CGTCON(3)

💅 CGTCON(3) 💅

okay so bestie, this is the cgtcon.f(3) page from the Library Functions Manual — header path says /home/abui...RC/cgtcon.f(3) and we are lowkey about to get into complex tridiagonal condition-number math. 💖 No cap.

🌸 NAME 🌸

cgtcon.f(3) — the source file this page points at is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cgtcon.f.

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

Here's the synopsis call, line break and all:

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

That's the CGTCON subroutine, bestie. 🫶

💫 Function/Subroutine Documentation 💫

Full signature with all the types and dimensions, copied exactly:

   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)

The routine is CGTCON. ✨

🎯 Purpose 🎯

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)))

It's giving condition-number detective energy, and honestly? Obsessed. 💅

🌈 Parameters 🌈

• NORM — 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 — INTEGER. The order of the matrix A. N >= 0.
• DL — COMPLEX array, dimension (N-1). The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by CGTTRF.
• D — COMPLEX array, dimension (N). The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
• DU — COMPLEX array, dimension (N-1). The (n-1) elements of the first superdiagonal of U.
• DU2 — COMPLEX array, dimension (N-2). The (n-2) elements of the second superdiagonal of U.
• IPIV — 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 — REAL. 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 — REAL. 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 — COMPLEX array, dimension (2*N).
• INFO — 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 👑

Generated automatically by Doxygen for LAPACK from the source code.

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