ZGBEQU(3)

🎀 NAME 🎀

okay so bestie, this is ZGBEQU(3) from the Library Functions Manual — yes, the whole manual name is folded in right here. The file behind the curtain is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgbequ.f, and it's giving major LAPACK energy. 💅

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✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

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

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💖 Function/Subroutine Documentation 💖

🌟 subroutine ZGBEQU 🌟

subroutine ZGBEQU (integer m, integer n, integer kl, integer ku, complex*16,
    dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )
    r, double precision, dimension( * ) c, double precision rowcnd, double
    precision colcnd, double precision amax, integer info)
    ZGBEQU

🌸 Purpose 🌸

okay so ZGBEQU 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. slay. ✨

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.

bestie, lowkey important: the reduction is not guaranteed — it just works well in practice, no cap.

💫 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*16 array, dimension (LDAB,N). The band matrix A, stored 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(m,j+kl).
• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1.
• 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 📌

Definition at line 152 of file zgbequ.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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cute sign-off, bestie: this footer vibe is LAPACK, Version 3.12.0, plus the path /home/abui...RC/zgbequ.f(3). that's the whole footer tea. 🫶💖