TESTING/LIN/stbt05.f(3)

📦
version 3.12.1 · 3 versions
, in arch rolling

🦋 TESTING/LIN/stbt05.f

Okay bestie, this page is from the Library Functions Manual, and it’s all about stbt05 — no cap, it’s a whole LAPACK testing subroutine 💅✨

🌸 NAME

TESTING/LIN/stbt05.f

✨ SYNOPSIS

🧩 Functions/Subroutines

subroutine stbt05 (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x,
    ldx, xact, ldxact, ferr, berr, reslts)

STBT05

📚 Function/Subroutine Documentation

subroutine stbt05 (character uplo, character trans, character diag, integer
    n, integer kd, 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)

STBT05

🎯 Purpose

Lowkey this one is doing error-bound checks 👑 STBT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a triangular band matrix. Periodt.

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(A)*abs(X) +abs(b))_i )
            and NZ = max. number of nonzeros in any row of A, plus 1

🧸 Parameters

🌸 UPLO

Type: CHARACTER*1. Specifies whether the matrix A is upper or lower triangular, bestie.

  • = 'U': Upper triangular
  • = 'L': Lower triangular

🦋 TRANS

Type: CHARACTER*1. Specifies the form of the system of equations.

  • = 'N': A * X = B (No transpose)
  • = 'T': A'* X = B (Transpose)
  • = 'C': A'* X = B (Conjugate transpose = Transpose)

🎀 DIAG

Type: CHARACTER*1. Specifies whether or not the matrix A is unit triangular.

  • = 'N': Non-unit triangular
  • = 'U': Unit triangular

⭐ N

Type: INTEGER. The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.

💫 KD

Type: INTEGER. The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.

🌈 NRHS

Type: INTEGER. The number of columns of the matrices X, B, and XACT. NRHS >= 0.

🍓 AB

Type: REAL array, dimension (LDAB,N). The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

💜 LDAB

Type: INTEGER. The leading dimension of the array AB. LDAB >= KD+1.

🧚 B

Type: REAL array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.

🔥 LDB

Type: INTEGER. The leading dimension of the array B. LDB >= max(1,N).

🫶 X

Type: REAL array, dimension (LDX,NRHS). The computed solution vectors. Each vector is stored as a column of the matrix X.

🌟 LDX

Type: INTEGER. The leading dimension of the array X. LDX >= max(1,N).

🎀 XACT

Type: REAL array, dimension (LDX,NRHS). The exact solution vectors. Each vector is stored as a column of the matrix XACT.

🦋 LDXACT

Type: INTEGER. The leading dimension of the array XACT. LDXACT >= max(1,N).

💖 FERR

Type: 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

Type: 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

Type: 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

Definition at line 187 of file stbt05.f.

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

mwah 💋 — LAPACK Version 3.12.0, page TESTING/LIN/stbt05.f(3). The footer doesn’t show a separate date line, bestie, so I’m not inventing one 🙈✨

📦 where this page comes from