TESTING/LIN/dtrt05.f(3)

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version 3.12.1 · 3 versions
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💖 NAME 💖

okay bestie, welcome to TESTING/LIN/dtrt05.f(3) — the manual page for TESTING/LIN/dtrt05.f, aka the DTRT05 test routine. iykyk 💅

🌈 SYNOPSIS 🌈

🧚 Functions/Subroutines 🧚

  • subroutine dtrt05 (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts) — DTRT05

💖 Function/Subroutine Documentation 💖

subroutine dtrt05 (character uplo, character trans, character diag, integer
     n, integer nrhs, double precision, dimension( lda, * ) a, integer lda,
     double precision, dimension( ldb, * ) b, integer ldb, double precision,
     dimension( ldx, * ) x, integer ldx, double precision, dimension( ldxact,
     * ) xact, integer ldxact, double precision, dimension( * ) ferr, double
     precision, dimension( * ) berr, double precision, dimension( * ) reslts)

DTRT05 is literally the main character here ✨

🎀 Purpose 🎀

okay so DTRT05 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. 🦋

RESLTS(1) = test of the error bound

RESLTS(1) = 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

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 matrix A is upper or lower triangular.

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

TRANS

TRANS is 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

DIAG is CHARACTER*1

Specifies whether or not the matrix A is unit triangular.

  • = 'N': Non-unit triangular
  • = 'U': Unit 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 DOUBLE PRECISION array, dimension (LDA,N)

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

The leading dimension of the array A. LDA >= max(1,N).

B

B is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 179 of file dtrt05.f.

💜 Author 💜

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signing off with major main character energy: this page is from LAPACK, version 3.12.0, and the manual-page tag is TESTING/LIN/dtrt05.f(3) — byeee, drink water, and may your triangular solves be slay 💅💖✨

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