DPTRFS(3)

💖 DPTRFS(3) 💖

okay bestie, welcome to the DPTRFS(3) page from the Library Functions Manual — section 3, LAPACK math, main character energy. Let's get into it. ✨

🌸 NAME 🌸

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

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

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

💖 Function/Subroutine Documentation 💖

the full typed signature is giving:

   subroutine DPTRFS (integer n, integer nrhs, double precision, dimension( * )
       d, double precision, dimension( * ) e, double precision, dimension( * )
       df, double precision, dimension( * ) ef, 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
       info)
       DPTRFS

🎀 Purpose 🎀

okay so DPTRFS literally improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal. It also provides error bounds and backward error estimates for the solution. That's the whole point, no cap. ✨

🧚 Parameters 🧚

• N — INTEGER. The order of the matrix A. N >= 0.
• NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
• D — DOUBLE PRECISION array, dimension (N). The n diagonal elements of the tridiagonal matrix A.
• E — DOUBLE PRECISION array, dimension (N-1). The (n-1) subdiagonal elements of the tridiagonal matrix A.
• DF — DOUBLE PRECISION array, dimension (N). The n diagonal elements of the diagonal matrix D from the factorization computed by DPTTRF.
• EF — DOUBLE PRECISION array, dimension (N-1). The (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization computed by DPTTRF.
• B — DOUBLE PRECISION array, dimension (LDB,NRHS). The right hand side matrix B.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — DOUBLE PRECISION array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by DPTTRS. On exit, the improved solution matrix X.
• LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• FERR — DOUBLE PRECISION 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 — 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 — DOUBLE PRECISION array, dimension (2*N).
• INFO — INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

💅 Internal Parameters 💅

• ITMAX — the maximum number of steps of iterative refinement. 👑

👑 Author 👑

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

📍 Definition at line 161 of file dptrfs.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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💖 sign-off: source is LAPACK, Version 3.12.0, and the footer path is /home/abui...RC/dptrfs.f(3). The footer didn't give a separate date, so I'm not making one up, bestie. Bye! 🫶✨