TESTING/LIN/cgtt05.f(3)

💖 TESTING/LIN/cgtt05.f(3) 💖

okay so welcome to the Library Functions Manual entry for TESTING/LIN/cgtt05.f — yes, the filename is also the title, she’s doing double duty 💅. This page is giving “LAPACK test routine that checks iterative-refinement error bounds for tridiagonal systems” energy, and honestly? Iconic.

✨ NAME ✨

TESTING/LIN/cgtt05.f

🌸 SYNOPSIS 🌸

🎀 Functions/Subroutines 🎀

subroutine cgtt05 (trans, n, nrhs, dl, d, du, b, ldb, x, ldx, xact,
    ldxact, ferr, berr, reslts)
    CGTT05

🦋 Function/Subroutine Documentation 🦋

subroutine cgtt05 (character trans, integer n, integer nrhs, complex,
    dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * )
    du, complex, dimension( ldb, * ) b, integer ldb, complex, dimension(
    ldx, * ) x, integer ldx, complex, dimension( ldxact, * ) xact, integer
    ldxact, real, dimension( * ) ferr, real, dimension( * ) berr, real,
    dimension( * ) reslts)
    CGTT05

💜 Purpose 💜

okay so CGTT05 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.

Then the receipts, bestie:

• 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

🌈 Parameters 🌈

• TRANS — TRANS is 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 — N is INTEGER. The number of rows of the matrices X and XACT. N >= 0.
• NRHS — NRHS is INTEGER. The number of columns of the matrices X and XACT. NRHS >= 0.
• DL — DL is COMPLEX array, dimension (N-1). The (n-1) sub-diagonal elements of A.
• D — D is COMPLEX array, dimension (N). The diagonal elements of A.
• DU — DU is COMPLEX array, dimension (N-1). The (n-1) super-diagonal elements of A.
• B — B is COMPLEX 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).
• X — X is COMPLEX array, dimension (LDX,NRHS). The computed solution vectors. Each vector is stored as a column of the matrix X.
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• XACT — XACT is COMPLEX array, dimension (LDX,NRHS). The exact solution vectors. Each vector is stored as a column of the matrix XACT.
• LDXACT — LDXACT is INTEGER. The leading dimension of the array XACT. LDXACT >= max(1,N).
• FERR — FERR is REAL 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 — BERR is REAL 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 — RESLTS is REAL 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 + (*) )

🌟 Author 🌟

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

Definition at line 163 of file cgtt05.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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xoxo, LAPACK 💖 — Version 3.12.0 — TESTING/LIN/cgtt05.f(3). The footer didn’t print a separate date, so no invented date, bestie; source = LAPACK, version = 3.12.0. 🫶