SRC/sgtrfs.f(3)

🩷 SRC/sgtrfs.f 🩷

okay so this page is from the Library Functions Manual, and the title is literally SRC/sgtrfs.f — welcome to the tridiagonal solver corner of the group chat. 💅

🌸 NAME 🌸

SRC/sgtrfs.f — that's the name, bestie. No cap. ✨

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

This is the callable icon:

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

💖 Function/Subroutine Documentation 💖

The full signature glow-up is:

   subroutine sgtrfs (character trans, integer n, integer nrhs, real,
       dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du,
       real, dimension( * ) dlf, real, dimension( * ) df, real, dimension( * )
       duf, real, dimension( * ) du2, 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)
       SGTRFS

🎀 Purpose 🎀

SGTRFS 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. that's the assignment, and it ate. 🔥

💅 Parameters 💅

• TRANS — TRANS is CHARACTER*1. 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 REAL array, dimension (N-1). The (n-1) subdiagonal elements of A.
• D — D is REAL array, dimension (N). The diagonal elements of A.
• DU — DU is REAL array, dimension (N-1). The (n-1) superdiagonal elements of A.
• DLF — DLF is REAL array, dimension (N-1). The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF.
• DF — DF is REAL array, dimension (N). The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
• DUF — DUF is REAL array, dimension (N-1). The (n-1) elements of the first superdiagonal of U.
• DU2 — DU2 is REAL 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 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 SGTTRS. 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 is the maximum number of steps of iterative refinement. periodt. 💅

👑 Author 👑

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

Definition at line 206 of file sgtrfs.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 signing off with the footer energy: LAPACK Version 3.12.0, SRC/sgtrfs.f(3). (There's no extra date in this footer, bestie — don't come for me.) 🫶