SRC/zlaqsb.f(3)

🌸 NAME 🌸

Bestie, this is the SRC/zlaqsb.f(3) page from the LAPACK Library Functions Manual. Yes, the whole page is literally named SRC/zlaqsb.f — iconic. 💅

💖 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. Slay. ✨

🌈 Function/Subroutine Documentation 🌈

📚 Subroutine signature 📚

   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. No cap. 🫶

✨ Purpose ✨

Okay so the whole vibe is this: ZLAQSB equilibrates a symmetric band matrix A using the scaling factors in the vector S. That's it, that's the mission. 💖

🎀 Parameters 🎀

• UPLO — UPLO is CHARACTER*1. It 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 COMPLEX*16 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**H *U or A = L*L**H of the band matrix A, in the same storage format as A. Obsessed with the storage format staying put. 🦋

• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• S — S is DOUBLE PRECISION array, dimension (N). 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. 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  • = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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 — 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 — 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, bestie: this page is from LAPACK Version 3.12.0, source page SRC/zlaqsb.f(3) — generated automatically by Doxygen for LAPACK from the source code. The original footer doesn't show a date, so I'm not inventing one. Periodt. 🎀