ZGTCON(3)

🌸 NAME 🌸

hey bestie 💖 this is the /home/abui...RC/zgtcon.f(3) page from the LAPACK Library Functions Manual. It's all about ZGTCON, the LAPACK subroutine that estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF 🦋. The source file in the original doc is:

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

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

🫶 Function/Subroutine Documentation 🫶

here's the full signature, no cap:

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

💫 Purpose 💫

okay so 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 🌟

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 🌟

N is INTEGER

The order of the matrix A. N >= 0.

🦋 DL 🦋

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 🦋

D is COMPLEX*16 array, dimension (N)

The n diagonal elements of the upper triangular matrix U from the LU factorization of A.

🌸 DU 🌸

DU is COMPLEX*16 array, dimension (N-1)

The (n-1) elements of the first superdiagonal of U.

🌸 DU2 🌸

DU2 is COMPLEX*16 array, dimension (N-2)

The (n-2) elements of the second superdiagonal of U.

🎀 IPIV 🎀

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 🎀

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 💖

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 💖

WORK is COMPLEX*16 array, dimension (2*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.

Definition at line 139 of file zgtcon.f.

🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code.

---

okay bestie, that's the whole page 💖 this is LAPACK Version 3.12.0, and the footer path is /home/abui...RC/zgtcon.f(3) — slay, go estimate those condition numbers responsibly ✨