SRC/cgeequ.f(3)

okay so this page is SRC/cgeequ.f(3) from the Library Functions Manual, and it's your bestie-approved guide to the cgeequ subroutine. it's giving “linear algebra but make it make sense” 💅✨

NAME 🎀

SRC/cgeequ.f — the page for cgeequ, the subroutine that computes row and column equilibration scale factors.

SYNOPSIS 🌸

Functions/Subroutines 🦋

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

Function/Subroutine Documentation 💖

Full signature, exactly as written:

   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 💫

CGEEQU 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 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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mwah 💖 this page is from LAPACK Version 3.12.0, and its source is SRC/cgeequ.f(3) — the footer didn’t give us a date, so we’re not inventing one 🫶✨