/home/abui.../cgeequb.f(3)

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cgeequb.f — okay bestie, this is the cgeequb.f(3) page from the Library Functions Manual, and it is literally all about the CGEEQUB subroutine. 💅✨

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✨ SYNOPSIS ✨

💖 Functions/Subroutines 💖

• subroutine CGEEQUB (m, n, a, lda, r, c, rowcnd, colcnd, amax, info) — the one and only subroutine on this page.

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

CGEEQUB — yep, that's the name, no cap. 🫶

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🦋 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 — main character subroutine energy, honestly. 👑

💫 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. 💖

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🎀 and that's the sign-off, bestie: LAPACK Version 3.12.0, on this cgeequb.f(3) source page — periodt. 💅✨