b DGEBD2 reduces a general matrix to bidiagonal form using an unblocked algorithm.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, M, N
*     ..
*     .. Array Arguments ..

*>
*> The right eigenvector v(j) of A satisfies
*>                  A * v(j) = lambda(j) * v(j)
*> where lambda(j) is its eigenvalue.
*> The left eigenvector u(j) of A satisfies
*>               u(j)**H * A = lambda(j) * u(j)**H
*> where u(j)**H denotes the conjugate-transpose of u(j).
*>
*> The computed eigenvectors are normalized to have Euclidean norm
*> equal to 1 and largest component real.
*> \endverbatim
*

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEeigen
*
*  =====================================================================
      SUBROUTINE DGEEV( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR,
     $                  LDVR, WORK, LWORK, INFO )
*
*  -- LAPACK driver routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          JOBVL, JOBVR
      INTEGER            INFO, LDA, LDVL, LDVR, LWORK, N
*     ..

*>
*> The right eigenvector v(j) of A satisfies
*>                  A * v(j) = lambda(j) * v(j)
*> where lambda(j) is its eigenvalue.
*> The left eigenvector u(j) of A satisfies
*>               u(j)**H * A = lambda(j) * u(j)**H
*> where u(j)**H denotes the conjugate-transpose of u(j).
*>
*> The computed eigenvectors are normalized to have Euclidean norm
*> equal to 1 and largest component real.
*>
*> Balancing a matrix means permuting the rows and columns to make it

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEeigen
*
*  =====================================================================
      SUBROUTINE DGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, WR, WI,
     $                   VL, LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM,
     $                   RCONDE, RCONDV, WORK, LWORK, IWORK, INFO )
*
*  -- LAPACK driver routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          BALANC, JOBVL, JOBVR, SENSE
      INTEGER            IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N
      DOUBLE PRECISION   ABNRM

      RETURN
*
*     End of DGEGV
*
      END
*> \brief \b DGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            IHI, ILO, INFO, LDA, N
*     ..
*     .. Array Arguments ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEsing
*
*> \par Further Details:
*  =====================
*>
*> \verbatim

*  =====================================================================
      SUBROUTINE DGEJSV( JOBA, JOBU, JOBV, JOBR, JOBT, JOBP,
     $                   M, N, A, LDA, SVA, U, LDU, V, LDV,
     $                   WORK, LWORK, IWORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      IMPLICIT    NONE
      INTEGER     INFO, LDA, LDU, LDV, LWORK, M, N
*     ..

*     ..
*     .. END OF DGEJSV
*     ..
      END
*
*> \brief \b DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, M, N
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DGEMQRT
*
      END
*> \brief \b DGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DGEQL2( M, N, A, LDA, TAU, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, M, N
*     ..
*     .. Array Arguments ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEcomputational
*
*> \par Further Details:
*  =====================

*>
*>  Each H(i) has the form
*>
*>     H(i) = I - tau * v * v**T
*>
*>  where tau is a real scalar, and v is a real/complex vector
*>  with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
*>  A(i+1:m,i), and tau in TAU(i).
*> \endverbatim
*
*> \par Contributors:

*>    X. Sun, Computer Science Dept., Duke University, USA
*>
*  =====================================================================
      SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, LWORK, M, N
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DGEQPF
*
      END
*> \brief \b DGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, M, N
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DGEQR2
*
      END
*> \brief \b DGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, M, N
*     ..
*     .. Array Arguments ..

      RETURN
*     
*     End of DGEQRT
*
      END
*> \brief \b DGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DGEQRT2( M, N, A, LDA, T, LDT, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER   INFO, LDA, LDT, M, N
*     ..
*     .. Array Arguments ..

   
*
*     End of DGEQRT2
*
      END
*> \brief \b DGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      RECURSIVE SUBROUTINE DGEQRT3( M, N, A, LDA, T, LDT, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER   INFO, LDA, M, N, LDT
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DGERFS
*
      END
*> \brief \b DGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DGERQ2( M, N, A, LDA, TAU, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, M, N
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DGERQF
*
      END
*> \brief \b DGESC2 solves a system of linear equations using the LU factorization with complete pivoting computed by sgetc2.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEauxiliary
*
*> \par Contributors:
*  ==================

*>     Umea University, S-901 87 Umea, Sweden.
*
*  =====================================================================
      SUBROUTINE DGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            LDA, N
      DOUBLE PRECISION   SCALE
*     ..

*>          If JOBZ = 'O',
*>            LWORK >= 3*min(M,N) + 
*>                     max(max(M,N),5*min(M,N)*min(M,N)+4*min(M,N)).
*>          If JOBZ = 'S' or 'A'
*>            LWORK >= 3*min(M,N) +
*>                     max(max(M,N),4*min(M,N)*min(M,N)+3*min(M,N)+max(M,N)).
*>          For good performance, LWORK should generally be larger.
*>          If LWORK = -1 but other input arguments are legal, WORK(1)
*>          returns the optimal LWORK.
*> \endverbatim
*>

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEsing
*
*> \par Contributors:
*  ==================

*>
*  =====================================================================
      SUBROUTINE DGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
     $                   LWORK, IWORK, INFO )
*
*  -- LAPACK driver routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          JOBZ
      INTEGER            INFO, LDA, LDU, LDVT, LWORK, M, N
*     ..

     $                    ILAENV( 1, 'DORMBR', 'QLN', N, N, N, -1 ) )
                  WRKBL = MAX( WRKBL, 3*N+N*
     $                    ILAENV( 1, 'DORMBR', 'PRT', N, N, N, -1 ) )
                  WRKBL = MAX( WRKBL, BDSPAC+3*N )
                  MAXWRK = WRKBL + N*N
                  MINWRK = BDSPAC + N*N + 2*N + M
               END IF
            ELSE
*
*              Path 5 (M at least N, but not much larger)
*

               LDWRKU = N
               ITAU = IU + LDWRKU*N
               NWORK = ITAU + N
*
*              Compute A=Q*R, copying result to U
*              (Workspace: need N*N+N+M, prefer N*N+N+M*NB)
*
               CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ),
     $                      LWORK-NWORK+1, IERR )
               CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
*
*              Generate Q in U
*              (Workspace: need N*N+N+M, prefer N*N+N+M*NB)
               CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ),
     $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
*
*              Produce R in A, zeroing out other entries
*

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEcomputational
*
*> \par Further Details:
*  =====================

*>
*  =====================================================================
      SUBROUTINE DGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V,
     $                   LDV, WORK, LWORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, LDV, LWORK, M, MV, N
      CHARACTER*1        JOBA, JOBU, JOBV
*     ..

 2399       CONTINUE
         END IF
      END IF
*
*     Undo scaling, if necessary (and possible).
      IF( ( ( SKL.GT.ONE ) .AND. ( SVA( 1 ).LT.( BIG / SKL) ) )
     $    .OR. ( ( SKL.LT.ONE ) .AND. ( SVA( MAX( N2, 1 ) ) .GT.
     $    ( SFMIN / SKL) ) ) ) THEN
         DO 2400 p = 1, N
            SVA( P ) = SKL*SVA( P )
 2400    CONTINUE
         SKL= ONE
      END IF
*
      WORK( 1 ) = SKL

      RETURN
*
*     End of DGESVX
*
      END
*> \brief \b DGETC2 computes the LU factorization with complete pivoting of the general n-by-n matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEauxiliary
*
*> \par Contributors:
*  ==================

*>     Umea University, S-901 87 Umea, Sweden.
*
*  =====================================================================
      SUBROUTINE DGETC2( N, A, LDA, IPIV, JPIV, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, N
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DGETC2
*
      END
*> \brief \b DGETF2 computes the LU factorization of a general m-by-n matrix using partial pivoting with row interchanges (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEcomputational
*
*  =====================================================================
      SUBROUTINE DGETF2( M, N, A, LDA, IPIV, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, M, N
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DGGSVP
*
      END
*> \brief \b DGSVJ0 pre-processor for the routine sgesvj.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \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 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP
      DOUBLE PRECISION   EPS, SFMIN, TOL
      CHARACTER*1        JOBV

      RETURN
*     ..
*     .. END OF DGSVJ0
*     ..
      END
*> \brief \b DGSVJ1 pre-processor for the routine sgesvj, applies Jacobi rotations targeting only particular pivots.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Contributors:
*  ==================

*
*  =====================================================================
      SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
     $                   EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   EPS, SFMIN, TOL
      INTEGER            INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP
      CHARACTER*1        JOBV

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGTcomputational
*
*  =====================================================================
      SUBROUTINE DGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
     $                   WORK, IWORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          NORM
      INTEGER            INFO, N
      DOUBLE PRECISION   ANORM, RCOND

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGTcomputational
*
*  =====================================================================
      SUBROUTINE DGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2,
     $                   IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK,
     $                   INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          TRANS
      INTEGER            INFO, LDB, LDX, N, NRHS
*     ..

      RETURN
*
*     End of DGTRFS
*
      END
*> \brief <b> DGTSV computes the solution to system of linear equations A * X = B for GT matrices <b>
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGTsolve
*
*  =====================================================================
      SUBROUTINE DGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
*
*  -- LAPACK driver routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDB, N, NRHS
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DGTSV
*
      END
*> \brief <b> DGTSVX computes the solution to system of linear equations A * X = B for GT matrices <b>
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGTsolve
*
*  =====================================================================
      SUBROUTINE DGTSVX( FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF,
     $                   DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR,
     $                   WORK, IWORK, INFO )
*
*  -- LAPACK driver routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          FACT, TRANS
      INTEGER            INFO, LDB, LDX, N, NRHS
      DOUBLE PRECISION   RCOND

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGTcomputational
*
*  =====================================================================
      SUBROUTINE DGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, N
*     ..
*     .. Array Arguments ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGTcomputational
*
*  =====================================================================
      SUBROUTINE DGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB,
     $                   INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          TRANS
      INTEGER            INFO, LDB, N, NRHS
*     ..

      END IF
*
*     End of DGTTRS
*
      END
*> \brief \b DGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGTcomputational
*
*  =====================================================================
      SUBROUTINE DGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            ITRANS, LDB, N, NRHS
*     ..
*     .. Array Arguments ..

      END IF
*
*     ==== End of DHSEQR ====
*
      END
*> \brief \b DISNAN tests input for NaN.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      LOGICAL FUNCTION DISNAN( DIN )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   DIN
*     ..
*

      RETURN
*
*     End of DLABAD
*
      END
*> \brief \b DLABRD reduces the first nb rows and columns of a general matrix to a bidiagonal form.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Further Details:
*  =====================

*>
*  =====================================================================
      SUBROUTINE DLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y,
     $                   LDY )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            LDA, LDX, LDY, M, N, NB
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DLABRD
*
      END
*> \brief \b DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Further Details:
*  =====================

*>  ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
*>
*  =====================================================================
      SUBROUTINE DLACN2( N, V, X, ISGN, EST, KASE, ISAVE )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            KASE, N
      DOUBLE PRECISION   EST
*     ..

      RETURN
*
*     End of DLACN2
*
      END
*> \brief \b DLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Contributors:
*  ==================

*>  ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
*>
*  =====================================================================
      SUBROUTINE DLACON( N, V, X, ISGN, EST, KASE )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            KASE, N
      DOUBLE PRECISION   EST
*     ..

      RETURN
*
*     End of DLACON
*
      END
*> \brief \b DLACPY copies all or part of one two-dimensional array to another.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLACPY( UPLO, M, N, A, LDA, B, LDB )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            LDA, LDB, M, N
*     ..

      RETURN
*
*     End of DLACPY
*
      END
*> \brief \b DLADIV performs complex division in real arithmetic, avoiding unnecessary overflow.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLADIV( A, B, C, D, P, Q )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   A, B, C, D, P, Q
*     ..
*

      RETURN
*
*     End of DLADIV
*
      END
*> \brief \b DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DLAE2( A, B, C, RT1, RT2 )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   A, B, C, RT1, RT2
*     ..
*

      RETURN
*
*     End of DLAE2
*
      END
 
*> \brief \b DLAEBZ computes the number of eigenvalues of a real symmetric tridiagonal matrix which are less than or equal to a given value, and performs other tasks required by the routine sstebz.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Further Details:
*  =====================

*  =====================================================================
      SUBROUTINE DLAEBZ( IJOB, NITMAX, N, MMAX, MINP, NBMIN, ABSTOL,
     $                   RELTOL, PIVMIN, D, E, E2, NVAL, AB, C, MOUT,
     $                   NAB, WORK, IWORK, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            IJOB, INFO, MINP, MMAX, MOUT, N, NBMIN, NITMAX
      DOUBLE PRECISION   ABSTOL, PIVMIN, RELTOL
*     ..

      RETURN
*
*     End of DLAEBZ
*
      END
*> \brief \b DLAED0 used by sstedc. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*> \par Contributors:
*  ==================

*
*  =====================================================================
      SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,
     $                   WORK, IWORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            ICOMPQ, INFO, LDQ, LDQS, N, QSIZ
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DLAED0
*
      END
*> \brief \b DLAED1 used by sstedc. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is tridiagonal.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*> \par Contributors:
*  ==================

*>
*  =====================================================================
      SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK,
     $                   INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            CUTPNT, INFO, LDQ, N
      DOUBLE PRECISION   RHO
*     ..

      RETURN
*
*     End of DLAED1
*
      END
*> \brief \b DLAED2 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*> \par Contributors:
*  ==================

*>
*  =====================================================================
      SUBROUTINE DLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W,
     $                   Q2, INDX, INDXC, INDXP, COLTYP, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, K, LDQ, N, N1
      DOUBLE PRECISION   RHO
*     ..

      RETURN
*
*     End of DLAED2
*
      END
*> \brief \b DLAED3 used by sstedc. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is tridiagonal.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*> \par Contributors:
*  ==================

*>
*  =====================================================================
      SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX,
     $                   CTOT, W, S, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, K, LDQ, N, N1
      DOUBLE PRECISION   RHO
*     ..

      RETURN
*
*     End of DLAED3
*
      END
*> \brief \b DLAED4 used by sstedc. Finds a single root of the secular equation.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*> \par Contributors:
*  ==================

*>     at Berkeley, USA
*>
*  =====================================================================
      SUBROUTINE DLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            I, INFO, N
      DOUBLE PRECISION   DLAM, RHO
*     ..

      RETURN
*
*     End of DLAED4
*
      END
*> \brief \b DLAED5 used by sstedc. Solves the 2-by-2 secular equation.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*> \par Contributors:
*  ==================

*>     at Berkeley, USA
*>
*  =====================================================================
      SUBROUTINE DLAED5( I, D, Z, DELTA, RHO, DLAM )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            I
      DOUBLE PRECISION   DLAM, RHO
*     ..

      RETURN
*
*     End OF DLAED5
*
      END
*> \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/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*> \par Further Details:
*  =====================

*>     at Berkeley, USA
*>
*  =====================================================================
      SUBROUTINE DLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      LOGICAL            ORGATI
      INTEGER            INFO, KNITER
      DOUBLE PRECISION   FINIT, RHO, TAU

      RETURN
*
*     End of DLAED6
*
      END
*> \brief \b DLAED7 used by sstedc. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is dense.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*> \par Contributors:
*  ==================

      SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q,
     $                   LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR,
     $                   PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK,
     $                   INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N,
     $                   QSIZ, TLVLS
      DOUBLE PRECISION   RHO

      RETURN
*
*     End of DLAED7
*
      END
*> \brief \b DLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*> \par Contributors:
*  ==================

*  =====================================================================
      SUBROUTINE DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO,
     $                   CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR,
     $                   GIVCOL, GIVNUM, INDXP, INDX, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            CUTPNT, GIVPTR, ICOMPQ, INFO, K, LDQ, LDQ2, N,
     $                   QSIZ
      DOUBLE PRECISION   RHO

      RETURN
*
*     End of DLAED8
*
      END
*> \brief \b DLAED9 used by sstedc. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*> \par Contributors:
*  ==================

*
*  =====================================================================
      SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W,
     $                   S, LDS, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, K, KSTART, KSTOP, LDQ, LDS, N
      DOUBLE PRECISION   RHO
*     ..

