CPTT05(3)

💅 CPTT05(3) — the manual page, but make it make sense

okay bestie, first things first: this page lives at /home/abui...IN/cptt05.f(3) in the Library Functions Manual, and the real file it's describing is this absolute icon right here:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/cptt05.f

yes that is a whole path. no I will not be shortening it. it's giving "build artifact realness" and we respect it. 🫶

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✨ SYNOPSIS ✨

Functions/Subroutines

so here's the star of the show, the main character herself:

subroutine CPTT05 (n, nrhs, d, e, b, ldb, x, ldx, xact, ldxact, ferr,
    berr, reslts)

CPTT05 — that's her. that's the name. 💅

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🦋 Function/Subroutine Documentation 🦋

the full signature, spelled all the way out

subroutine CPTT05 (integer n, integer nrhs, real, dimension( * ) d, complex,
    dimension( * ) e, complex, dimension( ldb, * ) b, integer ldb, complex,
    dimension( ldx, * ) x, integer ldx, complex, dimension( ldxact, * )
    xact, integer ldxact, real, dimension( * ) ferr, real, dimension( * )
    berr, real, dimension( * ) reslts)

CPTT05

🎀 Purpose 🎀

no cap, here's the whole point of her existence:

!>
!> CPTT05 tests the error bounds from iterative refinement for the
!> computed solution to a system of equations A*X = B, where A is a
!> Hermitian tridiagonal matrix of order n.
!>
!> RESLTS(1) = test of the error bound
!>           = norm(X - XACT) / ( norm(X) * FERR )
!>
!> A large value is returned if this ratio is not less than one.
!>
!> RESLTS(2) = residual from the iterative refinement routine
!>           = the maximum of BERR / ( NZ*EPS + (*) ), where
!>             (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
!>             and NZ = max. number of nonzeros in any row of A, plus 1
!>

like... she literally checks whether your iterative refinement error bounds are behaving. queen behavior honestly. 👑

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🌸 Parameters 🌸

okay this is the long part, but every single one matters, so lock in bestie 🔥

• N — N is INTEGER. the number of rows of the matrices X, B, and XACT, and also the order of the matrix A. constraint: N >= 0.
• NRHS — NRHS is INTEGER. the number of columns of the matrices X, B, and XACT. constraint: NRHS >= 0.
• D — D is REAL array, dimension (N). the n diagonal elements of the tridiagonal matrix A.
• E — E is COMPLEX array, dimension (N-1). the (n-1) subdiagonal elements of the tridiagonal matrix A. note the N-1, she's one shorter, that's just her vibe.
• B — B is COMPLEX 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. constraint: LDB >= max(1,N).
• X — X is COMPLEX array, dimension (LDX,NRHS). the computed solution vectors. each vector is stored as a column of the matrix X.
• LDX — LDX is INTEGER. the leading dimension of the array X. constraint: LDX >= max(1,N).
• XACT — XACT is COMPLEX array, dimension (LDX,NRHS). the exact solution vectors. each vector is stored as a column of the matrix XACT. yes, the dimension says LDX and not LDXACT — that's what the page says, so that's what I'm telling you. 🙈
• LDXACT — LDXACT is INTEGER. the leading dimension of the array XACT. constraint: LDXACT >= max(1,N).
• FERR — FERR is REAL array, dimension (NRHS). the estimated forward error bounds for each solution vector X. if XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X.
• BERR — BERR is REAL array, dimension (NRHS). the componentwise relative backward error of each solution vector — i.e., the smallest relative change in any entry of A or B that makes X an exact solution.
• RESLTS — RESLTS is REAL array, dimension (2). the maximum over the NRHS solution vectors of the ratios:

RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( NZ*EPS + (*) )

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👑 Author 👑

the legends themselves:

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

Definition at line 148 of file cptt05.f. (go look, she's there, line 148, iconic) ⭐

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🌈 Author (the meta one) 🌈

Generated automatically by Doxygen for LAPACK from the source code.

so nobody hand-wrote this page, a robot did it, and honestly? she ate. 💀✨

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and that's the whole page, bestie — every flag, every constraint, every array, all of it, untouched. now go forth and check those error bounds. 🌸🦋

— LAPACK, Version 3.12.0, living at /home/abui...IN/cptt05.f(3), and that's the tea 🎀