SRC/zgeequb.f(3)

💅 SRC/zgeequb.f 💅

okay so bestie, this is the SRC/zgeequb.f page from the Library Functions Manual. We're doing ZGEEQUB today — matrix equilibration, scaling factors, the whole vibe. 🦋✨

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🌸 NAME 🌸

SRC/zgeequb.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine zgeequb (m, n, a, lda, r, c, rowcnd, colcnd, amax, info) — ZGEEQUB

🦋 Function/Subroutine Documentation 🦋

Full signature, no cap, character-for-character:

subroutine zgeequb (integer m, integer n, complex*16, dimension( lda, * ) a,
       integer lda, double precision, dimension( * ) r, double precision,
       dimension( * ) c, double precision rowcnd, double precision colcnd,
       double precision amax, integer info)

ZGEEQUB

💖 Purpose 💖

Okay so ZGEEQUB computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number. R returns the row scale factors and C the column scale factors, chosen to try to make the largest element in each row and column of the matrix B with elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most the radix. ✨

R(i) and C(j) are restricted to be a power of the radix between SMLNUM = smallest safe number and BIGNUM = largest safe number. Use of these scaling factors is not guaranteed to reduce the condition number of A but works well in practice.

This routine differs from ZGEEQU by restricting the scaling factors to a power of the radix. Barring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled entries' magnitudes are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix). 💅

🎀 Parameters 🎀

M

M is INTEGER. It's the number of rows of the matrix A. Constraint: M >= 0.

N

N is INTEGER. It's the number of columns of the matrix A. Constraint: N >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N). The M-by-N matrix whose equilibration factors are to be computed.

LDA

LDA is INTEGER. The leading dimension of the array A. Constraint: LDA >= max(1,M).

R

R is DOUBLE PRECISION array, dimension (M). If INFO = 0 or INFO > M, R contains the row scale factors for A.

C

C is DOUBLE PRECISION array, dimension (N). If INFO = 0, C contains the column scale factors for A.

ROWCND

ROWCND is DOUBLE PRECISION. If INFO = 0 or INFO > M, ROWCND contains the ratio of the smallest R(i) to the largest R(i). If ROWCND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by R.

COLCND

COLCND is DOUBLE PRECISION. If INFO = 0, COLCND contains the ratio of the smallest C(i) to the largest C(i). If COLCND >= 0.1, it is not worth scaling by C.

AMAX

AMAX is DOUBLE PRECISION. Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.

INFO

INFO is INTEGER.

• = 0: successful exit
• < 0: if INFO = -i, the i-th argument had an illegal value
• > 0: if INFO = i, and i is
  • <= M: the i-th row of A is exactly zero
  • > M: the (i-M)-th column of A is exactly zero

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 145 of file zgeequb.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Source/version vibes: LAPACK Version 3.12.0, page SRC/zgeequb.f(3) — that's the footer, bestie. 💖🎀✨