SRC/dgtrfs.f(3)

🎀 NAME 🎀

SRC/dgtrfs.f(3) — okay bestie, this is from the Library Functions Manual, and it's giving “tridiagonal linear solver glow-up” energy. 💅

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✨ SYNOPSIS ✨

💖 Functions/Subroutines 💖

• subroutine dgtrfs — (trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info) — DGTRFS

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

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🦋 Function/Subroutine Documentation 🦋

🌸 subroutine dgtrfs 🌸

subroutine dgtrfs (character trans, integer n, integer nrhs, double
    precision, dimension( * ) dl, double precision, dimension( * ) d, double
    precision, dimension( * ) du, double precision, dimension( * ) dlf,
    double precision, dimension( * ) df, double precision, dimension( * )
    duf, double precision, dimension( * ) du2, 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)
    DGTRFS

DGTRFS

🫶 Purpose 🫶

DGTRFS 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. 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. 🎀
• 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 DOUBLE PRECISION array, dimension (N-1). The (n-1) subdiagonal elements of A. 🌈
• D — D is DOUBLE PRECISION array, dimension (N). The diagonal elements of A. ⭐
• DU — DU is DOUBLE PRECISION array, dimension (N-1). The (n-1) superdiagonal elements of A. 🦋
• DLF — DLF is DOUBLE PRECISION array, dimension (N-1). The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by DGTTRF. 👑
• DF — DF is DOUBLE PRECISION array, dimension (N). The n diagonal elements of the upper triangular matrix U from the LU factorization of A. 💖
• DUF — DUF is DOUBLE PRECISION array, dimension (N-1). The (n-1) elements of the first superdiagonal of U. 🎀
• DU2 — DU2 is DOUBLE PRECISION 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 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 DGTTRS. 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 is the maximum number of steps of iterative refinement. iykyk 💅

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👑 Author 👑

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

Definition at line 206 of file dgtrfs.f. 🔥

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. 🫶

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Signed off by LAPACK — Version 3.12.0 — for SRC/dgtrfs.f(3) — mwah 💋