TESTING/LIN/ctrt02.f(3)

📦
version 3.12.1 · 2 versions
, in arch rolling

🌸 NAME 🌸

TESTING/LIN/ctrt02.f — okay bestie, this is the page for ctrt02, and it lives in the Library Functions Manual 💅

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine ctrt02 (uplo, trans, diag, n, nrhs, a, lda, x, ldx, b, ldb,
    work, rwork, resid)

CTRT02 — that's the name, periodt ✨

💜 Function/Subroutine Documentation 💜

🎀 ctrt02 🎀

subroutine ctrt02 (character uplo, character trans, character diag, integer
    n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex,
    dimension( ldx, * ) x, integer ldx, complex, dimension( ldb, * ) b,
    integer ldb, complex, dimension( * ) work, real, dimension( * ) rwork,
    real resid)

CTRT02 💖

🎯 Purpose

CTRT02 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, A**T, or A**H, b is the column of B, x is the solution vector, and EPS is the machine epsilon. Slay, that's the whole vibe of what it checks 💅

🧸 Parameters

  • UPLO — UPLO is CHARACTER*1. It says 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)
  • DIAG — DIAG is CHARACTER*1. Says whether matrix A is unit triangular or not.
    • = '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 COMPLEX array, dimension (LDA,N). The triangular matrix A. If UPLO = 'U', the leading n by n upper triangular part of 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 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. No cap, that's important 👑
  • LDA — LDA is INTEGER. The leading dimension of array A. LDA >= max(1,N).
  • X — X is COMPLEX array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations.
  • LDX — LDX is INTEGER. The leading dimension of array X. LDX >= max(1,N).
  • 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 array B. LDB >= max(1,N).
  • WORK — WORK is COMPLEX array, dimension (N).
  • RWORK — RWORK is REAL array, dimension (N).
  • RESID — RESID is REAL. 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 📜

Definition at line 153 of file ctrt02.f.

🫶 Author 🫶

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okay that's the whole page, bestie 🫶 source/version: LAPACK Version 3.12.0; page: TESTING/LIN/ctrt02.f(3); date: not listed on this page 💀✨

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