SRC/sla_lin_berr.f(3)

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version 3.12.1 · 4 versions
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💖 SRC/sla_lin_berr.f(3) 💖

okay so this is the Library Functions Manual page for LAPACK, bestie — yes, the whole thing is about one little subroutine and it’s lowkey iconic. Let’s get into it. ✨

🌸 NAME 🌸

  • SRC/sla_lin_berr.f — the source file for this page. That’s the whole name section, no cap.

🦋 SYNOPSIS 🦋

Functions/Subroutines

  • subroutine sla_lin_berr (n, nz, nrhs, res, ayb, berr) — SLA_LIN_BERR computes a component-wise relative backward error. 💅

🎀 Function/Subroutine Documentation 🎀

🫶 subroutine sla_lin_berr

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

SLA_LIN_BERR computes a component-wise relative backward error. Periodt. 💖

✨ Purpose ✨

Okay so the formula is literally this:

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. 🧚

🍓 Parameters 🍓

  • N — INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0. 💖
  • NZ — INTEGER. We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to guard against spuriously zero residuals. Default value is N. 🛡️
  • NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrices AYB, RES, and BERR. NRHS >= 0. ✨
  • RES — REAL array, dimension (N,NRHS). The residual matrix, i.e., the matrix R in the relative backward error formula above. 📉
  • AYB — 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 sla_gerfsx_extended.f). 🔥
  • BERR — REAL array, dimension (NRHS). The componentwise relative backward error from the formula above. 👑

👑 Author 👑

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

Definition at line 100 of file sla_lin_berr.f. 📍

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. So yeah, not a human wrote this page — it’s the Doxygen machine. 💀

💖 That’s a wrap, bestie — this page comes from the LAPACK manual, version 3.12.0, and the source is SRC/sla_lin_berr.f(3). The footer doesn’t give a date in this copy, so no invented date from me. Bye! 💅✨

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