/home/abui...RC/dlasr.f(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 NAME

ok so this is the manual page for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlasr.f — yes that's the whole entire path, she's long, she's iconic, she's from the Library Functions Manual, bestie. dlasr.f(3), if you're nasty. ✨

🌸 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. that's the whole vibe, fr fr 🦋

🎀 Function/Subroutine Documentation

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. lowkey the entire personality of this routine tbh 💖

⭐ 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.
!>

okay so real talk — those matrices? she's showing you the shape of each rotation, and the last line is the flex: the rotations get performed without ever forming P(k) explicitly. no cap, that's the whole point. efficient queen behavior 👑✨

🧚 Parameters

  • SIDE — SIDE is CHARACTER*1. tells us whether the plane rotation matrix P gets applied to A on the left or on the right. the deets:
    • = 'L': Left, compute A := P*A
    • = 'R': Right, compute A:= A*P**T
  • PIVOT — PIVOT is CHARACTER*1. which plane is P(k) a plane rotation matrix for? choose ur fighter:
    • = '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. is P 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. ⚠️ and listen: if m <= 1, an immediate return is effected. she is NOT doing the work, she's leaving. periodt 💀
  • N — N is INTEGER. the number of columns of the matrix A. same energy: if n <= 1, an immediate return is effected. bye bestie 👋
  • C — C is DOUBLE PRECISION array, dimension:
(M-1) if SIDE = 'L'
(N-1) if SIDE = 'R'

these are the cosines c(k) of the plane rotations. the c's!! 🍓

  • S — S is DOUBLE PRECISION array, dimension:
(M-1) if SIDE = 'L'
(N-1) if SIDE = 'R'

these are the sines s(k) of the plane rotations. and just so u know exactly what she's cooking, 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. 💖 and heads up, on exit, A is overwritten by P*A if SIDE = 'L' or by A*P**T if SIDE = 'R'. so yeah she does NOT ask permission, she replaces ur data. slay but be aware 🙈
  • LDA — LDA is INTEGER. the leading dimension of the array A. constraint, and this one is not vibes-optional: 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

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