      RETURN
*
*     End of DLAED9
*
      END
*> \brief \b DLAEDA used by sstedc. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*> \par Contributors:
*  ==================

*
*  =====================================================================
      SUBROUTINE DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR,
     $                   GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            CURLVL, CURPBM, INFO, N, TLVLS
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DLAEDA
*
      END
*> \brief \b DLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B,
     $                   LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      LOGICAL            NOINIT, RIGHTV
      INTEGER            INFO, LDB, LDH, N
      DOUBLE PRECISION   BIGNUM, EPS3, SMLNUM, WI, WR

      RETURN
*
*     End of DLAEIN
*
      END
*> \brief \b DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   A, B, C, CS1, RT1, RT2, SN1
*     ..
*

      RETURN
*
*     End of DLAEV2
*
      END
*> \brief \b DLAEXC swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLAEXC( WANTQ, N, T, LDT, Q, LDQ, J1, N1, N2, WORK,
     $                   INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      LOGICAL            WANTQ
      INTEGER            INFO, J1, LDQ, LDT, N, N1, N2
*     ..

      RETURN
*
*     End of DLAEXC
*
      END
*> \brief \b DLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLAG2( A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1,
     $                  WR2, WI )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            LDA, LDB
      DOUBLE PRECISION   SAFMIN, SCALE1, SCALE2, WI, WR1, WR2
*     ..

*
*     End of DLAG2
*
      RETURN
      END
*> \brief \b DLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV,
     $                   SNV, CSQ, SNQ )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      LOGICAL            UPPER
      DOUBLE PRECISION   A1, A2, A3, B1, B2, B3, CSQ, CSU, CSV, SNQ,
     $                   SNU, SNV

      RETURN
*
*     End of DLAGS2
*
      END
*> \brief \b DLAGTF computes an LU factorization of a matrix T-λI, where T is a general tridiagonal matrix, and λ a scalar, using partial pivoting with row interchanges.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DLAGTF( N, A, LAMBDA, B, C, TOL, D, IN, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, N
      DOUBLE PRECISION   LAMBDA, TOL
*     ..

      RETURN
*
*     End of DLAGTF
*
      END
 
*> \brief \b DLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
     $                   B, LDB )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          TRANS
      INTEGER            LDB, LDX, N, NRHS
      DOUBLE PRECISION   ALPHA, BETA

      RETURN
*
*     End of DLAGTM
*
      END
*> \brief \b DLAGTS solves the system of equations (T-λI)x = y or (T-λI)Tx = y,where T is a general tridiagonal matrix and λ a scalar, using the LU factorization computed by slagtf.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, JOB, N
      DOUBLE PRECISION   TOL
*     ..

      END IF
*
*     End of DLAGTS
*
      END
*> \brief \b DLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Contributors:
*  ==================

*
*  =====================================================================
      SUBROUTINE DLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL,
     $                   CSR, SNR )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            LDA, LDB
      DOUBLE PRECISION   CSL, CSR, SNL, SNR
*     ..

      RETURN
*
*     End of DLAGV2
*
      END
*> \brief \b DLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Further Details:
*  =====================

*>
*  =====================================================================
      SUBROUTINE DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
     $                   ILOZ, IHIZ, Z, LDZ, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
      LOGICAL            WANTT, WANTZ
*     ..

      RETURN
*
*     End of DLAHQR
*
      END
*> \brief \b DLAHR2 reduces the specified number of first columns of a general rectangular matrix A so that elements below the specified subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Further Details:
*  =====================

*>  Mathematical Software, 32(2):180-194, June 2006.
*>
*  =====================================================================
      SUBROUTINE DLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            K, LDA, LDT, LDY, N, NB
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DLAHR2
*
      END
 
*> \brief \b DLAHRD reduces the first nb columns of a general rectangular matrix A so that elements below the k-th subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DLAHRD( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            K, LDA, LDT, LDY, N, NB
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DLAHRD
*
      END
*> \brief \b DLAIC1 applies one step of incremental condition estimation.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            J, JOB
      DOUBLE PRECISION   C, GAMMA, S, SEST, SESTPR
*     ..

      RETURN
*
*     End of DLAIC1
*
      END
*> \brief \b DLAISNAN tests input for NaN by comparing two arguments for inequality.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      LOGICAL FUNCTION DLAISNAN( DIN1, DIN2 )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   DIN1, DIN2
*     ..
*

*
*  .. Executable Statements ..
      DLAISNAN = (DIN1.NE.DIN2)
      RETURN
      END
*> \brief \b DLALN2 solves a 1-by-1 or 2-by-2 linear system of equations of the specified form.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLALN2( LTRANS, NA, NW, SMIN, CA, A, LDA, D1, D2, B,
     $                   LDB, WR, WI, X, LDX, SCALE, XNORM, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      LOGICAL            LTRANS
      INTEGER            INFO, LDA, LDB, LDX, NA, NW
      DOUBLE PRECISION   CA, D1, D2, SCALE, SMIN, WI, WR, XNORM

      RETURN
*
*     End of DLALN2
*
      END
*> \brief \b DLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Contributors:
*  ==================

*  =====================================================================
      SUBROUTINE DLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX,
     $                   PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM,
     $                   POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL,
     $                   LDGNUM, NL, NR, NRHS, SQRE
      DOUBLE PRECISION   C, S

      RETURN
*
*     End of DLALS0
*
      END
*> \brief \b DLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Contributors:
*  ==================

      SUBROUTINE DLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U,
     $                   LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR,
     $                   GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK,
     $                   IWORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS,
     $                   SMLSIZ
*     ..

      RETURN
*
*     End of DLALSA
*
      END
*> \brief \b DLALSD uses the singular value decomposition of A to solve the least squares problem.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Contributors:
*  ==================

*
*  =====================================================================
      SUBROUTINE DLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
     $                   RANK, WORK, IWORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDB, N, NRHS, RANK, SMLSIZ
      DOUBLE PRECISION   RCOND

      RETURN
*
*     End of DLALSD
*
      END
*> \brief \b DLAMRG creates a permutation list to merge the entries of two independently sorted sets into a single set sorted in ascending order.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DLAMRG( N1, N2, A, DTRD1, DTRD2, INDEX )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            DTRD1, DTRD2, N1, N2
*     ..
*     .. Array Arguments ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

*>     Jason Riedy, University of California, Berkeley, USA \n
*>
*  =====================================================================
      INTEGER FUNCTION DLANEG( N, D, LLD, SIGMA, PIVMIN, R )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            N, R
      DOUBLE PRECISION   PIVMIN, SIGMA
*     ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGBauxiliary
*
*  =====================================================================
      DOUBLE PRECISION FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB,
     $                 WORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          NORM
      INTEGER            KL, KU, LDAB, N
*     ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEauxiliary
*
*  =====================================================================
      DOUBLE PRECISION FUNCTION DLANGE( NORM, M, N, A, LDA, WORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          NORM
      INTEGER            LDA, M, N
*     ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      DOUBLE PRECISION FUNCTION DLANGT( NORM, N, DL, D, DU )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          NORM
      INTEGER            N
*     ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      DOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, WORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          NORM
      INTEGER            LDA, N
*     ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      DOUBLE PRECISION FUNCTION DLANSB( NORM, UPLO, N, K, AB, LDAB,
     $                 WORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          NORM, UPLO
      INTEGER            K, LDAB, N
*     ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*
*  =====================================================================
      DOUBLE PRECISION FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          NORM, TRANSR, UPLO
      INTEGER            N
*     ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      DOUBLE PRECISION FUNCTION DLANSP( NORM, UPLO, N, AP, WORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          NORM, UPLO
      INTEGER            N
*     ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          NORM
      INTEGER            N
*     ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleSYauxiliary
*
*  =====================================================================
      DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          NORM, UPLO
      INTEGER            LDA, N
*     ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      DOUBLE PRECISION FUNCTION DLANTB( NORM, UPLO, DIAG, N, K, AB,
     $                 LDAB, WORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, NORM, UPLO
      INTEGER            K, LDAB, N
*     ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      DOUBLE PRECISION FUNCTION DLANTP( NORM, UPLO, DIAG, N, AP, WORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, NORM, UPLO
      INTEGER            N
*     ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      DOUBLE PRECISION FUNCTION DLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
     $                 WORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, NORM, UPLO
      INTEGER            LDA, M, N
*     ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN
*     ..
*

      RETURN
*
*     End of DLANV2
*
      END
*> \brief \b DLAPLL measures the linear dependence of two vectors.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLAPLL( N, X, INCX, Y, INCY, SSMIN )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INCX, INCY, N
      DOUBLE PRECISION   SSMIN
*     ..

      RETURN
*
*     End of DLAPLL
*
      END
*> \brief \b DLAPMR rearranges rows of a matrix as specified by a permutation vector.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLAPMR( FORWRD, M, N, X, LDX, K )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      LOGICAL            FORWRD
      INTEGER            LDX, M, N
*     ..

*
*     End of ZLAPMT
*
      END
 
*> \brief \b DLAPMT performs a forward or backward permutation of the columns of a matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLAPMT( FORWRD, M, N, X, LDX, K )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      LOGICAL            FORWRD
      INTEGER            LDX, M, N
*     ..

      RETURN
*
*     End of DLAPMT
*
      END
*> \brief \b DLAPY2 returns sqrt(x2+y2).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      DOUBLE PRECISION FUNCTION DLAPY2( X, Y )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   X, Y
*     ..
*

      RETURN
*
*     End of DLAPY2
*
      END
*> \brief \b DLAPY3 returns sqrt(x2+y2+z2).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      DOUBLE PRECISION FUNCTION DLAPY3( X, Y, Z )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   X, Y, Z
*     ..
*

      RETURN
*
*     End of DLAPY3
*
      END
*> \brief \b DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGBauxiliary
*
*  =====================================================================
      SUBROUTINE DLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
     $                   AMAX, EQUED )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          EQUED
      INTEGER            KL, KU, LDAB, M, N
      DOUBLE PRECISION   AMAX, COLCND, ROWCND

      RETURN
*
*     End of DLAQGB
*
      END
*> \brief \b DLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEauxiliary
*
*  =====================================================================
      SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
     $                   EQUED )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          EQUED
      INTEGER            LDA, M, N
      DOUBLE PRECISION   AMAX, COLCND, ROWCND

      RETURN
*
*     End of DLAQGE
*
      END
*> \brief \b DLAQP2 computes a QR factorization with column pivoting of the matrix block.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Contributors:
*  ==================

*
*  =====================================================================
      SUBROUTINE DLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2,
     $                   WORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            LDA, M, N, OFFSET
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DLAQP2
*
      END
*> \brief \b DLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Contributors:
*  ==================

*
*  =====================================================================
      SUBROUTINE DLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1,
     $                   VN2, AUXV, F, LDF )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            KB, LDA, LDF, M, N, NB, OFFSET
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DLAQPS
*
      END
*> \brief \b DLAQR0 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
     $                   ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, LWORK, N
      LOGICAL            WANTT, WANTZ
*     ..

      WORK( 1 ) = DBLE( LWKOPT )
*
*     ==== End of DLAQR0 ====
*
      END
*> \brief \b DLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Contributors:
*  ==================

*>       University of Kansas, USA
*>
*  =====================================================================
      SUBROUTINE DLAQR1( N, H, LDH, SR1, SI1, SR2, SI2, V )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   SI1, SI2, SR1, SR2
      INTEGER            LDH, N
*     ..

            V( 3 ) = H31S*( H( 1, 1 )+H( 3, 3 )-SR1-SR2 ) +
     $               H21S*H( 3, 2 )
         END IF
      END IF
      END
 
*> \brief \b DLAQR2 performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Contributors:
*  ==================

*  =====================================================================
      SUBROUTINE DLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
     $                   IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T,
     $                   LDT, NV, WV, LDWV, WORK, LWORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            IHIZ, ILOZ, KBOT, KTOP, LDH, LDT, LDV, LDWV,
     $                   LDZ, LWORK, N, ND, NH, NS, NV, NW
      LOGICAL            WANTT, WANTZ

      WORK( 1 ) = DBLE( LWKOPT )
*
*     ==== End of DLAQR2 ====
*
      END
 
*> \brief \b DLAQR3 performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Contributors:
*  ==================

*  =====================================================================
      SUBROUTINE DLAQR3( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
     $                   IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T,
     $                   LDT, NV, WV, LDWV, WORK, LWORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            IHIZ, ILOZ, KBOT, KTOP, LDH, LDT, LDV, LDWV,
     $                   LDZ, LWORK, N, ND, NH, NS, NV, NW
      LOGICAL            WANTT, WANTZ

      WORK( 1 ) = DBLE( LWKOPT )
*
*     ==== End of DLAQR3 ====
*
      END
*> \brief \b DLAQR4 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Contributors:
*  ==================

*>
*  =====================================================================
      SUBROUTINE DLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
     $                   ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, LWORK, N
      LOGICAL            WANTT, WANTZ
*     ..

      WORK( 1 ) = DBLE( LWKOPT )
*
*     ==== End of DLAQR4 ====
*
      END
*> \brief \b DLAQR5 performs a single small-bulge multi-shift QR sweep.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Contributors:
*  ==================

*  =====================================================================
      SUBROUTINE DLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS,
     $                   SR, SI, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U,
     $                   LDU, NV, WV, LDWV, NH, WH, LDWH )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            IHIZ, ILOZ, KACC22, KBOT, KTOP, LDH, LDU, LDV,
     $                   LDWH, LDWV, LDZ, N, NH, NSHFTS, NV
      LOGICAL            WANTT, WANTZ

  220 CONTINUE
*
*     ==== End of DLAQR5 ====
*
      END
*> \brief \b DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          EQUED, UPLO
      INTEGER            KD, LDAB, N
      DOUBLE PRECISION   AMAX, SCOND

      RETURN
*
*     End of DLAQSB
*
      END
*> \brief \b DLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          EQUED, UPLO
      INTEGER            N
      DOUBLE PRECISION   AMAX, SCOND

      RETURN
*
*     End of DLAQSP
*
      END
*> \brief \b DLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleSYauxiliary
*
*  =====================================================================
      SUBROUTINE DLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          EQUED, UPLO
      INTEGER            LDA, N
      DOUBLE PRECISION   AMAX, SCOND

      RETURN
*
*     End of DLAQSY
*
      END
*> \brief \b DLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLAQTR( LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK,
     $                   INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      LOGICAL            LREAL, LTRAN
      INTEGER            INFO, LDT, N
      DOUBLE PRECISION   SCALE, W

      RETURN
*
*     End of DLAQTR
*
      END
*> \brief \b DLAR1V computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT - λI.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Contributors:
*  ==================

*  =====================================================================
      SUBROUTINE DLAR1V( N, B1, BN, LAMBDA, D, L, LD, LLD,
     $           PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA,
     $           R, ISUPPZ, NRMINV, RESID, RQCORR, WORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      LOGICAL            WANTNC
      INTEGER   B1, BN, N, NEGCNT, R
      DOUBLE PRECISION   GAPTOL, LAMBDA, MINGMA, NRMINV, PIVMIN, RESID,

      RETURN
*
*     End of DLAR1V
*
      END
*> \brief \b DLAR2V applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLAR2V( N, X, Y, Z, INCX, C, S, INCC )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INCC, INCX, N
*     ..
*     .. Array Arguments ..

