ZGTT05(3)

💅 ZGTT05(3) — the LAPACK test routine bestie 💅

okay so this page is from the Library Functions Manual, and we're talking about ZGTT05. It's a subroutine from LAPACK, and it tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a general tridiagonal matrix of order n and op(A) = A or A**T, depending on TRANS. (Yes, the tridiagonal girlies are eating.) ✨

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📛 NAME 📛

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zgtt05.f

That's the file path, no cap. 🫶

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🫶 SYNOPSIS 🫶

Functions/Subroutines

• ZGTT05 — the function/subroutine you came for, in all its icon behavior.

subroutine ZGTT05 (trans, n, nrhs, dl, d, du, b, ldb, x, ldx, xact,
    ldxact, ferr, berr, reslts)

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🧚 Function/Subroutine Documentation 🧚

subroutine ZGTT05

subroutine ZGTT05 (character trans, integer n, integer nrhs, complex*16,
    dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension(
    * ) du, complex*16, dimension( ldb, * ) b, integer ldb, complex*16,
    dimension( ldx, * ) x, integer ldx, complex*16, dimension( ldxact, * )
    xact, integer ldxact, double precision, dimension( * ) ferr, double
    precision, dimension( * ) berr, double precision, dimension( * ) reslts)

ZGTT05 — yes bestie, that's the whole vibe.

🎯 Purpose: 🎯

okay so the purpose is literally: ZGTT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a general tridiagonal matrix of order n and op(A) = A or A**T, depending on TRANS.

RESLTS(1) = test of the error bound
          = norm(X - XACT) / ( norm(X) * FERR )

A large value is returned if this ratio is not less than one.

RESLTS(2) = residual from the iterative refinement routine
          = the maximum of BERR / ( NZ*EPS + (*) ), where
            (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
            and NZ = max. number of nonzeros in any row of A, plus 1

That's the formula glow-up. 💅

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🌸 Parameters 🌸

• TRANS — CHARACTER*1. Specifies the form of the system of equations:
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose = Transpose)
• N — INTEGER. The number of rows of the matrices X and XACT. N >= 0.
• NRHS — INTEGER. The number of columns of the matrices X and XACT. NRHS >= 0.
• DL — COMPLEX*16 array, dimension (N-1). The (n-1) sub-diagonal elements of A.
• D — COMPLEX*16 array, dimension (N). The diagonal elements of A.
• DU — COMPLEX*16 array, dimension (N-1). The (n-1) super-diagonal elements of A.
• 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).
• X — COMPLEX*16 array, dimension (LDX,NRHS). The computed solution vectors. Each vector is stored as a column of the matrix X.
• LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• XACT — COMPLEX*16 array, dimension (LDX,NRHS). The exact solution vectors. Each vector is stored as a column of the matrix XACT.
• LDXACT — INTEGER. The leading dimension of the array XACT. LDXACT >= max(1,N).
• FERR — DOUBLE PRECISION array, dimension (NRHS). The estimated forward error bounds for each solution vector X. If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X.
• BERR — DOUBLE PRECISION array, dimension (NRHS). The componentwise relative backward error of each solution vector (i.e., the smallest relative change in any entry of A or B that makes X an exact solution).
• RESLTS — DOUBLE PRECISION array, dimension (2). The maximum over the NRHS solution vectors of the ratios:

RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( NZ*EPS + (*) )

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👑 Author 👑

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

📍 Definition at line 163 of file zgtt05.f.

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🎀 Author (auto-generated edition) 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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💖 okay bye bestie 💖 — this footer energy is LAPACK Version 3.12.0, from the path /home/abui...IN/zgtt05.f(3). There's literally no date in the footer, so no date to give you; don't come for me 💀. Mwah! 🫶