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version 1.15, 2016/08/27 15:34:32 version 1.16, 2017/06/17 10:53:57
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 *  *
 *  =========== DOCUMENTATION ===========  *  =========== DOCUMENTATION ===========
 *  *
 * Online html documentation available at   * Online html documentation available at
 *            http://www.netlib.org/lapack/explore-html/   *            http://www.netlib.org/lapack/explore-html/
 *  *
 *> \htmlonly  *> \htmlonly
 *> Download DLASR + dependencies   *> Download DLASR + dependencies
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasr.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasr.f">
 *> [TGZ]</a>   *> [TGZ]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasr.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasr.f">
 *> [ZIP]</a>   *> [ZIP]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasr.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasr.f">
 *> [TXT]</a>  *> [TXT]</a>
 *> \endhtmlonly   *> \endhtmlonly
 *  *
 *  Definition:  *  Definition:
 *  ===========  *  ===========
 *  *
 *       SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )  *       SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
 *   *
 *       .. Scalar Arguments ..  *       .. Scalar Arguments ..
 *       CHARACTER          DIRECT, PIVOT, SIDE  *       CHARACTER          DIRECT, PIVOT, SIDE
 *       INTEGER            LDA, M, N  *       INTEGER            LDA, M, N
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 *       .. Array Arguments ..  *       .. Array Arguments ..
 *       DOUBLE PRECISION   A( LDA, * ), C( * ), S( * )  *       DOUBLE PRECISION   A( LDA, * ), C( * ), S( * )
 *       ..  *       ..
 *    *
 *  *
 *> \par Purpose:  *> \par Purpose:
 *  =============  *  =============
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 *>  *>
 *> DLASR applies a sequence of plane rotations to a real matrix A,  *> DLASR applies a sequence of plane rotations to a real matrix A,
 *> from either the left or the right.  *> from either the left or the right.
 *>   *>
 *> When SIDE = 'L', the transformation takes the form  *> When SIDE = 'L', the transformation takes the form
 *>   *>
 *>    A := P*A  *>    A := P*A
 *>   *>
 *> and when SIDE = 'R', the transformation takes the form  *> and when SIDE = 'R', the transformation takes the form
 *>   *>
 *>    A := A*P**T  *>    A := A*P**T
 *>   *>
 *> where P is an orthogonal matrix consisting of a sequence of z plane  *> where P is an orthogonal matrix consisting of a sequence of z plane
 *> rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',  *> rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
 *> and P**T is the transpose of P.  *> and P**T is the transpose of P.
 *>   *>
 *> When DIRECT = 'F' (Forward sequence), then  *> When DIRECT = 'F' (Forward sequence), then
 *>   *>
 *>    P = P(z-1) * ... * P(2) * P(1)  *>    P = P(z-1) * ... * P(2) * P(1)
 *>   *>
 *> and when DIRECT = 'B' (Backward sequence), then  *> and when DIRECT = 'B' (Backward sequence), then
 *>   *>
 *>    P = P(1) * P(2) * ... * P(z-1)  *>    P = P(1) * P(2) * ... * P(z-1)
 *>   *>
 *> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation  *> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
 *>   *>
 *>    R(k) = (  c(k)  s(k) )  *>    R(k) = (  c(k)  s(k) )
 *>         = ( -s(k)  c(k) ).  *>         = ( -s(k)  c(k) ).
 *>   *>
 *> When PIVOT = 'V' (Variable pivot), the rotation is performed  *> When PIVOT = 'V' (Variable pivot), the rotation is performed
 *> for the plane (k,k+1), i.e., P(k) has the form  *> for the plane (k,k+1), i.e., P(k) has the form
 *>   *>
 *>    P(k) = (  1                                            )  *>    P(k) = (  1                                            )
 *>           (       ...                                     )  *>           (       ...                                     )
 *>           (              1                                )  *>           (              1                                )
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 *>           (                                1              )  *>           (                                1              )
 *>           (                                     ...       )  *>           (                                     ...       )
 *>           (                                            1  )  *>           (                                            1  )
 *>   *>
 *> where R(k) appears as a rank-2 modification to the identity matrix in  *> where R(k) appears as a rank-2 modification to the identity matrix in
 *> rows and columns k and k+1.  *> rows and columns k and k+1.
 *>   *>
 *> When PIVOT = 'T' (Top pivot), the rotation is performed for the  *> When PIVOT = 'T' (Top pivot), the rotation is performed for the
 *> plane (1,k+1), so P(k) has the form  *> plane (1,k+1), so P(k) has the form
 *>   *>
 *>    P(k) = (  c(k)                    s(k)                 )  *>    P(k) = (  c(k)                    s(k)                 )
 *>           (         1                                     )  *>           (         1                                     )
 *>           (              ...                              )  *>           (              ...                              )
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 *>           (                                 1             )  *>           (                                 1             )
 *>           (                                      ...      )  *>           (                                      ...      )
 *>           (                                             1 )  *>           (                                             1 )
 *>   *>
 *> where R(k) appears in rows and columns 1 and k+1.  *> where R(k) appears in rows and columns 1 and k+1.
 *>   *>
 *> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is  *> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
 *> performed for the plane (k,z), giving P(k) the form  *> performed for the plane (k,z), giving P(k) the form
 *>   *>
 *>    P(k) = ( 1                                             )  *>    P(k) = ( 1                                             )
 *>           (      ...                                      )  *>           (      ...                                      )
 *>           (             1                                 )  *>           (             1                                 )
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 *>           (                              ...              )  *>           (                              ...              )
 *>           (                                     1         )  *>           (                                     1         )
 *>           (                 -s(k)                    c(k) )  *>           (                 -s(k)                    c(k) )
 *>   *>
 *> where R(k) appears in rows and columns k and z.  The rotations are  *> where R(k) appears in rows and columns k and z.  The rotations are
 *> performed without ever forming P(k) explicitly.  *> performed without ever forming P(k) explicitly.
 *> \endverbatim  *> \endverbatim
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 *  Authors:  *  Authors:
 *  ========  *  ========
 *  *
 *> \author Univ. of Tennessee   *> \author Univ. of Tennessee
 *> \author Univ. of California Berkeley   *> \author Univ. of California Berkeley
 *> \author Univ. of Colorado Denver   *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.   *> \author NAG Ltd.
 *  *
 *> \date September 2012  *> \date December 2016
 *  *
 *> \ingroup auxOTHERauxiliary  *> \ingroup OTHERauxiliary
 *  *
 *  =====================================================================  *  =====================================================================
       SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )        SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
 *  *
 *  -- LAPACK auxiliary routine (version 3.4.2) --  *  -- LAPACK auxiliary routine (version 3.7.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     September 2012  *     December 2016
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          DIRECT, PIVOT, SIDE        CHARACTER          DIRECT, PIVOT, SIDE
Removed from v.1.15  
changed lines
  Added in v.1.16

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