SRC/sgbequb.f(3)

💖 SRC/sgbequb.f — Library Functions Manual, bestie ✨

🌸 NAME 🌸

SRC/sgbequb.f

✨ SYNOPSIS ✨

🧸 Functions/Subroutines

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

SGBEQUB

🌟 Function/Subroutine Documentation 🌟

subroutine sgbequb (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)

SGBEQUB

🎯 Purpose

Okay so SGBEQUB 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.

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 SGEEQU 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).

🧾 Parameters

• M — M is INTEGER. The number of rows of the matrix A. The rule is M >= 0.
• N — N is INTEGER. The number of columns of the matrix A. The rule is N >= 0.
• KL — KL is INTEGER. The number of subdiagonals within the band of A. The rule is KL >= 0.
• KU — KU is INTEGER. The number of superdiagonals within the band of A. The rule is KU >= 0.
• AB — AB is REAL 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. The rule is 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 158 of file sgbequb.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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Mwah 💋 — the footer says LAPACK Version 3.12.0, and the source/version is SRC/sgbequb.f(3); no separate date is listed there, so that's the whole cute send-off. 🫶