SRC/ssyequb.f(3)

🌸 SRC/ssyequb.f(3) 🌸

okay so bestie, welcome to the Library Functions Manual page for SRC/ssyequb.f — yes, that's the title, and we're folding the manual name right here like a lil name tag. 💖

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👑 NAME 👑

SRC/ssyequb.f

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine ssyequb (uplo, n, a, lda, s, scond, amax, work, info) — SSYEQUB

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🦋 Function/Subroutine Documentation 🦋

💅 subroutine ssyequb

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

SSYEQUB

🌟 Purpose

ok so SSYEQUB 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 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. 💅

🎀 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 REAL array, dimension (LDA,N)

The N-by-N symmetric 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 REAL 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

Definition at line 130 of file ssyequb.f.

🖋️ Author

Generated automatically by Doxygen for LAPACK from the source code.

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