SRC/sgeequb.f(3)

🌸 NAME 🌸

Okay bestie, this page is SRC/sgeequb.f(3) from the Library Functions Manual, and the name on the door is SRC/sgeequb.f 💖. It's the home of the sgeequb subroutine, and we're gonna get into every detail, no cap.

🦋 SYNOPSIS 🦋

🎀 Functions/Subroutines 🎀

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

💅 Function/Subroutine Documentation 💅

subroutine sgeequb (integer m, integer n, real, dimension( lda, * ) a,
    integer lda, real, dimension( * ) r, real, dimension( * ) c, real
    rowcnd, real colcnd, real amax, integer info)
    SGEEQUB

✨ Purpose ✨

SGEEQUB 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 SGEEQU 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 REAL 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 144 of file sgeequb.f.

📜 Author 📜

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okay bestie, that's the tea ☕ — footer check: LAPACK Version 3.12.0 and source SRC/sgeequb.f(3), stay scaled and slay 💅✨