CSYCON(3)

💅 CSYCON(3) — the "is my symmetric matrix ok or a total mess" check 🦋

ok so bestie, quick vibe check: this page lives in the LAPACK Library Functions Manual, and the actual file it's documenting is

(yeah the header up top truncates it to `/home/abui...RC/csycon.f(3)` because paths are dramatic like that 💀)

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# ✨ NAME ✨

`/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/csycon.f` — that's it, that's the name, the file *is* the main character 👑

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# 🌸 SYNOPSIS 🌸

## Functions/Subroutines

subroutine CSYCON (uplo, n, a, lda, ipiv, anorm, rcond, work, info) CSYCON

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# 🎀 Function/Subroutine Documentation 🎀

subroutine CSYCON (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, integer info) CSYCON

## 💜 Purpose:

> !>
> !> CSYCON estimates the reciprocal of the condition number (in the
> !> 1-norm) of a complex symmetric matrix A using the factorization
> !> A = U*D*U**T or A = L*D*L**T computed by CSYTRF.
> !>
> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the
> !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
> !>

no cap, that's the whole flex: it's estimating `norm(inv(A))` and then handing you back `RCOND = 1 / (ANORM * norm(inv(A)))` 🧚✨

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# 🔥 Parameters 🔥

ok this is the part where every single one of them shows up, so let's go, one by one, no skipping 🙈

### UPLO

> !>          UPLO is CHARACTER*1
> !>          Specifies whether the details of the factorization are stored
> !>          as an upper or lower triangular matrix.
> !>          = 'U':  Upper triangular, form is A = U*D*U**T;
> !>          = 'L':  Lower triangular, form is A = L*D*L**T.
> !>

### N

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

### A

> !>          A is COMPLEX array, dimension (LDA,N)
> !>          The block diagonal matrix D and the multipliers used to
> !>          obtain the factor U or L as computed by CSYTRF.
> !>

### LDA

> !>          LDA is INTEGER
> !>          The leading dimension of the array A.  LDA >= max(1,N).
> !>

### IPIV

> !>          IPIV is INTEGER array, dimension (N)
> !>          Details of the interchanges and the block structure of D
> !>          as determined by CSYTRF.
> !>

### ANORM

> !>          ANORM is REAL
> !>          The 1-norm of the original matrix A.
> !>

### RCOND

> !>          RCOND is 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

> !>          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
> !>

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# 🫶 Author 🫶

- Univ. of Tennessee
- Univ. of California Berkeley
- Univ. of Colorado Denver
- NAG Ltd.

📌 Definition at line 123 of file `csycon.f`.

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# ⭐ Author (yes, again, it's giving sequel energy) ⭐

Generated automatically by Doxygen for LAPACK from the source code. 🤖✨

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<pink>and that's the whole page bestie — every flag, every dimension, every `!>` comment, all present and accounted for, periodt 💅</pink>

<purple>sign-off szn: this iconic little number is `LAPACK` **Version 3.12.0**, and the footer goes out to `/home/abui...RC/csycon.f(3)` 🎀💖</purple>