CGEEQU(3)

💅 CGEEQU(3) — Library Functions Manual 💅

okay bestie, welcome to CGEEQU(3) from the Library Functions Manual. The page header path is /home/abui...RC/cgeequ.f(3) — yep, it’s giving “I appear on both sides of the header,” lowkey iconic. Let’s get into it. 🫶

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🎀 NAME 🎀

The name on this page is literally this path:

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

No cap, that’s the whole NAME section. 💖

🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

    subroutine CGEEQU (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)
        CGEEQU

🌈 Function/Subroutine Documentation 🌈

   subroutine CGEEQU (integer m, integer n, complex, dimension( lda, * ) a,
       integer lda, real, dimension( * ) r, real, dimension( * ) c, real
       rowcnd, real colcnd, real amax, integer info)
       CGEEQU

💖 Purpose 💖

okay so CGEEQU computes row and column scalings that are 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 — where the elements are 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. 💅

⚠️ caveat alert: the scaling is not guaranteed to reduce the condition number of A, but it works well in practice. fr fr.

🌸 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.
• A — A is COMPLEX array, dimension (LDA,N). The M-by-N matrix whose equilibration factors are to be computed.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= 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 138 of file cgeequ.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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💖 That’s the whole page, bestie 💖 — the footer says LAPACK Version 3.12.0 and /home/abui...RC/cgeequ.f(3). No date on this footer, just so you know. 🫶