SLANGB(3)

🎀 SLANGB(3) — like, the band-matrix norm girlie 🎀

okay bestie, so this page lives in the Library Functions Manual and it's literally about /home/abui...RC/slangb.f(3) — yes, the same path twice on the header line, that's just how the manual do. anyway, buckle up 🦋

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✨ NAME ✨

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

that's it. that's the name. it's giving "my whole identity is a build path" 💀 but slay, we move.

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

real function SLANGB (norm, n, kl, ku, ab, ldab, work)

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

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💖 Function/Subroutine Documentation 💖

real function SLANGB (character norm, integer n, integer kl, integer ku,
    real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)

so, again, no cap: SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general band matrix. iconic behaviour honestly 💅

🧚 Purpose 🧚

!> !> SLANGB returns the value of the one norm, or the Frobenius norm, or !> the infinity norm, or the element of largest absolute value of an !> n by n band matrix A, with kl sub-diagonals and ku super-diagonals. !>

like, it's an n by n band matrix A, lowkey hanging out with kl sub-diagonals and ku super-diagonals, and SLANGB is here to measure it. main character energy fr fr 🫶

⭐ Returns ⭐

SLANGB

!>
!>    SLANGB = ( 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 like, pick your fighter: norm1 is the one norm (maximum column sum), normI is the infinity norm (maximum row sum), and normF is the Frobenius norm (square root of sum of squares) 🌈

⚠️ heads up bestie: max(abs(A(i,j))) is not a consistent matrix norm. that's a real caveat, not me being dramatic. well — okay, it's also me being dramatic, but it's true. 💀

🌸 Parameters 🌸

• NORM — a CHARACTER*1. it specifies the value to be returned in SLANGB as described above. it's the vibe selector ✨
• N — an INTEGER, the order of the matrix A. N >= 0. and when N = 0, SLANGB is set to zero. tiny matrix, tiny answer, we love a clean edge case 🎀
• KL — an INTEGER, the number of sub-diagonals of the matrix A. KL >= 0.
• KU — an INTEGER, the number of super-diagonals of the matrix A. KU >= 0.
• AB — a REAL array, dimension (LDAB,N). this is the band matrix A, stored in rows 1 to KL+KU+1. the j-th column of A is stored in the j-th column of the array AB as follows:

AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

iykyk. that index gymnastics is literally the whole bit 🧚

• LDAB — an INTEGER, the leading dimension of the array AB. LDAB >= KL+KU+1. don't skimp on it 💅
• WORK — a REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. so she only shows up when infinity norm is invited. rude but valid 🙈

👑 Author 👑

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

Definition at line 122 of file slangb.f.

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🌟 Author (the other one) 🌟

Generated automatically by Doxygen for LAPACK from the source code. yes, a robot wrote the manpage. and now a gen z rewrote the manpage. the circle of life 🦋

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okay that's the whole page bestie, you ate that 💖✨

— xoxo, LAPACK Version 3.12.0, signed off from /home/abui...RC/slangb.f(3) 🫶🎀