SRC/zgeequ.f(3)

okay bestie, welcome to SRC/zgeequ.f(3) from the Library Functions Manual — this is the ZGEEQU subroutine page, and it’s giving matrix-equilibration main character energy. 💅✨

💖 NAME 💖

SRC/zgeequ.f — yes, that’s the name, no cap. 🎀

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✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

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

short version: one subroutine, zgeequ, doing its little scaling thing. 🦋

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👑 Function/Subroutine Documentation 👑

here’s the full signature, character-for-character, because we do not play with code:

subroutine zgeequ (integer m, integer n, complex*16, dimension( lda, * ) a,
    integer lda, double precision, dimension( * ) r, double precision,
    dimension( * ) c, double precision rowcnd, double precision colcnd,
    double precision amax, integer info)
    ZGEEQU

🎯 Purpose 🎯

okay so ZGEEQU 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 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 works well in practice. 🫶

🔥 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*16 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 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 138 of file zgeequ.f.

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code.

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LAPACK Version 3.12.0 — and the footer points at SRC/zgeequ.f(3). that’s the source/version and page info, bestie; no extra date in this footer, so I’m not inventing one. periodt. 💖✨