ZLAQHB(3)

💖 ZLAQHB(3) — Library Functions Manual 💖

okay so bestie, this page is from the Library Functions Manual, header path /home/abui...RC/zlaqhb.f(3). It’s giving LAPACK, it’s giving Hermitian band matrix scaling, and every single arg is about to get its moment. no cap, let’s go 💅

💖 NAME 💖

literally just this file path, bestie:

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

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

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

ZLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ. periodt.

🎀 Function/Subroutine Documentation 🎀

   subroutine ZLAQHB (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)

same energy, bigger signature: ZLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ.

🦋 Purpose: 🦋

ZLAQHB equilibrates a Hermitian band matrix A using the scaling factors in the vector S. that’s the whole purpose, and it ate. 💜

🌸 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 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.

• 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 — 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 — 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 zlaqhb.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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💖 Signing off from LAPACK Version 3.12.0, page path /home/abui...RC/zlaqhb.f(3). The page doesn’t print an explicit date, so we’re just gonna note that and vibe; it’s auto-generated by Doxygen for LAPACK from the source code. Bye bestie! 🫶