STRT05(3)

💅 STRT05(3) — Library Functions Manual 💅

okay bestie, welcome to the STRT05(3) page — yes, the Library Functions Manual one. The file tag up top is /home/abui...IN/strt05.f(3), and this whole thing is giving LAPACK testing energy. Let's get into it 💖

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/strt05.f

✨ SYNOPSIS ✨

Functions/Subroutines

       subroutine STRT05 (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx,
           xact, ldxact, ferr, berr, reslts)
           STRT05

🦋 Function/Subroutine Documentation 🦋

   subroutine STRT05 (character uplo, character trans, character diag, 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)
       STRT05

🎀 Purpose 🎀

okay so STRT05 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 = 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 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 REAL 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 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 179 of file strt05.f.

👑 Author 👑

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