DQRT11(3)

🎀 DQRT11(3) 🎀

okay bestie, so this is a page from the Library Functions Manual — it's the manpage for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dqrt11.f, and it's literally just sitting there in the LAPACK testing folder being iconic. 💅

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dqrt11.f

like, that's the whole name. that's the file. that's her. 🫶

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🌸 SYNOPSIS 🌸

Functions/Subroutines

double precision function DQRT11 (m, k, a, lda, tau, work, lwork)

DQRT11

no cap, that's the whole vibe check right there.

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💜 Function/Subroutine Documentation 💜

🦋 the actual signature 🦋

double precision function DQRT11 (integer m, integer k, double precision,
    dimension( lda, * ) a, integer lda, double precision, dimension( * )
    tau, double precision, dimension( lwork ) work, integer lwork)

DQRT11

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💖 Purpose 💖

!>
!> DQRT11 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).
!>

so basically she's out here computing the test ratio || Q'*Q - I || / (eps * m), where the orthogonal matrix Q is a product of elementary transformations — and every single one of those bad boys looks like H(k) = I - tau(k) v(k) v(k)' ✨. the tau(k) lives in TAU(k), and v(k) is an m-vector shaped like [ 0 ... 0 1 x(k) ]' where x(k) is a vector of length m-k chilling in A(k+1:m,k). periodt. 👑

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🌈 Parameters 🌈

• M

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

lowkey the row count of A. that's it, that's the job. 💅

• 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 the orthogonal-transformation lore. iykyk. 🧚

• A

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

a DOUBLE PRECISION array, dimension (LDA,K) — literally the (possibly partial) output of a QR reduction routine. she's giving "leftover glow-up". 🔥

• LDA

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

the leading dimension of A, bestie. the main character dimension. 👑

• TAU

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

a DOUBLE PRECISION array, dimension (K) — these are the scaling factors tau for the elementary transformations, exactly as computed by the QR factorization routine. no notes. 🎀

• WORK

!>          WORK is DOUBLE PRECISION array, dimension (LWORK)
!>

a DOUBLE PRECISION array, dimension (LWORK). the workspace. the grind. 🫶

• LWORK

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

the length of the array WORK, and heads up — LWORK >= M*M + M. fr fr, don't skip that. 😭

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👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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⭐ Definition at line 97 of file dqrt11.f. ⭐

like, line 97. we stan a precise citation. 📍

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 that's the whole page — brought to you by LAPACK, Version 3.12.0, dated /home/abui...IN/dqrt11.f(3) — slay, go compute that test ratio bestie 💖✨🎀🦋