ZGET54(3)

🦋 ZGET54(3) — the LAPACK check-my-decomposition girlie 🦋

okay so this page lives in the Library Functions Manual for LAPACK (yes, the /home/abui...IG/zget54.f(3) one, mwah 💅), and it's literally all about one lil Fortran subroutine that does a vibe check on your generalized decomposition. buckle up bestie, we're going in 🎀

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zget54.f — that's the whole glowing file path, and honestly she's that file. 👑

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine ZGET54 (n, a, lda, b, ldb, s, lds, t, ldt, u, ldu, v, ldv, work, result) — the icon herself, ZGET54 💖

subroutine ZGET54 (n, a, lda, b, ldb, s, lds, t, ldt, u, ldu, v, ldv,
    work, result)
    ZGET54

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👑 Function/Subroutine Documentation 👑

subroutine ZGET54 (integer n, complex*16, dimension( lda, * ) a, integer
    lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16,
    dimension( lds, * ) s, integer lds, complex*16, dimension( ldt, * ) t,
    integer ldt, complex*16, dimension( ldu, * ) u, integer ldu, complex*16,
    dimension( ldv, * ) v, integer ldv, complex*16, dimension( * ) work,
    double precision result)
    ZGET54

she's giving main character energy, fr fr 🌟

🧚 Purpose

!> !> ZGET54 checks a generalized decomposition of the form !> !> A = U*S*V' and B = U*T* V' !> !> where ' means conjugate transpose and U and V are unitary. !> !> Specifically, !> !> RESULT = ||( A - U*S*V', B - U*T*V' )|| / (||( A, B )||*n*ulp ) !>

so basically: you hand her your A, your B, and the whole factored situation, and she tells you how far off your reconstruction is, scaled by (||( A, B )||*n*ulp ). the way that this is literally just a normalized error check 😭🔥

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🍓 Parameters

• N

!> N is INTEGER !> The size of the matrix. If it is zero, DGET54 does nothing. !> It must be at least zero. !>

(yes she says DGET54 in the source, and no we do not correct our queen's typo 💀 — and also N has to be at least zero, okurr)

• A

!> A is COMPLEX*16 array, dimension (LDA, N) !> The original (unfactored) matrix A. !>

the raw, un-factored, pre-glow-up A ✨

• LDA

!> LDA is INTEGER !> The leading dimension of A. It must be at least 1 !> and at least N. !>

so it's gotta be at least 1 and at least N, no skipping 👏

• B

!> B is COMPLEX*16 array, dimension (LDB, N) !> The original (unfactored) matrix B. !>

the other original (unfactored) matrix, B 🫶

• LDB

!> LDB is INTEGER !> The leading dimension of B. It must be at least 1 !> and at least N. !>

at least 1, at least N. periodt 💅

• S

!> S is COMPLEX*16 array, dimension (LDS, N) !> The factored matrix S. !>

the factored one, she's been through something 🌸

• LDS

!> LDS is INTEGER !> The leading dimension of S. It must be at least 1 !> and at least N. !>

• T

!> T is COMPLEX*16 array, dimension (LDT, N) !> The factored matrix T. !>

• LDT

!> LDT is INTEGER !> The leading dimension of T. It must be at least 1 !> and at least N. !>

• U

!> U is COMPLEX*16 array, dimension (LDU, N) !> The orthogonal matrix on the left-hand side in the !> decomposition. !>

left-hand side icon 🎀

• LDU

!> LDU is INTEGER !> The leading dimension of U. LDU must be at least N and !> at least 1. !>

(LDU must be at least N and at least 1 — same vibe, slightly different word order, and we respect it 🙈)

• V

!> V is COMPLEX*16 array, dimension (LDV, N) !> The orthogonal matrix on the left-hand side in the !> decomposition. !>

yes, the source literally also says "left-hand side" for V — not me, not my fault, I'm just the messenger 🧚

• LDV

!> LDV is INTEGER !> The leading dimension of V. LDV must be at least N and !> at least 1. !>

• WORK

!> WORK is COMPLEX*16 array, dimension (3*N**2) !>

she needs room to cook — (3*N**2) of it 🔥

• RESULT

!> RESULT is DOUBLE PRECISION !> The value RESULT, It is currently limited to 1/ulp, to !> avoid overflow. Errors are flagged by RESULT=10/ulp. !>

⚠️ heads up bestie: RESULT is capped at 1/ulp so nothing overflows, and if things go wrong you get RESULT=10/ulp thrown at you 😭 that's your error flag, iykyk

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💜 Author

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

Definition at line 154 of file zget54.f. 📍

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🌈 Author

Generated automatically by Doxygen for LAPACK from the source code. 🤖 (the bot did her makeup and she ate, ngl)

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and that's the whole page, bestie — no cap, every flag, every dimension, every !> line accounted for 💖

LAPACK, Version 3.12.0 — and the source path on the footer is /home/abui...IG/zget54.f(3), so like… that's the whole sign-off, mwah 🫶✨🎀