DTRT02(3)

🦋 DTRT02(3) — Library Functions Manual 🦋

Bestie, this page comes from /home/abui...IN/dtrt02.f(3), and the manual name is Library Functions Manual. We are officially in our LAPACK triangular-residual era. 💅

✨ NAME ✨

The NAME tea is this exact file path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dtrt02.f

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🌸 SYNOPSIS 🌸

🎀 Functions/Subroutines 🎀

subroutine DTRT02 (uplo, trans, diag, n, nrhs, a, lda, x, ldx, b, ldb,
    work, resid)
    DTRT02

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🦋 Function/Subroutine Documentation 🦋

subroutine DTRT02 (character uplo, character trans, character diag, integer
    n, integer nrhs, double precision, dimension( lda, * ) a, integer lda,
    double precision, dimension( ldx, * ) x, integer ldx, double precision,
    dimension( ldb, * ) b, integer ldb, double precision, dimension( * )
    work, double precision resid)
    DTRT02

💖 Purpose 💖

Okay so DTRT02 computes the residual for the computed solution to a triangular system of linear equations op(A)*X = B, where A is a triangular matrix. 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. Slay, that's the whole vibe. 💅

⭐ Parameters ⭐

• UPLO — UPLO is CHARACTER*1. Specifies whether matrix A is upper or lower triangular: = 'U': Upper triangular, = 'L': Lower triangular.
• TRANS — TRANS is CHARACTER*1. Specifies the operation applied to A: = 'N': A * X = B (No transpose), = 'T': A**T * X = B (Transpose), = 'C': A**H * X = B (Conjugate transpose = Transpose).
• DIAG — DIAG is CHARACTER*1. Specifies whether or not matrix A is unit triangular: = 'N': Non-unit triangular, = 'U': Unit triangular.
• N — N is INTEGER. The order of matrix A. N >= 0.
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of matrices X and B. NRHS >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). 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.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• X — X is DOUBLE PRECISION array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations.
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• B — B is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N).
• RESID — RESID is DOUBLE PRECISION. The maximum over the number of right hand sides of norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ).

👑 Author 👑

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

Definition at line 148 of file dtrt02.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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🌈 Footer tea: LAPACK Version 3.12.0, file /home/abui...IN/dtrt02.f(3). No date is printed in the footer, so that's the whole sign-off, bestie — byeee 🫶💖