STPCON(3)

STPCON(3) 💅

ok so bestie, welcome to STPCON — it lives in the LAPACK fam, and today we're doing condition number estimation for a packed triangular matrix. yes it's a .f file. yes it's Fortran. no we're not scared. 🫶

the file in question? literally:

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

that's the one. that's our girl. 🌸

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✨ SYNOPSIS ✨

Functions/Subroutines 🎀

subroutine STPCON (norm, uplo, diag, n, ap, rcond, work, iwork, info)

STPCON — that's her name, that's her whole vibe.

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🦋 Function/Subroutine Documentation 🦋

subroutine STPCON (character norm, character uplo, character diag, integer
    n, real, dimension( * ) ap, real rcond, real, dimension( * ) work,
    integer, dimension( * ) iwork, integer info)

STPCON

🌟 Purpose 🌟

ok so picture this — STPCON estimates the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm. pick your fighter, both are valid. 👑

the way it works is: the norm of A gets computed, then an estimate is obtained for norm(inv(A)), and then the reciprocal of the condition number is computed as

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

periodt. that's the whole formula. 💜

🌈 Parameters 🌈

• NORM — NORM is CHARACTER*1. it specifies whether you want the 1-norm condition number or the infinity-norm condition number, so like, choose wisely bestie:
  • = '1' or 'O': 1-norm;
  • = 'I': Infinity-norm.
• UPLO — UPLO is CHARACTER*1. which triangle are we working with:
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• DIAG — DIAG is CHARACTER*1. is the diagonal doing anything or is it just decorative:
  • = 'N': A is non-unit triangular;
  • = 'U': A is unit triangular.
• N — N is INTEGER. the order of the matrix A. and listen: N >= 0. no negatives, no cap. 🚫
• AP — AP is REAL array, dimension (N*(N+1)/2). this is the upper or lower triangular matrix A, packed columnwise into a linear array. the j-th column of A is stored in the array AP like this:
  • if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
  • if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

and if DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1. so don't come for them, they're not even invited. 🙈

• RCOND — RCOND is REAL. the reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). it's giving main character output value honestly. ⭐
• WORK — WORK is REAL array, dimension (3*N). it's the workspace. it does the work. hence the name, iykyk. 🔥
• IWORK — IWORK is INTEGER array, dimension (N). integer workspace, also invited to the party. 🎀
• INFO — INFO is INTEGER. the vibe check at the end:
  • = 0: successful exit — slay, we ate; 💖
  • < 0: if INFO = -i, the i-th argument had an illegal value — not slay, something's wrong. 😭

👑 Author 👑

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

the whole squad really showed up for this one. 🫶

Definition at line 128 of file stpcon.f.

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🌸 Author (the meta one) 🌸

Generated automatically by Doxygen for LAPACK from the source code. so technically the robots wrote it, but we're the ones making it cute. 🤖✨

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and that's the whole page bestie! this one came to you courtesy of LAPACK, Version 3.12.0, and it was living at /home/abui...RC/stpcon.f(3) when we found it. go forth and estimate those condition numbers responsibly. 💅🦋💖