SRC/slacn2.f(3)

💅 SRC/slacn2.f 💅

okay so welcome to the Library Functions Manual page for SRC/slacn2.f(3) — yes bestie, we're deep in LAPACK territory and this subroutine is lowkey iconic. It estimates the 1-norm of a square real matrix using reverse communication for matrix-vector products, and it's giving "you do the matvec, I'll handle the norm estimate" energy. 🫶✨

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💖 NAME 💖

SRC/slacn2.f — that's the file, bestie. It's the home of slacn2, and the whole page is about that subroutine. 🎀

🌈 SYNOPSIS 🌈

🦋 Functions/Subroutines 🦋

subroutine slacn2 (n, v, x, isgn, est, kase, isave)

SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products. No cap. 💫

🔥 Function/Subroutine Documentation 🔥

subroutine slacn2 (integer n, real, dimension( * ) v, real, dimension( * )
    x, integer, dimension( * ) isgn, real est, integer kase, integer,
    dimension( 3 ) isave)

SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products. That's the whole vibe, and honestly it ate. 👑

🎯 Purpose 🎯

SLACN2 estimates the 1-norm of a square, real matrix A. Reverse communication is used for evaluating matrix-vector products. Periodt. 💅

🌸 Parameters 🌸

• N — INTEGER. The order of the matrix. N >= 1. So yes, there's at least one row and one column, bestie. 🍓
• V — REAL array, dimension (N). On the final return, V = A*W, where EST = norm(V)/norm(W) (W is not returned). It's giving "I saw W but I'm not handing it over." 🙈
• X — REAL array, dimension (N). On an intermediate return, X should be overwritten by:
  • A * X, if KASE=1,
  • A**T * X, if KASE=2,

and SLACN2 must be re-called with all the other parameters unchanged. Do not freestyle with the other params, okay? 😭

• ISGN — INTEGER array, dimension (N). That's it, that's the whole note. 💀
• EST — REAL. On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be unchanged from the previous call to SLACN2. On exit, EST is an estimate (a lower bound) for norm(A). It's a lower bound, so don't @ me. ✨
• KASE — INTEGER. On the initial call to SLACN2, 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 SLACN2, KASE will again be 0. The full circle moment. 🔄
• ISAVE — INTEGER array, dimension (3). ISAVE is used to save variables between calls to SLACN2. It's the little memory keeper. 🧚

👑 Author 👑

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

🔥 Further Details 🔥

Originally named SONEST, dated March 16, 1988. So yes, this icon has been serving since the 80s. 💜

This is a thread safe version of SLACON, which uses the array ISAVE in place of a SAVE statement, as follows:

SLACON     SLACN2
 JUMP     ISAVE(1)
 J        ISAVE(2)
 ITER     ISAVE(3)

🍓 Contributors 🍓

Nick Higham, University of Manchester. We stan. 🫶

🌈 References 🌈

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

Definition at line 135 of file slacn2.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. It's the meta author, bestie. 🤖💅

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okay bye bestie — this page is from LAPACK Version 3.12.0, and the file is SRC/slacn2.f(3). mwah 💋✨