*
*     End of DLAR2V
*
      RETURN
      END
*> \brief \b DLARF applies an elementary reflector to a general rectangular matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE
      INTEGER            INCV, LDC, M, N
      DOUBLE PRECISION   TAU

      RETURN
*
*     End of DLARF
*
      END
*> \brief \b DLARFB applies a block reflector or its transpose to a general rectangular matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Further Details:
*  =====================

*>
*  =====================================================================
      SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
     $                   T, LDT, C, LDC, WORK, LDWORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          DIRECT, SIDE, STOREV, TRANS
      INTEGER            K, LDC, LDT, LDV, LDWORK, M, N
*     ..

      DOUBLE PRECISION   ONE
      PARAMETER          ( ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      CHARACTER          TRANST
      INTEGER            I, J, LASTV, LASTC, lastv2
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILADLR, ILADLC
      EXTERNAL           LSAME, ILADLR, ILADLC

            IF( LSAME( SIDE, 'L' ) ) THEN
*
*              Form  H * C  or  H**T * C  where  C = ( C1 )
*                                                    ( C2 )
*
 
               LASTC = ILADLC( M, N, C, LDC )
*
*              W := C**T * V  =  (C1**T * V1 + C2**T * V2)  (stored in WORK)
*
*              W := C2**T
*
               DO 70 J = 1, K
                  CALL DCOPY( LASTC, C( M-K+J, 1 ), LDC,
     $                 WORK( 1, J ), 1 )
   70          CONTINUE
*
*              W := W * V2
*
               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
     $              LASTC, K, ONE, V( M-K+1, 1 ), LDV,
     $              WORK, LDWORK )
               IF( M.GT.K ) THEN
*
*                 W := W + C1**T*V1
*
                  CALL DGEMM( 'Transpose', 'No transpose',
     $                 LASTC, K, M-K, ONE, C, LDC, V, LDV,
     $                 ONE, WORK, LDWORK )
               END IF
*
*              W := W * T**T  or  W * T
*
               CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
*
*              C := C - V * W**T
*
               IF( M.GT.K ) THEN
*
*                 C1 := C1 - V1 * W**T
*
                  CALL DGEMM( 'No transpose', 'Transpose',
     $                 M-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,
     $                 ONE, C, LDC )
               END IF
*
*              W := W * V2**T
*
               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
     $              LASTC, K, ONE, V( M-K+1, 1 ), LDV,
     $              WORK, LDWORK )
*
*              C2 := C2 - W**T
*
               DO 90 J = 1, K
                  DO 80 I = 1, LASTC
                     C( M-K+J, I ) = C( M-K+J, I ) - WORK(I, J)
   80             CONTINUE
   90          CONTINUE
*
            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
*
*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
*
 
               LASTC = ILADLR( M, N, C, LDC )
*
*              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)
*
*              W := C2
*

  100          CONTINUE
*
*              W := W * V2
*
               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
     $              LASTC, K, ONE, V( N-K+1, 1 ), LDV,
     $              WORK, LDWORK )
               IF( N.GT.K ) THEN
*
*                 W := W + C1 * V1
*
                  CALL DGEMM( 'No transpose', 'No transpose',
     $                 LASTC, K, N-K, ONE, C, LDC, V, LDV,
     $                 ONE, WORK, LDWORK )
               END IF
*
*              W := W * T  or  W * T**T
*
               CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
*
*              C := C - W * V**T
*
               IF( N.GT.K ) THEN
*
*                 C1 := C1 - W * V1**T
*
                  CALL DGEMM( 'No transpose', 'Transpose',
     $                 LASTC, N-K, K, -ONE, WORK, LDWORK, V, LDV,
     $                 ONE, C, LDC )
               END IF
*
*              W := W * V2**T
*
               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
     $              LASTC, K, ONE, V( N-K+1, 1 ), LDV,
     $              WORK, LDWORK )
*
*              C2 := C2 - W
*
               DO 120 J = 1, K
                  DO 110 I = 1, LASTC
                     C( I, N-K+J ) = C( I, N-K+J ) - WORK(I, J)
  110             CONTINUE
  120          CONTINUE
            END IF
         END IF
*

            IF( LSAME( SIDE, 'L' ) ) THEN
*
*              Form  H * C  or  H**T * C  where  C = ( C1 )
*                                                    ( C2 )
*
 
               LASTC = ILADLC( M, N, C, LDC )
*
*              W := C**T * V**T  =  (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
*
*              W := C2**T
*
               DO 190 J = 1, K
                  CALL DCOPY( LASTC, C( M-K+J, 1 ), LDC,
     $                 WORK( 1, J ), 1 )
  190          CONTINUE
*
*              W := W * V2**T
*
               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
     $              LASTC, K, ONE, V( 1, M-K+1 ), LDV,
     $              WORK, LDWORK )
               IF( M.GT.K ) THEN
*
*                 W := W + C1**T * V1**T
*
                  CALL DGEMM( 'Transpose', 'Transpose',
     $                 LASTC, K, M-K, ONE, C, LDC, V, LDV,
     $                 ONE, WORK, LDWORK )
               END IF
*
*              W := W * T**T  or  W * T
*
               CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
*
*              C := C - V**T * W**T
*
               IF( M.GT.K ) THEN
*
*                 C1 := C1 - V1**T * W**T
*
                  CALL DGEMM( 'Transpose', 'Transpose',
     $                 M-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,
     $                 ONE, C, LDC )
               END IF
*
*              W := W * V2
*
               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
     $              LASTC, K, ONE, V( 1, M-K+1 ), LDV,
     $              WORK, LDWORK )
*
*              C2 := C2 - W**T
*
               DO 210 J = 1, K
                  DO 200 I = 1, LASTC
                     C( M-K+J, I ) = C( M-K+J, I ) - WORK(I, J)
  200             CONTINUE
  210          CONTINUE
*
            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
*
*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
*
 
               LASTC = ILADLR( M, N, C, LDC )
*
*              W := C * V**T  =  (C1*V1**T + C2*V2**T)  (stored in WORK)
*
*              W := C2
*
               DO 220 J = 1, K
                  CALL DCOPY( LASTC, C( 1, N-K+J ), 1,
     $                 WORK( 1, J ), 1 )
  220          CONTINUE
*
*              W := W * V2**T
*
               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
     $              LASTC, K, ONE, V( 1, N-K+1 ), LDV,
     $              WORK, LDWORK )
               IF( N.GT.K ) THEN
*
*                 W := W + C1 * V1**T
*
                  CALL DGEMM( 'No transpose', 'Transpose',
     $                 LASTC, K, N-K, ONE, C, LDC, V, LDV,
     $                 ONE, WORK, LDWORK )
               END IF
*
*              W := W * T  or  W * T**T
*
               CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
*
*              C := C - W * V
*
               IF( N.GT.K ) THEN
*
*                 C1 := C1 - W * V1
*
                  CALL DGEMM( 'No transpose', 'No transpose',
     $                 LASTC, N-K, K, -ONE, WORK, LDWORK, V, LDV,
     $                 ONE, C, LDC )
               END IF
*
*              W := W * V2
*
               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
     $              LASTC, K, ONE, V( 1, N-K+1 ), LDV,
     $              WORK, LDWORK )
*
*              C1 := C1 - W
*
               DO 240 J = 1, K
                  DO 230 I = 1, LASTC
                     C( I, N-K+J ) = C( I, N-K+J ) - WORK(I, J)
  230             CONTINUE
  240          CONTINUE
*
            END IF
*

      RETURN
*
*     End of DLARFB
*
      END
*> \brief \b DLARFG generates an elementary reflector (Householder matrix).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INCX, N
      DOUBLE PRECISION   ALPHA, TAU
*     ..

      RETURN
*
*     End of DLARFG
*
      END
*> \brief \b DLARFGP generates an elementary reflector (Householder matrix) with non-negatibe beta.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLARFGP( N, ALPHA, X, INCX, TAU )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INCX, N
      DOUBLE PRECISION   ALPHA, TAU
*     ..

      RETURN
*
*     End of DLARFGP
*
      END
*> \brief \b DLARFT forms the triangular factor T of a block reflector H = I - vtvH
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          DIRECT, STOREV
      INTEGER            K, LDT, LDV, N
*     ..

      RETURN
*
*     End of DLARFT
*
      END
*> \brief \b DLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLARFX( SIDE, M, N, V, TAU, C, LDC, WORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE
      INTEGER            LDC, M, N
      DOUBLE PRECISION   TAU

      RETURN
*
*     End of DLARFX
*
      END
*> \brief \b DLARGV generates a vector of plane rotations with real cosines and real sines.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLARGV( N, X, INCX, Y, INCY, C, INCC )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INCC, INCX, INCY, N
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DLARGV
*
      END
*> \brief \b DLARNV returns a vector of random numbers from a uniform or normal distribution.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DLARNV( IDIST, ISEED, N, X )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            IDIST, N
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DLARNV
*
      END
*> \brief \b DLARRA computes the splitting points with the specified threshold.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

*
*  =====================================================================
      SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM,
     $                    NSPLIT, ISPLIT, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, N, NSPLIT
      DOUBLE PRECISION    SPLTOL, TNRM
*     ..

      RETURN
*
*     End of DLARRA
*
      END
*> \brief \b DLARRB provides limited bisection to locate eigenvalues for more accuracy.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

*  =====================================================================
      SUBROUTINE DLARRB( N, D, LLD, IFIRST, ILAST, RTOL1,
     $                   RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK,
     $                   PIVMIN, SPDIAM, TWIST, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            IFIRST, ILAST, INFO, N, OFFSET, TWIST
      DOUBLE PRECISION   PIVMIN, RTOL1, RTOL2, SPDIAM
*     ..

      RETURN
*
*     End of DLARRB
*
      END
*> \brief \b DLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

*
*  =====================================================================
      SUBROUTINE DLARRC( JOBT, N, VL, VU, D, E, PIVMIN,
     $                            EIGCNT, LCNT, RCNT, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          JOBT
      INTEGER            EIGCNT, INFO, LCNT, N, RCNT
      DOUBLE PRECISION   PIVMIN, VL, VU

      RETURN
*
*     end of DLARRC
*
      END
*> \brief \b DLARRD computes the eigenvalues of a symmetric tridiagonal matrix to suitable accuracy.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLARRD( RANGE, ORDER, N, VL, VU, IL, IU, GERS,
     $                    RELTOL, D, E, E2, PIVMIN, NSPLIT, ISPLIT,
     $                    M, W, WERR, WL, WU, IBLOCK, INDEXW,
     $                    WORK, IWORK, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          ORDER, RANGE
      INTEGER            IL, INFO, IU, M, N, NSPLIT
      DOUBLE PRECISION    PIVMIN, RELTOL, VL, VU, WL, WU

      RETURN
*
*     End of DLARRD
*
      END
*> \brief \b DLARRE given the tridiagonal matrix T, sets small off-diagonal elements to zero and for each unreduced block Ti, finds base representations and eigenvalues.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Further Details:
*  =====================

      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 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          RANGE
      INTEGER            IL, INFO, IU, M, N, NSPLIT
      DOUBLE PRECISION  PIVMIN, RTOL1, RTOL2, SPLTOL, VL, VU

      RETURN
*
*     end of DLARRE
*
      END
*> \brief \b DLARRF finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

      SUBROUTINE DLARRF( N, D, L, LD, CLSTRT, CLEND,
     $                   W, WGAP, WERR,
     $                   SPDIAM, CLGAPL, CLGAPR, PIVMIN, SIGMA,
     $                   DPLUS, LPLUS, WORK, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            CLSTRT, CLEND, INFO, N
      DOUBLE PRECISION   CLGAPL, CLGAPR, PIVMIN, SIGMA, SPDIAM
*     ..

      RETURN
*
*     End of DLARRF
*
      END
*> \brief \b DLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

*  =====================================================================
      SUBROUTINE DLARRJ( N, D, E2, IFIRST, ILAST,
     $                   RTOL, OFFSET, W, WERR, WORK, IWORK,
     $                   PIVMIN, SPDIAM, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            IFIRST, ILAST, INFO, N, OFFSET
      DOUBLE PRECISION   PIVMIN, RTOL, SPDIAM
*     ..

      RETURN
*
*     End of DLARRJ
*
      END
*> \brief \b DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLARRK( N, IW, GL, GU,
     $                    D, E2, PIVMIN, RELTOL, W, WERR, INFO)
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER   INFO, IW, N
      DOUBLE PRECISION    PIVMIN, RELTOL, GL, GU, W, WERR
*     ..

      RETURN
*
*     End of DLARRK
*
      END
*> \brief \b DLARRR performs tests to decide whether the symmetric tridiagonal matrix T warrants expensive computations which guarantee high relative accuracy in the eigenvalues.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

*> Christof Voemel, University of California, Berkeley, USA
*
*  =====================================================================
      SUBROUTINE DLARRR( N, D, E, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            N, INFO
*     ..
*     .. Array Arguments ..

      RETURN
*
*     END OF DLARRR
*
      END
*> \brief \b DLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the eigenvalues of L D LT.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Contributors:
*  ==================

     $                   ISPLIT, M, DOL, DOU, MINRGP,
     $                   RTOL1, RTOL2, W, WERR, WGAP,
     $                   IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ,
     $                   WORK, IWORK, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            DOL, DOU, INFO, LDZ, M, N
      DOUBLE PRECISION   MINRGP, PIVMIN, RTOL1, RTOL2, VL, VU
*     ..

      RETURN
*
*     End of DLARRV
*
      END
*> \brief \b DLARSCL2 performs reciprocal diagonal scaling on a vector.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DLARSCL2 ( M, N, D, X, LDX )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            M, N, LDX
*     ..
*     .. Array Arguments ..

         END DO
      END DO
 
      RETURN
      END
*> \brief \b DLARTG generates a plane rotation with real cosine and real sine.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLARTG( F, G, CS, SN, R )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   CS, F, G, R, SN
*     ..
*

      RETURN
*
*     End of DLARTG
*
      END
*> \brief \b DLARTGP generates a plane rotation so that the diagonal is nonnegative.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLARTGP( F, G, CS, SN, R )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   CS, F, G, R, SN
*     ..
*

      RETURN
*
*     End of DLARTGP
*
      END
*> \brief \b DLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DLARTGS( X, Y, SIGMA, CS, SN )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION        CS, SIGMA, SN, X, Y
*     ..
*

*
*     End DLARTGS
*
      END
 
*> \brief \b DLARTV applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLARTV( N, X, INCX, Y, INCY, C, S, INCC )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INCC, INCX, INCY, N
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DLARTV
*
      END
*> \brief \b DLARUV returns a vector of n random real numbers from a uniform distribution.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DLARUV( ISEED, N, X )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            N
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DLARUV
*
      END
*> \brief \b DLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Contributors:
*  ==================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE
      INTEGER            INCV, L, LDC, M, N
      DOUBLE PRECISION   TAU

      RETURN
*
*     End of DLARZ
*
      END
*> \brief \b DLARZB applies a block reflector or its transpose to a general matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Contributors:
*  ==================

*>
*  =====================================================================
      SUBROUTINE DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
     $                   LDV, T, LDT, C, LDC, WORK, LDWORK )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          DIRECT, SIDE, STOREV, TRANS
      INTEGER            K, L, LDC, LDT, LDV, LDWORK, M, N
*     ..

      RETURN
*
*     End of DLARZB
*
      END
*> \brief \b DLARZT forms the triangular factor T of a block reflector H = I - vtvH.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Contributors:
*  ==================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          DIRECT, STOREV
      INTEGER            K, LDT, LDV, N
*     ..

