SRC/cgtcon.f(3)

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💖 NAME 💖

SRC/cgtcon.f

🌈 SYNOPSIS 🌈

🧩 Functions/Subroutines 🧩

  • subroutine cgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, info) — CGTCON

🛠️ Function/Subroutine Documentation 🛠️

subroutine cgtcon (character norm, integer n, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, integer info)
CGTCON

🎯 Purpose 🎯

Okay so CGTCON estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF. ✨

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). That’s the whole main-character formula, no cap. 💖

🎛️ Parameters 🎛️

  • NORM — NORM is CHARACTER*1. It 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. This is the order of the matrix A. N >= 0.
  • DL — DL is COMPLEX array, dimension (N-1). These are the (n-1) multipliers that define the matrix L from the LU factorization of A as computed by CGTTRF.
  • D — D is COMPLEX array, dimension (N). These are the n diagonal elements of the upper triangular matrix U from the LU factorization of A.
  • DU — DU is COMPLEX array, dimension (N-1). These are the (n-1) elements of the first superdiagonal of U.
  • DU2 — DU2 is COMPLEX array, dimension (N-2). These are the (n-2) elements of the second superdiagonal of U.
  • IPIV — IPIV is INTEGER array, dimension (N). These are 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 REAL. If NORM = '1' or 'O', this is the 1-norm of the original matrix A. If NORM = 'I', this is the infinity-norm of the original matrix A.
  • 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 an estimate of the 1-norm of inv(A) computed in this routine.
  • WORK — WORK is COMPLEX 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 cgtcon.f.

👑 Author 👑

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