TESTING/LIN/ztpt05.f(3)

✨ NAME ✨

Okay so this page lives in the Library Functions Manual, and the page itself is TESTING/LIN/ztpt05.f(3) — yes bestie, that's the manual-name situation folded in right here. It's literally all about the ztpt05 subroutine. 💅

🌸 SYNOPSIS 🌸

🧁 Functions/Subroutines 🧁

subroutine ztpt05 (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, xact,
    ldxact, ferr, berr, reslts)
    ZTPT05

🦋 Function/Subroutine Documentation 🦋

Here's the full signature, character for character, no cap:

   subroutine ztpt05 (character uplo, character trans, character diag, integer
       n, integer nrhs, complex*16, dimension( * ) ap, 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)
       ZTPT05

🎀 Purpose 🎀

Okay, the whole point: ZTPT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a triangular matrix in packed storage format. It's giving "trust but verify" energy, fr fr. 💖

Here's the RESLTS(1) situation:

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. That's the warning vibe, bestie. 😭

And here's RESLTS(2):

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 — CHARACTER*1. Specifies whether the matrix A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — 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 — CHARACTER*1. Specifies whether or not the matrix A is unit triangular.
  • = 'N': Non-unit triangular
  • = 'U': Unit triangular
• N — INTEGER. The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.
• NRHS — INTEGER. The number of columns of the matrices X, B, and XACT. NRHS >= 0.
• AP — COMPLEX*16 array, dimension (N*(N+1)/2). The upper or lower triangular 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.

If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

• B — COMPLEX*16 array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — COMPLEX*16 array, dimension (LDX,NRHS). The computed solution vectors. Each vector is stored as a column of the matrix X.
• LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• XACT — COMPLEX*16 array, dimension (LDX,NRHS). The exact solution vectors. Each vector is stored as a column of the matrix XACT.
• LDXACT — INTEGER. The leading dimension of the array XACT. LDXACT >= max(1,N).
• FERR — 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 — 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 — DOUBLE PRECISION array, dimension (2). The maximum over the NRHS solution vectors of the ratios: RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) and RESLTS(2) = BERR / ( (n+1)*EPS + (*) ).

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 173 of file ztpt05.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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💖 okay that's the whole page, bestie. The footer vibe is LAPACK Version 3.12.0, page TESTING/LIN/ztpt05.f(3). Mwah! 💖