      RETURN
*
*     End of DLARZT
*
      END
*> \brief \b DLAS2 computes singular values of a 2-by-2 triangular matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   F, G, H, SSMAX, SSMIN
*     ..
*

      RETURN
*
*     End of DLAS2
*
      END
*> \brief \b DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          TYPE
      INTEGER            INFO, KL, KU, LDA, M, N
      DOUBLE PRECISION   CFROM, CTO

      RETURN
*
*     End of DLASCL
*
      END
*> \brief \b DLASCL2 performs diagonal scaling on a vector.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DLASCL2 ( M, N, D, X, LDX )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            M, N, LDX
*     ..
*     .. Array Arguments ..

         END DO
      END DO
 
      RETURN
      END
*> \brief \b DLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

*>
*  =====================================================================
      SUBROUTINE DLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
     $                   WORK, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDU, LDVT, N, SMLSIZ, SQRE
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DLASD0
*
      END
*> \brief \b DLASD1 computes the SVD of an upper bidiagonal matrix B of the specified size. Used by sbdsdc.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

*>
*  =====================================================================
      SUBROUTINE DLASD1( NL, NR, SQRE, D, ALPHA, BETA, U, LDU, VT, LDVT,
     $                   IDXQ, IWORK, WORK, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDU, LDVT, NL, NR, SQRE
      DOUBLE PRECISION   ALPHA, BETA
*     ..

      RETURN
*
*     End of DLASD1
*
      END
*> \brief \b DLASD2 merges the two sets of singular values together into a single sorted set. Used by sbdsdc.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

*  =====================================================================
      SUBROUTINE DLASD2( NL, NR, SQRE, K, D, Z, ALPHA, BETA, U, LDU, VT,
     $                   LDVT, DSIGMA, U2, LDU2, VT2, LDVT2, IDXP, IDX,
     $                   IDXC, IDXQ, COLTYP, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, K, LDU, LDU2, LDVT, LDVT2, NL, NR, SQRE
      DOUBLE PRECISION   ALPHA, BETA
*     ..

      RETURN
*
*     End of DLASD2
*
      END
 
*> \brief \b DLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

*  =====================================================================
      SUBROUTINE DLASD3( NL, NR, SQRE, K, D, Q, LDQ, DSIGMA, U, LDU, U2,
     $                   LDU2, VT, LDVT, VT2, LDVT2, IDXC, CTOT, Z,
     $                   INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, K, LDQ, LDU, LDU2, LDVT, LDVT2, NL, NR,
     $                   SQRE
*     ..

      RETURN
*
*     End of DLASD3
*
      END
*> \brief \b DLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by dbdsdc.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLASD4 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasd4.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasd4.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasd4.f">
*> [TXT]</a>
*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )
*
*       .. Scalar Arguments ..
*       INTEGER            I, INFO, N
*       DOUBLE PRECISION   RHO, SIGMA
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   D( * ), DELTA( * ), WORK( * ), Z( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim

*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

*>     at Berkeley, USA
*>
*  =====================================================================
      SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            I, INFO, N
      DOUBLE PRECISION   RHO, SIGMA
*     ..

*
*  =====================================================================
*
*     .. Parameters ..
      INTEGER            MAXIT
      PARAMETER          ( MAXIT = 400 )
      DOUBLE PRECISION   ZERO, ONE, TWO, THREE, FOUR, EIGHT, TEN
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0,
     $                   THREE = 3.0D+0, FOUR = 4.0D+0, EIGHT = 8.0D+0,
     $                   TEN = 10.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            ORGATI, SWTCH, SWTCH3, GEOMAVG
      INTEGER            II, IIM1, IIP1, IP1, ITER, J, NITER
      DOUBLE PRECISION   A, B, C, DELSQ, DELSQ2, SQ2, DPHI, DPSI, DTIIM,
     $                   DTIIP, DTIPSQ, DTISQ, DTNSQ, DTNSQ1, DW, EPS,
     $                   ERRETM, ETA, PHI, PREW, PSI, RHOINV, SGLB,
     $                   SGUB, TAU, TAU2, TEMP, TEMP1, TEMP2, W
*     ..
*     .. Local Arrays ..
      DOUBLE PRECISION   DD( 3 ), ZZ( 3 )
*     ..
*     .. External Subroutines ..

            TEMP1 = SQRT( D( N )*D( N )+RHO )
            TEMP = Z( N-1 )*Z( N-1 ) / ( ( D( N-1 )+TEMP1 )*
     $             ( D( N )-D( N-1 )+RHO / ( D( N )+TEMP1 ) ) ) +
     $             Z( N )*Z( N ) / RHO
*
*           The following TAU2 is to approximate
*           SIGMA_n^2 - D( N )*D( N )
*
            IF( C.LE.TEMP ) THEN
               TAU = RHO
            ELSE
               DELSQ = ( D( N )-D( N-1 ) )*( D( N )+D( N-1 ) )
               A = -C*DELSQ + Z( N-1 )*Z( N-1 ) + Z( N )*Z( N )
               B = Z( N )*Z( N )*DELSQ
               IF( A.LT.ZERO ) THEN
                  TAU2 = TWO*B / ( SQRT( A*A+FOUR*B*C )-A )
               ELSE
                  TAU2 = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C )
               END IF
            END IF
*
*           It can be proved that
*               D(N)^2+RHO/2 <= SIGMA_n^2 < D(N)^2+TAU2 <= D(N)^2+RHO
*
         ELSE
            DELSQ = ( D( N )-D( N-1 ) )*( D( N )+D( N-1 ) )
            A = -C*DELSQ + Z( N-1 )*Z( N-1 ) + Z( N )*Z( N )
            B = Z( N )*Z( N )*DELSQ
*
*           The following TAU2 is to approximate
*           SIGMA_n^2 - D( N )*D( N )
*
            IF( A.LT.ZERO ) THEN
               TAU2 = TWO*B / ( SQRT( A*A+FOUR*B*C )-A )
            ELSE
               TAU2 = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C )
            END IF
*
*           It can be proved that
*           D(N)^2 < D(N)^2+TAU2 < SIGMA(N)^2 < D(N)^2+RHO/2
*
         END IF
*
*        The following TAU is to approximate SIGMA_n - D( N )
*
         TAU = TAU2 / ( D( N )+SQRT( D( N )*D( N )+TAU2 ) )
*
         SIGMA = D( N ) + TAU
         DO 30 J = 1, N
            DELTA( J ) = ( D( J )-D( N ) ) - TAU
            WORK( J ) = D( J ) + D( N ) + TAU
   30    CONTINUE
*
*        Evaluate PSI and the derivative DPSI
*
         DPSI = ZERO

*        Evaluate PHI and the derivative DPHI
*
         TEMP = Z( N ) / ( DELTA( N )*WORK( N ) )
         PHI = Z( N )*TEMP
         DPHI = TEMP*TEMP
         ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV  
*    $          + ABS( TAU2 )*( DPSI+DPHI )
*
         W = RHOINV + PHI + PSI
*
*        Test for convergence
*

     $      ETA = -W / ( DPSI+DPHI )
         TEMP = ETA - DTNSQ
         IF( TEMP.GT.RHO )
     $      ETA = RHO + DTNSQ
*
 
         ETA = ETA / ( SIGMA+SQRT( ETA+SIGMA*SIGMA ) )
         TAU = TAU + ETA
         SIGMA = SIGMA + ETA
*
         DO 50 J = 1, N
            DELTA( J ) = DELTA( J ) - ETA
            WORK( J ) = WORK( J ) + ETA
   50    CONTINUE
*
 
 
*        Evaluate PSI and the derivative DPSI
*
         DPSI = ZERO
         PSI = ZERO
         ERRETM = ZERO

   60    CONTINUE
         ERRETM = ABS( ERRETM )
*
*        Evaluate PHI and the derivative DPHI
*
         TAU2 = WORK( N )*DELTA( N )
         TEMP = Z( N ) / TAU2
         PHI = Z( N )*TEMP
         DPHI = TEMP*TEMP
         ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV  
*    $          + ABS( TAU2 )*( DPSI+DPHI )
*
         W = RHOINV + PHI + PSI
*
*        Main loop to update the values of the array   DELTA
*

     $         ETA = -W / ( DPSI+DPHI )
            TEMP = ETA - DTNSQ
            IF( TEMP.LE.ZERO )
     $         ETA = ETA / TWO
*
 
            ETA = ETA / ( SIGMA+SQRT( ETA+SIGMA*SIGMA ) )
            TAU = TAU + ETA
            SIGMA = SIGMA + ETA
*
            DO 70 J = 1, N
               DELTA( J ) = DELTA( J ) - ETA
               WORK( J ) = WORK( J ) + ETA
   70       CONTINUE
*
 
 
*           Evaluate PSI and the derivative DPSI
*
            DPSI = ZERO
            PSI = ZERO
            ERRETM = ZERO

   80       CONTINUE
            ERRETM = ABS( ERRETM )
*
*           Evaluate PHI and the derivative DPHI
*
            TAU2 = WORK( N )*DELTA( N )
            TEMP = Z( N ) / TAU2
            PHI = Z( N )*TEMP
            DPHI = TEMP*TEMP
            ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV  
*    $             + ABS( TAU2 )*( DPSI+DPHI )
*
            W = RHOINV + PHI + PSI
   90    CONTINUE
*
*        Return with INFO = 1, NITER = MAXIT and not converged

*
*        Calculate initial guess
*
         DELSQ = ( D( IP1 )-D( I ) )*( D( IP1 )+D( I ) )
         DELSQ2 = DELSQ / TWO
         SQ2=SQRT( ( D( I )*D( I )+D( IP1 )*D( IP1 ) ) / TWO )
         TEMP = DELSQ2 / ( D( I )+SQ2 )
         DO 100 J = 1, N
            WORK( J ) = D( J ) + D( I ) + TEMP
            DELTA( J ) = ( D( J )-D( I ) ) - TEMP
  100    CONTINUE
*

  120    CONTINUE
         C = RHOINV + PSI + PHI
         W = C + Z( I )*Z( I ) / ( WORK( I )*DELTA( I ) ) +
     $       Z( IP1 )*Z( IP1 ) / ( WORK( IP1 )*DELTA( IP1 ) )
*
         GEOMAVG = .FALSE.
         IF( W.GT.ZERO ) THEN
*
*           d(i)^2 < the ith sigma^2 < (d(i)^2+d(i+1)^2)/2
*
*           We choose d(i) as origin.
*
            ORGATI = .TRUE.
            II = I
            SGLB = ZERO
            SGUB = DELSQ2  / ( D( I )+SQ2 )
            A = C*DELSQ + Z( I )*Z( I ) + Z( IP1 )*Z( IP1 )
            B = Z( I )*Z( I )*DELSQ
            IF( A.GT.ZERO ) THEN
               TAU2 = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) )
            ELSE
               TAU2 = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C )
            END IF
*
*           TAU2 now is an estimation of SIGMA^2 - D( I )^2. The
*           following, however, is the corresponding estimation of
*           SIGMA - D( I ).
*
            TAU = TAU2 / ( D( I )+SQRT( D( I )*D( I )+TAU2 ) )
            TEMP = SQRT(EPS)
            IF( (D(I).LE.TEMP*D(IP1)).AND.(ABS(Z(I)).LE.TEMP)
     $                               .AND.(D(I).GT.ZERO) ) THEN
               TAU = MIN( TEN*D(I), SGUB )
               GEOMAVG = .TRUE.
            END IF
         ELSE
*
*           (d(i)^2+d(i+1)^2)/2 <= the ith sigma^2 < d(i+1)^2/2
*
*           We choose d(i+1) as origin.
*
            ORGATI = .FALSE.
            II = IP1
            SGLB = -DELSQ2  / ( D( II )+SQ2 )
            SGUB = ZERO
            A = C*DELSQ - Z( I )*Z( I ) - Z( IP1 )*Z( IP1 )
            B = Z( IP1 )*Z( IP1 )*DELSQ
            IF( A.LT.ZERO ) THEN
               TAU2 = TWO*B / ( A-SQRT( ABS( A*A+FOUR*B*C ) ) )
            ELSE
               TAU2 = -( A+SQRT( ABS( A*A+FOUR*B*C ) ) ) / ( TWO*C )
            END IF
*
*           TAU2 now is an estimation of SIGMA^2 - D( IP1 )^2. The
*           following, however, is the corresponding estimation of
*           SIGMA - D( IP1 ).
*
            TAU = TAU2 / ( D( IP1 )+SQRT( ABS( D( IP1 )*D( IP1 )+
     $            TAU2 ) ) )
         END IF
*
 
 
         SIGMA = D( II ) + TAU
         DO 130 J = 1, N
            WORK( J ) = D( J ) + D( II ) + TAU
            DELTA( J ) = ( D( J )-D( II ) ) - TAU
  130    CONTINUE
 
 
 
 
 
 
 
 
         IIM1 = II - 1
         IIP1 = II + 1
*
*        Evaluate PSI and the derivative DPSI
*

*
         TEMP = Z( II ) / ( WORK( II )*DELTA( II ) )
         DW = DPSI + DPHI + TEMP*TEMP
         TEMP = Z( II )*TEMP
         W = W + TEMP
         ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV 
     $          + THREE*ABS( TEMP ) 
*    $          + ABS( TAU2 )*DW
*
*        Test for convergence
*
         IF( ABS( W ).LE.EPS*ERRETM ) THEN
            GO TO 240
         END IF
*
         IF( W.LE.ZERO ) THEN
            SGLB = MAX( SGLB, TAU )
         ELSE
            SGUB = MIN( SGUB, TAU )
         END IF
*
*        Calculate the new step
*
         NITER = NITER + 1

            ZZ( 2 ) = Z( II )*Z( II )
            DD( 1 ) = DTIIM
            DD( 2 ) = DELTA( II )*WORK( II )
            DD( 3 ) = DTIIP
            CALL DLAED6( NITER, ORGATI, C, DD, ZZ, W, ETA, INFO )
*
            IF( INFO.NE.0 ) THEN
*
*              If INFO is not 0, i.e., DLAED6 failed, switch back 
*              to 2 pole interpolation.
*
               SWTCH3 = .FALSE.
               INFO = 0
               DTIPSQ = WORK( IP1 )*DELTA( IP1 )
               DTISQ = WORK( I )*DELTA( I )
               IF( ORGATI ) THEN
                  C = W - DTIPSQ*DW + DELSQ*( Z( I ) / DTISQ )**2
               ELSE
                  C = W - DTISQ*DW - DELSQ*( Z( IP1 ) / DTIPSQ )**2
               END IF
               A = ( DTIPSQ+DTISQ )*W - DTIPSQ*DTISQ*DW
               B = DTIPSQ*DTISQ*W
               IF( C.EQ.ZERO ) THEN
                  IF( A.EQ.ZERO ) THEN
                     IF( ORGATI ) THEN
                        A = Z( I )*Z( I ) + DTIPSQ*DTIPSQ*( DPSI+DPHI )
                     ELSE
                        A = Z( IP1 )*Z( IP1 ) + DTISQ*DTISQ*( DPSI+DPHI)
                     END IF
                  END IF
                  ETA = B / A
               ELSE IF( A.LE.ZERO ) THEN
                  ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C )
               ELSE
                  ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) )
               END IF
            END IF
         END IF
*
*        Note, eta should be positive if w is negative, and
*        eta should be negative otherwise. However,
*        if for some reason caused by roundoff, eta*w > 0,
*        we simply use one Newton step instead. This way
*        will guarantee eta*w < 0.
*
         IF( W*ETA.GE.ZERO )
     $      ETA = -W / DW
 
 
 
*
         ETA = ETA / ( SIGMA+SQRT( SIGMA*SIGMA+ETA ) )
         TEMP = TAU + ETA
 
         IF( TEMP.GT.SGUB .OR. TEMP.LT.SGLB ) THEN
            IF( W.LT.ZERO ) THEN
               ETA = ( SGUB-TAU ) / TWO
            ELSE
               ETA = ( SGLB-TAU ) / TWO
            END IF
            IF( GEOMAVG ) THEN
               IF( W .LT. ZERO ) THEN
                  IF( TAU .GT. ZERO ) THEN
                     ETA = SQRT(SGUB*TAU)-TAU
                  END IF
               ELSE
                  IF( SGLB .GT. ZERO ) THEN
                     ETA = SQRT(SGLB*TAU)-TAU
                  END IF
               END IF
            END IF
         END IF
*
 
 
 
         PREW = W
*
         TAU = TAU + ETA
         SIGMA = SIGMA + ETA
*
         DO 170 J = 1, N
            WORK( J ) = WORK( J ) + ETA
            DELTA( J ) = DELTA( J ) - ETA
  170    CONTINUE
*

            PHI = PHI + Z( J )*TEMP
            DPHI = DPHI + TEMP*TEMP
            ERRETM = ERRETM + PHI
  190    CONTINUE
*
         TAU2 = WORK( II )*DELTA( II )
         TEMP = Z( II ) / TAU2
         DW = DPSI + DPHI + TEMP*TEMP
         TEMP = Z( II )*TEMP
         W = RHOINV + PHI + PSI + TEMP
         ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV 
     $          + THREE*ABS( TEMP ) 
 
 
 
 
*    $          + ABS( TAU2 )*DW
 
*
         SWTCH = .FALSE.
         IF( ORGATI ) THEN
            IF( -W.GT.ABS( PREW ) / TEN )
     $         SWTCH = .TRUE.

