SRC/dlasr.f(3)

From the Library Functions Manual, this is SRC/dlasr.f — the DLASR page, now with main-character energy. 💅✨

💖 NAME 💖

SRC/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 🌸

subroutine dlasr (character side, character pivot, character direct, integer m, integer n, double precision, dimension( * ) c, double precision, dimension( * ) s, double precision, dimension( lda, * ) a, integer lda)

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

💫 Purpose 💫

Okay bestie, here’s the vibe: 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 — 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 — 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 — 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 — INTEGER. The number of rows of the matrix A. If m <= 1, an immediate return is effected.
• N — INTEGER. The number of columns of the matrix A. If n <= 1, an immediate return is effected.
• C — DOUBLE PRECISION array, dimension

(M-1) if SIDE = 'L'
(N-1) if SIDE = 'R'

The cosines c(k) of the plane rotations.

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

Definition at line 198 of file dlasr.f.

🌈 AUTHOR 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Later, bestie — this one is from LAPACK, Version 3.12.0, source SRC/dlasr.f(3). 💜✨🫶