STPT02(3)

💅 STPT02(3) — like, the Library Functions Manual entry, bestie 🎀

okay so this is the STPT02 page from the Library Functions Manual, and the file it lives in is literally:

/home/abuild/rpmbuild/BUILD/lapack-
static-3.12.0-build/lapack-3.12.0/TESTING/LIN/stpt02.f

that's the NAME, no cap. it's a .f file, it's Fortran, it's giving "we test things here" ✨

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✨ SYNOPSIS ✨

Functions/Subroutines 🦋

• subroutine STPT02 (uplo, trans, diag, n, nrhs, ap, x, ldx, b, ldb, work, resid) — the whole squad, assembled. also: it's STPT02. that's it. that's the subtitle. 💀

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🌸 Function/Subroutine Documentation 🌸

subroutine STPT02 (character uplo, character trans, character diag, integer
    n, integer nrhs, real, dimension( * ) ap, real, dimension( ldx, * ) x,
    integer ldx, real, dimension( ldb, * ) b, integer ldb, real, dimension(
    * ) work, real resid)

STPT02 — yes queen, that's the name again, she's consistent 👑

🎯 Purpose 🎯

!> !> STPT02 computes the residual for the computed solution to a !> triangular system of linear equations op(A)*X = B, when the !> triangular matrix A is stored in packed format. The test ratio is !> the maximum over !> norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ), !> where op(A) = A or A**T, b is the column of B, x is the solution !> vector, and EPS is the machine epsilon. !> The norm used is the 1-norm. !>

so basically, bestie: she's checking how good your answer is 🫶 she takes the residual of the computed solution to a triangular system op(A)*X = B, where A is triangular and stored in packed format — and the test ratio is the max over that whole fraction up there. and the norm? the 1-norm, always, periodt. 🔥

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💖 Parameters 💖

• UPLO — UPLO is CHARACTER*1. tells you whether A is upper or lower triangular: = 'U': upper triangular ⬆️, = 'L': lower triangular ⬇️.
• TRANS — TRANS is CHARACTER*1. the operation being applied to A: = 'N': A * X = B (No transpose), = 'T': A**T * X = B (Transpose), = 'C': A**H * X = B (Conjugate transpose = Transpose). yes she said conjugate transpose equals transpose, for real matrices it literally does, iykyk 🧚
• DIAG — DIAG is CHARACTER*1. is the matrix A unit triangular or not: = 'N': non-unit triangular, = 'U': unit triangular.
• N — N is INTEGER. the order of the matrix A. N >= 0. 💫
• NRHS — NRHS is INTEGER. how many right hand sides — aka the number of columns of the matrices X and B. NRHS >= 0.
• AP — AP is REAL array, dimension (N*(N+1)/2). the upper or lower triangular matrix A, packed columnwise in a linear array. the j-th column of A sits in AP like this:
  • if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
  • if UPLO = 'L', AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.

copy those indices exactly, do NOT freestyle them, that's the whole vibe check 😭

• X — X is REAL array, dimension (LDX,NRHS). the computed solution vectors for the system of linear equations. the main character, honestly 👑
• LDX — LDX is INTEGER. the leading dimension of the array X. LDX >= max(1,N). 🍓
• B — B is REAL array, dimension (LDB,NRHS). the right hand side vectors for the system of linear equations.
• LDB — LDB is INTEGER. the leading dimension of the array B. LDB >= max(1,N).
• WORK — WORK is REAL array, dimension (N). that's it. that's the whole description. she works. 💀
• RESID — RESID is REAL. the maximum over the number of right hand sides of norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ). this is the answer-answer, the final score, the moment 🌈

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👑 Author 👑

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

the whole collective ate, fr fr 💅

Definition at line 140 of file stpt02.f.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. so nobody hand-wrote this page, a robot did it, and we respect the robot 🙈

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and that's the whole page, bestie — no notes, no cap, slay 🎀

lowkey reminder: every number, every = 'U', every AP((j-1)*j/2 + i) index stays exactly as written. she's cute but she's also precise. periodt. 💅

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sign-off time: this icon was running the LAPACK edition of the docs, Version 3.12.0, and the file was living at /home/abui...IN/stpt02.f(3) — mwah, bye bestie 🦋💖