TESTING/LIN/ztrt02.f(3)

🎀 NAME 🎀

okay so bestie, this is the manual page for TESTING/LIN/ztrt02.f(3) — Library Functions Manual energy, no cap. The main character here is ztrt02, a subroutine that checks residuals for triangular solves, and she is lowkey iconic. 💅

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✨ SYNOPSIS ✨

🌟 Functions/Subroutines 🌟

subroutine ztrt02 (uplo, trans, diag, n, nrhs, a, lda, x, ldx, b, ldb,
    work, rwork, resid)

ZTRT02

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💖 Function/Subroutine Documentation 💖

subroutine ztrt02 (character uplo, character trans, character diag, integer
    n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda,
    complex*16, dimension( ldx, * ) x, integer ldx, complex*16, dimension(
    ldb, * ) b, integer ldb, complex*16, dimension( * ) work, double
    precision, dimension( * ) rwork, double precision resid)

ZTRT02

🌸 Purpose 🌸

ZTRT02 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. slay. ✨

🦋 Parameters 🦋

• UPLO — UPLO is CHARACTER*1 and specifies whether the matrix A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — TRANS is CHARACTER*1 and 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 — DIAG is CHARACTER*1 and 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.
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
• A — A is 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. periodt.

• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• X — X is COMPLEX*16 array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations.
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• B — B is COMPLEX*16 array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• WORK — WORK is COMPLEX*16 array, dimension (N).
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N).
• RESID — RESID is DOUBLE PRECISION. 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 ztrt02.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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💖 okay that’s the whole page, bestie — LAPACK Version 3.12.0, page TESTING/LIN/ztrt02.f(3), signing off with main character energy. mwah 💅✨