DGBRFS(3)

💅 DGBRFS(3) — dgbrfs.f 💅

okay bestie, welcome to the dgbrfs.f(3) page from the Library Functions Manual ✨ this is the whole vibe, and yes, we're keeping every single detail.

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgbrfs.f — literally the file this page is about, no cap 🫶

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✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

subroutine DGBRFS (trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv,
    b, ldb, x, ldx, ferr, berr, work, iwork, info)
    DGBRFS

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🦋 Function/Subroutine Documentation 🦋

subroutine DGBRFS (...)

subroutine DGBRFS (character trans, integer n, integer kl, integer ku,
    integer nrhs, double precision, dimension( ldab, * ) ab, integer ldab,
    double precision, dimension( ldafb, * ) afb, integer ldafb, 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)
    DGBRFS

🎯 Purpose 🎯

okay so DGBRFS improves the computed solution to a system of linear equations when the coefficient matrix is banded, and it provides error bounds and backward error estimates for the solution. that's the whole main character job, periodt 💅

💖 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.
• KL — KL is INTEGER; the number of subdiagonals within the band of A. KL >= 0.
• KU — KU is INTEGER; the number of superdiagonals within the band of A. KU >= 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.
• AB — AB is DOUBLE PRECISION array, dimension (LDAB,N); the original band matrix A, stored in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows:

AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

• LDAB — LDAB is INTEGER; the leading dimension of the array AB. LDAB >= KL+KU+1.
• AFB — AFB is DOUBLE PRECISION array, dimension (LDAFB,N); details of the LU factorization of the band matrix A, as computed by DGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
• LDAFB — LDAFB is INTEGER; the leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.
• IPIV — IPIV is INTEGER array, dimension (N); the pivot indices from DGBTRF; 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 DGBTRS. 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

= 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. that's the internal bestie doing the loop-counting 💫

👑 Author 👑

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

🎀 Definition at line 202 of file dgbrfs.f. 🎀

literally line 202, bestie, right there in dgbrfs.f 📍

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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