SRC/dptcon.f(3)

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version 3.12.1 · 7 versions
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💅 SRC/dptcon.f(3) — Library Functions Manual 💅

Okay bestie, this is the manual page for SRC/dptcon.f from the Library Functions Manual. It’s a LAPACK situation, and the main character is DPTCON. Let’s get into it, no cap. ✨

💖 NAME 💖

SRC/dptcon.f

🌸 SYNOPSIS 🌸

🦋 Functions/Subroutines 🦋

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

👑 Function/Subroutine Documentation 👑

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. It uses 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)))

That’s the formula, periodt. ✨

🎀 Parameters 🎀

  • N — N is INTEGER. The order of 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 DPTTRF.
  • E — E is 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 — ANORM is DOUBLE PRECISION. The 1-norm of the original matrix A.
  • RCOND — RCOND is DOUBLE PRECISION. The reciprocal of the condition number of matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the 1-norm of inv(A) computed in this routine.
  • WORK — WORK 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

🫶 Author 🫶

  • 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 🌈

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That’s the whole vibe, bestie. Catch you later — this page came from LAPACK Version 3.12.0, file SRC/dptcon.f(3). 💖✨

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