SRC/spoequb.f(3)

💖 SRC/spoequb.f 💖

okay bestie, welcome to the Library Functions Manual page for SRC/spoequb.f. this is a LAPACK Fortran routine and it's giving very “small file, serious math” energy. ✨

🌸 NAME 🌸

SRC/spoequb.f

that's the name, no notes 💅

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine spoequb (n, a, lda, s, scond, amax, info)
    SPOEQUB

💅 Function/Subroutine Documentation 💅

subroutine spoequb (integer n, real, dimension( lda, * ) a, integer lda,
    real, dimension( * ) s, real scond, real amax, integer info)

SPOEQUB

Purpose

SPOEQUB computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings.

This routine differs from SPOEQU 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 diagonal entries are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix).

Parameters

• N — N is INTEGER. The order of the matrix A. N >= 0.
• A — A is REAL array, dimension (LDA,N). The N-by-N symmetric positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• S — S is REAL array, dimension (N). If INFO = 0, S contains the scale factors for A.
• SCOND — SCOND is REAL. If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S. (the page literally says S in that ratio line, bestie — preserving it exactly 🙈)
• 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, the i-th diagonal element is nonpositive.

Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

📍 Definition at line 117 of file spoequb.f. 📍

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

---

okay that's the whole page, bestie — go equilibrate something cute 🫶💖

footer deets: LAPACK, Version 3.12.0, page SRC/spoequb.f(3). no date line to report 💅