TESTING/LIN/ctrt03.f(3)

🌸 TESTING/LIN/ctrt03.f 🌸

okay so bestie, welcome to this page from the LAPACK Library Functions Manual. The main character is TESTING/LIN/ctrt03.f, and it is lowkey all about checking the residual for a scaled triangular solve. very niche, very iconic. 💅

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✨ NAME ✨

TESTING/LIN/ctrt03.f

🦋 SYNOPSIS 🦋

Functions/Subroutines

       subroutine ctrt03 (uplo, trans, diag, n, nrhs, a, lda, scale, cnorm,
           tscal, x, ldx, b, ldb, work, resid)
           CTRT03

💖 Function/Subroutine Documentation 💖

subroutine ctrt03 — the whole signature, bestie

subroutine ctrt03 (character uplo, character trans, character diag, integer
    n, integer nrhs, complex, dimension( lda, * ) a, integer lda, real
    scale, real, dimension( * ) cnorm, real tscal, complex, dimension( ldx,
    * ) x, integer ldx, complex, dimension( ldb, * ) b, integer ldb,
    complex, dimension( * ) work, real resid)
    CTRT03

Purpose

okay so CTRT03 computes the residual for the solution to a scaled triangular system of equations:

A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b.

Here A is a triangular matrix, A**T denotes the transpose of A, A**H denotes the conjugate transpose of A, s is a scalar, and x and b are N by NRHS matrices. The test ratio is the maximum over the number of right hand sides of

norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),

where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon. no cap, that formula is the whole vibe. 🎀

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 = s*b (No transpose)
  • = 'T': A**T *x = s*b (Transpose)
  • = 'C': A**H *x = s*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).
• SCALE — REAL. The scaling factor s used in solving the triangular system.
• CNORM — REAL array, dimension (N). The 1-norms of the columns of A, not counting the diagonal.
• TSCAL — REAL. The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.
• 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).
• RESID — REAL. The maximum over the number of right hand sides of

norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).

Author

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

Definition at line 169 of file ctrt03.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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that's the whole page, bestie 💜 — footer flavor: LAPACK Version 3.12.0, source TESTING/LIN/ctrt03.f(3), and no separate date shown, so no invented date energy here 🙈 periodt. 🫶