STPT03(3)

💅 STPT03(3) — Library Functions Manual, bestie 💅

okay so this is the STPT03(3) page from the Library Functions Manual. It’s giving “LAPACK testing routine that checks residuals,” and honestly? iconic. Let’s get into it. 🫶

📁 NAME 📁

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/stpt03.f — that’s the whole NAME section, no cap. Just the full source-file path, being its main-character self. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine STPT03 (uplo, trans, diag, n, nrhs, ap, scale, cnorm, tscal,
    x, ldx, b, ldb, work, resid)
    STPT03

🦋 Function/Subroutine Documentation 🦋

subroutine STPT03 (character uplo, character trans, character diag, integer
    n, integer nrhs, real, dimension( * ) ap, real scale, real, dimension( *
    ) cnorm, real tscal, real, dimension( ldx, * ) x, integer ldx, real,
    dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, real
    resid)
    STPT03

🌸 Purpose 🌸

So here’s the tea: STPT03 computes the residual for the solution to a scaled triangular system of equations A*x = s*b or A'*x = s*b when the triangular matrix A is stored in packed format. Here A' is the transpose of A, s is a scalar, and x and b are N by NRHS matrices.

The test ratio is the maximum over the number of right hand sides of:

norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS )

where op(A) denotes A or A', and EPS is the machine epsilon. Slay. ✨

🎀 Parameters 🎀

• UPLO — CHARACTER*1. Tells you whether the matrix A is upper or lower triangular. = 'U': Upper triangular. = 'L': Lower triangular.
• TRANS — CHARACTER*1. Tells you which operation is applied to A. = 'N': A*x = s*b (No transpose). = 'T': A'*x = s*b (Transpose). = 'C': A'*x = s*b (Conjugate transpose = Transpose).
• DIAG — CHARACTER*1. Tells you whether or not the matrix A is unit triangular. = 'N': Non-unit triangular. = 'U': Unit triangular.
• N — INTEGER. The order of the matrix A. N >= 0.
• NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
• AP — REAL 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.

• SCALE — REAL. The scaling factor s used in solving the triangular system.
• CNORM — REAL array, dimension (N). The 1-norms of the columns of A, not counting the diagonal.
• TSCAL — REAL. The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.
• X — REAL array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations.
• LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• B — REAL 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).
• WORK — REAL array, dimension (N).
• RESID — REAL. The maximum over the number of right hand sides of:

norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS )

👑 Author 👑

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

Definition at line 159 of file stpt03.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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That’s the whole vibe check, bestie: the footer says LAPACK Version 3.12.0 and /home/abui...IN/stpt03.f(3) — periodt. 💖✨🎀