SRC/zptrfs.f(3)

🌸 NAME 🌸

SRC/zptrfs.f — the ZPTRFS routine, bestie, straight from the Library Functions Manual. It's the one that improves your computed solution and gives you error-bound receipts. 💅

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🌈 SYNOPSIS 🌈

Functions/Subroutines

   subroutine zptrfs (uplo, n, nrhs, d, e, df, ef, b, ldb, x, ldx, ferr,
       berr, work, rwork, info)
       ZPTRFS

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🎀 Function/Subroutine Documentation 🎀

Here's the full signature, exactly as the page serves it, no cap:

   subroutine zptrfs (character uplo, integer n, integer nrhs, double
       precision, dimension( * ) d, complex*16, dimension( * ) e, double
       precision, dimension( * ) df, complex*16, dimension( * ) ef, 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)
       ZPTRFS

🎯 Purpose

ZPTRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution. It's giving "your answer, but with a security blanket and a math receipt." ✨

🧸 Parameters

• UPLO — UPLO is CHARACTER*1. Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix A is stored and the form of the factorization:
  • = 'U': E is the superdiagonal of A, and A = U**H*D*U;
  • = 'L': E is the subdiagonal of A, and A = L*D*L**H.
  • (The two forms are equivalent if A is real.)
• 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 DOUBLE PRECISION array, dimension (N). The n real diagonal elements of the tridiagonal matrix A.
• E — E is COMPLEX*16 array, dimension (N-1). The (n-1) off-diagonal elements of the tridiagonal matrix A (see UPLO).
• DF — DF is DOUBLE PRECISION array, dimension (N). The n diagonal elements of the diagonal matrix D from the factorization computed by ZPTTRF.
• EF — EF is COMPLEX*16 array, dimension (N-1). The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization computed by ZPTTRF (see UPLO).
• 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 ZPTTRS. 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 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 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 (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

🧚 Internal Parameters

ITMAX is the maximum number of steps of iterative refinement. It's the "one more little glow-up pass" limit, bestie. 🪄

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 181 of file zptrfs.f.

✨ Author (generated edition) ✨

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, that's the whole page — xoxo, your LAPACK gen-z Unix bestie 💅✨🦋. Footer glow: LAPACK, Version 3.12.0, page SRC/zptrfs.f(3). 🎀