DTPT02(3)

💅 DTPT02 (3) — bestie, it's a LAPACK test routine

ok so real talk, this whole page lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dtpt02.f (the header and footer crop it down to /home/abui...IN/dtpt02.f(3) because apparently even manpage headers have a character limit, iconic of them honestly). It's from the library functions manual, and it's giving "small but mighty" ✨

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🌸 SYNOPSIS

Functions/Subroutines

subroutine DTPT02 (uplo, trans, diag, n, nrhs, ap, x, ldx, b, ldb, work,
    resid)

DTPT02 🫶

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🎀 Function/Subroutine Documentation

subroutine DTPT02 (character uplo, character trans, character diag, integer
    n, integer nrhs, double precision, dimension( * ) ap, double precision,
    dimension( ldx, * ) x, integer ldx, double precision, dimension( ldb, *
    ) b, integer ldb, double precision, dimension( * ) work, double
    precision resid)

DTPT02 💖

✨ Purpose

!> DTPT02 computes the residual for the computed solution to a !> triangular system of linear equations op(A)*X = B, when the !> triangular matrix A is stored in packed format. The test ratio is !> the maximum over !> norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ), !> where op(A) = A or A**T, b is the column of B, x is the solution !> vector, and EPS is the machine epsilon. !> The norm used is the 1-norm. !>

So bestie, DTPT02 is the vibe-checker 👑 — it computes the residual for your computed solution to a triangular system of linear equations op(A)*X = B, when the triangular matrix A is stored in packed format. The test ratio is the max over:

norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),

where op(A) = A or A**T, b is the column of B, x is the solution vector, and EPS is the machine epsilon. The norm used is the 1-norm. no cap, that's the whole personality 🧚

🦋 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 operation applied to A.
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * 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 order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
• AP — AP is DOUBLE PRECISION 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((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
  • if UPLO = 'L', AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
• X — X is DOUBLE PRECISION array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations.
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• B — B is DOUBLE PRECISION 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).
• WORK — WORK is DOUBLE PRECISION array, dimension (N).
• RESID — RESID is DOUBLE PRECISION. The maximum over the number of right hand sides of

norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ).

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 140 of file dtpt02.f. 🔥

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⭐ Author (the meta one)

Generated automatically by Doxygen for LAPACK from the source code. (not a human, just a very diligent little robot 🫶)

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ok that's the whole page, mwah 💋 — LAPACK, Version 3.12.0, and this beauty was filed on /home/abui...IN/dtpt02.f(3). go forth and residual-check, bestie 🌈🎀