SRC/dsyequb.f(3)

💖 NAME 💖

SRC/dsyequb.f — from the Library Functions Manual, bestie. That's the whole name, no notes, periodt.

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine dsyequb (uplo, n, a, lda, s, scond, amax, work, info)

DSYEQUB

DSYEQUB — the main character of this page, no cap.

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🫶 Function/Subroutine Documentation 🫶

subroutine dsyequb (character uplo, integer n, double precision, dimension(
    lda, * ) a, integer lda, double precision, dimension( * ) s, double
    precision scond, double precision amax, double precision, dimension( * )
    work, integer info)

DSYEQUB

🎯 Purpose

Okay so DSYEQUB computes row and column scalings intended to equilibrate a symmetric matrix A — with respect to the Euclidean norm — and reduce its condition number.

The scale factors S are computed by the BIN algorithm (see the 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, fr fr.

🎀 Parameters

• UPLO — CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — INTEGER
  • The order of the matrix A. N >= 0.
• A — DOUBLE PRECISION array, dimension (LDA,N)
  • The N-by-N symmetric matrix whose scaling factors are to be computed.
• LDA — INTEGER
  • The leading dimension of the array A. LDA >= max(1,N).
• S — DOUBLE PRECISION array, dimension (N)
  • If INFO = 0, S contains the scale factors for A.
• SCOND — 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 — DOUBLE PRECISION
  • 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 — DOUBLE PRECISION array, dimension (2*N)
• 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.

📚 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 130 of file dsyequb.f.

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🦋 Author

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That's the whole page, bestie — footer vibe check: LAPACK Version 3.12.0 and SRC/dsyequb.f(3). 💅✨