CTRT01(3)

📦 version 3.12.0, in opensuse-leap 16.0

Hey bestie 💖 welcome to CTRT01(3), hanging out in the Library Functions Manual. This is a LAPACK testing-lin situation, and the vibe is: check the residual of a triangular matrix times its inverse. No cap.

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/ctrt01.f

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

CTRT01

💖 Function/Subroutine Documentation 💖

🦋 subroutine CTRT01 🦋

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 ✨

Okay so 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. Obsessed with a clean residual, honestly.

🌈 Parameters 🌈

  • UPLO — UPLO is CHARACTER*1. Specifies whether the matrix A is upper or lower triangular.
    • = 'U': Upper triangular
    • = 'L': Lower triangular
  • DIAG — DIAG is CHARACTER*1. Specifies whether or not the matrix A is unit triangular.
    • = 'N': Non-unit triangular
    • = 'U': Unit triangular
  • N — N is INTEGER. The order of the matrix A. N >= 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 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).
  • AINV — AINV is COMPLEX array, dimension (LDAINV,N). On entry, the (triangular) inverse of the matrix A, in the same storage format as A. On exit, the contents of AINV are destroyed.
  • LDAINV — LDAINV is INTEGER. The leading dimension of the array AINV. LDAINV >= max(1,N).
  • RCOND — RCOND is REAL. The reciprocal condition number of A, computed as 1/(norm(A) * norm(AINV)).
  • RWORK — RWORK is REAL array, dimension (N).
  • RESID — RESID is REAL. 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 👑

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