SRC/sgerfs.f(3)

hey bestie 💖 welcome to SRC/sgerfs.f(3) — that’s the page title, and it lives in the Library Functions Manual. no cap, this one is a Fortran subroutine situation, so grab a lil snack and let’s get into it ✨

🎀 NAME 🎀

SRC/sgerfs.f — that’s the whole name, iconic and to the point 💅

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

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

SGERFS is the name, and yes it’s giving main-character linear algebra 😌

🦋 Function/Subroutine Documentation 🦋

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

💖 Purpose 💖

SGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. literally its whole job 🫶

🌸 Parameters 🌸

• TRANS — TRANS is CHARACTER*1. It specifies the form of the system of equations:
  • = '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 REAL 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 REAL array, dimension (LDAF,N). The factors L and U from the factorization A = P*L*U as computed by SGETRF.
• 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 SGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
• B — B is REAL 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 REAL array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by SGETRS. 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 REAL 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 REAL 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 REAL array, dimension (3*N).
• IWORK — IWORK is INTEGER array, dimension (N).
• INFO — INFO is INTEGER:
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

🔥 Internal Parameters 🔥

• ITMAX — 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 📍

Definition at line 183 of file sgerfs.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page bestie — the footer says SRC/sgerfs.f(3) and LAPACK Version 3.12.0. mwah 💋✨