SPTCON(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 SPTCON(3) — Library Functions Manual, bestie edition 💅

✨ NAME ✨

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

That’s the file this page is serving, no cap. 💖

🦋 SYNOPSIS 🦋

📚 Functions/Subroutines 📚

subroutine SPTCON (n, d, e, anorm, rcond, work, info)

SPTCON

🦋 Function/Subroutine Documentation 🦋

subroutine SPTCON (integer n, real, dimension( * ) d, real, dimension( * ) e, real anorm, real rcond, real, dimension( * ) work, integer info)

SPTCON

✨ Purpose: ✨

Okay so bestie, SPTCON 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 SPTTRF. 💅

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))). Periodt. 💖

🎀 Parameters 🎀

  • N — N is INTEGER. The order of the matrix A. N >= 0. 🌸
  • D — D is REAL array, dimension (N). The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by SPTTRF. 🍓
  • E — E is REAL 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 SPTTRF. 🦋
  • ANORM — ANORM is REAL. The 1-norm of the original matrix A. 👑
  • RCOND — RCOND is REAL. 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 — WORK is REAL 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 sptcon.f. 📌

🌸 Author 🌸

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