CTBRFS(3)

✨ CTBRFS(3) — error bounds & backward error for triangular band solves ✨

okay so bestie, this is a page from the LAPACK crew (Version 3.12.0), and it lives at this absolutely unhinged path:

💖 NAME 💖

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

yes that's the whole name section. it's giving "file path as a personality." iykyk 🫶

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine CTBRFS (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x,
    ldx, ferr, berr, work, rwork, info)

CTBRFS 🌟

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🌸 Function/Subroutine Documentation 🌸

subroutine CTBRFS (character uplo, character trans, character diag, integer
    n, integer kd, integer nrhs, complex, dimension( ldab, * ) ab, integer
    ldab, complex, dimension( ldb, * ) b, integer ldb, complex, dimension(
    ldx, * ) x, integer ldx, real, dimension( * ) ferr, real, dimension( * )
    berr, complex, dimension( * ) work, real, dimension( * ) rwork, integer
    info)

CTBRFS 💅

🎀 Purpose 🎀

!> !> CTBRFS provides error bounds and backward error estimates for the !> solution to a system of linear equations with a triangular band !> coefficient matrix. !> !> The solution matrix X must be computed by CTBTRS or some other !> means before entering this routine. CTBRFS does not do iterative !> refinement because doing so cannot improve the backward error. !>

so like — this routine does not solve anything, bestie. it grades the solution you already have 😭 you gotta get X from CTBTRS (or wherever, no judgement) before you knock on this door. and no, it does not do iterative refinement, because apparently that cannot improve the backward error. periodt. 🔥

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💜 Parameters 💜

• UPLO — UPLO is CHARACTER*1
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• TRANS — TRANS is CHARACTER*1, and it specifies the form of the system of equations:
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose)
• DIAG — 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. N >= 0. 👑
• KD — KD is INTEGER; the number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
• NRHS — NRHS is INTEGER; the number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• AB — AB is COMPLEX array, dimension (LDAB,N). it's 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 like this:
  • 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).

and heads up 🫶 — if DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

• LDAB — LDAB is INTEGER; the leading dimension of the array AB. LDAB >= KD+1. no cap.
• B — B is COMPLEX array, dimension (LDB,NRHS); the right hand side matrix B. 💖
• LDB — LDB is INTEGER; the leading dimension of the array B. LDB >= max(1,N).
• X — X is COMPLEX array, dimension (LDX,NRHS); the solution matrix X. this is the main character of the whole operation ngl ⭐
• LDX — LDX is INTEGER; the leading dimension of the array X. LDX >= max(1,N).
• FERR — FERR is REAL array, dimension (NRHS); the estimated forward error bound for each solution vector X(j) (the j-th column of the solution matrix X). if XTRUE is the true solution corresponding to X(j), then FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest element in X(j). the estimate is as reliable as the estimate for RCOND, and it's almost always a slight overestimate of the true error. humble queen behavior 💅
• BERR — BERR is REAL array, dimension (NRHS); the componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution). 👑
• WORK — WORK is COMPLEX array, dimension (2*N).
• RWORK — RWORK is REAL array, dimension (N).
• INFO — INFO is INTEGER
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value 💀

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🌈 Author 🌈

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

Definition at line 186 of file ctbrfs.f. 📍

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. (iconic of her, honestly — no human typed this, the machine did, and it ate 🤖✨)

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that's the whole page bestie, go forth and compute your error bounds 💖

this has been LAPACK Version 3.12.0, dated and filed under /home/abui...RC/ctbrfs.f(3) — mwah, slay, see u in the next manpage 🎀🦋💜