DGERFS(3)

✨ DGERFS(3) — Library Functions Manual, but make it cute ✨

okay bestie, welcome to the glow-up of the DGERFS(3) page. This is the manual page for the file at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgerfs.f — yes, that whole path is the NAME. iconic, honestly. 🫶

💖 NAME 💖

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

That's it. That's the name. 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

the whole function/subroutine moment:

       subroutine DGERFS (trans, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x,
           ldx, ferr, berr, work, iwork, info)
           DGERFS

🦋 Function/Subroutine Documentation 🦋

subroutine DGERFS (...)

full signature, character-for-character, no cap:

   subroutine DGERFS (character trans, integer n, integer nrhs, double
       precision, dimension( lda, * ) a, integer lda, double precision,
       dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv,
       double precision, dimension( ldb, * ) b, integer ldb, double precision,
       dimension( ldx, * ) x, integer ldx, double precision, dimension( * )
       ferr, double precision, dimension( * ) berr, double precision,
       dimension( * ) work, integer, dimension( * ) iwork, integer info)
       DGERFS

Purpose: 💡

okay so the whole point: DGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. that's the mission. 🔥

Parameters 🎀

• TRANS — TRANS is CHARACTER*1. It specifies the form of the system of equations, and the options are:
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose = Transpose)
• N — N is INTEGER. The order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). The original N-by-N matrix A.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• AF — AF is DOUBLE PRECISION array, dimension (LDAF,N). The factors L and U from the factorization A = P*L*U as computed by DGETRF.
• LDAF — LDAF is INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).
• IPIV — IPIV is INTEGER array, dimension (N). The pivot indices from DGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
• B — B is DOUBLE PRECISION array, dimension (LDB,NRHS). The right hand side matrix B.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — X is DOUBLE PRECISION array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by DGETRS. On exit, the improved solution matrix X.
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• FERR — FERR is DOUBLE PRECISION array, dimension (NRHS). The estimated forward error bound for each solution vector X(j) (the j-th column of the solution matrix X). If XTRUE is the true solution corresponding to X(j), FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest element in X(j). The estimate is as reliable as the estimate for RCOND, and is almost always a slight overestimate of the true error.
• BERR — BERR is DOUBLE PRECISION array, dimension (NRHS). The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).
• WORK — WORK is DOUBLE PRECISION array, dimension (3*N).
• IWORK — IWORK is INTEGER array, dimension (N).
• INFO — INFO is INTEGER. Exit status tea:
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

Internal Parameters: 🧚

• ITMAX — is the maximum number of steps of iterative refinement.

Author 👑

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

Definition at line 183 of file dgerfs.f.

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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that's the whole page, bestie — every detail kept, all vibes upgraded. signed with love by LAPACK Version 3.12.0, with the footer path /home/abui...RC/dgerfs.f(3) 🫶💖✨