clasr.f(3)

NAME
clasr.f -

SYNOPSIS

  Functions/Subroutines
subroutine clasr (SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA)
CLASR applies a sequence of plane rotations to a general rectangular matrix.

Function/Subroutine Documentation

  subroutine clasr (characterSIDE, characterPIVOT, characterDIRECT, integerM, integerN, real, dimension( * )C, real, dimension( * )S, complex, dimension( lda, * )A, integerLDA)

CLASR applies a sequence of plane rotations to a general rectangular matrix.

Purpose:

     CLASR applies a sequence of real plane rotations to a complex matrix
     A, from either the left or the right.
     When SIDE = 'L', the transformation takes the form
        A := P*A
     and when SIDE = 'R', the transformation takes the form
        A := A*P**T
     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',
     and P**T is the transpose of P.

     When DIRECT = 'F' (Forward sequence), then

        P = P(z-1) * ... * P(2) * P(1)

     and when DIRECT = 'B' (Backward sequence), then

        P = P(1) * P(2) * ... * P(z-1)

     where P(k) is a plane rotation matrix defined by the 2-by-2 rotation

        R(k) = (  c(k)  s(k) )
             = ( -s(k)  c(k) ).

     When PIVOT = 'V' (Variable pivot), the rotation is performed
     for the plane (k,k+1), i.e., P(k) has the form

        P(k) = (  1                                            )
               (       ...                                     )
               (              1                                )
               (                   c(k)  s(k)                  )
               (                  -s(k)  c(k)                  )
               (                                1              )
               (                                     ...       )
               (                                            1  )

     where R(k) appears as a rank-2 modification to the identity matrix in
     rows and columns k and k+1.

     When PIVOT = 'T' (Top pivot), the rotation is performed for the
     plane (1,k+1), so P(k) has the form

        P(k) = (  c(k)                    s(k)                 )
               (         1                                     )
               (              ...                              )
               (                     1                         )
               ( -s(k)                    c(k)                 )
               (                                 1             )
               (                                      ...      )
               (                                             1 )

     where R(k) appears in rows and columns 1 and k+1.

     Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
     performed for the plane (k,z), giving P(k) the form

        P(k) = ( 1                                             )
               (      ...                                      )
               (             1                                 )
               (                  c(k)                    s(k) )
               (                         1                     )
               (                              ...              )
               (                                     1         )
               (                 -s(k)                    c(k) )

     where R(k) appears in rows and columns k and z.  The rotations are
     performed without ever forming P(k) explicitly.

Parameters:
    SIDE

              SIDE is CHARACTER*1
              Specifies whether the plane rotation matrix P is applied to
              A on the left or the right.
              = 'L':  Left, compute A := P*A
              = 'R':  Right, compute A:= A*P**T

    PIVOT

              PIVOT is CHARACTER*1
              Specifies the plane for which P(k) is a plane rotation
              matrix.
              = 'V':  Variable pivot, the plane (k,k+1)
              = 'T':  Top pivot, the plane (1,k+1)
              = 'B':  Bottom pivot, the plane (k,z)

    DIRECT

              DIRECT is CHARACTER*1
              Specifies whether P is a forward or backward sequence of
              plane rotations.
              = 'F':  Forward, P = P(z-1)*...*P(2)*P(1)
              = 'B':  Backward, P = P(1)*P(2)*...*P(z-1)

    M

              M is INTEGER
              The number of rows of the matrix A.  If m <= 1, an immediate
              return is effected.

    N

              N is INTEGER
              The number of columns of the matrix A.  If n <= 1, an
              immediate return is effected.

    C

              C is REAL array, dimension
                      (M-1) if SIDE = 'L'
                      (N-1) if SIDE = 'R'
              The cosines c(k) of the plane rotations.

    S

              S is REAL array, dimension
                      (M-1) if SIDE = 'L'
                      (N-1) if SIDE = 'R'
              The sines s(k) of the plane rotations.  The 2-by-2 plane
              rotation part of the matrix P(k), R(k), has the form
              R(k) = (  c(k)  s(k) )
                     ( -s(k)  c(k) ).

    A

              A is COMPLEX array, dimension (LDA,N)
              The M-by-N matrix A.  On exit, A is overwritten by P*A if
              SIDE = 'R' or by A*P**T if SIDE = 'L'.

    LDA

              LDA is INTEGER
              The leading dimension of the array A.  LDA >= max(1,M).

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    September 2012

Definition at line 201 of file clasr.f.

Author

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