         DO 230 NITER = ITER, MAXIT
*
*           Test for convergence
*
            IF( ABS( W ).LE.EPS*ERRETM ) THEN
*     $          .OR. (SGUB-SGLB).LE.EIGHT*ABS(SGUB+SGLB) ) THEN
               GO TO 240
            END IF
*
            IF( W.LE.ZERO ) THEN
               SGLB = MAX( SGLB, TAU )
            ELSE
               SGUB = MIN( SGUB, TAU )
            END IF
*
*           Calculate the new step
*
            IF( .NOT.SWTCH3 ) THEN
               DTIPSQ = WORK( IP1 )*DELTA( IP1 )
               DTISQ = WORK( I )*DELTA( I )

               END IF
               DD( 1 ) = DTIIM
               DD( 2 ) = DELTA( II )*WORK( II )
               DD( 3 ) = DTIIP
               CALL DLAED6( NITER, ORGATI, C, DD, ZZ, W, ETA, INFO )
*
               IF( INFO.NE.0 ) THEN
*
*                 If INFO is not 0, i.e., DLAED6 failed, switch 
*                 back to two pole interpolation
*
                  SWTCH3 = .FALSE.
                  INFO = 0
                  DTIPSQ = WORK( IP1 )*DELTA( IP1 )
                  DTISQ = WORK( I )*DELTA( I )
                  IF( .NOT.SWTCH ) THEN
                     IF( ORGATI ) THEN
                        C = W - DTIPSQ*DW + DELSQ*( Z( I )/DTISQ )**2
                     ELSE
                        C = W - DTISQ*DW - DELSQ*( Z( IP1 )/DTIPSQ )**2
                     END IF
                  ELSE
                     TEMP = Z( II ) / ( WORK( II )*DELTA( II ) )
                     IF( ORGATI ) THEN
                        DPSI = DPSI + TEMP*TEMP
                     ELSE
                        DPHI = DPHI + TEMP*TEMP
                     END IF
                     C = W - DTISQ*DPSI - DTIPSQ*DPHI
                  END IF
                  A = ( DTIPSQ+DTISQ )*W - DTIPSQ*DTISQ*DW
                  B = DTIPSQ*DTISQ*W
                  IF( C.EQ.ZERO ) THEN
                     IF( A.EQ.ZERO ) THEN
                        IF( .NOT.SWTCH ) THEN
                           IF( ORGATI ) THEN
                              A = Z( I )*Z( I ) + DTIPSQ*DTIPSQ*
     $                            ( DPSI+DPHI )
                           ELSE
                              A = Z( IP1 )*Z( IP1 ) +
     $                            DTISQ*DTISQ*( DPSI+DPHI )
                           END IF
                        ELSE
                           A = DTISQ*DTISQ*DPSI + DTIPSQ*DTIPSQ*DPHI
                        END IF
                     END IF
                     ETA = B / A
                  ELSE IF( A.LE.ZERO ) THEN
                     ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C )
                  ELSE
                     ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) )
                  END IF
               END IF
            END IF
*
*           Note, eta should be positive if w is negative, and
*           eta should be negative otherwise. However,
*           if for some reason caused by roundoff, eta*w > 0,
*           we simply use one Newton step instead. This way
*           will guarantee eta*w < 0.
*
            IF( W*ETA.GE.ZERO )
     $         ETA = -W / DW
 
 
 
*
            ETA = ETA / ( SIGMA+SQRT( SIGMA*SIGMA+ETA ) )
            TEMP=TAU+ETA
 
            IF( TEMP.GT.SGUB .OR. TEMP.LT.SGLB ) THEN
               IF( W.LT.ZERO ) THEN
                  ETA = ( SGUB-TAU ) / TWO
               ELSE
                  ETA = ( SGLB-TAU ) / TWO
               END IF
               IF( GEOMAVG ) THEN
                  IF( W .LT. ZERO ) THEN
                     IF( TAU .GT. ZERO ) THEN
                        ETA = SQRT(SGUB*TAU)-TAU
                     END IF
                  ELSE
                     IF( SGLB .GT. ZERO ) THEN
                        ETA = SQRT(SGLB*TAU)-TAU
                     END IF
                  END IF
               END IF
            END IF
*
            PREW = W
 
*
            TAU = TAU + ETA
            SIGMA = SIGMA + ETA
*
            DO 200 J = 1, N
               WORK( J ) = WORK( J ) + ETA
               DELTA( J ) = DELTA( J ) - ETA
  200       CONTINUE
*
 
 
*           Evaluate PSI and the derivative DPSI
*
            DPSI = ZERO
            PSI = ZERO
            ERRETM = ZERO

               PHI = PHI + Z( J )*TEMP
               DPHI = DPHI + TEMP*TEMP
               ERRETM = ERRETM + PHI
  220       CONTINUE
*
            TAU2 = WORK( II )*DELTA( II )
            TEMP = Z( II ) / TAU2
            DW = DPSI + DPHI + TEMP*TEMP
            TEMP = Z( II )*TEMP
            W = RHOINV + PHI + PSI + TEMP
            ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV 
     $             + THREE*ABS( TEMP ) 
*    $             + ABS( TAU2 )*DW
*
            IF( W*PREW.GT.ZERO .AND. ABS( W ).GT.ABS( PREW ) / TEN )
     $         SWTCH = .NOT.SWTCH
*
 
 
 
 
 
 
  230    CONTINUE
*
*        Return with INFO = 1, NITER = MAXIT and not converged
*
         INFO = 1

      RETURN
*
*     End of DLASD4
*
      END
*> \brief \b DLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

*>     at Berkeley, USA
*>
*  =====================================================================
      SUBROUTINE DLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            I
      DOUBLE PRECISION   DSIGMA, RHO
*     ..

      RETURN
*
*     End of DLASD5
*
      END
*> \brief \b DLASD6 computes the SVD of an updated upper bidiagonal matrix obtained by merging two smaller ones by appending a row. Used by sbdsdc.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

      SUBROUTINE DLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA,
     $                   IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM,
     $                   LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK,
     $                   IWORK, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL,
     $                   NR, SQRE
      DOUBLE PRECISION   ALPHA, BETA, C, S

      RETURN
*
*     End of DLASD6
*
      END
*> \brief \b DLASD7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by sbdsdc.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

      SUBROUTINE DLASD7( ICOMPQ, NL, NR, SQRE, K, D, Z, ZW, VF, VFW, VL,
     $                   VLW, ALPHA, BETA, DSIGMA, IDX, IDXP, IDXQ,
     $                   PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM,
     $                   C, S, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL,
     $                   NR, SQRE
      DOUBLE PRECISION   ALPHA, BETA, C, S

      RETURN
*
*     End of DLASD7
*
      END
*> \brief \b DLASD8 finds the square roots of the roots of the secular equation, and stores, for each element in D, the distance to its two nearest poles. Used by sbdsdc.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

*>
*  =====================================================================
      SUBROUTINE DLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR,
     $                   DSIGMA, WORK, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            ICOMPQ, INFO, K, LDDIFR
*     ..
*     .. Array Arguments ..

*
*     End of DLASD8
*
      END
 
*> \brief \b DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

*  =====================================================================
      SUBROUTINE DLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K,
     $                   DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL,
     $                   PERM, GIVNUM, C, S, WORK, IWORK, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DLASDA
*
      END
*> \brief \b DLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

*>
*  =====================================================================
      SUBROUTINE DLASDQ( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT,
     $                   U, LDU, C, LDC, WORK, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU, SQRE
*     ..

      RETURN
*
*     End of DLASDQ
*
      END
*> \brief \b DLASDT creates a tree of subproblems for bidiagonal divide and conquer. Used by sbdsdc.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Contributors:
*  ==================

*>     California at Berkeley, USA
*>
*  =====================================================================
      SUBROUTINE DLASDT( N, LVL, ND, INODE, NDIML, NDIMR, MSUB )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            LVL, MSUB, N, ND
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DLASDT
*
      END
*> \brief \b DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLASET( UPLO, M, N, ALPHA, BETA, A, LDA )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            LDA, M, N
      DOUBLE PRECISION   ALPHA, BETA

      RETURN
*
*     End of DLASET
*
      END
*> \brief \b DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DLASQ1( N, D, E, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, N
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DLASQ1
*
      END
 
*> \brief \b DLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DLASQ2( N, Z, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, N
*     ..
*     .. Array Arguments ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL,
     $                   ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1,
     $                   DN2, G, TAU )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      LOGICAL            IEEE
      INTEGER            I0, ITER, N0, NDIV, NFAIL, PP
      DOUBLE PRECISION   DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G,

      RETURN
*
*     End of DLASQ3
*
      END
*> \brief \b DLASQ4 computes an approximation to the smallest eigenvalue using values of d from the previous transform. Used by sbdsqr.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*> \par Further Details:
*  =====================

*>
*  =====================================================================
      SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN,
     $                   DN1, DN2, TAU, TTYPE, G )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            I0, N0, N0IN, PP, TTYPE
      DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU
*     ..

      RETURN
*
*     End of DLASQ4
*
      END
*> \brief \b DLASQ5 computes one dqds transform in ping-pong form. Used by sbdsqr and sstegr.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2,
     $                   DN, DNM1, DNM2, IEEE, EPS )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      LOGICAL            IEEE
      INTEGER            I0, N0, PP
      DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU,

      RETURN
*
*     End of DLASQ5
*
      END
*> \brief \b DLASQ6 computes one dqd transform in ping-pong form. Used by sbdsqr and sstegr.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN,
     $                   DNM1, DNM2 )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            I0, N0, PP
      DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DNM1, DNM2
*     ..

      RETURN
*
*     End of DLASQ6
*
      END
*> \brief \b DLASR applies a sequence of plane rotations to a general rectangular matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          DIRECT, PIVOT, SIDE
      INTEGER            LDA, M, N
*     ..

      RETURN
*
*     End of DLASR
*
      END
*> \brief \b DLASRT sorts numbers in increasing or decreasing order.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DLASRT( ID, N, D, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          ID
      INTEGER            INFO, N
*     ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INCX, N
      DOUBLE PRECISION   SCALE, SUMSQ
*     ..

      RETURN
*
*     End of DLASSQ
*
      END
*> \brief \b DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN
*     ..
*

      RETURN
*
*     End of DLASV2
*
      END
*> \brief \b DLASWP performs a series of row interchanges on a general rectangular matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DLASWP( N, A, LDA, K1, K2, IPIV, INCX )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INCX, K1, K2, LDA, N
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DLASWP
*
      END
*> \brief \b DLASY2 solves the Sylvester matrix equation where the matrices are of order 1 or 2.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleSYauxiliary
*
*  =====================================================================
      SUBROUTINE DLASY2( LTRANL, LTRANR, ISGN, N1, N2, TL, LDTL, TR,
     $                   LDTR, B, LDB, SCALE, X, LDX, XNORM, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      LOGICAL            LTRANL, LTRANR
      INTEGER            INFO, ISGN, LDB, LDTL, LDTR, LDX, N1, N2
      DOUBLE PRECISION   SCALE, XNORM

      RETURN
*
*     End of DLASY2
*
      END
*> \brief \b DLASYF computes a partial factorization of a real symmetric matrix, using the diagonal pivoting method.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleSYcomputational
*
*  =====================================================================
      SUBROUTINE DLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, KB, LDA, LDW, N, NB
*     ..

      RETURN
*
*     End of DLASYF
*
      END
*> \brief \b DLATBS solves a triangular banded system of equations.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Further Details:
*  =====================

*>
*  =====================================================================
      SUBROUTINE DLATBS( UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X,
     $                   SCALE, CNORM, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, NORMIN, TRANS, UPLO
      INTEGER            INFO, KD, LDAB, N
      DOUBLE PRECISION   SCALE

      RETURN
*
*     End of DLATBS
*
      END
*> \brief \b DLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Further Details:
*  =====================

*>
*  =====================================================================
      SUBROUTINE DLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV,
     $                   JPIV )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            IJOB, LDZ, N
      DOUBLE PRECISION   RDSCAL, RDSUM
*     ..

      RETURN
*
*     End of DLATDF
*
      END
*> \brief \b DLATPS solves a triangular system of equations with the matrix held in packed storage.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Further Details:
*  =====================

*>
*  =====================================================================
      SUBROUTINE DLATPS( UPLO, TRANS, DIAG, NORMIN, N, AP, X, SCALE,
     $                   CNORM, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, NORMIN, TRANS, UPLO
      INTEGER            INFO, N
      DOUBLE PRECISION   SCALE

      RETURN
*
*     End of DLATPS
*
      END
*> \brief \b DLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiagonal form by an orthogonal similarity transformation.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            LDA, LDW, N, NB
*     ..

      RETURN
*
*     End of DLATRD
*
      END
*> \brief \b DLATRS solves a triangular system of equations with the scale factor set to prevent overflow.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Further Details:
*  =====================

*>
*  =====================================================================
      SUBROUTINE DLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE,
     $                   CNORM, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, NORMIN, TRANS, UPLO
      INTEGER            INFO, LDA, N
      DOUBLE PRECISION   SCALE

      RETURN
*
*     End of DLATRS
*
      END
*> \brief \b DLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Contributors:
*  ==================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DLATRZ( M, N, L, A, LDA, TAU, WORK )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            L, LDA, M, N
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DLATZM
*
      END
*> \brief \b DLAUU2 computes the product UUH or LHL, where U and L are upper or lower triangular matrices (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLAUU2( UPLO, N, A, LDA, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, N
*     ..

      RETURN
*
*     End of DLAUU2
*
      END
*> \brief \b DLAUUM computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DLAUUM( UPLO, N, A, LDA, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, N
*     ..

*
*     End DORCSD
*
      END
 
*> \brief \b DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DORG2L( M, N, K, A, LDA, TAU, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, K, LDA, M, N
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DORG2L
*
      END
*> \brief \b DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DORG2R( M, N, K, A, LDA, TAU, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, K, LDA, M, N
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DORGQR
*
      END
*> \brief \b DORGR2 generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DORGR2( M, N, K, A, LDA, TAU, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, K, LDA, M, N
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DORGTR
*
      END
*> \brief \b DORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
     $                   WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE, TRANS
      INTEGER            INFO, K, LDA, LDC, M, N
*     ..

