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

💅 slasr.f(3) — Library Functions Manual 💅

Hii bestie, welcome to /home/abui...RC/slasr.f(3), straight out of the Library Functions Manual. It’s giving linear algebra, it’s giving LAPACK, and we’re keeping every single detail. 💖

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slasr.f — the file this page is about, periodt.

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✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

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

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📚 Function/Subroutine Documentation 📚

The signature is literally this:

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

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

🎯 Purpose 🎯

Okay so SLASR applies a sequence of plane rotations to a real matrix A, from either the left or the right. No cap. 💅

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. Values:
  • '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. Values:
  • '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. Values:
  • '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 — REAL array, dimension (M-1) if SIDE = 'L' and (N-1) if SIDE = 'R'. The cosines c(k) of the plane rotations.
• S — REAL array, dimension (M-1) if SIDE = 'L' and (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 — REAL 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 — 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 slasr.f.

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🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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Okay that’s the whole page, bestie. Source/version/date check: the source is LAPACK, the version is Version 3.12.0, and the footer path is /home/abui...RC/slasr.f(3). There’s no separate date in the footer, so I’m not inventing one — periodt. 💖✨