ZGTRFS(3)

💖 zgtrfs.f(3) 💖

Okay bestie, welcome to the Library Functions Manual entry for zgtrfs.f(3). This one is a Fortran situation, and yes, we’re keeping every single detail — no cap.

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🌸 NAME 🌸

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

That’s the whole NAME section. It’s literally giving “the file path is the moment.” 💅

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine ZGTRFS (trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv,
    b, ldb, x, ldx, ferr, berr, work, rwork, info)
    ZGTRFS

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🦋 Function/Subroutine Documentation 🦋

subroutine ZGTRFS (character trans, integer n, integer nrhs, complex*16,
    dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension(
    * ) du, complex*16, dimension( * ) dlf, complex*16, dimension( * ) df,
    complex*16, dimension( * ) duf, complex*16, dimension( * ) du2, integer,
    dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb,
    complex*16, dimension( ldx, * ) x, integer ldx, double precision,
    dimension( * ) ferr, double precision, dimension( * ) berr, complex*16,
    dimension( * ) work, double precision, dimension( * ) rwork, integer
    info)
    ZGTRFS

🎀 Purpose 🎀

Bestie, here’s the vibe: ZGTRFS improves the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution. Iconic behavior. 💖

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💜 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)
• 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 matrix B. NRHS >= 0.
• DL — DL is COMPLEX*16 array, dimension (N-1). The (n-1) subdiagonal elements of A.
• D — D is COMPLEX*16 array, dimension (N). The diagonal elements of A.
• DU — DU is COMPLEX*16 array, dimension (N-1). The (n-1) superdiagonal elements of A.
• DLF — DLF is COMPLEX*16 array, dimension (N-1). The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by ZGTTRF.
• DF — DF is COMPLEX*16 array, dimension (N). The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
• DUF — DUF is COMPLEX*16 array, dimension (N-1). The (n-1) elements of the first superdiagonal of U.
• DU2 — DU2 is COMPLEX*16 array, dimension (N-2). The (n-2) elements of the second superdiagonal of U.
• IPIV — IPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.
• B — B is COMPLEX*16 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 COMPLEX*16 array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by ZGTTRS. 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 COMPLEX*16 array, dimension (2*N).
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N).
• INFO — INFO is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

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🧚 Internal Parameters 🧚

ITMAX is the maximum number of steps of iterative refinement. That’s the whole note. Slay. ✨

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👑 Author 👑

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

Definition at line 207 of file zgtrfs.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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So yeah, that’s the zgtrfs.f(3) page, bestie: LAPACK Version 3.12.0, and the footer path is /home/abui...RC/zgtrfs.f(3). 🫶💖✨