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

🎀 NAME 🎀

ok so bestie, this page is literally all about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cgbequb.f — yes that's the whole path as the name, she's extra like that 💅 (it's a LAPACK source file, from the Library Functions Manual section 3, iykyk).

---

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine CGBEQUB (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)
• CGBEQUB

---

🦋 Function/Subroutine Documentation 🦋

subroutine CGBEQUB (integer m, integer n, integer kl, integer ku, complex,
    dimension( ldab, * ) ab, integer ldab, real, dimension( * ) r, real,
    dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)

CGBEQUB

💖 Purpose:

!> !> CGBEQUB 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 CGEEQU 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). !>

okay so real talk, this routine's whole vibe is equilibration — she computes row and column scalings that try to make an M-by-N matrix A behave and bring its condition number down. R comes back with the row scale factors, C with the column ones, and they're picked so that the biggest element in each row/column of the matrix B — where B(i,j)=R(i)*A(i,j)*C(j) — has an absolute value of at most the radix ✨

And here's the tea: R(i) and C(j) are restricted to be a power of the radix, sitting between SMLNUM = smallest safe number and BIGNUM = largest safe number. Using these factors is not guaranteed to reduce the condition number of A, but in practice it works well 💅

Also she differs from CGEEQU by restricting the scaling factors to a power of the radix. Barring over- and underflow, scaling by these factors adds literally zero additional rounding errors. But (and this is the plot twist 😭) the scaled entries' magnitudes are no longer approximately 1 — they land between sqrt(radix) and 1/sqrt(radix).

---

🌸 Parameters 🌸

M

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

Number of rows in A, bestie. Requirement: M >= 0 🫶

N

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

Number of columns in A. Requirement: N >= 0 🫶

KL

!> KL is INTEGER !> The number of subdiagonals within the band of A. KL >= 0. !>

How many subdiagonals live inside the band of A. Requirement: KL >= 0 👑

KU

!> KU is INTEGER !> The number of superdiagonals within the band of A. KU >= 0. !>

How many superdiagonals live inside the band of A. Requirement: KU >= 0 👑

AB

!> AB is COMPLEX array, dimension (LDAB,N) !> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. !> The j-th column of A is stored in the j-th column of the !> array AB as follows: !> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) !>

AB is a COMPLEX array with dimension (LDAB,N). On entry it's the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A gets stored in the j-th column of the array AB, like this, fr fr:

AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)

LDAB

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

The leading dimension of the array A. Requirement: LDAB >= max(1,M) 🧚

R

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

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

C

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

REAL array, dimension (N). If INFO = 0, C contains the column scale factors for A 💖

ROWCND

!> ROWCND is REAL !> 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. !>

REAL. If INFO = 0 or INFO > M, ROWCND holds the ratio of the smallest R(i) to the largest R(i). And heads up: if ROWCND >= 0.1 and AMAX is neither too large nor too small, it's not worth scaling by R — so like, don't bother 🙈

COLCND

!> COLCND is REAL !> 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. !>

REAL. If INFO = 0, COLCND holds the ratio of the smallest C(i) to the largest C(i). If COLCND >= 0.1, it's not worth scaling by C 🙈

AMAX

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

REAL. Absolute value of the largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled — that's not a drill ⚠️

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, and she's the whole mood report:

• = 0: successful exit, we ate 🎉
• < 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 159 of file cgbequb.f.

---

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. (not her writing it herself, she's a bot bestie, iconic behavior honestly 🤖💅)

---

LAPACK — Version 3.12.0 🦋 and this icon is literally /home/abui.../cgbequb.f(3), mwah, go equilibrate something, ily, bye 💖🎀✨