CPTCON(3)

💖 NAME 💖

okay bestie, you’re in the Library Functions Manual, and this page is literally all about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cptcon.f. no cap, that’s the file. 🦋

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

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👑 Function/Subroutine Documentation 👑

subroutine CPTCON (integer n, real, dimension( * ) d, complex, dimension( * ) e, real anorm, real rcond, real, dimension( * ) rwork, integer info)
    CPTCON

🌸 Purpose 🌸

okay so CPTCON computes the reciprocal of the condition number — in the 1-norm, bestie — of a complex Hermitian positive definite tridiagonal matrix. it does this using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRF. iconic behavior tbh. 💅

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. periodt.
• D — D is REAL array, dimension (N). these are the n diagonal elements of the diagonal matrix D from the factorization of A, as computed by CPTTRF. slay.
• E — E is COMPLEX array, dimension (N-1). these are the (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization of A, as computed by CPTTRF. 🫶
• ANORM — ANORM is REAL. it’s the 1-norm of the original matrix A. yes ma’am.
• RCOND — RCOND is REAL. this is 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. big main-character energy. 🔥
• RWORK — RWORK is REAL array, dimension (N). that’s the whole vibe.
• 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 118 of file cptcon.f.

🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code.

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✨ cute sign-off: LAPACK Version 3.12.0 — source file /home/abui...RC/cptcon.f(3); the only date on this page is the Higham citation’s January 1986. iykyk. 💜🎀