TESTING/LIN/ztrt03.f(3)

🌸 NAME 🌸

okay bestie, this manual page is literally named TESTING/LIN/ztrt03.f 💅 and yes, we're folding the manual name in right here: it's from the Library Functions Manual, and the page title is TESTING/LIN/ztrt03.f(3).

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine ztrt03 (uplo, trans, diag, n, nrhs, a, lda, scale, cnorm,
    tscal, x, ldx, b, ldb, work, resid)

ZTRT03 👑

🎀 Function/Subroutine Documentation 🎀

subroutine ztrt03 (character uplo, character trans, character diag, integer
    n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, double
    precision scale, double precision, dimension( * ) cnorm, double
    precision tscal, complex*16, dimension( ldx, * ) x, integer ldx,
    complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( *
    ) work, double precision resid)

ZTRT03 is the main character here, no cap ✨

Purpose

ZTRT03 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 💖

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*16 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 — DOUBLE PRECISION. The scaling factor s used in solving the triangular system.
• CNORM — DOUBLE PRECISION array, dimension (N). The 1-norms of the columns of A, not counting the diagonal.
• TSCAL — DOUBLE PRECISION. The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A 🦋
• X — COMPLEX*16 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*16 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*16 array, dimension (N).
• RESID — DOUBLE PRECISION. 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 ztrt03.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

---

okay that's the whole vibe, bestie 💖 this page came from LAPACK Version 3.12.0 and TESTING/LIN/ztrt03.f(3) — mwah, bye! 🌸👑