SRC/sptrfs.f(3)

Okay bestie, this is the manual page for SRC/sptrfs.f in the Library Functions Manual — welcome to the group chat 💅.

💖 NAME 💖

SRC/sptrfs.f — that’s the name, no cap.

---

✨ SYNOPSIS ✨

Under Functions/Subroutines, the listing is this iconic little signature:

subroutine sptrfs (n, nrhs, d, e, df, ef, b, ldb, x, ldx, ferr, berr, work, info)

And the routine’s name is literally SPTRFS 🫶.

---

🫶 Function/Subroutine Documentation 🫶

Here’s the full declaration, bestie, copied exactly so nobody comes for me:

subroutine sptrfs (integer n, integer nrhs, real, dimension( * ) d, real, dimension( * ) e, real, dimension( * ) df, real, dimension( * ) ef, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * ) work, integer info)

The routine is SPTRFS 💜.

🌸 Purpose 🌸

SPTRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and it provides error bounds and backward error estimates for the solution. Slay, honestly ✨.

🦋 Parameters 🦋

• 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.
• D — D is REAL array, dimension (N). The n diagonal elements of the tridiagonal matrix A.
• E — E is REAL array, dimension (N-1). The (n-1) subdiagonal elements of the tridiagonal matrix A.
• DF — DF is REAL array, dimension (N). The n diagonal elements of the diagonal matrix D from the factorization computed by SPTTRF.
• EF — EF is REAL array, dimension (N-1). The (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization computed by SPTTRF.
• 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 SPTTRS. 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 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).
• 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 (2*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. That’s the whole tea 🍓.

🌈 Author 🌈

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

🧚 Definition at line 🧚

Definition at line 161 of file sptrfs.f.

---

💅 Author 💅

Generated automatically by Doxygen for LAPACK from the source code.

---

That’s the whole page, bestie — this footer energy comes from LAPACK Version 3.12.0 and the source page SRC/sptrfs.f(3). The original footer has no date stamped on it, so I’m not inventing one, periodt. 🎀