STBCON(3)

💅 STBCON(3) — like, the LAPACK triangular-band condition-number girlie ✨

okay so this is a page from the Library Functions Manual (yep, that's the manual name, we're folding it in, you're welcome 🫶) and it's all about STBCON, a Fortran subroutine from LAPACK that does exactly one thing and does it iconically.

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🌸 NAME 🌸

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

that's the file, bestie. that's literally the whole NAME section. it's giving "my name is on the roster and that's enough" 💀

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🎀 SYNOPSIS 🎀

Functions/Subroutines

subroutine STBCON (norm, uplo, diag, n, kd, ab, ldab, rcond, work,
    iwork, info)

STBCON ✨ (yes it gets its own little line, main character energy fr)

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🦋 Function/Subroutine Documentation 🦋

subroutine STBCON (character norm, character uplo, character diag, integer
    n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real rcond,
    real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

STBCON

✨ Purpose ✨

!> STBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. 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)) ). !>

so basically: it looks at your triangular band matrix A, gets the norm of A, gets an estimate of norm(inv(A)) (an estimate, okay, not the whole truth, we're being efficient 💅), and then hands you back the reciprocal of the condition number with

RCOND = 1 / ( norm(A) * norm(inv(A)) )

like. that's the whole vibe. one number, so much power 🔥

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🌈 Parameters 🌈

• NORM — NORM is CHARACTER*1. it's the "which flavour of condition number do you want" switch, and here are your options, no substitutions:

!> NORM is CHARACTER*1 !> Specifies whether the 1-norm condition number or the !> infinity-norm condition number is required: !> = '1' or 'O': 1-norm; !> = 'I': Infinity-norm. !>

so '1' or 'O' gets you the 1-norm (yes, both letters, they're the same thing, don't ask 🙈), and 'I' gets you the Infinity-norm.

• UPLO — UPLO is CHARACTER*1. which triangle are we even talking about:

!> UPLO is CHARACTER*1 !> = 'U': A is upper triangular; !> = 'L': A is lower triangular. !>

• DIAG — DIAG is CHARACTER*1. is your diagonal doing the most or is it just vibing at 1:

!> DIAG is CHARACTER*1 !> = 'N': A is non-unit triangular; !> = 'U': A is unit triangular. !>

• N — N is INTEGER. the order of the matrix A. and the rule is N >= 0, periodt.

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

• KD — KD is INTEGER. how many superdiagonals or subdiagonals your triangular band matrix A is packing. KD >= 0, no cap.

!> KD is INTEGER !> The number of superdiagonals or subdiagonals of the !> triangular band matrix A. KD >= 0. !>

• AB — AB is REAL array, dimension (LDAB,N). this is the actual matrix, stored in the first kd+1 rows of the array. the j-th column of A lives in the j-th column of AB, and the indexing is like this:

!> AB is REAL array, dimension (LDAB,N) !> The upper or lower triangular band matrix A, stored in the !> first kd+1 rows of the array. The j-th column of A is stored !> in the j-th column of the array AB as follows: !> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; !> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). !> If DIAG = 'U', the diagonal elements of A are not referenced !> and are assumed to be 1. !>

okay important: if DIAG = 'U', those diagonal entries of A are not referenced at all, they're just assumed to be 1. so don't be out here stressing about what you put on the diagonal when DIAG = 'U', it's literally not being read 😭

• LDAB — LDAB is INTEGER. the leading dimension of the array AB, and it has to be LDAB >= KD+1.

!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KD+1. !>

• RCOND — RCOND is REAL. the moment we've all been waiting for: the reciprocal of the condition number of A, computed as RCOND = 1/(norm(A) * norm(inv(A))).

!> 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 REAL array, dimension (3*N).

!> WORK is REAL array, dimension (3*N) !>

• IWORK — IWORK is INTEGER array, dimension (N).

!> IWORK is INTEGER array, dimension (N) !>

• INFO — INFO is INTEGER. the receipts:

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

so 0 means slay, we're done, everything's fine 🌟 and if INFO = -i then it's negative and the i-th argument had an illegal value — someone didn't read the constraints above, and honestly? it shows 💀

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👑 Author 👑

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

Definition at line 141 of file stbcon.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!! 💖 this footer energy: LAPACK, Version 3.12.0, dated /home/abui...RC/stbcon.f(3) — mwah, iconic, no notes 🎀✨🦋