SRC/zlasr.f(3)

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💖 SRC/zlasr.f(3) 💖

okay bestie, welcome to the Library Functions Manual page for SRC/zlasr.f — the one and only spot where ZLASR applies a sequence of plane rotations to a general rectangular matrix. it’s giving linear algebra main character energy, fr fr. 💅

✨ NAME ✨

SRC/zlasr.f — that’s the page name, bestie. The subroutine living here is zlasr, and it applies a sequence of plane rotations to a general rectangular matrix.

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine zlasr (side, pivot, direct, m, n, c, s, a, lda)
    ZLASR applies a sequence of plane rotations to a general rectangular
    matrix.

🌸 Function/Subroutine Documentation 🌸

Here’s the full signature, bestie — no cap, this is the exact shape:

subroutine zlasr (character side, character pivot, character direct, integer
    m, integer n, double precision, dimension( * ) c, double precision,
    dimension( * ) s, complex*16, dimension( lda, * ) a, integer lda)

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

🎯 Purpose 🎯

okay so ZLASR applies a sequence of real plane rotations to a complex matrix A, from either the left or the right. yes, real rotations on a complex matrix — she contains multitudes. 🦋

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. iconic behavior, honestly. ✨

🧚 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 COMPLEX*16 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.

Definition at line 199 of file zlasr.f.

💖 Author 💖

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