SRC/cspcon.f(3)

💅 SRC/cspcon.f

okay so this is a page from the LAPACK Library Functions Manual, and honestly? it's giving "quietly doing the most important math in the room" energy. bestie, let's get into it 🫶

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✨ NAME ✨

SRC/cspcon.f — the file that brings you CSPCON, a Fortran subroutine living its best life estimating condition numbers. no cap. 🌸

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🦋 SYNOPSIS 🦋

Functions/Subroutines

• subroutine cspcon (uplo, n, ap, ipiv, anorm, rcond, work, info) — that's the one and only CSPCON 👑

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👑 Function/Subroutine Documentation 👑

subroutine cspcon (character uplo, integer n, complex, dimension( * ) ap,
    integer, dimension( * ) ipiv, real anorm, real rcond, complex,
    dimension( * ) work, integer info)

CSPCON — say it with me. iconic name. 🌟

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🎀 Purpose 🎀

!> CSPCON estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF.

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

so basically: it gets an estimate for norm(inv(A)), then flips it around into RCOND = 1 / (ANORM * norm(inv(A))). math girl summer 💅✨

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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 = U*D*U**T; !> = 'L': Lower triangular, form is A = L*D*L**T.

it's a single character telling you how the factorization got stored — upper or lower, pick your fighter. 'U' gives you A = U*D*U**T, 'L' gives you A = L*D*L**T. no in-between, it's not that kind of parameter. 🦋

• N

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

the order of matrix A. and it's N >= 0, so no negative nonsense please, we're not doing that here. 😭

• AP

!> AP is COMPLEX array, dimension (N*(N+1)/2) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by CSPTRF, stored as a !> packed triangular matrix.

this is the whole vibe: the block diagonal matrix D plus the multipliers used to get factor U or L, exactly as CSPTRF computed them, all packed into a triangular matrix. dimension is (N*(N+1)/2) — packed means packed, bestie, no wasted space. 🍓

• IPIV

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

all the deets on the interchanges and the block structure of D, straight from CSPTRF. dimension (N). iykyk. 🔥

• ANORM

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

it's REAL, and it's literally just the 1-norm of the original matrix A. main character energy, no complications. ⭐

• 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.

also REAL. this is the whole point of the routine: the reciprocal of the condition number of A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the estimate of the 1-norm of inv(A) computed right here in this routine. she did that. 💖

• WORK

!> WORK is COMPLEX array, dimension (2*N)

scratch space, COMPLEX, dimension (2*N). be nice to her, she's just holding your stuff. 💜

• INFO

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

the vibes report: 0 means successful exit (slay ✨), and < 0 means if INFO = -i, the i-th argument had an illegal value — so 👀 check your arguments, bestie, that's on you not her.

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🧚 Author 🧚

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

four whole institutions, one legendary subroutine. periodt. 🌟

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Definition at line 117 of file cspcon.f. 🎀

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🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code. (the robots made this page, but the math was human 💅)

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and that's the whole page, bestie 🫶 — LAPACK, Version 3.12.0, dated, from SRC/cspcon.f(3). go forth and estimate those condition numbers. slay 🌈✨🦋