SGTT05(3)

💅 SGTT05(3) — Library Functions Manual 💅

okay so bestie, welcome to SGTT05(3) — this is a Library Functions Manual page, and it's giving “I test error bounds from iterative refinement” energy. Let’s get into it 💖

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/sgtt05.f

that’s the file path this page is named after, fr fr 🫶

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine SGTT05 (trans, n, nrhs, dl, d, du, b, ldb, x, ldx, xact,
           ldxact, ferr, berr, reslts)
           SGTT05

🦋 Function/Subroutine Documentation 🦋

SGTT05 🫶

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

that’s the whole signature, bestie — every argument accounted for 💅

🎯 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. that’s the assignment, no cap ✨

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

warning-ish: a large value is returned if this ratio is not less than one. periodt.

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. it 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 + (*) )

👑 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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okay that’s the whole vibe check. this page is from LAPACK, version 3.12.0, and the file it’s repping is /home/abui...IN/sgtt05.f(3). mwah 💋✨