CLA_LIN_BERR(3)

💖 CLA_LIN_BERR(3) 💖

okay bestie, welcome to CLA_LIN_BERR(3) from the Library Functions Manual. This is the group chat for a LAPACK subroutine that computes a component-wise relative backward error, and yes it's giving math-girlie main character energy. 🧮✨

🏷️ NAME 🏷️

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

That's the source file path, bestie. Keep it exactly like that. 🫶

📚 SYNOPSIS 📚

🧚 Functions/Subroutines 🧚

subroutine CLA_LIN_BERR (n, nz, nrhs, res, ayb, berr)
    CLA_LIN_BERR computes a component-wise relative backward error.

💅 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.

So like, this is the full signature, and the vibe is: it computes a component-wise relative backward error. No cap. 😌

🎯 Purpose 🎯

Here's the exact formula moment, preserved for the group chat:

!>
!>    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.
!>

Translation: it takes the max over i of abs(R(i)) divided by ( abs(op(A_s))*abs(Y) + abs(B_s) )(i), and abs(Z) means the componentwise absolute value of matrix or vector Z. 💖

🧮 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 array, dimension (N,NRHS). The residual matrix, i.e., the matrix R in the relative backward error formula above.
• 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).
• BERR — BERR is REAL array, dimension (NRHS). The componentwise relative backward error from the formula above.

👑 Author (routine edition) 👑

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

Definition at line 100 of file cla_lin_berr.f.

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code.

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Okay that's the page, bestie. Final footer vibe check: this is LAPACK Version 3.12.0, and the source path on the footer is /home/abui..._lin_berr.f(3). Slay, bye 💅💖