CPPT05(3)

✨ NAME ✨

Bestie, this is the CPPT05 page from the Library Functions Manual 💅, and the exact source file is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/cppt05.f. That's the whole name/address situation, no cap.

🌸 SYNOPSIS 🌸

✨ Functions/Subroutines ✨

subroutine CPPT05 (uplo, n, nrhs, ap, b, ldb, x, ldx, xact, ldxact,
    ferr, berr, reslts)

And the subroutine itself is, obviously, CPPT05 👑.

💖 Function/Subroutine Documentation 💖

subroutine CPPT05 (character uplo, integer n, integer nrhs, complex,
    dimension( * ) ap, complex, dimension( ldb, * ) b, integer ldb, complex,
    dimension( ldx, * ) x, integer ldx, complex, dimension( ldxact, * )
    xact, integer ldxact, real, dimension( * ) ferr, real, dimension( * )
    berr, real, dimension( * ) reslts)

CPPT05 again, because main character energy ✨.

🎯 Purpose

Okay so listen: CPPT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a Hermitian matrix in packed storage format. Obsessed with the specificity, honestly. 🫶

The result ratios are:

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 )

⚠️ That "large value" line is important, bestie — if the ratio is not less than one, the routine returns a large value. Keep that in mind.

📝 Parameters

💅 UPLO

UPLO is CHARACTER*1. It says whether the upper or lower triangular part of the Hermitian matrix A is stored.

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

Constraint: N >= 0.

🧮 NRHS

NRHS is INTEGER. It's the number of columns of the matrices X, B, and XACT.

Constraint: NRHS >= 0.

🍓 AP

AP is a COMPLEX array, dimension (N*(N+1)/2). It holds the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:

if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

🍓 B

B is a COMPLEX 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.

Constraint: LDB >= max(1,N).

🦋 X

X is a COMPLEX 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.

Constraint: LDX >= max(1,N).

🦋 XACT

XACT is a COMPLEX 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.

Constraint: LDXACT >= max(1,N).

🎀 FERR

FERR is a REAL 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 a REAL array, dimension (NRHS). It's 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 a REAL 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 155 of file cppt05.f.

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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And that's the tea ☕💖. Footer vibe check: source/version is LAPACK Version 3.12.0, and the page path is /home/abui...IN/cppt05.f(3). The original footer doesn't show a date, so I'm not inventing one, bestie. Byeee 🫶✨