ZLAQSB(3)

NAME

okay so bestie, this is the zlaqsb.f(3) page from the Library Functions Manual — LAPACK edition ✨. The source file this whole thing is about is:

• /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zlaqsb.f — yep, that’s the exact file path, no cap 💅

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SYNOPSIS

Functions/Subroutines

• subroutine ZLAQSB (uplo, n, kd, ab, ldab, s, scond, amax, equed) — ZLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. 🫶

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🌸 Function/Subroutine Documentation 🌸

subroutine ZLAQSB (character uplo, integer n, integer kd, complex*16,
       dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )
       s, double precision scond, double precision amax, character equed)

ZLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. ✨

💖 Purpose

okay so the actual glow-up: ZLAQSB equilibrates a symmetric band matrix A using the scaling factors in the vector S. That’s the vibe 💅

✨ Parameters ✨

UPLO

UPLO is CHARACTER*1 and tells us whether the upper or lower triangular part of the symmetric matrix A is stored, bestie:

• = 'U': Upper triangular
• = 'L': Lower triangular

N

N is INTEGER — it’s the order of the matrix A. Constraint: N >= 0. ✅

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'. Constraint: KD >= 0. 🦋

AB

AB is a COMPLEX*16 array, dimension (LDAB,N). On entry, it holds 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, the triangular factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H of the band matrix A, in the same storage format as A. 🔥

LDAB

LDAB is INTEGER — the leading dimension of the array AB. Constraint: LDAB >= KD+1. 🎀

S

S is a DOUBLE PRECISION array, dimension (N). These are the scale factors for A. 💖

SCOND

SCOND is DOUBLE PRECISION — ratio of the smallest S(i) to the largest S(i). 🧚

AMAX

AMAX is DOUBLE PRECISION — absolute value of largest matrix entry. ⭐

EQUED

EQUED is CHARACTER*1 and says whether or not equilibration was done:

• = 'N': No equilibration.
• = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S). 💅

🫶 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.
• 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.

Author

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

📍 Definition at line 140 of file zlaqsb.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

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<cute sign-off time, bestie: source/version is LAPACK Version 3.12.0, and the page path is /home/abui...RC/zlaqsb.f(3) — that’s the footer tea, periodt ☕💜