SRC/dtrrfs.f(3)

okay so bestie, welcome to SRC/dtrrfs.f(3) from the Library Functions Manual — this page is giving LAPACK error-bound realness and we are seated 💅

💖 NAME 💖

SRC/dtrrfs.f — the DTRRFS girlies are here to give you error bounds and backward error estimates for triangular linear systems ✨

🌸 SYNOPSIS 🌸

🎀 Functions/Subroutines 🎀

subroutine dtrrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx,
    ferr, berr, work, iwork, info)
    DTRRFS

🦋 Function/Subroutine Documentation 🦋

subroutine dtrrfs (character uplo, character trans, character diag, integer
    n, integer nrhs, double precision, dimension( lda, * ) a, integer lda,
    double precision, dimension( ldb, * ) b, integer ldb, double precision,
    dimension( ldx, * ) x, integer ldx, double precision, dimension( * )
    ferr, double precision, dimension( * ) berr, double precision,
    dimension( * ) work, integer, dimension( * ) iwork, integer info)
    DTRRFS

🌟 DTRRFS 🌟

🎯 Purpose 🎯

okay so DTRRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. no cap, that's the whole vibe 🔥

the solution matrix X must be computed by DTRTRS or some other means before entering this routine. and listen: DTRRFS does not do iterative refinement because doing so cannot improve the backward error. periodt 💅

🧸 Parameters 🧸

• UPLO — UPLO is CHARACTER*1; = 'U': A is upper triangular; = 'L': A is lower triangular.
• TRANS — TRANS is CHARACTER*1; 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 = 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.
• NRHS — NRHS is INTEGER; the number of right hand sides, i.e., the number of columns of the matrices B and X. 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).
• B — B is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDX,NRHS); the solution matrix X.
• LDX — LDX is INTEGER; the leading dimension of the array X. LDX >= max(1,N).
• FERR — FERR is DOUBLE PRECISION 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), 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 is almost always a slight overestimate of the true error. bestie, it's lowkey overestimating on purpose 🙈
• BERR — BERR is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (3*N).
• IWORK — IWORK is INTEGER array, dimension (N).
• INFO — INFO is INTEGER; = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value.

👑 Author 👑

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

Definition at line 180 of file dtrrfs.f.

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🌈 Author 🌈

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