SRC/dlaqsb.f(3)

💅 SRC/dlaqsb.f — the glow-up your band matrix deserves

okay bestie, gather round, because today we're talking about DLAQSB — a literal icon from the LAPACK library, living her best life at line 139 of dlaqsb.f. she scales symmetric/Hermitian band matrices using scaling factors computed by spbequ, and honestly? she ate. 💖

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines

subroutine dlaqsb (uplo, n, kd, ab, ldab, s, scond, amax, equed)

DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. no cap, that's the whole vibe.

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🦋 Function/Subroutine Documentation 🦋

subroutine dlaqsb (character uplo, integer n, integer kd,
     double precision, dimension( ldab, * ) ab, integer ldab,
     double precision, dimension( * ) s, double precision scond,
     double precision amax, character equed)

DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. she's giving main character energy fr fr.

🌸 Purpose

DLAQSB equilibrates a symmetric band matrix A using the scaling factors in the vector S. literally her whole job and she does it flawlessly 💅

🎀 Parameters

• UPLO — UPLO is CHARACTER*1. it tells us whether the upper or lower triangular part of the symmetric matrix A is stored, and here are your options:
  • = 'U': Upper triangular 👑
  • = 'L': Lower triangular 🦋
• N — N is INTEGER. the order of the matrix A. N >= 0. respect the N, bestie, she's not optional.
• KD — KD is INTEGER. the number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. must have KD >= 0. keep it positive (or zero), ok?
• AB — AB is DOUBLE PRECISION array, dimension (LDAB,N). ooooh this is the juicy one:
  • On entry: the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:
    • if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    • if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
  • On exit, if INFO = 0, you get the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A, in the same storage format as A. it's giving transformation arc ✨
• LDAB — LDAB is INTEGER. the leading dimension of the array AB. must be LDAB >= KD+1. don't skimp on the leading dimension bestie, she needs her space.
• S — S is DOUBLE PRECISION array, dimension (N). the scale factors for A. iconic.
• SCOND — SCOND is DOUBLE PRECISION. the ratio of the smallest S(i) to the largest S(i). tiny queen, big queen, the ratio is the moment 🎀
• AMAX — AMAX is DOUBLE PRECISION. absolute value of largest matrix entry. she's the biggest vibe in the matrix fr fr.
• EQUED — EQUED is CHARACTER*1. tells you whether or not equilibration was done, and here's the tea:
  • = 'N': No equilibration. nope, didn't happen 🙈
  • = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S). yes bestie, slay 💅

🔥 Internal Parameters

• THRESH is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors. if SCOND < THRESH, scaling is done. periodt.
• LARGE and SMALL are threshold values used to decide if scaling should be done based on the absolute size of the largest matrix element. if AMAX > LARGE or AMAX < SMALL, scaling is done. two little gatekeepers, love that for us 🫶

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👑 Author 👑

the absolute legends who made this happen:

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

Definition at line 139 of file dlaqsb.f. iykyk.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. the robots did this one, and they lowkey snapped ✨

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LAPACK — Version 3.12.0 💜 and that's the whole page bestie, SRC/dlaqsb.f(3) signed, sealed, delivered, no cap 🎀🦋💖