SRC/zla_lin_berr.f(3)

💖 SRC/zla_lin_berr.f(3) 💖

Okay bestie, welcome to the Library Functions Manual page for SRC/zla_lin_berr.f(3) — this is the zla_lin_berr subroutine and she is here to compute a component-wise relative backward error. No cap. ✨

✨ NAME ✨

SRC/zla_lin_berr.f

✨ SYNOPSIS ✨

Functions/Subroutines

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

🦋 Function/Subroutine Documentation 🦋

subroutine zla_lin_berr (integer n, integer nz, integer nrhs, complex*16, dimension( n, nrhs ) res, double precision, dimension( n, nrhs ) ayb, double precision, dimension( nrhs ) berr)

ZLA_LIN_BERR computes a component-wise relative backward error.

🎀 Purpose 🎀

So the whole point, bestie: ZLA_LIN_BERR computes componentwise relative backward error from this formula:

max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )

And abs(Z) is the componentwise absolute value of the matrix or vector Z. That’s the vibe. ✨

🌸 Parameters 🌸

• N — N is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
• NZ — NZ is 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 — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices AYB, RES, and BERR. NRHS >= 0.
• RES — RES is COMPLEX*16 array, dimension (N,NRHS). The residual matrix, i.e., the matrix R in the relative backward error formula above.
• AYB — AYB is DOUBLE PRECISION 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 zla_gerfsx_extended.f).
• BERR — BERR is DOUBLE PRECISION 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 zla_lin_berr.f.

👑 Author (Doxygen-generated) 👑

Generated automatically by Doxygen for LAPACK from the source code.

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xoxo bestie — signed off with LAPACK Version 3.12.0, source SRC/zla_lin_berr.f(3), and no date in the footer, so that’s the whole tea 💅🫶