SRC/cgeequb.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

💖 NAME 💖

okay so this page is from the Library Functions Manual and the name is literally SRC/cgeequb.f. bestie, it’s giving “subroutine documentation but make it cute.” 💅

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

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

🎀 Function/Subroutine Documentation 🎀

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

💅 Purpose 💅

okay so CGEEQUB 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 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 CGEEQU 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. 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 145 of file cgeequb.f.

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

okay that’s the whole thing, bestie. footer vibes: LAPACK Version 3.12.0, page SRC/cgeequb.f(3) — and there’s no date on that footer line, so we’re not making one up. bye 💅✨

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