SQRT11(3)

💅 SQRT11(3) — like, the LAPACK library functions manual, bestie 🎀

okay so real talk: this is a page from the LAPACK library functions manual, and it's about a lil Fortran function called SQRT11 that lives in sqrt11.f(3). she's a test-ratio girlie, she's in the TESTING/LIN directory, and she's here to check your orthogonal matrix's vibe. let's get into it ✨

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/sqrt11.f

that's literally her whole address, no cap. that's where the file lives 🫶

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✨ SYNOPSIS ✨

🦋 Functions/Subroutines

real function SQRT11 (m, k, a, lda, tau, work, lwork)

SQRT11 — yes that's just the name again, she's not doing a whole subtitle okay 😭

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💖 Function/Subroutine Documentation 💖

real function SQRT11 (integer m, integer k, real, dimension( lda, * ) a,
    integer lda, real, dimension( * ) tau, real, dimension( lwork ) work,
    integer lwork)

SQRT11

⭐ Purpose:

ok so here's the moment. SQRT11 computes the test ratio

      || Q'*Q - I || / (eps * m)

where the orthogonal matrix Q is represented as a product of elementary transformations. each transformation has the form

   H(k) = I - tau(k) v(k) v(k)'

where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form [ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored in A(k+1:m,k).

like she's literally measuring how close Q'*Q is to the identity, scaled by eps * m. that's the whole gig. iconic. 💅

🎀 Parameters

• M

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

how many rows your matrix A is serving. that's the row count, periodt.

• K

!>          K is INTEGER
!>          The number of columns of A whose subdiagonal entries
!>          contain information about orthogonal transformations.
!>

the number of columns of A whose subdiagonal entries are carrying intel about the orthogonal transformations 🕵️‍♀️

• A

!>          A is REAL array, dimension (LDA,K)
!>          The (possibly partial) output of a QR reduction routine.
!>

a real array, dimension (LDA,K) — it's the (possibly partial!) output of a QR reduction routine. possibly partial, she's flexible like that.

• LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.
!>

the leading dimension of A. the big one. the boss dimension.

• TAU

!>          TAU is REAL array, dimension (K)
!>          The scaling factors tau for the elementary transformations as
!>          computed by the QR factorization routine.
!>

a real array, dimension (K) — these are the scaling factors tau for the elementary transformations, exactly as the QR factorization routine computed them. no notes. 👑

• WORK

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

a real array, dimension (LWORK). it's just the workspace, she's doing her job.

• LWORK

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

the length of the array WORK. and like, LWORK >= M*M + M — that's not a suggestion bestie, that's the rule fr fr 🙈

🧚 Author

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

the whole squad contributed, we love a collab 🌈

Definition at line 97 of file sqrt11.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

like yes, a robot wrote the docs. she's still slaying.

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okay bye bestie!! this page is LAPACK, Version 3.12.0, and the whole thing lives at /home/abui...IN/sqrt11.f(3) if you ever need to find her again 💜✨ stay orthogonal, drink water 🍓💀