SRC/clangt.f(3)

✨ SRC/clangt.f ✨

Ok so bestie, welcome to the LAPACK Library Functions Manual, and today's main character is SRC/clangt.f 🎀 like yes she's a Fortran file, yes she's iconic, let's get into it.

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🌸 NAME 🌸

SRC/clangt.f — no cap, that's literally the name, that's the whole name section, we move 💅

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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.

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👑 Function/Subroutine Documentation 👑

real function clangt (character norm, integer n, complex, dimension( * ) dl,
    complex, dimension( * ) d, complex, dimension( * ) 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. she does exactly one job and she ate 🔥

💜 Purpose:

!>
!> 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.
!>

🍓 Returns

CLANGT

!>
!>    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.
!>

⚠️ bestie read that last line again: max(abs(A(i,j))) is not a consistent matrix norm. it's just vibes measuring the biggest element, that's it, don't @ me 😭

🌈 Parameters

• NORM

!>          NORM is CHARACTER*1
!>          Specifies the value to be returned in CLANGT as described
!>          above.
!>

• N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.  When N = 0, CLANGT is
!>          set to zero.
!>

(so if N is 0, she just hands you zero, no drama, no division, we love a graceful edge case 💖)

• DL

!>          DL is COMPLEX array, dimension (N-1)
!>          The (n-1) sub-diagonal elements of A.
!>

• D

!>          D is COMPLEX array, dimension (N)
!>          The diagonal elements of A.
!>

• DU

!>          DU is COMPLEX array, dimension (N-1)
!>          The (n-1) super-diagonal elements of A.
!>

so like: DL is under her, D is her, DU is over her — tridiagonal main character energy for real 👑

⭐ Author

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

Definition at line 105 of file clangt.f. 🫶

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💫 Author (of this doc, not of the math) 💫

Generated automatically by Doxygen for LAPACK from the source code. not me writing it by hand, the robot did it, and honestly? slayed 🤖✨

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LAPACK — Version 3.12.0 💖 that's the tea, that's the version, that's the whole page for SRC/clangt.f. go forth and norm responsibly, bestie 🦋🎀💅