DGBEQU(3)

DGBEQU(3) 💅

okay bestie, welcome to the Library Functions Manual page for DGBEQU(3). The header shows /home/abui...RC/dgbequ.f(3), and we are absolutely about to get into the whole band-matrix scaling situation. No cap.

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💖 NAME 💖

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

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✨ SYNOPSIS ✨

Functions/Subroutines

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

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🦋 Function/Subroutine Documentation 🦋

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

Purpose

okay so DGBEQU 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 it works well in practice. slay for practical vibes only.

Parameters

here's the whole cast, bestie — no skips:

• 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 DOUBLE PRECISION 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 at line 151 of file dgbequ.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the page, bestie 💜 Footer check: LAPACK Version 3.12.0 and /home/abui...RC/dgbequ.f(3) — there's no separate date printed in the footer, so that's the whole sign-off tea. bye! 🎀