CSYCON_3(3)

💖 CSYCON_3(3) — Library Functions Manual ✨

okay so bestie, this little icon lives in the Library Functions Manual and honestly? she's doing a lot. she's a subroutine, she's doing condition-number estimation, she's got opinions about your factorization. let's get into it 🫶

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📛 NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/csycon_3.f

like... that's her whole government name 😭 that's the file. that's it. that's the NAME section.

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine CSYCON_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)

CSYCON_3

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🧚 FUNCTION/SUBROUTINE DOCUMENTATION 🧚

subroutine CSYCON_3 (character uplo, integer n, complex, dimension( lda, * )
a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv,
real anorm, real rcond, complex, dimension( * ) work, integer info)

CSYCON_3

🎀 Purpose 🎀

okay so CSYCON_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization computed by CSYTRF_RK or CSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

This routine uses BLAS3 solver CSYTRS_3. slay 💅

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💅 Parameters 💅

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 = P*U*D*(U**T)*(P**T);
• = 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T).

N

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

A

A is COMPLEX array, dimension (LDA,N). Diagonal of the block diagonal matrix D and factors U or L as computed by CSYTRF_RK and CSYTRF_BK:

1. ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and
2. If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A.

LDA

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

E

E is COMPLEX array, dimension (N).

On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where:

• If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
• If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases. like, she's just sitting there. unbothered. unreferenced. 💀

IPIV

IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CSYTRF_RK or CSYTRF_BK.

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). that's the workspace bestie, give her room to breathe 🦋

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.

🌈 Contributors 🌈

• June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley
• September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

⭐ Definition ⭐

Definition at line 164 of file csycon_3.f.

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🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page, bestie 🫶 go forth and estimate those condition numbers responsibly. no cap, RCOND is about to be so real.

💖 LAPACK — Version 3.12.0 — /home/abui.../csycon_3.f(3) 💖 — mwah, that's the footer, that's the sign-off, the vibes are immaculate, periodt. 🎀🌸