DLACON(3)

💅 DLACON(3) — the reverse-communication 1-norm estimator ✨

okay so bestie, welcome to the Library Functions Manual corner of the group chat 💖. This page is for DLACON, and it’s giving “we estimate a 1-norm together via reverse communication” main-character energy. It’s not a solo mission — you and the subroutine keep passing X back and forth. Iconic. 🦋

🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlacon.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine DLACON (n, v, x, isgn, est, kase) — DLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

🌸 Function/Subroutine Documentation 🌸

Here’s the signature, copied exactly because we do not mess with the source, periodt:

subroutine DLACON (integer n, double precision, dimension( * ) v, double precision, dimension( * ) x, integer, dimension( * ) isgn, double precision est, integer kase)

DLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

🌈 Purpose 🌈

The source literally says:

!>
!> DLACON estimates the 1-norm of a square, real matrix A.
!> Reverse communication is used for evaluating matrix-vector products.
!>

So yeah: square, real matrix A, 1-norm estimation, and reverse communication for matrix-vector products. Slay. 💜

💖 Parameters 💖

• N — N is INTEGER; the order of the matrix. N >= 1. 👑
• V — V is DOUBLE PRECISION array, dimension (N). On the final return:

V = A*W,  where  EST = norm(V)/norm(W)
(W is not returned).

so W is lowkey not invited to the return party, but the formula is still iconic.

• X — X is DOUBLE PRECISION array, dimension (N). On an intermediate return, X should be overwritten by:

A * X,   if KASE=1,
A**T * X,  if KASE=2,

and DLACON must be re-called with all the other parameters unchanged. No cap — same parameters, bestie. 🫶

• ISGN — ISGN is INTEGER array, dimension (N). That’s the whole note; it’s giving mysterious side character. 🙈
• EST — EST is DOUBLE PRECISION. On entry with KASE = 1 or 2 and JUMP = 3, EST should be unchanged from the previous call to DLACON. On exit, EST is an estimate (a lower bound) for norm(A). Yes, JUMP appears in the note even though it’s not in the arg list — that’s literally what the page says. 💀
• KASE — KASE is INTEGER. On the initial call to DLACON, KASE should be 0. On an intermediate return, KASE will be 1 or 2, indicating whether X should be overwritten by A * X or A**T * X. On the final return from DLACON, KASE will again be 0. Full-circle moment. ⭐

👑 Author 👑

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

🫶 Contributors 🫶

• Nick Higham, University of Manchester.
• Originally named SONEST, dated March 16, 1988.

📚 References 📚

N.J. Higham, "FORTRAN codes for estimating the one-norm ofa real or complex matrix, with applications to condition estimation", ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.

(That ofa is exactly how it appears, bestie — we preserve the source’s quirks. 💅)

🧭 Definition at line 114 of file dlacon.f 🧭

Definition at line 114 of file dlacon.f.

🤖 Author (the Doxygen one) 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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💖 bye bestie! This page is LAPACK Version 3.12.0, source /home/abui...RC/dlacon.f(3). Stay slay, and remember: reverse communication is just a conversation with extra steps. ✨