STBT03(3)

💅 STBT03(3) — like, the triangular band residual checker bestie

okay so real talk, this page lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/stbt03.f (yes that's a whole journey, don't @ me) and it's chillin' in the Library Functions Manual section. it's giving "test routine that verifies your triangular solve actually ate." 🦋

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine STBT03 (uplo, trans, diag, n, kd, nrhs, ab, ldab, scale,
    cnorm, tscal, x, ldx, b, ldb, work, resid)

STBT03. that's her. that's the whole name. iconic behavior honestly. 👑

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🎀 Function/Subroutine Documentation 🎀

subroutine STBT03 (character uplo, character trans, character diag, integer
    n, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integer
    ldab, real scale, real, dimension( * ) cnorm, real tscal, real,
    dimension( ldx, * ) x, integer ldx, real, dimension( ldb, * ) b, integer
    ldb, real, dimension( * ) work, real resid)

STBT03 💖

Purpose: 🌸

sooo what she does — STBT03 computes the residual for the solution to a scaled triangular system of equations A*x = s*b or A'*x = s*b when A is a triangular band matrix. 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. basically she's the vibe check for your triangular solve. no cap. ✨

Parameters 🔥

• UPLO — UPLO is CHARACTER*1. tells you whether the matrix A is upper or lower triangular. and the options are:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — TRANS is CHARACTER*1. specifies the operation applied to A. choices below bestie:
  • = 'N': A *x = b (No transpose)
  • = 'T': A'*x = b (Transpose)
  • = 'C': A'*x = b (Conjugate transpose = Transpose)
• DIAG — DIAG is CHARACTER*1. specifies whether or not the matrix A is unit triangular. pick your fighter:
  • = 'N': Non-unit triangular
  • = 'U': Unit triangular
• N — N is INTEGER. the order of the matrix A. N >= 0. lowkey the main character here.
• KD — KD is INTEGER. the number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 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.
• AB — AB is REAL array, dimension (LDAB,N). this is the upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. the j-th column of A is stored in the j-th column of the array AB as follows:
  • if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
  • if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

(yes she's specific. respect it. 💅)

• LDAB — LDAB is INTEGER. the leading dimension of the array AB. LDAB >= KD+1.
• SCALE — SCALE is REAL. the scaling factor s used in solving the triangular system.
• CNORM — CNORM is REAL array, dimension (N). the 1-norms of the columns of A, not counting the diagonal. read that again, bestie, the diagonal is NOT invited to this party. 🙈
• TSCAL — TSCAL is REAL. the scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A. so like, the norms got a glow-up first.
• X — X is REAL array, dimension (LDX,NRHS). the computed solution vectors for the system of linear equations. the answer your code thinks it found. 🧚
• LDX — LDX is INTEGER. the leading dimension of the array X. LDX >= max(1,N).
• B — B is REAL array, dimension (LDB,NRHS). the right hand side vectors for the system of linear equations. the original ask, fr fr.
• LDB — LDB is INTEGER. the leading dimension of the array B. LDB >= max(1,N).
• WORK — WORK is REAL array, dimension (N). scratch space, doing unpaid labor, we love her. 🫶
• RESID — RESID is REAL. the maximum over the number of right hand sides of

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

so it's the final score. if RESID is tiny, you slayed. if it's big… 💀

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👑 Author 👑

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

Definition at line 172 of file stbt03.f. 📍

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⭐ Author ⭐

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

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and that's the whole page, bestie. LAPACK, Version 3.12.0, brought to you from /home/abui...IN/stbt03.f(3) — mwah 💋, go check those residuals. 🌈💜