DSYCON_3(3)

💅 DSYCON_3 💅

okay so welcome to the Library Functions Manual, bestie — this page lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsycon_3.f and honestly? she's a whole vibe. 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/dsycon_3.f

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine DSYCON_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work,
    iwork, info)

DSYCON_3 💖

🦋 Function/Subroutine Documentation 🦋

subroutine DSYCON_3 (character uplo, integer n, double precision, dimension(
    lda, * ) a, integer lda, double precision, dimension( * ) e, integer,
    dimension( * ) ipiv, double precision anorm, double precision rcond,
    double precision, dimension( * ) work, integer, dimension( * ) iwork,
    integer info)

DSYCON_3 ✨

🎀 Purpose 🎀

!> DSYCON_3 estimates the reciprocal of the condition number (in the !> 1-norm) of a real symmetric matrix A using the factorization !> computed by DSYTRF_RK or DSYTRF_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 DSYTRS_3.

like, she's literally estimating how sketchy your matrix is, no cap 🫶

🌈 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).

'U' for upper, 'L' for lower — pick your fighter, iykyk 💅

N

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

A

!> A is DOUBLE PRECISION array, dimension (LDA,N) !> Diagonal of the block diagonal matrix D and factors U or L !> as computed by DSYTRF_RK and DSYTRF_BK: !> a) 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 !> b) 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 DOUBLE PRECISION 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.

bestie the note is important!! for a 1-by-1 block E(k) is literally not referenced in either UPLO case. don't come for me, that's just what the source says 🍓

IPIV

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

ANORM

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

RCOND

!> RCOND is DOUBLE PRECISION !> 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 DOUBLE PRECISION array, dimension (2*N)

IWORK

!> IWORK is INTEGER array, dimension (N)

INFO

!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value

heads up: if INFO comes back negative it's giving "you passed me something illegal," and INFO = -i tells you exactly which argument (the i-th one) was the problem. slay that debugging, bestie 🔥

👑 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 at line 169 of file dsycon_3.f.

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page, periodt 💜 okay so this masterpiece of a manpage is from LAPACK, Version 3.12.0, and it lives at /home/abui.../dsycon_3.f(3) — mwah, icon behavior, no notes 🎀✨