CGBEQU(3)

💅 CGBEQU(3) — Library Functions Manual 💅

okay so this is the page for CGBEQU, bestie. Manual name: Library Functions Manual. Let’s get into it, no cap.

📛 NAME 📛

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

🌈 SYNOPSIS 🌈

🦋 Functions/Subroutines 🦋

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

🎀 Function/Subroutine Documentation 🎀

subroutine CGBEQU (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)
    CGBEQU

✨ Purpose ✨

okay so CGBEQU is literally out here computing row and column scalings that are intended to equilibrate an M-by-N band matrix A and reduce its condition number. R gives back the row scale factors and C gives back the column scale factors — they’re chosen trying 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. Using these scaling factors is not guaranteed to reduce the condition number of A, but it works well in practice. Periodt.

🌸 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). 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 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 152 of file cgbequ.f.

🧚 Author 🧚

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xoxo, LAPACK Version 3.12.0, from /home/abui...RC/cgbequ.f(3) — the footer has no date, bestie, so I’m not inventing one 💖✨