SPBT02(3)

💅 SPBT02(3) — like, the manual page, bestie

okay so real quick: this is a page from the Library Functions Manual, and the star of the show is spbt02.f(3) — yes the whole path situation is a lot, we'll get to it. buckle up 🎀

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/spbt02.f

like... that's the name. that's literally the whole name. it's giving "my full legal name on a government form" energy 😭 but slay, we respect it.

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine SPBT02 (uplo, n, kd, nrhs, a, lda, x, ldx, b, ldb, rwork,
    resid)

SPBT02 — that's her. that's the subroutine. 👑

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🌸 Function/Subroutine Documentation 🌸

subroutine SPBT02 (character uplo, integer n, integer kd, integer nrhs,
    real, dimension( lda, * ) a, integer lda, real, dimension( ldx, * ) x,
    integer ldx, real, dimension( ldb, * ) b, integer ldb, real, dimension(
    * ) rwork, real resid)

SPBT02 — okay so here's the full glow-up, every single argument typed out exactly, no cap. 💖

🎯 Purpose 🎯

!> !> SPBT02 computes the residual for a solution of a symmetric banded !> system of equations A*x = b: !> RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS) !> where EPS is the machine precision. !>

so basically she checks your work. you solved A*x = b, and she's like "bestie... let me verify that real quick" and hands you back RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS), where EPS is the machine precision. a whole vibe check for your linear algebra. 💅

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🧚 Parameters 🧚

okay so these are the arguments, one by one, each one more iconic than the last:

• UPLO — it's CHARACTER*1, and it says which triangle of the symmetric matrix A we're storing: = 'U': upper triangular, = 'L': lower triangular. pick a side, king. 👑
• N — INTEGER, the number of rows and columns of the matrix A. N >= 0. no negatives, we don't do that here.
• KD — INTEGER, the number of super-diagonals of A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0. she's the band width, the moment, the range. 🌈
• NRHS — INTEGER, the number of right hand sides. NRHS >= 0. plural queens rise up.
• A — REAL array, dimension (LDA,N). this is the original symmetric band matrix A. if UPLO = 'U', the upper triangular part of A is stored as a band matrix; if UPLO = 'L', the lower triangular part of A is stored. the columns of the appropriate triangle are stored in the columns of A and the diagonals of the triangle are stored in the rows of A. see SPBTRF for further details — she's the reference, iykyk. 📚
• LDA — INTEGER. the leading dimension of the array A. LDA >= max(1,KD+1). respect the leading dimension fr fr.
• X — REAL array, dimension (LDX,NRHS). the computed solution vectors for the system of linear equations. this is your answer, main character energy. 💖
• LDX — INTEGER, the leading dimension of the array X. LDX >= max(1,N).
• B — REAL array, dimension (LDB,NRHS). on entry, the right hand side vectors for the system of linear equations. on exit, B is overwritten with the difference B - A*X. ⚠️ she does NOT come back the same, bestie — that array is getting rewritten whether you like it or not.
• LDB — INTEGER, the leading dimension of the array B. LDB >= max(1,N).
• RWORK — REAL array, dimension (N). that's it. that's the whole description. she's a mystery but we love her. 🫶
• RESID — REAL. the maximum over the number of right hand sides of norm(B - A*X) / ( norm(A) * norm(X) * EPS ). the final verdict. the score. the moment of truth. ⭐

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👑 Author 👑

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

the whole squad, honestly. 💜

Definition at line 134 of file spbt02.f. — go look, she's right there. 🔥

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🌺 Author (again, but different) 🌺

Generated automatically by Doxygen for LAPACK from the source code. so like... a robot wrote this page. and now i'm rewriting the robot's page. we're all just doing our part. 🦋

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💀 quick reminder: nothing here changed, every flag, bound, dimension and overwrite notice is exactly as written — i just made it fun.

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and that's the page!! LAPACK, Version 3.12.0, dated /home/abui...IN/spbt02.f(3) — mwah, sending you off with a kiss, go solve your symmetric banded system responsibly 💅✨🎀