CTRT02(3)

👑 CTRT02(3) — Library Functions Manual glow-up 👑

okay so bestie, welcome to the Library Functions Manual page for CTRT02(3). This is LAPACK's little residual-checking subroutine, and it is lowkey doing a lot. Let's get into it 💅

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/ctrt02.f

That's the source file this page is serving, periodt. 💖

✨ SYNOPSIS ✨

🫶 Functions/Subroutines

       subroutine CTRT02 (uplo, trans, diag, n, nrhs, a, lda, x, ldx, b, ldb,
           work, rwork, resid)

CTRT02 is giving "I compute residuals for triangular systems" and honestly? iconic. 🦋

🦋 Function/Subroutine Documentation 🦋

   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 — yes, that's the name, and she's consistent. 💅

💅 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. No cap, that's the whole vibe check. ✨

🎀 Parameters 🎀

• UPLO — CHARACTER*1. Specifies whether the matrix A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — 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 — CHARACTER*1. Specifies whether or not the matrix A is unit triangular.
  • = 'N': Non-unit triangular
  • = 'U': Unit triangular
• N — INTEGER. The order of the matrix A. N >= 0.
• NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
• A — 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• X — COMPLEX array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations.
• LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• B — COMPLEX array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• WORK — COMPLEX array, dimension (N).
• RWORK — REAL array, dimension (N).
• RESID — 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 153 of file ctrt02.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. 💖

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okay bestie, that's the whole page. The footer says LAPACK Version 3.12.0 and points at /home/abui...IN/ctrt02.f(3). Date? Not printed in this footer, so we're not inventing one — keeping it accurate is the main character move. 🫶✨