TESTING/LIN/sgtt05.f(3)

💖 SGTT05 — tridiagonal error-bound vibe check, bestie 💖

okay so this is the manual page for TESTING/LIN/sgtt05.f(3) from the Library Functions Manual, and it’s giving “I test iterative-refinement error bounds for a general tridiagonal matrix” energy. iconic. let’s get into it ✨

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🌸 NAME 🌸

TESTING/LIN/sgtt05.f — yes bestie, that’s literally the file this whole page is about 🫶

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine sgtt05 (trans, n, nrhs, dl, d, du, b, ldb, x, ldx, xact,
     ldxact, ferr, berr, reslts)

SGTT05 is the subroutine name, and it’s the main character here 👑

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🫶 Function/Subroutine Documentation 🫶

subroutine sgtt05 (character trans, integer n, integer nrhs, real,
     dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du,
     real, dimension( ldb, * ) b, integer ldb, real, dimension( ldx, * ) x,
     integer ldx, real, dimension( ldxact, * ) xact, integer ldxact, real,
     dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * )
     reslts)

SGTT05

🎀 Purpose 🎀

okay so SGTT05 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. no cap, that’s the whole warning.

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

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🌈 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 REAL array, dimension (N-1).
• The (n-1) sub-diagonal elements of A.

💅 D

• D is REAL array, dimension (N).
• The diagonal elements of A.

💅 DU

• DU is REAL array, dimension (N-1).
• The (n-1) super-diagonal elements of A.

💅 B

• B is REAL 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 REAL 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 REAL 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 + (*) )

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👑 Author 👑

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

📌 Definition at line 163 of file sgtt05.f.

🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 — this cutie is from LAPACK Version 3.12.0, for the page TESTING/LIN/sgtt05.f(3). slay and goodbye 💖✨