SRC/dgeequb.f(3)

🌸 NAME 🌸

SRC/dgeequb.f(3) — okay bestie, this is the manual page for SRC/dgeequb.f, living its best life in the Library Functions Manual 💅✨

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

That’s the iconic DGEEQUB subroutine, showing up exactly like this:

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

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💖 Function/Subroutine Documentation 💖

🦋 The dgeequb subroutine 🦋

Full signature, no cap:

subroutine dgeequb (integer m, integer n, double precision, dimension( lda,
* ) a, integer lda, double precision, dimension( * ) r, double
precision, dimension( * ) c, double precision rowcnd, double precision
colcnd, double precision amax, integer info)

This is DGEEQUB, and the whole function is giving “let me balance your matrix so it behaves” energy 😌✨

🌈 Purpose 🌈

DGEEQUB 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 DGEEQU 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 DOUBLE PRECISION 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 144 of file dgeequb.f. 🦋

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code. 💖

Cute little sign-off bestie: this is LAPACK Version 3.12.0 energy, and that’s the whole page — mwah 💋✨🌸