SRC/slangb.f(3)

🌈 SRC/slangb.f 🌈

SRC/slangb.f — yup, that's the page, bestie. It's from the Library Functions Manual and it's here to explain slangb, the real function that measures a general band matrix. 💅

🌸 NAME 🌸

SRC/slangb.f — the function page itself. Iconic, honestly. 🎀

🦋 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 general band matrix. ✨

🎀 Function/Subroutine Documentation 🎀

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

SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. No cap, that's the whole gig. 😌

💖 Purpose 💖

Okay so 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. It's giving "matrix measurement main character." 🔥

🔥 Returns 🔥

SLANGB is defined like this, bestie:

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. ⚠️

🫶 Parameters 🫶

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in SLANGB as described above. 💅
• N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, SLANGB is set to zero. 🎀
• KL — KL is INTEGER. The number of sub-diagonals of the matrix A. KL >= 0. 🌸
• KU — KU is INTEGER. The number of super-diagonals of the matrix A. KU >= 0. 🦋
• AB — AB is REAL array, dimension (LDAB,N). 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).

• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1. ✨
• WORK — WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. 💜

🧚 Author 🧚

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

Definition at line 122 of file slangb.f. 👑

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. ✨

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That's the whole thing, bestie. Footer tea at the very bottom: LAPACK, Version 3.12.0, source SRC/slangb.f(3). Mwah 💋💅