SGBT05(3)

Manual: Library Functions Manual · page: sgbt05.f(3) 💖

🌸 NAME 🌸

Okay bestie, this page is for the file /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/sgbt05.f — yes, the NAME section is literally just that whole path, and we respect her for it. 👑

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine SGBT05 (trans, n, kl, ku, nrhs, ab, ldab, b, ldb, x, ldx,
    xact, ldxact, ferr, berr, reslts)
    SGBT05

💅 Function/Subroutine Documentation 💅

The full signature is giving main-character Fortran energy:

subroutine SGBT05 (character trans, integer n, integer kl, integer ku,
    integer nrhs, real, dimension( ldab, * ) ab, integer ldab, 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)
    SGBT05

🌟 Purpose 🌟

SGBT05 tests the error bounds from iterative refinement for the computed solution to a system of equations op(A)*X = B, where A is a general band matrix of order n with kl subdiagonals and ku superdiagonals and op(A) = A or A**T, depending on TRANS. 💜

The result formulas are iconic and exact:

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. That's the vibe check saying “nope,” no cap. 😭

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. Bestie, pick your fighter:
  • = '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, B, and XACT, and the order of the matrix A. N >= 0.
• KL — KL is INTEGER. The number of subdiagonals within the band of A. KL >= 0.
• KU — KU is INTEGER. The number of superdiagonals within the band of A. KU >= 0.
• NRHS — NRHS is INTEGER. The number of columns of the matrices X, B, and XACT. NRHS >= 0.
• AB — AB is REAL array, dimension (LDAB,N). The original band matrix A, stored in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1.
• 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. (Yes, the dimension says LDX in the source text — we’re keeping it exactly as written, bestie. 🙈)
• 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 174 of file sgbt05.f.

💖 Author 💖

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