      RETURN
*
*     End of DORM2L
*
      END
*> \brief \b DORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
     $                   WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE, TRANS
      INTEGER            INFO, K, LDA, LDC, M, N
*     ..

      RETURN
*
*     End of DORMHR
*
      END
*> \brief \b DORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
     $                   WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE, TRANS
      INTEGER            INFO, K, LDA, LDC, M, N
*     ..

      RETURN
*
*     End of DORMQR
*
      END
*> \brief \b DORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DORMR2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
     $                   WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE, TRANS
      INTEGER            INFO, K, LDA, LDC, M, N
*     ..

      RETURN
*
*     End of DORMR2
*
      END
*> \brief \b DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Contributors:
*  ==================

*>
*  =====================================================================
      SUBROUTINE DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
     $                   WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE, TRANS
      INTEGER            INFO, K, L, LDA, LDC, M, N
*     ..

      RETURN
*
*     End of DPBSVX
*
      END
*> \brief \b DPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DPBTF2( UPLO, N, KD, AB, LDAB, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, KD, LDAB, N
*     ..

      RETURN
*
*     End of DPOSVX
*
      END
*> \brief \b DPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doublePOcomputational
*
*  =====================================================================
      SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, N
*     ..

      RETURN
*
*     End of DPPTRS
*
      END
*> \brief \b DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric or complex Hermitian positive semi-definite matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   TOL
      INTEGER            INFO, LDA, N, RANK
      CHARACTER          UPLO

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doublePTcomputational
*
*> \par Further Details:
*  =====================
*>
*> \verbatim

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DPTCON( N, D, E, ANORM, RCOND, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, N
      DOUBLE PRECISION   ANORM, RCOND
*     ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doublePTcomputational
*
*  =====================================================================
      SUBROUTINE DPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          COMPZ
      INTEGER            INFO, LDZ, N
*     ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doublePTcomputational
*
*  =====================================================================
      SUBROUTINE DPTRFS( N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR,
     $                   BERR, WORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDB, LDX, N, NRHS
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DPTRFS
*
      END
*> \brief <b> DPTSV computes the solution to system of linear equations A * X = B for PT matrices</b>
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doublePTsolve
*
*  =====================================================================
      SUBROUTINE DPTSV( N, NRHS, D, E, B, LDB, INFO )
*
*  -- LAPACK driver routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDB, N, NRHS
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DPTSV
*
      END
*> \brief <b> DPTSVX computes the solution to system of linear equations A * X = B for PT matrices</b>
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doublePTsolve
*
*  =====================================================================
      SUBROUTINE DPTSVX( FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
     $                   RCOND, FERR, BERR, WORK, INFO )
*
*  -- LAPACK driver routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          FACT
      INTEGER            INFO, LDB, LDX, N, NRHS
      DOUBLE PRECISION   RCOND

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doublePTcomputational
*
*  =====================================================================
      SUBROUTINE DPTTRF( N, D, E, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, N
*     ..
*     .. Array Arguments ..

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doublePTcomputational
*
*  =====================================================================
      SUBROUTINE DPTTRS( N, NRHS, D, E, B, LDB, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDB, N, NRHS
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DPTTRS
*
      END
*> \brief \b DPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doublePTcomputational
*
*  =====================================================================
      SUBROUTINE DPTTS2( N, NRHS, D, E, B, LDB )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            LDB, N, NRHS
*     ..
*     .. Array Arguments ..

      RETURN
*
*     End of DPTTS2
*
      END
*> \brief \b DRSCL multiplies a vector by the reciprocal of a real scalar.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE DRSCL( N, SA, SX, INCX )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            INCX, N
      DOUBLE PRECISION   SA
*     ..

*> \endverbatim
*>
*> \param[in] LIWORK
*> \verbatim
*>          LIWORK is INTEGER
*>          The dimension of the array IWORK.
*>          If JOBZ  = 'N' or N <= 1, LIWORK must be at least 1.
*>          If JOBZ  = 'V' and N > 2, LIWORK must be at least 3 + 5*N.
*>
*>          If LIWORK = -1, then a workspace query is assumed; the
*>          routine only calculates the optimal sizes of the WORK and

      RETURN
*
*     End of DSBTRD
*
      END
*> \brief \b DSFRK performs a symmetric rank-k operation for matrix in RFP format.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DSFRK( TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA,
     $                  C )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   ALPHA, BETA
      INTEGER            K, LDA, N
      CHARACTER          TRANS, TRANSR, UPLO

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Contributors:
*  ==================

*  =====================================================================
      SUBROUTINE DSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
     $                   M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK,
     $                   IWORK, LIWORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          JOBZ, RANGE
      LOGICAL            TRYRAC
      INTEGER            IL, INFO, IU, LDZ, NZC, LIWORK, LWORK, M, N

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleSYeigen
*
*> \par Contributors:
*  ==================

*>
*  =====================================================================
      SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK,
     $                   LIWORK, INFO )
*
*  -- LAPACK driver routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          JOBZ, UPLO
      INTEGER            INFO, LDA, LIWORK, LWORK, N
*     ..

      INDWK2 = INDWRK + N*N
      LLWRK2 = LWORK - INDWK2 + 1
*
      CALL DSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ),
     $             WORK( INDWRK ), LLWORK, IINFO )
 
*
*     For eigenvalues only, call DSTERF.  For eigenvectors, first call
*     DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
*     tridiagonal matrix, then call DORMTR to multiply it by the
*     Householder transformations stored in A.

         CALL DSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N,
     $                WORK( INDWK2 ), LLWRK2, IWORK, LIWORK, INFO )
         CALL DORMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ),
     $                WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO )
         CALL DLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA )
 
      END IF
*
*     If matrix was scaled, then rescale eigenvalues appropriately.
*
      IF( ISCALE.EQ.1 )

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleSYeigen
*
*> \par Contributors:
*  ==================

*  =====================================================================
      SUBROUTINE DSYEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
     $                   ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK,
     $                   IWORK, LIWORK, INFO )
*
*  -- LAPACK driver routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          JOBZ, RANGE, UPLO
      INTEGER            IL, INFO, IU, LDA, LDZ, LIWORK, LWORK, M, N
      DOUBLE PRECISION   ABSTOL, VL, VU

*     that corresponding to eigenvectors that fail to converge in
*     DSTEIN.  This information is discarded; if any fail, the driver
*     returns INFO > 0.
      INDIFL = INDISP + N
*     INDIWO is the offset of the remaining integer workspace.
      INDIWO = INDIFL + N
 
*
*     Call DSYTRD to reduce symmetric matrix to tridiagonal form.
*
      CALL DSYTRD( UPLO, N, A, LDA, WORK( INDD ), WORK( INDE ),

      RETURN
*
*     End of DSYEVX
*
      END
*> \brief \b DSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleSYcomputational
*
*  =====================================================================
      SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, ITYPE, LDA, LDB, N
*     ..

      RETURN
*
*     End of DSYSVX
*
      END
*> \brief \b DSYSWAPR applies an elementary permutation on the rows and columns of a symmetric matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleSYauxiliary
*
*  =====================================================================
      SUBROUTINE DSYSWAPR( UPLO, N, A, LDA, I1, I2)
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER        UPLO
      INTEGER          I1, I2, LDA, N
*     ..

          END DO
*
      ENDIF
      END SUBROUTINE DSYSWAPR
 
*> \brief \b DSYTD2 reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal similarity transformation (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleSYcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DSYTD2( UPLO, N, A, LDA, D, E, TAU, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, N
*     ..

      RETURN
*
*     End of DSYTD2
*
      END
*> \brief \b DSYTF2 computes the factorization of a real symmetric indefinite matrix, using the diagonal pivoting method (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleSYcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*
*  =====================================================================
      SUBROUTINE DSYTF2( UPLO, N, A, LDA, IPIV, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, N
*     ..

*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DSYTRI2 computes the inverse of a DOUBLE PRECISION symmetric indefinite matrix
*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
*> DSYTRF. DSYTRI2 sets the LEADING DIMENSION of the workspace
*> before calling DSYTRI2X that actually computes the inverse.
*> \endverbatim
*

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleSYcomputational
*
*  =====================================================================
      SUBROUTINE DSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, LWORK, N
*     ..

      RETURN
*
*     End of DTBTRS
*
      END
*> \brief \b DTFSM solves a matrix equation (one operand is a triangular matrix in RFP format).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
*  =====================

*
*  =====================================================================
      SUBROUTINE DTFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A,
     $                  B, LDB )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          TRANSR, DIAG, SIDE, TRANS, UPLO
      INTEGER            LDB, M, N
      DOUBLE PRECISION   ALPHA

      RETURN
*
*     End of DTFTRI
*
      END
*> \brief \b DTFTTP copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          TRANSR, UPLO
      INTEGER            INFO, N
*     ..

      RETURN
*
*     End of DTFTTP
*
      END
*> \brief \b DTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*
*  =====================================================================
      SUBROUTINE DTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          TRANSR, UPLO
      INTEGER            INFO, N, LDA
*     ..

      RETURN
*
*     End of DTGEVC
*
      END
*> \brief \b DTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogonal equivalence transformation.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEauxiliary
*
*> \par Further Details:
*  =====================

*>
*  =====================================================================
      SUBROUTINE DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                   LDZ, J1, N1, N2, WORK, LWORK, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      LOGICAL            WANTQ, WANTZ
      INTEGER            INFO, J1, LDA, LDB, LDQ, LDZ, LWORK, N, N1, N2
*     ..

      RETURN
*
*     End of DTGSNA
*
      END
*> \brief \b DTGSY2 solves the generalized Sylvester equation (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleSYauxiliary
*
*> \par Contributors:
*  ==================

*  =====================================================================
      SUBROUTINE DTGSY2( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
     $                   LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL,
     $                   IWORK, PQ, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          TRANS
      INTEGER            IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF, M, N,
     $                   PQ

      RETURN
*     
*     End of DTPQRT
*
      END
 
*> \brief \b DTPQRT2 computes a QR factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DTPQRT2( M, N, L, A, LDA, B, LDB, T, LDT, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER   INFO, LDA, LDB, LDT, N, M, L
*     ..
*     .. Array Arguments ..

   
*
*     End of DTPQRT2
*
      END
*> \brief \b DTPRFB applies a real or complex "triangular-pentagonal" blocked reflector to a real or complex matrix, which is composed of two blocks.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERauxiliary
*
*> \par Further Details:
*  =====================

*>
*  =====================================================================
      SUBROUTINE DTPRFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, 
     $                   V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER DIRECT, SIDE, STOREV, TRANS
      INTEGER   K, L, LDA, LDB, LDT, LDV, LDWORK, M, N
*     ..

      RETURN
*
*     End of DTPTRS
*
      END
*> \brief \b DTPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DTPTTF( TRANSR, UPLO, N, AP, ARF, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          TRANSR, UPLO
      INTEGER            INFO, N
*     ..

      RETURN
*
*     End of DTPTTF
*
      END
*> \brief \b DTPTTR copies a triangular matrix from the standard packed format (TP) to the standard full format (TR).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DTPTTR( UPLO, N, AP, A, LDA, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, N, LDA
*     ..

      RETURN
*
*     End of DTRSYL
*
      END
*> \brief \b DTRTI2 computes the inverse of a triangular matrix (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, UPLO
      INTEGER            INFO, LDA, N
*     ..

      RETURN
*
*     End of DTRTRS
*
      END
*> \brief \b DTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
*  =====================

*> \endverbatim
*
*  =====================================================================
      SUBROUTINE DTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          TRANSR, UPLO
      INTEGER            INFO, N, LDA
*     ..

      RETURN
*
*     End of DTRTTF
*
      END
*> \brief \b DTRTTP copies a triangular matrix from the standard full format (TR) to the standard packed format (TP).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DTRTTP( UPLO, N, A, LDA, AP, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, N, LDA
*     ..

         RETURN
      END IF
*
      RETURN
      END
*> \brief \b ILADLC scans a matrix for its last non-zero column.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      INTEGER FUNCTION ILADLC( M, N, A, LDA )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            M, N, LDA
*     ..
*     .. Array Arguments ..

            END DO
         END DO
      END IF
      RETURN
      END
*> \brief \b ILADLR scans a matrix for its last non-zero row.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 

*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      INTEGER FUNCTION ILADLR( M, N, A, LDA )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            M, N, LDA
*     ..
*     .. Array Arguments ..

