SGERQF(3)

✨ SGERQF(3) ✨

okay bestie, so this page lives in the Library Functions Manual collection and the file it's documenting is literally this whole vibe:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgerqf.f

like that's the whole NAME section, no cap 🫶

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine SGERQF (m, n, a, lda, tau, work, lwork, info)

and yes, it's just SGERQF. icon behavior honestly 👑

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🦋 Function/Subroutine Documentation 🦋

subroutine SGERQF (integer m, integer n, real, dimension( lda, * ) a,
    integer lda, real, dimension( * ) tau, real, dimension( * ) work,
    integer lwork, integer info)

SGERQF

🎀 Purpose 🎀

okay so here's the tea, straight from the source:

!>
!> SGERQF computes an RQ factorization of a real M-by-N matrix A:
!> A = R * Q.
!>

like it takes your matrix and serves you a whole R times Q, periodt 🔥

⭐ Parameters ⭐

• M — the glow-up begins:

!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.
!>

• N —

!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!>

• A — bestie this is THE main character array:

!>          A is REAL array, dimension (LDA,N)
!>          On entry, the M-by-N matrix A.
!>          On exit,
!>          if m <= n, the upper triangle of the subarray
!>          A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R;
!>          if m >= n, the elements on and above the (m-n)-th subdiagonal
!>          contain the M-by-N upper trapezoidal matrix R;
!>          the remaining elements, with the array TAU, represent the
!>          orthogonal matrix Q as a product of min(m,n) elementary
!>          reflectors (see Further Details).
!>

• LDA —

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>

• TAU — the scalar factors, lowkey iconic:

!>          TAU is REAL array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors (see Further
!>          Details).
!>

• WORK —

!>          WORK is REAL array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!>

• LWORK — read this one carefully bestie, it's giving rules:

!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise.
!>          For optimum performance LWORK >= M*NB, where NB is
!>          the optimal blocksize.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA.
!>

• INFO — the vibe check at the end:

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

👑 Author 👑

the whole squad behind this:

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🌈 Further Details 🌈

okay this is where it gets good — the matrix Q is literally built out of elementary reflectors:

!>
!>  The matrix Q is represented as a product of elementary reflectors
!>
!>     Q = H(1) H(2) . . . H(k), where k = min(m,n).
!>
!>  Each H(i) has the form
!>
!>     H(i) = I - tau * v * v**T
!>
!>  where tau is a real scalar, and v is a real vector with
!>  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
!>  A(m-k+i,1:n-k+i-1), and tau in TAU(i).
!>

like, tau is a real scalar, v is a real vector, and the zeros and the 1 land exactly where they land. iykyk 💅

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Definition at line 138 of file sgerqf.f.

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🙈 Author 🙈

Generated automatically by Doxygen for LAPACK from the source code.

bestie did you catch that? it's autogenerated, don't @ me 🫶

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💖 and that's the whole page!! 💖 this one came to you from LAPACK, Version 3.12.0, and it's filed as /home/abui...RC/sgerqf.f(3) — mwah, kiss the source, she ate 🌸✨💜