CPOEQU(3)

📦 version 3.12.0, in opensuse-leap 16.0

🌸 CPOEQU(3) — Library Functions Manual 🌸

🎀 NAME 🎀

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

That’s the NAME situation, bestie — it’s literally just the path, and we respect it. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

  • subroutine CPOEQU (n, a, lda, s, scond, amax, info) — CPOEQU

💖 Function/Subroutine Documentation 💖

🌟 CPOEQU 🌟

subroutine CPOEQU (integer n, complex, dimension( lda, * ) a, integer lda,
       real, dimension( * ) s, real scond, real amax, integer info)

CPOEQU — yes, the name again, it’s giving main character energy. ✨

🎯 Purpose 🎯

Okay so CPOEQU 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). The scale factors live in S, and they’re 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. Slay. 💖

🧾 Parameters 🧾

  • N — INTEGER. The order of the matrix A. N >= 0.
  • A — COMPLEX 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • S — REAL array, dimension (N). If INFO = 0, S contains the scale factors for A.
  • SCOND — REAL. 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 — REAL. Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.
  • INFO — 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 cpoequ.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

LAPACK Version 3.12.0 — /home/abui...RC/cpoequ.f(3) ✨ (that’s the footer source/version, and no separate date is listed there, bestie). Periodt. 🫶💅

📦 where this page comes from