ZTRT05(3)

💖 ZTRT05(3) 💖

okay so this is the LAPACK Library Functions Manual page for ZTRT05, and its header path is /home/abui...IN/ztrt05.f(3). grab a lil snack 🍓, bestie, we're getting into it.

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✨ NAME ✨

the NAME line is literally just this path — no fancy label, just the file, periodt:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/ztrt05.f

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🌸 SYNOPSIS 🌸

🌈 Functions/Subroutines 🌈

subroutine ZTRT05 (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx,
    xact, ldxact, ferr, berr, reslts)
    ZTRT05

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🦋 Function/Subroutine Documentation 🦋

here's the full signature, bestie — no cap, this is exactly it:

subroutine ZTRT05 (character uplo, character trans, character diag, integer
       n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda,
       complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension(
       ldx, * ) x, integer ldx, complex*16, dimension( ldxact, * ) xact,
       integer ldxact, double precision, dimension( * ) ferr, double precision,
       dimension( * ) berr, double precision, dimension( * ) reslts)
       ZTRT05

🎀 Purpose 🎀

okay so ZTRT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a triangular n by n matrix. it's giving "vibe check but for numerical accuracy" ✨

the ratios are:

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

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 )

and yeah — a large value is returned if this ratio is not less than one. so if that number is big, the routine is basically side-eyeing you 🚩😭

💅 Parameters 💅

UPLO

UPLO is CHARACTER*1. it specifies whether the matrix A is upper or lower triangular:

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

TRANS

TRANS is CHARACTER*1. it 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

DIAG is CHARACTER*1. it specifies whether or not the matrix A is unit triangular:

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

N

N is INTEGER. it's the number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.

NRHS

NRHS is INTEGER. it's the number of columns of the matrices X, B, and XACT. NRHS >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N). it's the triangular matrix A. if UPLO = 'U', the leading n by n upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. if UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. if DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.

LDA

LDA is INTEGER. it's the leading dimension of the array A. LDA >= max(1,N).

B

B is COMPLEX*16 array, dimension (LDB,NRHS). these are the right hand side vectors for the system of linear equations.

LDB

LDB is INTEGER. it's the leading dimension of the array B. LDB >= max(1,N).

X

X is COMPLEX*16 array, dimension (LDX,NRHS). these are the computed solution vectors. each vector is stored as a column of the matrix X.

LDX

LDX is INTEGER. it's the leading dimension of the array X. LDX >= max(1,N).

XACT

XACT is COMPLEX*16 array, dimension (LDX,NRHS). these are the exact solution vectors. each vector is stored as a column of the matrix XACT.

LDXACT

LDXACT is INTEGER. it's the leading dimension of the array XACT. LDXACT >= max(1,N).

FERR

FERR is DOUBLE PRECISION array, dimension (NRHS). these are 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 DOUBLE PRECISION array, dimension (NRHS). this is 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 DOUBLE PRECISION array, dimension (2). it's 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 180 of file ztrt05.f.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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that's the whole page, bestie 🫶 — it's LAPACK Version 3.12.0, and the footer path is /home/abui...IN/ztrt05.f(3). mwah, bye! 💅✨