Rev 60211	Rev 62769
Line 5540...	Line 5540...
5540	`RETURN`	5540	`RETURN`
5541	`*`	5541	`*`
5542	`* End of DGBSVX`	5542	`* End of DGBSVX`
5543	`*`	5543	`*`
5544	`END`	5544	`END`
5545	`*> \brief \b DGBTF2`	5545	`*> \brief \b DGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.`
5546	`*`	5546	`*`
5547	`* =========== DOCUMENTATION ===========`	5547	`* =========== DOCUMENTATION ===========`
5548	`*`	5548	`*`
5549	`* Online html documentation available at`	5549	`* Online html documentation available at`
5550	`* http://www.netlib.org/lapack/explore-html/`	5550	`* http://www.netlib.org/lapack/explore-html/`
Line 5657...	Line 5657...
5657	`*> \author Univ. of Tennessee`	5657	`*> \author Univ. of Tennessee`
5658	`*> \author Univ. of California Berkeley`	5658	`*> \author Univ. of California Berkeley`
5659	`*> \author Univ. of Colorado Denver`	5659	`*> \author Univ. of Colorado Denver`
5660	`*> \author NAG Ltd.`	5660	`*> \author NAG Ltd.`
5661	`*`	5661	`*`
5662	`*> \date November 2011`	5662	`*> \date September 2012`
5663	`*`	5663	`*`
5664	`*> \ingroup doubleGBcomputational`	5664	`*> \ingroup doubleGBcomputational`
5665	`*`	5665	`*`
5666	`*> \par Further Details:`	5666	`*> \par Further Details:`
5667	`* =====================`	5667	`* =====================`
Line 5687...	Line 5687...
5687	`*> \endverbatim`	5687	`*> \endverbatim`
5688	`*>`	5688	`*>`
5689	`* =====================================================================`	5689	`* =====================================================================`
5690	`SUBROUTINE DGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO )`	5690	`SUBROUTINE DGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO )`
5691	`*`	5691	`*`
5692	`* -- LAPACK computational routine (version 3.4.0) --`	5692	`* -- LAPACK computational routine (version 3.4.2) --`
5693	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	5693	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
5694	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	5694	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
5695	`* November 2011`	5695	`* September 2012`
5696	`*`	5696	`*`
5697	`* .. Scalar Arguments ..`	5697	`* .. Scalar Arguments ..`
5698	`INTEGER INFO, KL, KU, LDAB, M, N`	5698	`INTEGER INFO, KL, KU, LDAB, M, N`
5699	`* ..`	5699	`* ..`
5700	`* .. Array Arguments ..`	5700	`* .. Array Arguments ..`
Line 7275...	Line 7275...
7275	`RETURN`	7275	`RETURN`
7276	`*`	7276	`*`
7277	`* End of DGEBAL`	7277	`* End of DGEBAL`
7278	`*`	7278	`*`
7279	`END`	7279	`END`
7280	`*> \brief \b DGEBD2`	7280	`*> \brief \b DGEBD2 reduces a general matrix to bidiagonal form using an unblocked algorithm.`
7281	`*`	7281	`*`
7282	`* =========== DOCUMENTATION ===========`	7282	`* =========== DOCUMENTATION ===========`
7283	`*`	7283	`*`
7284	`* Online html documentation available at`	7284	`* Online html documentation available at`
7285	`* http://www.netlib.org/lapack/explore-html/`	7285	`* http://www.netlib.org/lapack/explore-html/`
Line 7409...	Line 7409...
7409	`*> \author Univ. of Tennessee`	7409	`*> \author Univ. of Tennessee`
7410	`*> \author Univ. of California Berkeley`	7410	`*> \author Univ. of California Berkeley`
7411	`*> \author Univ. of Colorado Denver`	7411	`*> \author Univ. of Colorado Denver`
7412	`*> \author NAG Ltd.`	7412	`*> \author NAG Ltd.`
7413	`*`	7413	`*`
7414	`*> \date November 2011`	7414	`*> \date September 2012`
7415	`*`	7415	`*`
7416	`*> \ingroup doubleGEcomputational`	7416	`*> \ingroup doubleGEcomputational`
7417	`*`	7417	`*`
7418	`*> \par Further Details:`	7418	`*> \par Further Details:`
7419	`* =====================`	7419	`* =====================`
Line 7466...	Line 7466...
7466	`*> \endverbatim`	7466	`*> \endverbatim`
7467	`*>`	7467	`*>`
7468	`* =====================================================================`	7468	`* =====================================================================`
7469	`SUBROUTINE DGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO )`	7469	`SUBROUTINE DGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO )`
7470	`*`	7470	`*`
7471	`* -- LAPACK computational routine (version 3.4.0) --`	7471	`* -- LAPACK computational routine (version 3.4.2) --`
7472	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	7472	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
7473	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	7473	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
7474	`* November 2011`	7474	`* September 2012`
7475	`*`	7475	`*`
7476	`* .. Scalar Arguments ..`	7476	`* .. Scalar Arguments ..`
7477	`INTEGER INFO, LDA, M, N`	7477	`INTEGER INFO, LDA, M, N`
7478	`* ..`	7478	`* ..`
7479	`* .. Array Arguments ..`	7479	`* .. Array Arguments ..`
Line 10063...	Line 10063...
10063	`*>`	10063	`*>`
10064	`*> The right eigenvector v(j) of A satisfies`	10064	`*> The right eigenvector v(j) of A satisfies`
10065	`> A v(j) = lambda(j) * v(j)`	10065	`> A v(j) = lambda(j) * v(j)`
10066	`*> where lambda(j) is its eigenvalue.`	10066	`*> where lambda(j) is its eigenvalue.`
10067	`*> The left eigenvector u(j) of A satisfies`	10067	`*> The left eigenvector u(j) of A satisfies`
10068	`> u(j)T A = lambda(j) * u(j)**T`	10068	`> u(j)H A = lambda(j) * u(j)**H`
10069	`> where u(j)*T denotes the transpose of u(j).`	10069	`> where u(j)*H denotes the conjugate-transpose of u(j).`
10070	`*>`	10070	`*>`
10071	`*> The computed eigenvectors are normalized to have Euclidean norm`	10071	`*> The computed eigenvectors are normalized to have Euclidean norm`
10072	`*> equal to 1 and largest component real.`	10072	`*> equal to 1 and largest component real.`
10073	`*> \endverbatim`	10073	`*> \endverbatim`
10074	`*`	10074	`*`
Line 10201...	Line 10201...
10201	`*> \author Univ. of Tennessee`	10201	`*> \author Univ. of Tennessee`
10202	`*> \author Univ. of California Berkeley`	10202	`*> \author Univ. of California Berkeley`
10203	`*> \author Univ. of Colorado Denver`	10203	`*> \author Univ. of Colorado Denver`
10204	`*> \author NAG Ltd.`	10204	`*> \author NAG Ltd.`
10205	`*`	10205	`*`
10206	`*> \date November 2011`	10206	`*> \date September 2012`
10207	`*`	10207	`*`
10208	`*> \ingroup doubleGEeigen`	10208	`*> \ingroup doubleGEeigen`
10209	`*`	10209	`*`
10210	`* =====================================================================`	10210	`* =====================================================================`
10211	`SUBROUTINE DGEEV( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR,`	10211	`SUBROUTINE DGEEV( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR,`
10212	`$ LDVR, WORK, LWORK, INFO )`	10212	`$ LDVR, WORK, LWORK, INFO )`
10213	`*`	10213	`*`
10214	`* -- LAPACK driver routine (version 3.4.0) --`	10214	`* -- LAPACK driver routine (version 3.4.2) --`
10215	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	10215	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
10216	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	10216	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
10217	`* November 2011`	10217	`* September 2012`
10218	`*`	10218	`*`
10219	`* .. Scalar Arguments ..`	10219	`* .. Scalar Arguments ..`
10220	`CHARACTER JOBVL, JOBVR`	10220	`CHARACTER JOBVL, JOBVR`
10221	`INTEGER INFO, LDA, LDVL, LDVR, LWORK, N`	10221	`INTEGER INFO, LDA, LDVL, LDVR, LWORK, N`
10222	`* ..`	10222	`* ..`
Line 10589...	Line 10589...
10589	`*>`	10589	`*>`
10590	`*> The right eigenvector v(j) of A satisfies`	10590	`*> The right eigenvector v(j) of A satisfies`
10591	`> A v(j) = lambda(j) * v(j)`	10591	`> A v(j) = lambda(j) * v(j)`
10592	`*> where lambda(j) is its eigenvalue.`	10592	`*> where lambda(j) is its eigenvalue.`
10593	`*> The left eigenvector u(j) of A satisfies`	10593	`*> The left eigenvector u(j) of A satisfies`
10594	`> u(j)T A = lambda(j) * u(j)**T`	10594	`> u(j)H A = lambda(j) * u(j)**H`
10595	`> where u(j)*T denotes the transpose of u(j).`	10595	`> where u(j)*H denotes the conjugate-transpose of u(j).`
10596	`*>`	10596	`*>`
10597	`*> The computed eigenvectors are normalized to have Euclidean norm`	10597	`*> The computed eigenvectors are normalized to have Euclidean norm`
10598	`*> equal to 1 and largest component real.`	10598	`*> equal to 1 and largest component real.`
10599	`*>`	10599	`*>`
10600	`*> Balancing a matrix means permuting the rows and columns to make it`	10600	`*> Balancing a matrix means permuting the rows and columns to make it`
Line 10830...	Line 10830...
10830	`*> \author Univ. of Tennessee`	10830	`*> \author Univ. of Tennessee`
10831	`*> \author Univ. of California Berkeley`	10831	`*> \author Univ. of California Berkeley`
10832	`*> \author Univ. of Colorado Denver`	10832	`*> \author Univ. of Colorado Denver`
10833	`*> \author NAG Ltd.`	10833	`*> \author NAG Ltd.`
10834	`*`	10834	`*`
10835	`*> \date November 2011`	10835	`*> \date September 2012`
10836	`*`	10836	`*`
10837	`*> \ingroup doubleGEeigen`	10837	`*> \ingroup doubleGEeigen`
10838	`*`	10838	`*`
10839	`* =====================================================================`	10839	`* =====================================================================`
10840	`SUBROUTINE DGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, WR, WI,`	10840	`SUBROUTINE DGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, WR, WI,`
10841	`$ VL, LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM,`	10841	`$ VL, LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM,`
10842	`$ RCONDE, RCONDV, WORK, LWORK, IWORK, INFO )`	10842	`$ RCONDE, RCONDV, WORK, LWORK, IWORK, INFO )`
10843	`*`	10843	`*`
10844	`* -- LAPACK driver routine (version 3.4.0) --`	10844	`* -- LAPACK driver routine (version 3.4.2) --`
10845	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	10845	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
10846	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	10846	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
10847	`* November 2011`	10847	`* September 2012`
10848	`*`	10848	`*`
10849	`* .. Scalar Arguments ..`	10849	`* .. Scalar Arguments ..`
10850	`CHARACTER BALANC, JOBVL, JOBVR, SENSE`	10850	`CHARACTER BALANC, JOBVL, JOBVR, SENSE`
10851	`INTEGER IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N`	10851	`INTEGER IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N`
10852	`DOUBLE PRECISION ABNRM`	10852	`DOUBLE PRECISION ABNRM`
Line 12525...	Line 12525...
12525	`RETURN`	12525	`RETURN`
12526	`*`	12526	`*`
12527	`* End of DGEGV`	12527	`* End of DGEGV`
12528	`*`	12528	`*`
12529	`END`	12529	`END`
12530	`*> \brief \b DGEHD2`	12530	`*> \brief \b DGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.`
12531	`*`	12531	`*`
12532	`* =========== DOCUMENTATION ===========`	12532	`* =========== DOCUMENTATION ===========`
12533	`*`	12533	`*`
12534	`* Online html documentation available at`	12534	`* Online html documentation available at`
12535	`* http://www.netlib.org/lapack/explore-html/`	12535	`* http://www.netlib.org/lapack/explore-html/`
Line 12633...	Line 12633...
12633	`*> \author Univ. of Tennessee`	12633	`*> \author Univ. of Tennessee`
12634	`*> \author Univ. of California Berkeley`	12634	`*> \author Univ. of California Berkeley`
12635	`*> \author Univ. of Colorado Denver`	12635	`*> \author Univ. of Colorado Denver`
12636	`*> \author NAG Ltd.`	12636	`*> \author NAG Ltd.`
12637	`*`	12637	`*`
12638	`*> \date November 2011`	12638	`*> \date September 2012`
12639	`*`	12639	`*`
12640	`*> \ingroup doubleGEcomputational`	12640	`*> \ingroup doubleGEcomputational`
12641	`*`	12641	`*`
12642	`*> \par Further Details:`	12642	`*> \par Further Details:`
12643	`* =====================`	12643	`* =====================`
Line 12676...	Line 12676...
12676	`*> \endverbatim`	12676	`*> \endverbatim`
12677	`*>`	12677	`*>`
12678	`* =====================================================================`	12678	`* =====================================================================`
12679	`SUBROUTINE DGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )`	12679	`SUBROUTINE DGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )`
12680	`*`	12680	`*`
12681	`* -- LAPACK computational routine (version 3.4.0) --`	12681	`* -- LAPACK computational routine (version 3.4.2) --`
12682	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	12682	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
12683	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	12683	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
12684	`* November 2011`	12684	`* September 2012`
12685	`*`	12685	`*`
12686	`* .. Scalar Arguments ..`	12686	`* .. Scalar Arguments ..`
12687	`INTEGER IHI, ILO, INFO, LDA, N`	12687	`INTEGER IHI, ILO, INFO, LDA, N`
12688	`* ..`	12688	`* ..`
12689	`* .. Array Arguments ..`	12689	`* .. Array Arguments ..`
Line 13493...	Line 13493...
13493	`*> \author Univ. of Tennessee`	13493	`*> \author Univ. of Tennessee`
13494	`*> \author Univ. of California Berkeley`	13494	`*> \author Univ. of California Berkeley`
13495	`*> \author Univ. of Colorado Denver`	13495	`*> \author Univ. of Colorado Denver`
13496	`*> \author NAG Ltd.`	13496	`*> \author NAG Ltd.`
13497	`*`	13497	`*`
13498	`*> \date November 2011`	13498	`*> \date September 2012`
13499	`*`	13499	`*`
13500	`*> \ingroup doubleGEcomputational`	13500	`*> \ingroup doubleGEsing`
13501	`*`	13501	`*`
13502	`*> \par Further Details:`	13502	`*> \par Further Details:`
13503	`* =====================`	13503	`* =====================`
13504	`*>`	13504	`*>`
13505	`*> \verbatim`	13505	`*> \verbatim`
Line 13578...	Line 13578...
13578	`* =====================================================================`	13578	`* =====================================================================`
13579	`SUBROUTINE DGEJSV( JOBA, JOBU, JOBV, JOBR, JOBT, JOBP,`	13579	`SUBROUTINE DGEJSV( JOBA, JOBU, JOBV, JOBR, JOBT, JOBP,`
13580	`$ M, N, A, LDA, SVA, U, LDU, V, LDV,`	13580	`$ M, N, A, LDA, SVA, U, LDU, V, LDV,`
13581	`$ WORK, LWORK, IWORK, INFO )`	13581	`$ WORK, LWORK, IWORK, INFO )`
13582	`*`	13582	`*`
13583	`* -- LAPACK computational routine (version 3.4.0) --`	13583	`* -- LAPACK computational routine (version 3.4.2) --`
13584	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	13584	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
13585	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	13585	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
13586	`* November 2011`	13586	`* September 2012`
13587	`*`	13587	`*`
13588	`* .. Scalar Arguments ..`	13588	`* .. Scalar Arguments ..`
13589	`IMPLICIT NONE`	13589	`IMPLICIT NONE`
13590	`INTEGER INFO, LDA, LDU, LDV, LWORK, M, N`	13590	`INTEGER INFO, LDA, LDU, LDV, LWORK, M, N`
13591	`* ..`	13591	`* ..`
Line 14879...	Line 14879...
14879	`* ..`	14879	`* ..`
14880	`* .. END OF DGEJSV`	14880	`* .. END OF DGEJSV`
14881	`* ..`	14881	`* ..`
14882	`END`	14882	`END`
14883	`*`	14883	`*`
14884	`*> \brief \b DGELQ2`	14884	`*> \brief \b DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.`
14885	`*`	14885	`*`
14886	`* =========== DOCUMENTATION ===========`	14886	`* =========== DOCUMENTATION ===========`
14887	`*`	14887	`*`
14888	`* Online html documentation available at`	14888	`* Online html documentation available at`
14889	`* http://www.netlib.org/lapack/explore-html/`	14889	`* http://www.netlib.org/lapack/explore-html/`
Line 14977...	Line 14977...
14977	`*> \author Univ. of Tennessee`	14977	`*> \author Univ. of Tennessee`
14978	`*> \author Univ. of California Berkeley`	14978	`*> \author Univ. of California Berkeley`
14979	`*> \author Univ. of Colorado Denver`	14979	`*> \author Univ. of Colorado Denver`
14980	`*> \author NAG Ltd.`	14980	`*> \author NAG Ltd.`
14981	`*`	14981	`*`
14982	`*> \date November 2011`	14982	`*> \date September 2012`
14983	`*`	14983	`*`
14984	`*> \ingroup doubleGEcomputational`	14984	`*> \ingroup doubleGEcomputational`
14985	`*`	14985	`*`
14986	`*> \par Further Details:`	14986	`*> \par Further Details:`
14987	`* =====================`	14987	`* =====================`
