SPOT05(3)

okay bestie, welcome to the spot05.f(3) page 💅 it lives in the Library Functions Manual, and it’s all about SPOT05 — a Fortran subroutine that checks error bounds like it’s doing a vibe check on your linear solve. no cap, every detail is here. grab a strawberry drink 🍓 and let’s go.

🌸 NAME 🌸

the NAME is literally this exact file path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/spot05.f

iconic, chaotic, but that’s the name 💖

✨ SYNOPSIS ✨

Functions/Subroutines

here’s the callable thing, bestie:

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

💫 Function/Subroutine Documentation 💫

this is the full documentation flex. the signature is long and dramatic, but it’s exactly this:

   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

🎀 Purpose 🎀

bestie, the purpose is this: 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. it’s giving quality control for your solve 🔥

RESLTS(1) is the test of the error bound:

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 failing 😭

RESLTS(2) is the residual from the iterative refinement routine:

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 🧩

every parameter matters, no skipping 💅

UPLO

UPLO is CHARACTER*1 and tells us whether we’re storing the upper or lower triangular part of the symmetric matrix A.

• = '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 👑

the author squad is: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd. 💜

Definition at line 162 of file spot05.f.

👑 Author 👑

this page was generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie. signing off from LAPACK Version 3.12.0, page /home/abui...IN/spot05.f(3) 💖✨ go forth, check those error bounds, and slay. periodt.