/home/abui.../zgeqrt2.f(3)

💖 zgeqrt2.f — LAPACK Library Functions Manual 💖

okay bestie, so this one lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgeqrt2.f and it's part of the LAPACK manual, and honestly? she's a whole icon. it's giving linear algebra but make it fashion. let's get into it ✨

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgeqrt2.f

that's her. that's the file. no cap, that whole path is a mouthful but we respect the build directory aesthetic 🎀

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine ZGEQRT2 (m, n, a, lda, t, ldt, info)

ZGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

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💅 Function/Subroutine Documentation 💅

subroutine ZGEQRT2 (integer m, integer n, complex*16, dimension( lda, * ) a,
    integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integer
    info)

ZGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

⭐ Purpose:

!>
!> ZGEQRT2 computes a QR factorization of a complex M-by-N matrix A,
!> using the compact WY representation of Q.
!>

like literally she takes your matrix and does the whole QR glow-up with the compact WY representation of Q. main character energy fr fr 🔥

🎀 Parameters

• M

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

the row count, bestie. and yes, M >= N — that's not a suggestion, that's the law 💀

• N

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

column count. N >= 0, so zero is allowed, we love a low-maintenance dimension 🙈

• 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.
!>

okay so on entry it's just your cute little complex M-by-N matrix A. on exit? transformation. the elements on and above the diagonal? that's R, the N-by-N upper triangular queen 👑. the elements below the diagonal? those are the columns of V. see below for the details, iykyk 💜

• LDA

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

leading dimension of A. must be LDA >= max(1,M). respect the boundary or else 😭

• 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.
!>

T is the N-by-N upper triangular factor of the block reflector, slay. elements on and above the diagonal = the block reflector T. elements below the diagonal = not used, they're just vibing, leave them alone 🫶

• LDT

!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= max(1,N).
!>

leading dimension of T, and it's gotta be LDT >= max(1,N). periodt.

• INFO

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

the vibe check of return codes:

• = 0 → successful exit, we ate, no notes ✨
• < 0 → if INFO = -i, the i-th argument had an illegal value. not me pointing fingers at argument number i 💀

🌈 Author

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

four whole institutions collaborated on this. collaborative queen behavior 🧚

🔥 Further Details:

!>
!>  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
!>
!>               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.  The
!>  block reflector H is then given by
!>
!>               H = I - V * T * V**H
!>
!>  where V**H is the conjugate transpose of V.
!>

okay so here's the tea ☕ — the matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal. example time: if M=5 and N=3, the matrix V is:

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

the vi's are the vectors that define H(i), and they get returned inside the matrix A. the 1's along the diagonal of V are not stored in A — they're implied, they don't need a whole storage slot, lowkey iconic 🌟

and then the block reflector H is given by:

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

where V**H is the conjugate transpose of V. conjugate transpose!! she's fancy 💅

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⭐ Definition ⭐

Definition at line 126 of file zgeqrt2.f.

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🫶 Author

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and that's the whole page bestie, no crumbs left behind 🍓

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