SRC/claqhe.f(3)

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okay so this is the SRC/claqhe.f(3) page from the Library Functions Manual, and it's giving “tiny but important numeric glow-up” energy 💅✨

💖 NAME 💖

SRC/claqhe.f

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

  • subroutine claqhe (uplo, n, a, lda, s, scond, amax, equed) — CLAQHE scales a Hermitian matrix.

🌸 Function/Subroutine Documentation 🌸

🎀 the subroutine itself 🎀

subroutine claqhe (character uplo, integer n, complex, dimension( lda, * )
    a, integer lda, real, dimension( * ) s, real scond, real amax, character
    equed)

CLAQHE scales a Hermitian matrix. periodt 💅

🦋 Purpose 🦋

okay so CLAQHE equilibrates a Hermitian matrix A using the scaling factors in the vector S. that's the whole main-character job, no cap ✨

🍓 Parameters 🍓

💜 UPLO

UPLO is CHARACTER*1.

It specifies whether the upper or lower triangular part of the Hermitian matrix A is stored.

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

💜 N

N is INTEGER.

The order of the matrix A. N >= 0.

💜 A

A is COMPLEX array, dimension (LDA,N).

On entry, it's the Hermitian matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

On exit, if EQUED = 'Y', the equilibrated matrix:

diag(S) * A * diag(S)

💜 LDA

LDA is INTEGER.

The leading dimension of the array A. LDA >= max(N,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.

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  • = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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

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 133 of file claqhe.f.

👑 Author 👑

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