CGET07(3)

💅 CGET07(3) — Library Functions Manual edition 💖

Bestie, welcome to the group chat for CGET07 — she lives in the Library Functions Manual, and she is here to test error bounds. Obsessed. ✨

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/cget07.f

🦋 SYNOPSIS 🦋

🧚 Functions/Subroutines

subroutine CGET07 (trans, n, nrhs, a, lda, b, ldb, x, ldx, xact, ldxact, ferr, chkferr, berr, reslts)

CGET07 — yeah, that’s the whole vibe. 🫶

🌸 Function/Subroutine Documentation 🌸

subroutine CGET07 (character trans, integer n, integer nrhs, complex,
    dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b,
    integer ldb, complex, dimension( ldx, * ) x, integer ldx, complex,
    dimension( ldxact, * ) xact, integer ldxact, real, dimension( * ) ferr,
    logical chkferr, real, dimension( * ) berr, real, dimension( * ) reslts)

CGET07 — yes, her name again, main character energy. 👑

🎯 Purpose

Okay so CGET07 tests the error bounds from iterative refinement for the computed solution to a system of equations op(A)*X = B, where A is a general n by n matrix and op(A) = A or A**T, depending on TRANS. 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. Watch out, bestie — that’s the warning vibe. 💀

RESLTS(2) = residual from the iterative refinement routine
          = the maximum of BERR / ( (n+1)*EPS + (*) ), where
            (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )

🧸 Parameters

🔁 TRANS

TRANS is CHARACTER*1

Specifies the form of the system of equations.

= 'N':  A * X = B     (No transpose)
= 'T':  A**T * X = B  (Transpose)
= 'C':  A**H * X = B  (Conjugate transpose = Transpose)

🔢 N

N is INTEGER

The number of rows of the matrices X and XACT. N >= 0.

🔢 NRHS

NRHS is INTEGER

The number of columns of the matrices X and XACT. NRHS >= 0.

🧊 A

A is COMPLEX array, dimension (LDA,N)

The original n by n matrix A.

📏 LDA

LDA is INTEGER

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

🧊 B

B is COMPLEX 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 COMPLEX 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 COMPLEX 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.

✅ CHKFERR

CHKFERR is LOGICAL

Set to .TRUE. to check FERR, .FALSE. not to check FERR. When the test system is ill-conditioned, the solution in XACT may be incorrect.

🧪 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 164 of file cget07.f.

🫶 Author

Generated automatically by Doxygen for LAPACK from the source code.

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💖 Cute sign-off: this page is from LAPACK Version 3.12.0, and the source path is /home/abui...IN/cget07.f(3). The footer didn’t give me a separate date, so I’m not inventing one — periodt. 🫶