DTRT01(3)

okay bestie, welcome to the /home/abui...IN/dtrt01.f(3) page from the Library Functions Manual 💅✨

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🌸 NAME 🌸

bestie, the NAME line is literally this file path. The original had it wrapped after lapack-, exactly like this:

/home/abuild/rpmbuild/BUILD/lapack-
static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dtrt01.f

joined up, that’s:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dtrt01.f

no cap, that’s the whole name line 🫶

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💅 SYNOPSIS 💅

🧚 Functions/Subroutines 🧚

• subroutine DTRT01 (uplo, diag, n, a, lda, ainv, ldainv, rcond, work, resid) — this is the one, the main character 😌
• DTRT01 — and yeah, the subroutine is literally named DTRT01

subroutine DTRT01 (uplo, diag, n, a, lda, ainv, ldainv, rcond, work,
    resid)
    DTRT01

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🦋 Function/Subroutine Documentation 🦋

subroutine DTRT01 (character uplo, character diag, integer n, double
    precision, dimension( lda, * ) a, integer lda, double precision,
    dimension( ldainv, * ) ainv, integer ldainv, double precision rcond,
    double precision, dimension( * ) work, double precision resid)
    DTRT01

✨ Purpose ✨

okay so DTRT01 computes the residual for a triangular matrix A times its inverse, and the formula is giving:

RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),

where EPS is the machine epsilon. periodt 💫

🎀 Parameters 🎀

• UPLO — UPLO is CHARACTER*1. It specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular; = 'L': Lower triangular. pick your triangle, bestie 🔺
• DIAG — DIAG is CHARACTER*1. It specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular; = 'U': Unit triangular. so iconic of it 💅
• N — N is INTEGER. The order of the matrix A. N >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). It’s the triangular matrix A. If UPLO = 'U', the leading n by n upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1. slay the storage format 🔥
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• AINV — AINV is DOUBLE PRECISION array, dimension (LDAINV,N). On entry, it’s the (triangular) inverse of the matrix A, in the same storage format as A. On exit, the contents of AINV are destroyed.

bestie, listen: AINV gets destroyed on exit. not a drill 💀

• LDAINV — LDAINV is INTEGER. The leading dimension of the array AINV. LDAINV >= max(1,N).
• RCOND — RCOND is DOUBLE PRECISION. The reciprocal condition number of A, computed as 1/(norm(A) * norm(AINV)). math girlie behavior 🧮✨
• WORK — WORK is DOUBLE PRECISION array, dimension (N). it’s the workspace, doing its little job 🫶
• RESID — RESID is DOUBLE PRECISION. It’s:

norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )

and that’s the whole residual vibe check 💖

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👑 Author 👑

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

Definition at line 122 of file dtrt01.f. 🧚

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🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page! signing off from LAPACK Version 3.12.0 at /home/abui...IN/dtrt01.f(3) 💖✨