SRC/claqhb.f(3)

🌸 NAME 🌸

This is the SRC/claqhb.f page from the Library Functions Manual, bestie 💖 — and it's all about one little icon: claqhb.

✨ SYNOPSIS ✨

💖 Functions/Subroutines 💖

• subroutine claqhb (uplo, n, kd, ab, ldab, s, scond, amax, equed) — CLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ.

🫶 Function/Subroutine Documentation 🫶

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

Okay so CLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ. Periodt 💅

🎀 Purpose: 🎀

Real talk: CLAQHB equilibrates an Hermitian band matrix A using the scaling factors in the vector S. That's the whole vibe ✨.

🌈 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. It's the order of the matrix A. N >= 0.
• KD — KD is INTEGER. It's 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 array, dimension (LDAB,N).
  • On entry, it's 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's 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. It's the leading dimension of the array AB. LDAB >= KD+1.
• S — S is REAL array, dimension (N). These are the scale factors for A.
• SCOND — SCOND is REAL. It's the ratio of the smallest S(i) to the largest S(i).
• AMAX — AMAX is REAL. It's the absolute value of the largest matrix entry.
• EQUED — EQUED is CHARACTER*1. It 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  • = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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 140 of file claqhb.f.

👑 Author (auto-generated cutie) 👑

Generated automatically by Doxygen for LAPACK from the source code.

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