SRC/zptcon.f(3)

🎀 SRC/zptcon.f(3) 🎀

Okay bestie, welcome to the Library Functions Manual entry for SRC/zptcon.f. This is the whole page, and we’re keeping every little detail — no cap. 💅

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🌸 NAME 🌸

SRC/zptcon.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

subroutine zptcon (n, d, e, anorm, rcond, rwork, info)
    ZPTCON

🔥 Function/Subroutine Documentation 🔥

subroutine zptcon (integer n, double precision, dimension( * ) d,
    complex*16, dimension( * ) e, double precision anorm, double precision
    rcond, double precision, dimension( * ) rwork, integer info)
    ZPTCON

This one is literally called ZPTCON, and she’s here to do condition-number math on a complex Hermitian positive definite tridiagonal matrix. Iconic behavior, honestly. 👑

🌟 Purpose 🌟

ZPTCON computes the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization:

A = L*D*L**H

or:

A = U**H*D*U

Both of those are computed by ZPTTRF. 💖

Norm(inv(A)) is computed by a direct method, and the reciprocal of the condition number is computed as:

RCOND = 1 / (ANORM * norm(inv(A))).

💜 Parameters 💜

• N — N is INTEGER. The order of the matrix A. N >= 0. Slay. 🦋
• D — D is DOUBLE PRECISION array, dimension (N). The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by ZPTTRF.
• E — E is COMPLEX*16 array, dimension (N-1). The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization of A, as computed by ZPTTRF.
• ANORM — ANORM is DOUBLE PRECISION. The 1-norm of the original matrix A.
• RCOND — RCOND is DOUBLE PRECISION. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the 1-norm of inv(A) computed in this routine. Math girlie pop off. 🧮✨
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N). That’s the whole description, bestie — no extra lore.
• INFO — INFO is INTEGER.
  • = 0: successful exit. We love a happy ending. 🫶
  • < 0: if INFO = -i, the i-th argument had an illegal value. Rude, but at least it tells you which one. 😭

🌈 Author 🌈

Shoutout to the whole author squad:

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

🦋 Further Details 🦋

The method used is described in Nicholas J. Higham, , SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.

🎀 Definition at line 118 of file zptcon.f. 🎀

Definition at line 118 of file zptcon.f.

👑 Author 👑

And the auto-generated author credit says:

Generated automatically by Doxygen for LAPACK from the source code.

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💖 That’s the whole page, bestie! 💖 Signing off from the Library Functions Manual: LAPACK, Version 3.12.0, for SRC/zptcon.f(3). The footer doesn’t give a date, so I’m not inventing one — periodt. 🫶💅