SRC/slangt.f(3)

💅 SRC/slangt.f — like, the manual page, bestie

okay so this is the page for SRC/slangt.f, and it's a whole serve. it lives in the LAPACK Library Functions Manual, and honestly? it ate. let's get into it 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines

• real function slangt (norm, n, dl, d, du) — SLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix. that's the whole assignment, no cap 💅

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🦋 Function/Subroutine Documentation 🦋

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

SLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix. it's giving "one function, four moods" and honestly we love that for it ✨

🌸 Purpose 🌸

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

like literally just vibe-checking a real tridiagonal matrix A and telling you how big it is, in whichever flavour you asked for 🫶

💖 Returns 💖

SLANGT

!>
!>    SLANGT = ( 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.
!>

so it's a little choose-your-own-adventure situation 👑

• max(abs(A(i,j))) when NORM = 'M' or 'm'
• norm1(A) when NORM = '1', 'O' or 'o'
• normI(A) when NORM = 'I' or 'i'
• normF(A) when 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. no cap, it said what it said 💀

🎀 Parameters 🎀

• NORM — NORM is CHARACTER*1. specifies the value to be returned in SLANGT as described above. it's the main character of this whole operation, fr fr 👑
• N — N is INTEGER. the order of the matrix A. N >= 0. when N = 0, SLANGT is set to zero. zero matrix? zero output. balanced. 💅
• DL — DL is REAL array, dimension (N-1). the (n-1) sub-diagonal elements of A. the understudies, lowkey 🦋
• D — D is REAL array, dimension (N). the diagonal elements of A. main character energy, obviously ✨
• DU — DU is REAL array, dimension (N-1). the (n-1) super-diagonal elements of A. the other understudies, equally iconic 🌸

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👑 Author 👑

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

the whole squad really showed up and said "we made this" 🫶 periodt.

Definition at line 105 of file slangt.f. go look, iykyk 🙈

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🌟 Author (yes, again) 🌟

Generated automatically by Doxygen for LAPACK from the source code. not me being auto-generated and still slaying 😭💅

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kay so that's the whole page, bestie — that was LAPACK, Version 3.12.0, serving you SRC/slangt.f(3) realness. mwah, drink some water, go call your matrix tridiagonal 💜