SRC/ctbcon.f(3)

✨ NAME ✨

SRC/ctbcon.f — that's the name, bestie. This page is from the Library Functions Manual, and the title is SRC/ctbcon.f(3). Header info folded in near the top, exactly like we're supposed to. 💅

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

okay so the function lineup is literally one iconic subroutine, ctbcon, and it's giving CTBCON. Here's the synopsis, verbatim because we do not play with code:

subroutine ctbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work,
    rwork, info)
    CTBCON

🦋 Function/Subroutine Documentation 🦋

subroutine ctbcon (character norm, character uplo, character diag, integer
    n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real
    rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer
    info)
    CTBCON

🎀 Purpose 🎀

okay so CTBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as:

RCOND = 1 / ( norm(A) * norm(inv(A)) ).

That's the whole glow-up. ✨

🍓 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.
• UPLO — UPLO is CHARACTER*1
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• DIAG — DIAG is CHARACTER*1
  • = 'N': A is non-unit triangular;
  • = 'U': A is unit triangular.
• N — N is INTEGER. The order of the matrix A. N >= 0.
• KD — KD is INTEGER. The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
• AB — AB is COMPLEX array, dimension (LDAB,N). The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• RCOND — RCOND is REAL. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
• WORK — WORK is COMPLEX array, dimension (2*N).
• RWORK — RWORK is REAL array, dimension (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 141 of file ctbcon.f.

💅 Author 💅

Generated automatically by Doxygen for LAPACK from the source code.

---

okay bestie, that's the whole page. The footer vibe is LAPACK Version 3.12.0 and SRC/ctbcon.f(3), and we're out. 💖✨🫶