SLAQSB(3)

🌸 NAME 🌸

okay so welcome to the slaqsb.f(3) page from the Library Functions Manual — the header page path is /home/abui...RC/slaqsb.f(3), and the NAME section is literally this source-file path, bestie:

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

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

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

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💖 Function/Subroutine Documentation 💖

the full signature is giving:

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

SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. periodt.

🎀 Purpose 🎀

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

🦋 Parameters 🦋

UPLO

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

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

N

N is INTEGER. The order of the matrix A. 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'. KD >= 0.

AB

AB is REAL array, dimension (LDAB,N).

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, 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.

LDAB

LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+1.

S

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

SCOND

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

AMAX

AMAX is REAL. Absolute value of largest matrix entry.

EQUED

EQUED is CHARACTER*1. Specifies 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• 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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 139 of file slaqsb.f.

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💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

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source/version sign-off: LAPACK, Version 3.12.0. The footer also gives the page path /home/abui...RC/slaqsb.f(3), and there’s no date shown on this footer, bestie. mwah 💖💅