ZTBT02(3)

💅 ZTBT02 — like, the whole manual, bestie

okay so before we even get into it: the manual name is ztbt02.f(3) (yes, that's the page, that's the vibe), and the actual file we're documenting lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/ztbt02.f. she's a Fortran file, she's in the LIN testing directory, she's iconic, that's the whole header situation, moving on ✨

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/ztbt02.f

that's it. that's the name. it's a whole path. lowkey obsessed with how extra that is 🎀

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🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

subroutine ZTBT02 (uplo, trans, diag, n, kd, nrhs, ab, ldab, x, ldx, b,
    ldb, work, rwork, resid)
    ZTBT02

🌈 Function/Subroutine Documentation 🌈

subroutine ZTBT02 (character uplo, character trans, character diag, integer
    n, integer kd, integer nrhs, complex*16, dimension( ldab, * ) ab,
    integer ldab, complex*16, dimension( ldx, * ) x, integer ldx,
    complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( *
    ) work, double precision, dimension( * ) rwork, double precision resid)
    ZTBT02

💜 Purpose 💜

okay so here's what she actually does, and it's honestly so useful. ZTBT02 computes the residual for the computed solution to a triangular system of linear equations op(A)*X = B, when A is a triangular band matrix. and the test ratio? it's the maximum over

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

where op(A) = A, A**T, or A**H, b is the column of B, x is the solution vector, and EPS is the machine epsilon. math girlie things 🧚

🎀 Parameters 🎀

• UPLO — is CHARACTER*1, and she specifies whether the matrix A is upper or lower triangular. the options are:
  • = 'U': Upper triangular 👑
  • = 'L': Lower triangular
• TRANS — is CHARACTER*1, specifies the operation applied to A. the lineup:
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose)
• DIAG — is CHARACTER*1, specifies whether or not the matrix A is unit triangular. so:
  • = 'N': Non-unit triangular
  • = 'U': Unit triangular
• N — is INTEGER, the order of the matrix A. N >= 0. no negative girlies allowed 🚫
• KD — is INTEGER, the number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
• NRHS — is INTEGER, the number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
• AB — is COMPLEX*16 array, dimension (LDA,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).
• LDAB — is INTEGER, the leading dimension of the array AB. LDAB >= max(1,KD+1). respect the constraint bestie 💅
• X — is COMPLEX*16 array, dimension (LDX,NRHS). the computed solution vectors for the system of linear equations. the main character of this whole operation tbh ⭐
• LDX — is INTEGER, the leading dimension of the array X. LDX >= max(1,N).
• B — is COMPLEX*16 array, dimension (LDB,NRHS). the right hand side vectors for the system of linear equations.
• LDB — is INTEGER, the leading dimension of the array B. LDB >= max(1,N).
• WORK — is COMPLEX*16 array, dimension (N). just a lil workspace, doing her thing 🫶
• RWORK — is DOUBLE PRECISION array, dimension (N). more workspace, this time the real kind.
• RESID — is DOUBLE PRECISION, and this is the moment: the maximum over the number of right hand sides of

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

that's the whole point of the routine fr fr 🔥

ngl, watch those dimension rules — LDAB >= max(1,KD+1) and LDX >= max(1,N) and LDB >= max(1,N) are not suggestions, they're the law 💀

👑 Author 👑

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

the whole squad, no cap 🫡

Definition at line 157 of file ztbt02.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. yes she was autogenerated, yes she still ate 💅✨

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and that's the page bestie!! 🎀 this whole thing is from LAPACK, Version 3.12.0, and the footer path was /home/abui...IN/ztbt02.f(3) — you're welcome, go forth and check those residuals 🌈💖