la_lin_berr(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

💖 la_lin_berr(3) 💖

okay so bestie, grab your iced coffee, because we're about to get into la_lin_berr — that's the one in the Library Functions Manual and it's literally all about backward error. no cap. 🧚

✨ NAME ✨

la_lin_berr — la_lin_berr: backward error. that's it, that's the name, she's straightforward and she knows it 💅

🦋 SYNOPSIS 🦋

🌸 Functions 🌸

  • subroutine cla_lin_berr (n, nz, nrhs, res, ayb, berr) — CLA_LIN_BERR computes a component-wise relative backward error.
  • subroutine dla_lin_berr (n, nz, nrhs, res, ayb, berr) — DLA_LIN_BERR computes a component-wise relative backward error.
  • subroutine sla_lin_berr (n, nz, nrhs, res, ayb, berr) — SLA_LIN_BERR computes a component-wise relative backward error.
  • subroutine zla_lin_berr (n, nz, nrhs, res, ayb, berr) — ZLA_LIN_BERR computes a component-wise relative backward error.

like yes, they're four flavors of the exact same thing — that's the whole vibe check, it's the c/d/s/z quartet and they're all iconic in their own way 👑

🌈 Detailed Description 🌈

so the Detailed Description is just… "Function Documentation." that's the entire tea. she said "scroll down, bestie, the real content is in the subsections" 🫶

👑 Function 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.

💜 Purpose:

!>
!>    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.
!>

🎀 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 🌸

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

Definition at line 100 of file cla_lin_berr.f.

🔥 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:

!>
!>    DLA_LIN_BERR computes component-wise 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 component-wise absolute value of the 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 DOUBLE PRECISION 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 dla_gerfsx_extended.f).
  • BERR — BERR is DOUBLE PRECISION array, dimension (NRHS). the component-wise 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 dla_lin_berr.f.

⭐ 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.

💜 Purpose:

!>
!>    SLA_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.
!>

🎀 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 REAL 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 sla_gerfsx_extended.f).
  • BERR — BERR is 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.

🔥 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:

!>
!>    ZLA_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.
!>

🎀 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.

ok so quick heads up bestie: NZ is the one doing the quiet heavy lifting here 🫶 — that (NZ+1)*SLAMCH( 'Safe minimum' ) nudge to R(i) is literally there to guard against spuriously zero residuals, and its default value is N. don't sleep on it.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. (not me writing my own bio, the robots did it 🤖✨)

and that's the whole page, bestie!! 🎀 mwah 💋 — signed, sealed, and delivered straight from LAPACK, Version 3.12.0, on the la_lin_berr(3) page. slay. periodt. 🌈

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