SRC/zlaqsy.f(3)

🌸 NAME 🌸

SRC/zlaqsy.f — bestie, this page lives in the Library Functions Manual, (3) section, and it’s all about zlaqsy. Linear algebra but make it main character energy 💅✨.

✨ SYNOPSIS ✨

Functions/Subroutines

• zlaqsy — ZLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.

subroutine zlaqsy (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)

🛠️ Function/Subroutine Documentation 🛠️

zlaqsy scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ — no cap, that’s literally the whole vibe ✨.

subroutine zlaqsy (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)

🎯 Purpose

ZLAQSY equilibrates a symmetric matrix A using the scaling factors in the vector S. Periodt 💖.

🧸 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.
• A — A is COMPLEX*16 array, dimension (LDA,N). On entry, it’s the symmetric 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 is: diag(S) * A * diag(S).

• LDA — LDA is INTEGER. It’s the leading dimension of the array A. LDA >= max(N,1).
• S — S is DOUBLE PRECISION array, dimension (N). These are the scale factors for A.
• SCOND — SCOND is DOUBLE PRECISION. It’s the ratio of the smallest S(i) to the largest S(i).
• AMAX — AMAX is DOUBLE PRECISION. 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 'N' = No equilibration; 'Y' = Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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 133 of file zlaqsy.f.

🫶 Author

Generated automatically by Doxygen for LAPACK from the source code.

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💖 Okay bestie, that’s the tea: source/version is LAPACK Version 3.12.0, file SRC/zlaqsy.f(3). Go forth and equilibrate responsibly 😭✨🦋