DLA_LIN_BERR(3)

💅 DLA_LIN_BERR(3) 💅

okay so you opened the DLA_LIN_BERR(3) page from the Library Functions Manual — the title path is /home/abui..._lin_berr.f(3), and the source file behind it is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dla_lin_berr.f. literally LAPACK royalty, no cap. 👑

✨ NAME ✨

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

🦋 SYNOPSIS 🦋

Functions/Subroutines

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

🌸 Function/Subroutine Documentation 🌸

subroutine DLA_LIN_BERR (integer n, integer nz, integer nrhs, double precision, dimension( n, nrhs ) res, double precision, dimension( n, nrhs ) ayb, double precision, dimension( nrhs ) berr)

DLA_LIN_BERR computes a component-wise relative backward error.

🎀 Purpose 🎀

the formula is the whole main character, bestie:

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

and abs(Z) is the component-wise absolute value of the matrix or vector Z. periodt. 💅

🍓 Parameters 🍓

N

N is INTEGER. it's the number of linear equations, i.e., the order of the matrix A. constraint: N >= 0. slay. ✨

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. this is the little safety net, okay? 🫶

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 DOUBLE PRECISION array, dimension (N,NRHS). it's the residual matrix, i.e., the matrix R in the relative backward error formula above. the drama is in the residuals. 😭

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 dla_gerfsx_extended.f).

BERR

BERR is DOUBLE PRECISION array, dimension (NRHS). the component-wise relative backward error from the formula above. iconic output. 👑

🌈 Author 🌈

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

📌 Definition at line 100 of file dla_lin_berr.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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