DPTCON(3)

DPTCON(3) — Library Functions Manual 💅

okay so bestie, welcome to the Library Functions Manual page for DPTCON. This is the whole file-path situation, preserved exactly:

✨ NAME ✨

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

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🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

• subroutine DPTCON (n, d, e, anorm, rcond, work, info)
  • DPTCON

🦋 Function/Subroutine Documentation 🦋

Here’s the full signature, no cap, character-for-character:

subroutine DPTCON (integer n, double precision, dimension( * ) d, double
     precision, dimension( * ) e, double precision anorm, double precision
     rcond, double precision, dimension( * ) work, integer info)

DPTCON

🎯 Purpose 🎯

okay so DPTCON computes the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by DPTTRF.

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 — INTEGER. The order of the matrix A. N >= 0.
• D — DOUBLE PRECISION array, dimension (N). The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by DPTTRF.
• E — DOUBLE PRECISION 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 DPTTRF.
• ANORM — DOUBLE PRECISION. The 1-norm of the original matrix A.
• RCOND — 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.
• WORK — DOUBLE PRECISION array, dimension (N).
• INFO — INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

👑 Author 👑

Shoutout to the author squad, literally iconic:

• 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 117 of file dptcon.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie 🫶 — the footer sign-off is giving LAPACK Version 3.12.0 and the path /home/abui...RC/dptcon.f(3), so yeah, source/version preserved, mwah 💖✨