TESTING/LIN/crzt01.f(3)

✨ TESTING/LIN/crzt01.f ✨

okay bestie so this is a page out of LAPACK — the TESTING/LIN corner of it, to be exact — and it's all about one little Fortran function called crzt01. it's giving "quality control girlie" energy, fr fr 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• real function crzt01 (m, n, a, af, lda, tau, work, lwork) — CRZT01

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🦋 Function/Subroutine Documentation 🦋

real function crzt01 (integer m, integer n, complex, dimension( lda, * ) a,
    complex, dimension( lda, * ) af, integer lda, complex, dimension( * )
    tau, complex, dimension( lwork ) work, integer lwork)

CRZT01 — that's literally her name, no notes 🎀

💖 Purpose

!>
!> CRZT01 returns
!>      || A - R*Q || / ( M * eps * ||A|| )
!> for an upper trapezoidal A that was factored with CTZRZF.
!>

so like. she computes that ratio up there 👆 — the norm of A - R*Q, divided by M * eps * ||A|| — for an upper trapezoidal A that was factored with CTZRZF. it's a whole vibe check for your factorization 🔥 (and the emojis-optional part: the math is exact, keep every piece of it 💜)

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🎀 Parameters 🎀

M

!>          M is INTEGER
!>          The number of rows of the matrices A and AF.
!>

the row count, bestie. how many rows live in A and AF. periodt 💅

N

!>          N is INTEGER
!>          The number of columns of the matrices A and AF.
!>

same but for columns — N is the number of columns of A and AF. iconic 🌸

A

!>          A is COMPLEX array, dimension (LDA,N)
!>          The original upper trapezoidal M by N matrix A.
!>

this is the original A, an upper trapezoidal M by N matrix, sitting in a COMPLEX array with dimension (LDA,N). she's the before picture 📸

AF

!>          AF is COMPLEX array, dimension (LDA,N)
!>          The output of CTZRZF for input matrix A.
!>          The lower triangle is not referenced.
!>

AF is the after picture — the output of CTZRZF for input matrix A, in a COMPLEX array of dimension (LDA,N). and heads up: the lower triangle is not referenced. don't even worry about it, she's just not looking there 🙈

LDA

!>          LDA is INTEGER
!>          The leading dimension of the arrays A and AF.
!>

the leading dimension of both A and AF. yes both. shared. slay 💫

TAU

!>          TAU is COMPLEX array, dimension (M)
!>          Details of the  Householder transformations as returned by
!>          CTZRZF.
!>

TAU is a COMPLEX array of dimension (M) holding all the little details of the Householder transformations as returned by CTZRZF. the backstory, if you will ✨

WORK

!>          WORK is COMPLEX array, dimension (LWORK)
!>

WORK is a COMPLEX array of dimension (LWORK). scratch space, doing her thing 🫶

LWORK

!>          LWORK is INTEGER
!>          The length of the array WORK.  LWORK >= m*n + m.
!>

LWORK is an INTEGER — the length of the array WORK. and the rule is LWORK >= m*n + m. no cap, memorize it 📏💀

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👑 Author 👑

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

the whole friend group came together for this one, we love to see it 🌈

Definition at line 96 of file crzt01.f. 🎯

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side note from the docs themselves: this page was Generated automatically by Doxygen for LAPACK from the source code. — so if anything's funky, blame the robots, not me 🤖💀

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and that's the whole page, bestie!! 💖✨🦋🌸🎀

<cute>mwah 💋 — LAPACK, Version 3.12.0 💜 (that's the source/version and date energy, right there in the footer, folded into this little sign-off 🫶)</cute>