SRC/zheequb.f(3)

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🎀 SRC/zheequb.f(3) — Library Functions Manual 🎀

💖 NAME 💖

SRC/zheequb.f — bestie, that's literally the file name. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

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

ZHEEQUB

🦋 Function/Subroutine Documentation 🦋

subroutine zheequb (character uplo, integer n, complex*16, dimension( lda, *
    ) a, integer lda, double precision, dimension( * ) s, double precision
    scond, double precision amax, complex*16, dimension( * ) work, integer
    info)

ZHEEQUB

🌸 Purpose 🌸

Okay so ZHEEQUB 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. No cap. 💅

💜 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*16 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 DOUBLE PRECISION array, dimension (N)

If INFO = 0, S contains the scale factors for A.

🍓 SCOND

SCOND is 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

AMAX is 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

WORK is COMPLEX*16 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 zheequb.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

Okay bestie, that's the whole vibe. This page is from LAPACK Version 3.12.0 and the source file is SRC/zheequb.f(3). Slay. 💖✨

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