CLAQSB(3)

💖 CLAQSB(3) 💖

okay so bestie, this is CLAQSB(3) from the Library Functions Manual. The header path is /home/abui...RC/claqsb.f(3) — that's the exact header vibe, no cap. It's a LAPACK subroutine page, and it's lowkey giving main character energy. 🫶

🌸 NAME 🌸

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

✨ SYNOPSIS ✨

Functions/Subroutines

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

🦋 Function/Subroutine Documentation 🦋

Here's the full signature, fr fr:

subroutine CLAQSB (character uplo, integer n, integer kd, complex,
    dimension( ldab, * ) ab, integer ldab, real, dimension( * ) s, real
    scond, real amax, character equed)

CLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. Yep, same icon energy as the synopsis.

🎯 Purpose 🎯

CLAQSB equilibrates a symmetric band matrix A using the scaling factors in the vector S.

🌟 Parameters 🌟

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

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

N is INTEGER: the order of the matrix A. N >= 0.

KD is INTEGER: the number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.

AB is COMPLEX 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, it holds 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 is INTEGER: the leading dimension of the array AB. LDAB >= KD+1.

S is REAL array, dimension (N): the scale factors for A.

SCOND is REAL: ratio of the smallest S(i) to the largest S(i).

AMAX is REAL: absolute value of largest matrix entry.

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• = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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 claqsb.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Cute little footer sign-off, bestie: LAPACK, Version 3.12.0, and the path /home/abui...RC/claqsb.f(3) in the footer's date spot — no separate date shown, so that's the whole tea. 💖✨