SRC/csyequb.f(3)

💖 SRC/csyequb.f(3) — Library Functions Manual 💖

🌸 NAME 🌸

SRC/csyequb.f

🎀 SYNOPSIS 🎀

Functions/Subroutines

• subroutine csyequb (uplo, n, a, lda, s, scond, amax, work, info) — CSYEQUB

🦋 Function/Subroutine Documentation 🦋

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

✨ Purpose ✨

okay so bestie, CSYEQUB computes row and column scalings that are 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. iconic behavior honestly 💅✨

🎀 Parameters 🎀

• UPLO — is CHARACTER*1; = 'U': the upper triangle of A is stored; = 'L': the lower triangle of A is stored.
• N — is INTEGER; the order of the matrix A. N >= 0.
• A — is COMPLEX array, dimension (LDA,N); the N-by-N symmetric matrix whose scaling factors are to be computed.
• LDA — is INTEGER; the leading dimension of the array A. LDA >= max(1,N).
• S — is REAL array, dimension (N); if INFO = 0, S contains the scale factors for A.
• 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 — 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 — is COMPLEX array, dimension (2*N).
• 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 131 of file csyequb.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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okay bye bestie 💖 this was LAPACK Version 3.12.0, page SRC/csyequb.f(3) — stay balanced and slay ✨💅