SRC/cheequb.f(3)

📦
version 3.12.1 · 7 versions
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🌸 NAME 🌸

okay bestie, this is the Library Functions Manual page for SRC/cheequb.f, and the header calls it SRC/cheequb.f(3). The whole page is about CHEEQUB, and the docs are lowkey iconic. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

  • subroutine cheequb (uplo, n, a, lda, s, scond, amax, work, info) — CHEEQUB. That's the subroutine, front and center. 🫶

💖 Function/Subroutine Documentation 💖

🧚 subroutine cheequb

   subroutine cheequb (character uplo, integer n, complex, dimension( lda, * )
       a, integer lda, real, dimension( * ) s, real scond, real amax, complex,
       dimension( * ) work, integer info)

CHEEQUB — yes, that's the name in all caps, and it's giving main character energy. 👑

🎀 Purpose:

okay so CHEEQUB computes row and column scalings intended to equilibrate a Hermitian matrix A (with respect to the Euclidean norm) and reduce its condition number. The scale factors S are computed by the BIN algorithm (see references) so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of the smallest possible condition number over all possible diagonal scalings. That's the whole glow-up: matrix equilibration, no cap. Slay. ✨🔥

🎀 Parameters

okay here's the full parameter lineup, no skips, no missing parameters:

  • UPLO — UPLO is CHARACTER*1
    • = 'U': Upper triangle of A is stored;
    • = 'L': Lower triangle of A is stored.
  • N — N is INTEGER; the order of the matrix A. N >= 0.
  • A — A is COMPLEX array, dimension (LDA,N); the N-by-N Hermitian matrix whose scaling factors are to be computed.
  • LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,N).
  • S — S is REAL array, dimension (N); if INFO = 0, S contains the scale factors for A.
  • SCOND — SCOND is 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 — AMAX is REAL; largest absolute value of any matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.
  • WORK — WORK is COMPLEX array, dimension (2*N).
  • 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.

🎀 References:

🎀 Definition at line 131 of file cheequb.f.

🦋 Author 🦋

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okay bye bestie! the footer signs off with LAPACK Version 3.12.0 and SRC/cheequb.f(3) — that's the source/version energy, no separate date line, and this page is officially over. iykyk 💖✨🌈💜

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