TESTING/LIN/spot05.f(3)

🦋 TESTING/LIN/spot05.f(3) 🦋

okay so this is the TESTING/LIN/spot05.f(3) page from the Library Functions Manual, and it’s giving “LAPACK testing routine with receipts” energy. We’re gonna go through every parameter like it’s a group project that actually slaps. 💅

✨ NAME ✨

TESTING/LIN/spot05.f

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine spot05 (uplo, n, nrhs, a, lda, b, ldb, x, ldx, xact, ldxact,
    ferr, berr, reslts)
    SPOT05

✨ Function/Subroutine Documentation ✨

🫶 subroutine spot05

subroutine spot05 (character uplo, integer n, integer nrhs, real, dimension(
    lda, * ) a, integer lda, 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)
    SPOT05

SPOT05 — yes bestie, that’s the name. 🎀

🎀 Purpose 🎀

SPOT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a symmetric n by n matrix. no cap. 🧚

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 / ( (n+1)*EPS + (*) ), where
            (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )

💖 Parameters 💖

• UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — N is INTEGER. The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER. The number of columns of the matrices X, B, and XACT. NRHS >= 0.
• A — A is REAL array, dimension (LDA,N). The symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• 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 / ( (n+1)*EPS + (*) )

👑 Author 👑

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

Definition at line 162 of file spot05.f.

💀 Author 💀

Generated automatically by Doxygen for LAPACK from the source code.

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and that’s the whole page, bestie 🫶 — LAPACK Version 3.12.0, page TESTING/LIN/spot05.f(3). periodt. 💅