SRC/cgeqrt2.f(3)

✨ SRC/cgeqrt2.f ✨

okay bestie, buckle up — this one is from the LAPACK manual, section 3, and it's honestly kind of iconic 💅

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🌸 NAME 🌸

SRC/cgeqrt2.f — that's literally it, that's the name, no notes 🎀

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🦋 SYNOPSIS 🦋

Functions/Subroutines

• subroutine cgeqrt2 (m, n, a, lda, t, ldt, info) — CGEQRT2 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 cgeqrt2 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info)

CGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. slay 🫶

💜 Purpose:

!>
!> CGEQRT2 computes a QR factorization of a complex M-by-N matrix A,
!> using the compact WY representation of Q.
!>

🍓 Parameters

M

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

N

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

A

!>          A is COMPLEX 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.
!>

LDA

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

T

!>          T is COMPLEX 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.
!>

LDT

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

INFO

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

lowkey important: INFO never lies. = 0 means you ate and left no crumbs, < 0 means argument number i showed up with an illegal value and got read for filth 💀

🧚 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

— the whole squad, fr fr 🌈

⭐ 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 picture this: V is giving lower-triangular-but-make-it-fashion, the vi vectors live under the diagonal and they're the ones that define H(i), and they get handed back to you inside A 🎀 meanwhile those 1's along the diagonal of V? not stored in A, they're just vibes ✨ and the block reflector H is, literally,

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

where V**H is the conjugate transpose of V. conjugate transpose is main character energy, no cap 👑

Definition at line 126 of file cgeqrt2.f.

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💖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page bestie, every single detail accounted for, nothing skipped, we ate and left zero crumbs 💅✨

okay bye, this was LAPACK Version 3.12.0, generated by Doxygen for LAPACK straight from the source code — mwah 😘 🦋💖🌸