SRC/cgbequb.f(3)

🎀 SRC/cgbequb.f 🎀

okay so bestie, this one is from the Library Functions Manual, and it’s the page for CGBEQUB. it’s giving “LAPACK subroutine that does careful scaling math” and we are keeping literally every detail, no cap 💅

✨ NAME ✨

SRC/cgbequb.f

🦋 SYNOPSIS 🦋

Functions/Subroutines

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

🌈 Function/Subroutine Documentation 🌈

💖 subroutine cgbequb — CGBEQUB 💖

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 returns 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. it’s giving precise, iykyk 🎯

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 it works well in practice. lowkey important caveat, bestie 🎀

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). iconic tradeoff, fr fr ✨

🍓 Parameters 🍓

M

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

N

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

KL

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

KU

KU is INTEGER. The number of superdiagonals within the band of A. 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)

LDAB

LDAB is INTEGER. The leading dimension of the array A. 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.

C

C is 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.

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.

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.

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 159 of file cgbequb.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie that’s the whole page! 💖 this cutie is LAPACK Version 3.12.0, source SRC/cgbequb.f(3) — and the footer didn’t include a date, so no fake date from me, just facts and a lil sparkle. periodt 🫶💅