ZPOEQU(3)

ZPOEQU(3) 💖

okay so bestie, welcome to ZPOEQU(3) from the Library Functions Manual ✨ header file tag: /home/abui...RC/zpoequ.f(3). She’s a LAPACK subroutine with main character energy, and her whole vibe is computing scalings so a Hermitian positive definite matrix behaves. No cap.

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✨ NAME ✨

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

literally the source file for this subroutine, periodt 💅

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines

subroutine ZPOEQU (n, a, lda, s, scond, amax, info)

ZPOEQU

🦋 Function/Subroutine Documentation 🦋

subroutine ZPOEQU (integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, integer info)

ZPOEQU

💜 Purpose 💜

Okay so ZPOEQU computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings. It’s giving “make the diagonal all ones and keep the condition number from spiraling,” and honestly? iconic 🔥

🎀 Parameters 🎀

🍓 N

N is INTEGER — the order of the matrix A. N >= 0. ✨

🍓 A

A is COMPLEX*16 array, dimension (LDA,N) — the N-by-N Hermitian positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced. 👑

🍓 LDA

LDA is INTEGER — the leading dimension of the array A. LDA >= max(1,N). 💅

🍓 S

S is DOUBLE PRECISION array, dimension (N) — if INFO = 0, S contains the scale factors for A. 🫶

🍓 SCOND

SCOND is DOUBLE PRECISION — if INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S. 🌸

🍓 AMAX

AMAX is DOUBLE PRECISION — absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled. 😭

🍓 INFO

INFO is INTEGER

= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, the i-th diagonal element is nonpositive.

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 112 of file zpoequ.f.

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code.

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source/version sign-off, bestie: LAPACK Version 3.12.0, file tag /home/abui...RC/zpoequ.f(3). Date? The footer didn’t show one, so I’m not inventing one — no cap, facts only 🫶💅