SRC/spoequ.f(3)

🦋 SRC/spoequ.f 🦋

okay bestie, welcome to the SRC/spoequ.f(3) page from the Library Functions Manual — the main-character file here is literally SRC/spoequ.f, and it's all about the spoequ subroutine 💅✨

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✨ NAME ✨

SRC/spoequ.f

that's the file, periodt 🫶

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine spoequ (n, a, lda, s, scond, amax, info)
    SPOEQU

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👑 Function/Subroutine Documentation 👑

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

SPOEQU — iconic, no cap 💜

🦋 Purpose 🦋

okay so SPOEQU 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. obsessed 💖

🌈 Parameters 🌈

N

N is INTEGER. It's the order of the matrix A. N >= 0. 🎀

A

A is REAL array, dimension (LDA,N). It's the N-by-N symmetric positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced, bestie 👀.

LDA

LDA is INTEGER. It's 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. slay ✨

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. iykyk 🦋

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. important vibe check ⚠️

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 111 of file spoequ.f. 📌

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🫶 Author 🫶

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

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that's the whole tea, bestie — cute sign-off from LAPACK Version 3.12.0, source SRC/spoequ.f(3) 🌈💅🫶