ZPTCON(3)

🌸 ZPTCON(3) — the LAPACK girlies' guide to condition numbers 🌸

okay so bestie, welcome to the zptcon.f(3) page 💅 this one lives in the Library Functions Manual and it's about the very specific, very iconic act of asking "how badly-conditioned is my Hermitian positive definite tridiagonal matrix, actually?" 🦋

it lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zptcon.f, no cap.

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✨ SYNOPSIS ✨

Functions/Subroutines 🎀

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

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💖 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

🧚 Purpose 🧚

ok so, literally the whole point:

!>
!> 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 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))).
!>

like, it takes the factorization your girl ZPTTRF already produced and does the ✨norm of the inverse✨ thing — direct method, no games — and then flips it into a reciprocal. it's giving measurement, periodt. 👑

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🌈 Parameters 🌈

• N — N is INTEGER. the order of the matrix A. and listen: N >= 0. that's the vibe check. 💀

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

• 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. it already did the work, bestie, we're just reading it back. 🍓

!>          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. note the N-1 — it's one shorter, don't come for me, that's just how tridiagonal off-diagonals are. 🎀

!>          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. you gotta bring this in yourself, it's not computed here, iykyk. 💜

!>          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. this is the output. this is the moment. main character energy fr fr. ⭐

!>          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.
!>

• RWORK — RWORK is DOUBLE PRECISION array, dimension (N). workspace! give it N doubles and let it cook. 🫶

!>          RWORK is DOUBLE PRECISION array, dimension (N)
!>

• INFO — INFO is INTEGER. the receipts:

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

so 0 means slay, and anything negative means argument number i was a mess. 🙈

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👑 Author 👑

these legends:

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

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🔥 Further Details: 🔥

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

so if you wanna read the lore, that's the citation. Higham really said "let me explain" and we respect it. 💅

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Definition at line 118 of file zptcon.f. 🦋

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🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code.

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okay and finally, the little sign-off: this whole thing is LAPACK, Version 3.12.0, and the page is /home/abui...RC/zptcon.f(3) — that's from the source/version and date line at the bottom, mwah 💋 go forth and compute your condition numbers, bestie, you're gonna do amazing 🎀✨