SRC/sgbequ.f(3)

💅 SRC/sgbequ.f ✨

okay bestie, buckle up, because this one is a LAPACK subroutine page and we're gonna make it make sense 🫶

🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine sgbequ (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info) — the whole vibe, one line. this is SGBEQU 💖

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🦋 Function/Subroutine Documentation 🦋

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

this is SGBEQU, no cap 👑

⭐ Purpose

!> !> SGBEQU computes row and column scalings intended to equilibrate an !> M-by-N band 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 absolute value 1. !> !> R(i) and C(j) are restricted to be 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. !>

so like, it takes your band matrix A and tries to make everything chill by scaling rows and columns so the biggest element in each row/col of B (where B(i,j)=R(i)*A(i,j)*C(j), iykyk) has absolute value 1. the scale factors R(i) and C(j) get clamped between SMLNUM (smallest safe number) and BIGNUM (largest safe number). and ngl, it's not guaranteed to reduce the condition number — it just works well in practice. it's giving "trust me bro, empirically" 💀

🎀 Parameters

• M — M is INTEGER. the number of rows of the matrix A, and M >= 0. fr fr, no negative rows bestie.
• N — N is INTEGER. the number of columns of the matrix A, and N >= 0. same energy 💅
• KL — KL is INTEGER. the number of subdiagonals within the band of A, and KL >= 0.
• KU — KU is INTEGER. the number of superdiagonals within the band of A, and KU >= 0.
• AB — AB is REAL array, dimension (LDAB,N). this is the band matrix A, stored in rows 1 to KL+KU+1. the j-th column of A lives in the j-th column of the array AB, like this:

AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).

iconic indexing, honestly 🌈

• LDAB — LDAB is INTEGER. the leading dimension of the array AB, and LDAB >= KL+KU+1. don't skimp on it 🙈
• R — R is REAL array, dimension (M). if INFO = 0, or INFO > M, then R contains the row scale factors for A. 💖
• C — C is REAL array, dimension (N). if INFO = 0, then C contains the column scale factors for A.
• ROWCND — ROWCND is REAL. if INFO = 0 or INFO > M, then ROWCND contains the ratio of the smallest R(i) to the largest R(i). and if ROWCND >= 0.1 and AMAX is neither too large nor too small, then it's literally not worth scaling by R. skip it ✨
• COLCND — COLCND is REAL. if INFO = 0, then COLCND contains the ratio of the smallest C(i) to the largest C(i). if COLCND >= 0.1, it's not worth scaling by C. periodt.
• AMAX — AMAX is 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. like, that's your sign 🚨
• INFO — INFO is INTEGER, and it's the vibe check:
  • = 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 151 of file sgbequ.f.

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💜 Author (the meta one)

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page bestie, you ate that 🍓✨ this cutie was brought to you by LAPACK, Version 3.12.0, dated SRC/sgbequ.f(3) — mwah, go scale some matrices responsibly 🧚💖