CGTT05(3)

💖 CGTT05(3) — cgtt05.f 💖

okay bestie, welcome to the Library Functions Manual page for CGTT05(3) / cgtt05.f ✨ this is the LAPACK testing subroutine that does error-bound checks for iterative refinement, and we’re gonna make it make sense. 🫶

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🌸 NAME 🌸

The name here is literally this source path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/cgtt05.f

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💫 SYNOPSIS 💫

Functions/Subroutines

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

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🧚 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

CGTT05 is the main character here 👑 — a subroutine, and yes, it’s named exactly like that.

✨ Purpose: ✨

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. 💅

The results land in RESLTS, 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

So yeah — if that first ratio is not less than one, a large value comes back. That’s the vibe check. 🚨

🌈 Parameters 🌈

TRANS

TRANS is CHARACTER*1

It specifies the form of the system of equations, and it has exactly these options:

• = '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. 🧚

yes bestie, the original says LDX right there for XACT, so we’re keeping it exactly as written — no “fixing” lore. 🙈

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.

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🪄 Author 🪄

Generated automatically by Doxygen for LAPACK from the source code.

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Signed off with footer energy: LAPACK, Version 3.12.0, and the page path /home/abui...IN/cgtt05.f(3) — no separate date line in sight, so that’s the whole footer vibe. 💜💅✨