SRC/cheequb.f(3)

🌸 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:

• Livne, O.E. and Golub, G.H., "Scaling by Binormalization", Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
• DOI 10.1023/B:NUMA.0000016606.32820.69
• Tech report version:
  • http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

🎀 Definition at line 131 of file cheequb.f.

🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code.

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