TESTING/LIN/ctrt01.f(3)

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✨ TESTING/LIN/ctrt01.f — CTRT01 ✨

Okay bestie, welcome to the TESTING/LIN/ctrt01.f page from the Library Functions Manual — it's giving section 3 energy, and we're gonna get through every single detail together. 💅🦋

🌸 NAME 🌸

TESTING/LIN/ctrt01.f — that's the file on the page, and that's the name, periodt. 💖

🦋 SYNOPSIS 🦋

🌟 Functions/Subroutines 🌟

  • subroutine ctrt01 (uplo, diag, n, a, lda, ainv, ldainv, rcond, rwork, resid) — CTRT01
       subroutine ctrt01 (uplo, diag, n, a, lda, ainv, ldainv, rcond, rwork,
           resid)
           CTRT01

💖 Function/Subroutine Documentation 💖

   subroutine ctrt01 (character uplo, character diag, integer n, complex,
       dimension( lda, * ) a, integer lda, complex, dimension( ldainv, * )
       ainv, integer ldainv, real rcond, real, dimension( * ) rwork, real
       resid)
       CTRT01

🎀 Purpose 🎀

           !>
           !> CTRT01 computes the residual for a triangular matrix A times its
           !> inverse:
           !>    RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
           !> where EPS is the machine epsilon.
           !>

So basically it's computing the residual for a triangular matrix A times its inverse, with that exact formula. No cap, that's the whole vibe. ✨

🌈 Parameters 🌈

💜 UPLO

UPLO is CHARACTER*1. It specifies whether the matrix A is upper or lower triangular:

  • = 'U': Upper triangular
  • = 'L': Lower triangular

💜 DIAG

DIAG is CHARACTER*1. It specifies whether or not the matrix A is unit triangular:

  • = 'N': Non-unit triangular
  • = 'U': Unit triangular

💜 N

N is INTEGER. It's the order of the matrix A, and N >= 0.

💜 A

A is COMPLEX 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. 🫶

💜 LDA

LDA is INTEGER. It's the leading dimension of the array A, and LDA >= max(1,N).

💜 AINV

AINV is COMPLEX 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. So yeah, she's not coming back the same, bestie. 💀

💜 LDAINV

LDAINV is INTEGER. It's the leading dimension of the array AINV, and LDAINV >= max(1,N).

💜 RCOND

RCOND is REAL. It's the reciprocal condition number of A, computed as 1/(norm(A) * norm(AINV)).

💜 RWORK

RWORK is REAL array, dimension (N).

💜 RESID

RESID is REAL, and it's exactly:

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

👑 Author 👑

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

Definition at line 123 of file ctrt01.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

And that's the whole page, bestie! 💖 The footer energy is LAPACK Version 3.12.0 on TESTING/LIN/ctrt01.f(3) — no date is listed in the footer, so don't come for me about a calendar date, periodt. 🫶✨

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