SRC/zgtcon.f(3)

💅 SRC/zgtcon.f(3) 💅

okay so bestie, welcome to the Library Functions Manual entry for SRC/zgtcon.f — and no cap, this is the ZGTCON glow-up page. It’s a LAPACK routine, it’s giving complex tridiagonal-matrix condition-number realness, and we’re gonna read it together. 🫶

🌸 NAME 🌸

SRC/zgtcon.f

✨ SYNOPSIS ✨

Functions/Subroutines

       subroutine zgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work,
           info)

• ZGTCON — that’s the subroutine name, and yes it’s literally the main character of this page. 👑

🦋 Function/Subroutine Documentation 🦋

subroutine zgtcon (...) — ZGTCON

   subroutine zgtcon (character norm, integer n, complex*16, dimension( * ) dl,
       complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16,
       dimension( * ) du2, integer, dimension( * ) ipiv, double precision
       anorm, double precision rcond, complex*16, dimension( * ) work, integer
       info)

ZGTCON — okay bestie, here’s the whole signature, every argument in its exact little spot. 💖

Purpose:

ZGTCON estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

• NORM is CHARACTER*1. Specifies whether the 1-norm condition number or the infinity-norm condition number is required:
  • = '1' or 'O': 1-norm;
  • = 'I': Infinity-norm.
• N is INTEGER. The order of the matrix A. N >= 0.
• DL is COMPLEX*16 array, dimension (N-1). The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by ZGTTRF.
• D is COMPLEX*16 array, dimension (N). The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
• DU is COMPLEX*16 array, dimension (N-1). The (n-1) elements of the first superdiagonal of U.
• DU2 is COMPLEX*16 array, dimension (N-2). The (n-2) elements of the second superdiagonal of U.
• IPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.
• ANORM is DOUBLE PRECISION. If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A.
• RCOND is DOUBLE PRECISION. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.
• WORK is COMPLEX*16 array, dimension (2*N).
• 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.

📌 Definition at line 139 of file zgtcon.f.

👑 Author

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mwah 💋 — that’s the whole page, bestie. It’s from LAPACK, Version 3.12.0, and the page is SRC/zgtcon.f(3). 💖✨