SRC/ctpcon.f(3)

✨ NAME ✨

SRC/ctpcon.f — this iconic page is from the Library Functions Manual, and we’re folding that manual-name moment in right here instead of doing a boring header-line copy. 💖

📚 SYNOPSIS 📚

🧩 Functions/Subroutines 🧩

subroutine ctpcon (norm, uplo, diag, n, ap, rcond, work, rwork, info)
    CTPCON

🛠 Function/Subroutine Documentation 🛠

🌟 subroutine ctpcon 🌟

subroutine ctpcon (character norm, character uplo, character diag, integer
     n, complex, dimension( * ) ap, real rcond, complex, dimension( * ) work,
     real, dimension( * ) rwork, integer info)

CTPCON — that’s the name, no cap. 👑

🎯 Purpose 🎯

Okay so CTPCON estimates the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm. Literally its whole vibe.

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)) ).

🧾 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.

🔤 UPLO 🔤

UPLO is CHARACTER*1 — tells us which triangle is serving:

• = 'U': A is upper triangular;
• = 'L': A is lower triangular.

🔤 DIAG 🔤

DIAG is CHARACTER*1 — unit or non-unit, bestie:

• = 'N': A is non-unit triangular;
• = 'U': A is unit triangular.

🔢 N 🔢

N is INTEGER — the order of the matrix A. N >= 0.

🧺 AP 🧺

AP is COMPLEX array, dimension (N*(N+1)/2) — the upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:

• if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
• if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 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) — that’s the complex work array, periodt.

🌸 RWORK 🌸

RWORK is REAL array, dimension (N) — that’s the real work array.

🚦 INFO 🚦

INFO is INTEGER — the exit-status moment:

• = 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 128 of file ctpcon.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie — signing off with LAPACK, Version 3.12.0, for SRC/ctpcon.f(3) 🫶✨💅