ZPTRFS(3)

💅 ZPTRFS(3) — Library Functions Manual 💅

okay so bestie, welcome to the ZPTRFS page from the LAPACK girlies. This is literally a Library Functions Manual moment, and the source path floating around at the top is /home/abui...RC/zptrfs.f(3). ✨

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zptrfs.f — yeah, the entire path is the NAME entry. It’s giving “I am the source file” energy, no cap. 🫶

🦋 SYNOPSIS 🦋

Functions/Subroutines

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

🔥 Function/Subroutine Documentation 🔥

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.

💖 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.

👑 Author 👑

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

Definition at line 181 of file zptrfs.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole manual page bestie 💖 this one is LAPACK Version 3.12.0, and the footer path is /home/abui...RC/zptrfs.f(3). slay. 🎀