ZTPT05(3)

🌸 NAME 🌸

okay so bestie, this page is ztpt05.f(3) from the Library Functions Manual, and the NAME is literally this whole path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/ztpt05.f

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✨ SYNOPSIS ✨

🌟 Functions/Subroutines 🌟

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

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

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🫶 Function/Subroutine Documentation 🫶

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

ZTPT05

💖 Purpose 💖

bestie, 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. no cap, that's the whole job 💅

RESLTS(1) = test of the error bound
          = norm(X - XACT) / ( norm(X) * FERR )

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 )

A large value is returned if this ratio is not less than one. so yeah, that's the vibe check 🔥

🌈 Parameters 🌈

• UPLO — UPLO is CHARACTER*1 and it says whether matrix A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — TRANS is CHARACTER*1 and it says what form the system of equations is in.
  • = 'N': A * X = B (No transpose)
  • = 'T': A'* X = B (Transpose)
  • = 'C': A'* X = B (Conjugate transpose = Transpose)
• DIAG — DIAG is CHARACTER*1 and it says whether or not matrix A is unit triangular.
  • = 'N': Non-unit triangular
  • = 'U': Unit triangular
• N — N is INTEGER. It's the number of rows of the matrices X, B, and XACT, and the order of matrix A. N >= 0.
• NRHS — NRHS is INTEGER. It's the number of columns of the matrices X, B, and XACT. NRHS >= 0.
• AP — AP is COMPLEX*16 array, dimension (N*(N+1)/2). It's 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 — B is COMPLEX*16 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. LDB >= max(1,N).
• X — X is COMPLEX*16 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. LDX >= max(1,N).
• XACT — XACT is COMPLEX*16 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. LDXACT >= max(1,N).
• FERR — FERR is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (NRHS). This is 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). 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 173 of file ztpt05.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie 🫶 it's from LAPACK Version 3.12.0, source path /home/abui...IN/ztpt05.f(3), and the footer didn't give us a date so we're not inventing one — slay responsibly 💅✨