SRC/clasr.f(3)

🌸 NAME 🌸

okay so this page is SRC/clasr.f, from the Library Functions Manual — yes bestie, we’re deep in LAPACK land and this one is all about CLASR, which applies a sequence of plane rotations to a general rectangular matrix. Periodt. 💅

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✨ 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.

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🛠️ Function/Subroutine Documentation 🛠️

💖 subroutine clasr 💖

subroutine clasr (character side, character pivot, character direct, integer
m, integer n, real, dimension( * ) c, real, dimension( * ) s, complex,
dimension( lda, * ) a, integer lda)

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

🌟 Purpose 🌟

okay so here’s the tea: 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. It 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. It 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. It 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 a REAL array, dimension

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

The cosines c(k) of the plane rotations.

S — S is a 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 a 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.

Definition at line 199 of file clasr.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay bye bestie 💖 this page is from LAPACK Version 3.12.0, source SRC/clasr.f(3), and that’s the footer tea. No cap. 🫶✨