SRC/cla_lin_berr.f(3)

💅 NAME 💅

SRC/cla_lin_berr.f — bestie, this is the Fortran file that computes a component-wise relative backward error, and honestly? It's kind of the moment. ✨

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine cla_lin_berr (n, nz, nrhs, res, ayb, berr)

CLA_LIN_BERR computes a component-wise relative backward error. That's the whole vibe. 🎀

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🌸 Function/Subroutine Documentation 🌸

subroutine cla_lin_berr (integer n, integer nz, integer nrhs, complex,
    dimension( n, nrhs ) res, real, dimension( n, nrhs ) ayb, real,
    dimension( nrhs ) berr)

CLA_LIN_BERR computes a component-wise relative backward error. Say it with me now — component-wise relative backward error. Iconic. 👑

✨ Purpose ✨

Okay so here's the actual formula, and yes you're gonna want to screenshot this:

!>
!>    CLA_LIN_BERR computes componentwise relative backward error from
!>    the formula
!>        max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
!>    where abs(Z) is the componentwise absolute value of the matrix
!>    or vector Z.
!>

So abs(Z)? That's just the component-wise absolute value of the matrix or vector Z. Easy. No cap. 🧚

🫶 Parameters 🫶

• N — N is INTEGER. The number of linear equations, i.e., the order of the matrix A. And it's gotta be N >= 0, periodt.
• NZ — NZ is INTEGER. Lowkey the safety net of this whole operation: we add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to guard against spuriously zero residuals. Default value is N. 💖
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices AYB, RES, and BERR. Constraint: NRHS >= 0.
• RES — RES is COMPLEX array, dimension (N,NRHS). The residual matrix, i.e., the matrix R in the relative backward error formula above. Main character matrix, honestly. 🌟
• AYB — AYB is REAL array, dimension (N, NRHS). The denominator in the relative backward error formula above, i.e., the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B are from iterative refinement (see cla_gerfsx_extended.f). Iykyk. 🔥
• BERR — BERR is REAL array, dimension (NRHS). The componentwise relative backward error from the formula above. The final boss output. 💀✨

👑 Author 👑

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

Definition at line 100 of file cla_lin_berr.f.

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🌈 Author (again, but Doxygen this time) 🌈

Generated automatically by Doxygen for LAPACK from the source code. Not me, not you — Doxygen did that. 🙈

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Okay bestie, that's the whole page, every last flag and formula intact, no details dropped, we ate and left zero crumbs. 🍓

Stay safe out there, guard those spuriously zero residuals, and remember: only trust a backward error that's component-wise. 💅

✨ LAPACK, Version 3.12.0 · SRC/cla_lin_berr.f(3) · mwah, love u, bye ✨ 🎀🦋💜