/home/abui.../zgeqrt3.f(3)

✨ ZGEQRT3 ✨

okay so bestie, this is a LAPACK manual page for zgeqrt3.f and I'm about to make it make sense. it's literally giving "recursive QR factorization" energy and I'm obsessed. 💖

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgeqrt3.f

like, that's the file path bestie, no cap. 🎀

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✨ SYNOPSIS ✨

✨ Functions/Subroutines ✨

recursive subroutine ZGEQRT3 (m, n, a, lda, t, ldt, info)

ZGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. periodt. 💅

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✨ Function/Subroutine Documentation ✨

recursive subroutine ZGEQRT3 (integer m, integer n, complex*16, dimension(
    lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer
    ldt, integer info)

ZGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. yes, I said it twice. it's iconic. 🌟

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✨ Purpose ✨

okay so the actual purpose, and it's literally this:

!>
!> ZGEQRT3 recursively computes a QR factorization of a complex M-by-N
!> matrix A, using the compact WY representation of Q.
!>
!> Based on the algorithm of Elmroth and Gustavson,
!> IBM J. Res. Develop. Vol 44 No. 4 July 2000.
!>

so like, we're doing QR factorization but make it recursive, and it's based on Elmroth and Gustavson's algorithm from IBM J. Res. Develop. Vol 44 No. 4 July 2000. iykyk. 🔥

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✨ Parameters ✨

• M — M is INTEGER. the number of rows of the matrix A. M >= N. (yes bestie, rows have to be greater than or equal to columns, that's the vibe check 💅)
• N — N is INTEGER. the number of columns of the matrix A. N >= 0. (zero is allowed, she's flexible like that 🦋)
• A — A is COMPLEX*16 array, dimension (LDA,N). on entry, the complex M-by-N matrix A. on exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; the elements below the diagonal are the columns of V. see below for further details. (she's giving transformation, she's giving glow-up ✨)
• LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,M). (don't skimp on the leading dimension bestie, she needs room to breathe 🌸)
• T — T is COMPLEX*16 array, dimension (LDT,N). the N-by-N upper triangular factor of the block reflector. the elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. see below for further details. (upper triangular only, the rest is literally n/a 💀)
• LDT — LDT is INTEGER. the leading dimension of the array T. LDT >= max(1,N). (same energy as LDA but for T, keep up 🫶)
• INFO — INFO is INTEGER. and here's the tea:
  • = 0: successful exit (slay! 🎉)
  • < 0: if INFO = -i, the i-th argument had an illegal value (not me getting called out on argument i 😭)

bestie if INFO comes back negative it means one of your arguments is giving illegal value energy. check yourself before you wreck yourself. 💀

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✨ Author ✨

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

like, the whole academic avengers assembled for this one. 👑

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✨ Further Details ✨

okay so here's where it gets juicy. the matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal. for example, if M=5 and N=3, the matrix V is literally:

V = (  1       )
    ( v1  1    )
    ( v1 v2  1 )
    ( v1 v2 v3 )
    ( v1 v2 v3 )

where the vi's represent the vectors which define H(i), which are returned in the matrix A. the 1's along the diagonal of V are not stored in A. (not me being extra and storing the ones implicitly 🙈)

the block reflector H is then given by:

H = I - V * T * V**H

where V**H is the conjugate transpose of V. (conjugate transpose is her full government name, respect it 💅)

for details of the algorithm, see Elmroth and Gustavson (cited above). like, go read the paper bestie, it's giving academic excellence. 📚

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Definition at line 131 of file zgeqrt3.f.

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✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code. (the robots did this, not me, but I'm presenting it with flair ✨🤖)

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that's literally the whole vibe. this page was auto-magically generated by Doxygen for LAPACK from the source code, so don't come for me if the formatting is a little extra. 😘

~~ LAPACK Version 3.12.0 ~~ Dropped: /home/abui.../zgeqrt3.f(3) ~*~ 💖