/home/abui.../dgeequb.f(3)

💅 NAME 💅

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgeequb.f

okay so bestie, this is the manual page for that file — it's a LAPACK source file, and the actual star of the show is a Fortran subroutine called DGEEQUB. she balances matrices. she's iconic. let's get into it 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine DGEEQUB (m, n, a, lda, r, c, rowcnd, colcnd, amax, info) — the whole function, one line, she's neat like that 🫶

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🌸 Function/Subroutine Documentation 🌸

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

yep, that's her full signature, no cap 💜

Purpose:

!>
!> DGEEQUB 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 DGEEQU 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).
!>

so like — she computes row and column scalings to equilibrate an M-by-N matrix A and reduce its condition number 🔥. R gives you the row scale factors, C gives you the column scale factors, and the goal is making the biggest element in each row and column of the matrix B (where 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 locked to being a power of the radix between SMLNUM = smallest safe number and BIGNUM = largest safe number. And real talk: using these scaling factors is not guaranteed to reduce the condition number of A, but it works well in practice 😌.

The way she differs from DGEEQU? she restricts the scaling factors to a power of the radix. Barring over- and underflow, scaling by these factors introduces no additional rounding errors. But heads up — the scaled entries' magnitudes are no longer approximately 1, they lie between sqrt(radix) and 1/sqrt(radix). it's giving "trade-off, but make it precise" ✨

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🌈 Parameters 🌈

M

!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.
!>

integer, it's the number of rows of A, and M >= 0 — no negative rows, we don't do that here 🙈

N

!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!>

integer, the number of columns of A, and N >= 0 obviously 💅

A

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          The M-by-N matrix whose equilibration factors are
!>          to be computed.
!>

double precision array, dimension (LDA,N) — the M-by-N matrix whose equilibration factors are to be computed. she's the whole reason we're here 👑

LDA

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

integer, the leading dimension of the array A, and LDA >= max(1,M). respect the leading dimension bestie 🧚

R

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

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.
!>

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.
!>

double precision. If INFO = 0 or INFO > M, ROWCND contains the ratio of the smallest R(i) to the largest R(i). And lowkey — if ROWCND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by R. save yourself the trouble 😌

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.
!>

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 — same energy, column edition 💅

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.
!>

double precision — absolute value of the largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled. like, actually do it 🔥

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
!>

integer, the vibe check:

• = 0 — successful exit, slay 💖
• < 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

zero rows and columns are real, and she will tell you about them 🫶

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👑 Author 👑

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

the whole collective, fr fr 🌟

🎀 Definition at line 144 of file dgeequb.f. 🎀

like, line 144, exactly — iykyk 💜

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⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. yes, a robot wrote the page, but the math is all hers 🤖✨

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that's the whole thing bestie, no skipped options, no invented lore, every single constraint preserved 💅

LAPACK · Version 3.12.0 · /home/abui.../dgeequb.f(3) — mwah, that's the sign-off 🍓💖