Line 15002...	Line 15002...
15002	`*> \endverbatim`	15002	`*> \endverbatim`
15003	`*>`	15003	`*>`
15004	`* =====================================================================`	15004	`* =====================================================================`
15005	`SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO )`	15005	`SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO )`
15006	`*`	15006	`*`
15007	`* -- LAPACK computational routine (version 3.4.0) --`	15007	`* -- LAPACK computational routine (version 3.4.2) --`
15008	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	15008	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
15009	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	15009	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
15010	`* November 2011`	15010	`* September 2012`
15011	`*`	15011	`*`
15012	`* .. Scalar Arguments ..`	15012	`* .. Scalar Arguments ..`
15013	`INTEGER INFO, LDA, M, N`	15013	`INTEGER INFO, LDA, M, N`
15014	`* ..`	15014	`* ..`
15015	`* .. Array Arguments ..`	15015	`* .. Array Arguments ..`
Line 18425...	Line 18425...
18425	`RETURN`	18425	`RETURN`
18426	`*`	18426	`*`
18427	`* End of DGEMQRT`	18427	`* End of DGEMQRT`
18428	`*`	18428	`*`
18429	`END`	18429	`END`
18430	`*> \brief \b DGEQL2`	18430	`*> \brief \b DGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.`
18431	`*`	18431	`*`
18432	`* =========== DOCUMENTATION ===========`	18432	`* =========== DOCUMENTATION ===========`
18433	`*`	18433	`*`
18434	`* Online html documentation available at`	18434	`* Online html documentation available at`
18435	`* http://www.netlib.org/lapack/explore-html/`	18435	`* http://www.netlib.org/lapack/explore-html/`
Line 18525...	Line 18525...
18525	`*> \author Univ. of Tennessee`	18525	`*> \author Univ. of Tennessee`
18526	`*> \author Univ. of California Berkeley`	18526	`*> \author Univ. of California Berkeley`
18527	`*> \author Univ. of Colorado Denver`	18527	`*> \author Univ. of Colorado Denver`
18528	`*> \author NAG Ltd.`	18528	`*> \author NAG Ltd.`
18529	`*`	18529	`*`
18530	`*> \date November 2011`	18530	`*> \date September 2012`
18531	`*`	18531	`*`
18532	`*> \ingroup doubleGEcomputational`	18532	`*> \ingroup doubleGEcomputational`
18533	`*`	18533	`*`
18534	`*> \par Further Details:`	18534	`*> \par Further Details:`
18535	`* =====================`	18535	`* =====================`
Line 18550...	Line 18550...
18550	`*> \endverbatim`	18550	`*> \endverbatim`
18551	`*>`	18551	`*>`
18552	`* =====================================================================`	18552	`* =====================================================================`
18553	`SUBROUTINE DGEQL2( M, N, A, LDA, TAU, WORK, INFO )`	18553	`SUBROUTINE DGEQL2( M, N, A, LDA, TAU, WORK, INFO )`
18554	`*`	18554	`*`
18555	`* -- LAPACK computational routine (version 3.4.0) --`	18555	`* -- LAPACK computational routine (version 3.4.2) --`
18556	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	18556	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
18557	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	18557	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
18558	`* November 2011`	18558	`* September 2012`
18559	`*`	18559	`*`
18560	`* .. Scalar Arguments ..`	18560	`* .. Scalar Arguments ..`
18561	`INTEGER INFO, LDA, M, N`	18561	`INTEGER INFO, LDA, M, N`
18562	`* ..`	18562	`* ..`
18563	`* .. Array Arguments ..`	18563	`* .. Array Arguments ..`
Line 19027...	Line 19027...
19027	`*> \author Univ. of Tennessee`	19027	`*> \author Univ. of Tennessee`
19028	`*> \author Univ. of California Berkeley`	19028	`*> \author Univ. of California Berkeley`
19029	`*> \author Univ. of Colorado Denver`	19029	`*> \author Univ. of Colorado Denver`
19030	`*> \author NAG Ltd.`	19030	`*> \author NAG Ltd.`
19031	`*`	19031	`*`
19032	`*> \date November 2011`	19032	`*> \date September 2012`
19033	`*`	19033	`*`
19034	`*> \ingroup doubleGEcomputational`	19034	`*> \ingroup doubleGEcomputational`
19035	`*`	19035	`*`
19036	`*> \par Further Details:`	19036	`*> \par Further Details:`
19037	`* =====================`	19037	`* =====================`
Line 19044...	Line 19044...
19044	`*>`	19044	`*>`
19045	`*> Each H(i) has the form`	19045	`*> Each H(i) has the form`
19046	`*>`	19046	`*>`
19047	`> H(i) = I - tau v * v**T`	19047	`> H(i) = I - tau v * v**T`
19048	`*>`	19048	`*>`
19049	`*> where tau is a real/complex scalar, and v is a real/complex vector`	19049	`*> where tau is a real scalar, and v is a real/complex vector`
19050	`*> with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in`	19050	`*> with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in`
19051	`*> A(i+1:m,i), and tau in TAU(i).`	19051	`*> A(i+1:m,i), and tau in TAU(i).`
19052	`*> \endverbatim`	19052	`*> \endverbatim`
19053	`*`	19053	`*`
19054	`*> \par Contributors:`	19054	`*> \par Contributors:`
Line 19058...	Line 19058...
19058	`*> X. Sun, Computer Science Dept., Duke University, USA`	19058	`*> X. Sun, Computer Science Dept., Duke University, USA`
19059	`*>`	19059	`*>`
19060	`* =====================================================================`	19060	`* =====================================================================`
19061	`SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )`	19061	`SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )`
19062	`*`	19062	`*`
19063	`* -- LAPACK computational routine (version 3.4.0) --`	19063	`* -- LAPACK computational routine (version 3.4.2) --`
19064	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	19064	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
19065	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	19065	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
19066	`* November 2011`	19066	`* September 2012`
19067	`*`	19067	`*`
19068	`* .. Scalar Arguments ..`	19068	`* .. Scalar Arguments ..`
19069	`INTEGER INFO, LDA, LWORK, M, N`	19069	`INTEGER INFO, LDA, LWORK, M, N`
19070	`* ..`	19070	`* ..`
19071	`* .. Array Arguments ..`	19071	`* .. Array Arguments ..`
Line 19578...	Line 19578...
19578	`RETURN`	19578	`RETURN`
19579	`*`	19579	`*`
19580	`* End of DGEQPF`	19580	`* End of DGEQPF`
19581	`*`	19581	`*`
19582	`END`	19582	`END`
19583	`*> \brief \b DGEQR2`	19583	`*> \brief \b DGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.`
19584	`*`	19584	`*`
19585	`* =========== DOCUMENTATION ===========`	19585	`* =========== DOCUMENTATION ===========`
19586	`*`	19586	`*`
19587	`* Online html documentation available at`	19587	`* Online html documentation available at`
19588	`* http://www.netlib.org/lapack/explore-html/`	19588	`* http://www.netlib.org/lapack/explore-html/`
Line 19676...	Line 19676...
19676	`*> \author Univ. of Tennessee`	19676	`*> \author Univ. of Tennessee`
19677	`*> \author Univ. of California Berkeley`	19677	`*> \author Univ. of California Berkeley`
19678	`*> \author Univ. of Colorado Denver`	19678	`*> \author Univ. of Colorado Denver`
19679	`*> \author NAG Ltd.`	19679	`*> \author NAG Ltd.`
19680	`*`	19680	`*`
19681	`*> \date November 2011`	19681	`*> \date September 2012`
19682	`*`	19682	`*`
19683	`*> \ingroup doubleGEcomputational`	19683	`*> \ingroup doubleGEcomputational`
19684	`*`	19684	`*`
19685	`*> \par Further Details:`	19685	`*> \par Further Details:`
19686	`* =====================`	19686	`* =====================`
Line 19701...	Line 19701...
19701	`*> \endverbatim`	19701	`*> \endverbatim`
19702	`*>`	19702	`*>`
19703	`* =====================================================================`	19703	`* =====================================================================`
19704	`SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO )`	19704	`SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO )`
19705	`*`	19705	`*`
19706	`* -- LAPACK computational routine (version 3.4.0) --`	19706	`* -- LAPACK computational routine (version 3.4.2) --`
19707	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	19707	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
19708	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	19708	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
19709	`* November 2011`	19709	`* September 2012`
19710	`*`	19710	`*`
19711	`* .. Scalar Arguments ..`	19711	`* .. Scalar Arguments ..`
19712	`INTEGER INFO, LDA, M, N`	19712	`INTEGER INFO, LDA, M, N`
19713	`* ..`	19713	`* ..`
19714	`* .. Array Arguments ..`	19714	`* .. Array Arguments ..`
Line 19770...	Line 19770...
19770	`RETURN`	19770	`RETURN`
19771	`*`	19771	`*`
19772	`* End of DGEQR2`	19772	`* End of DGEQR2`
19773	`*`	19773	`*`
19774	`END`	19774	`END`
19775	`*> \brief \b DGEQR2P`	19775	`*> \brief \b DGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.`
19776	`*`	19776	`*`
19777	`* =========== DOCUMENTATION ===========`	19777	`* =========== DOCUMENTATION ===========`
19778	`*`	19778	`*`
19779	`* Online html documentation available at`	19779	`* Online html documentation available at`
19780	`* http://www.netlib.org/lapack/explore-html/`	19780	`* http://www.netlib.org/lapack/explore-html/`
Line 19868...	Line 19868...
19868	`*> \author Univ. of Tennessee`	19868	`*> \author Univ. of Tennessee`
19869	`*> \author Univ. of California Berkeley`	19869	`*> \author Univ. of California Berkeley`
19870	`*> \author Univ. of Colorado Denver`	19870	`*> \author Univ. of Colorado Denver`
19871	`*> \author NAG Ltd.`	19871	`*> \author NAG Ltd.`
19872	`*`	19872	`*`
19873	`*> \date November 2011`	19873	`*> \date September 2012`
19874	`*`	19874	`*`
19875	`*> \ingroup doubleGEcomputational`	19875	`*> \ingroup doubleGEcomputational`
19876	`*`	19876	`*`
19877	`*> \par Further Details:`	19877	`*> \par Further Details:`
19878	`* =====================`	19878	`* =====================`
Line 19893...	Line 19893...
19893	`*> \endverbatim`	19893	`*> \endverbatim`
19894	`*>`	19894	`*>`
19895	`* =====================================================================`	19895	`* =====================================================================`
19896	`SUBROUTINE DGEQR2P( M, N, A, LDA, TAU, WORK, INFO )`	19896	`SUBROUTINE DGEQR2P( M, N, A, LDA, TAU, WORK, INFO )`
19897	`*`	19897	`*`
19898	`* -- LAPACK computational routine (version 3.4.0) --`	19898	`* -- LAPACK computational routine (version 3.4.2) --`
19899	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	19899	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
19900	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	19900	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
19901	`* November 2011`	19901	`* September 2012`
19902	`*`	19902	`*`
19903	`* .. Scalar Arguments ..`	19903	`* .. Scalar Arguments ..`
19904	`INTEGER INFO, LDA, M, N`	19904	`INTEGER INFO, LDA, M, N`
19905	`* ..`	19905	`* ..`
19906	`* .. Array Arguments ..`	19906	`* .. Array Arguments ..`
Line 20720...	Line 20720...
20720	`RETURN`	20720	`RETURN`
20721	`*`	20721	`*`
20722	`* End of DGEQRT`	20722	`* End of DGEQRT`
20723	`*`	20723	`*`
20724	`END`	20724	`END`
20725	`*> \brief \b DGEQRT2`	20725	`*> \brief \b DGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.`
20726	`*`	20726	`*`
20727	`* =========== DOCUMENTATION ===========`	20727	`* =========== DOCUMENTATION ===========`
20728	`*`	20728	`*`
20729	`* Online html documentation available at`	20729	`* Online html documentation available at`
20730	`* http://www.netlib.org/lapack/explore-html/`	20730	`* http://www.netlib.org/lapack/explore-html/`
Line 20819...	Line 20819...
20819	`*> \author Univ. of Tennessee`	20819	`*> \author Univ. of Tennessee`
20820	`*> \author Univ. of California Berkeley`	20820	`*> \author Univ. of California Berkeley`
20821	`*> \author Univ. of Colorado Denver`	20821	`*> \author Univ. of Colorado Denver`
20822	`*> \author NAG Ltd.`	20822	`*> \author NAG Ltd.`
20823	`*`	20823	`*`
20824	`*> \date November 2011`	20824	`*> \date September 2012`
20825	`*`	20825	`*`
20826	`*> \ingroup doubleGEcomputational`	20826	`*> \ingroup doubleGEcomputational`
20827	`*`	20827	`*`
20828	`*> \par Further Details:`	20828	`*> \par Further Details:`
20829	`* =====================`	20829	`* =====================`
Line 20849...	Line 20849...
20849	`*> \endverbatim`	20849	`*> \endverbatim`
20850	`*>`	20850	`*>`
20851	`* =====================================================================`	20851	`* =====================================================================`
20852	`SUBROUTINE DGEQRT2( M, N, A, LDA, T, LDT, INFO )`	20852	`SUBROUTINE DGEQRT2( M, N, A, LDA, T, LDT, INFO )`
20853	`*`	20853	`*`
20854	`* -- LAPACK computational routine (version 3.4.0) --`	20854	`* -- LAPACK computational routine (version 3.4.2) --`
20855	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	20855	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
20856	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	20856	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
20857	`* November 2011`	20857	`* September 2012`
20858	`*`	20858	`*`
20859	`* .. Scalar Arguments ..`	20859	`* .. Scalar Arguments ..`
20860	`INTEGER INFO, LDA, LDT, M, N`	20860	`INTEGER INFO, LDA, LDT, M, N`
20861	`* ..`	20861	`* ..`
20862	`* .. Array Arguments ..`	20862	`* .. Array Arguments ..`
Line 20947...	Line 20947...
20947		20947
20948	`*`	20948	`*`
20949	`* End of DGEQRT2`	20949	`* End of DGEQRT2`
20950	`*`	20950	`*`
20951	`END`	20951	`END`
20952	`*> \brief \b DGEQRT3`	20952	`*> \brief \b DGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.`
20953	`*`	20953	`*`
20954	`* =========== DOCUMENTATION ===========`	20954	`* =========== DOCUMENTATION ===========`
20955	`*`	20955	`*`
20956	`* Online html documentation available at`	20956	`* Online html documentation available at`
20957	`* http://www.netlib.org/lapack/explore-html/`	20957	`* http://www.netlib.org/lapack/explore-html/`
Line 21049...	Line 21049...
21049	`*> \author Univ. of Tennessee`	21049	`*> \author Univ. of Tennessee`
21050	`*> \author Univ. of California Berkeley`	21050	`*> \author Univ. of California Berkeley`
21051	`*> \author Univ. of Colorado Denver`	21051	`*> \author Univ. of Colorado Denver`
21052	`*> \author NAG Ltd.`	21052	`*> \author NAG Ltd.`
21053	`*`	21053	`*`
21054	`*> \date November 2011`	21054	`*> \date September 2012`
21055	`*`	21055	`*`
21056	`*> \ingroup doubleGEcomputational`	21056	`*> \ingroup doubleGEcomputational`
21057	`*`	21057	`*`
21058	`*> \par Further Details:`	21058	`*> \par Further Details:`
21059	`* =====================`	21059	`* =====================`
Line 21081...	Line 21081...
21081	`*> \endverbatim`	21081	`*> \endverbatim`
21082	`*>`	21082	`*>`
21083	`* =====================================================================`	21083	`* =====================================================================`
21084	`RECURSIVE SUBROUTINE DGEQRT3( M, N, A, LDA, T, LDT, INFO )`	21084	`RECURSIVE SUBROUTINE DGEQRT3( M, N, A, LDA, T, LDT, INFO )`
21085	`*`	21085	`*`
21086	`* -- LAPACK computational routine (version 3.4.0) --`	21086	`* -- LAPACK computational routine (version 3.4.2) --`
21087	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`	21087	`* -- LAPACK is a software package provided by Univ. of Tennessee, --`
21088	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`	21088	`* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--`
21089	`* November 2011`	21089	`* September 2012`
21090	`*`	21090	`*`
21091	`* .. Scalar Arguments ..`	21091	`* .. Scalar Arguments ..`
21092	`INTEGER INFO, LDA, M, N, LDT`	21092	`INTEGER INFO, LDA, M, N, LDT`
21093	`* ..`	21093	`* ..`
21094	`* .. Array Arguments ..`	21094	`* .. Array Arguments ..`
Line 21643...	Line 21643...
21643	`RETURN`	21643	`RETURN`
21644	`*`	21644	`*`
21645	`* End of DGERFS`	21645	`* End of DGERFS`
21646	`*`	21646	`*`
21647	`END`	21647	`END`
21648	`*> \brief \b DGERQ2`	21648	`*> \brief \b DGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.`
21649	`*`	21649	`*`

The R Project SVN R

(root)/trunk/src/modules/lapack/dlapack.f – Rev 60211 → 62769