dlasr.f man page

dlasr.f —

Synopsis

Functions/Subroutines

subroutine dlasr (SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA)
DLASR applies a sequence of plane rotations to a general rectangular matrix.

Function/Subroutine Documentation

subroutine dlasr (characterSIDE, characterPIVOT, characterDIRECT, integerM, integerN, double precision, dimension( * )C, double precision, dimension( * )S, double precision, dimension( lda, * )A, integerLDA)

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

Purpose:

DLASR applies a sequence of plane rotations to a real 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 DOUBLE PRECISION array, dimension
        (M-1) if SIDE = 'L'
        (N-1) if SIDE = 'R'
The cosines c(k) of the plane rotations.

S

S is DOUBLE PRECISION 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 DOUBLE PRECISION 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 200 of file dlasr.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

dlasr(3) is an alias of dlasr.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK