CLANGT(3)

🦋 CLANGT(3) — the tridiagonal norm girlie 💅

ok so bestie, this page lives at clangt.f(3) in the manual, and honestly? it's giving "small but mighty". it's a Fortran thing, it's a LAPACK thing, and it's about to explain exactly one (1) function to you. buckle up 🎀

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/clangt.f

like. yes. that's the whole name. it's a whole absolute path and it ate, no notes 💀

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🌸 SYNOPSIS 🌸

Functions/Subroutines

real function CLANGT (norm, n, dl, d, du)

CLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix. periodt. 👑

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💜 Function/Subroutine Documentation 💜

real function CLANGT (character norm, integer n, complex, dimension( * ) dl,
    complex, dimension( * ) d, complex, dimension( * ) du)

ok so full signature reveal: CLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix. same energy as before, just with the full type list because we're being thorough bestie 🫶

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🔥 Purpose 🔥

lowkey the main character moment of the whole page:

!>
!> CLANGT  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> complex tridiagonal matrix A.
!>

so it's a complex tridiagonal matrix A, and you get to pick which flavour of "how big is this" you want. choose your fighter, iykyk ✨

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⭐ Returns ⭐

it returns CLANGT, and the definition is this absolute icon of a piecewise block — not me copying it exactly because precision is the vibe:

!>
!>    CLANGT = ( max(abs(A(i,j))), NORM = 'M' or 'm'
!>             (
!>             ( norm1(A),         NORM = '1', 'O' or 'o'
!>             (
!>             ( normI(A),         NORM = 'I' or 'i'
!>             (
!>             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
!>
!> where  norm1  denotes the  one norm of a matrix (maximum column sum),
!> normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
!> normF  denotes the  Frobenius norm of a matrix (square root of sum of
!> squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
!>

🚨 important caveat alert 🚨 max(abs(A(i,j))) is not a consistent matrix norm. that's canon, bestie, don't come for me.

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💖 Parameters 💖

• NORM — NORM is CHARACTER*1, and it specifies the value to be returned in CLANGT as described above. it's literally the "which norm tho" knob 🌈
• N — N is INTEGER, the order of the matrix A. N >= 0. and when N = 0, CLANGT is set to zero. zero girlies rise 🎀
• DL — DL is COMPLEX array, dimension (N-1), holding the (n-1) sub-diagonal elements of A. the underlings of the diagonal, fr fr ✨
• D — D is COMPLEX array, dimension (N), holding the diagonal elements of A. main character energy, obviously 👑
• DU — DU is COMPLEX array, dimension (N-1), holding the (n-1) super-diagonal elements of A. the over-achievers above the diagonal 💅

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👑 Author 👑

the whole squad gets credit:

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

we stan a collaborative effort 🫶

also: Definition at line 105 of file clangt.f. — line 105 specifically, no cap 📍

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💜 Author (again, yes really) 💜

Generated automatically by Doxygen for LAPACK from the source code.

it wasn't written by a person, it was birthed by Doxygen. iconic behaviour honestly 🤖✨

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🌈 Sign-off 🌈

so that's the whole page bestie — this is LAPACK, Version 3.12.0, and the file is chillin' at /home/abui...RC/clangt.f(3). go forth and compute your norms, you're gonna slay it, mwah 💋💖