TESTING/LIN/dtbt02.f(3)

okay bestie, welcome to TESTING/LIN/dtbt02.f(3) from the Library Functions Manual — the LAPACK page for a subroutine that is literally the vibe check for triangular band solves. 💖✨

🌸 NAME 🌸

TESTING/LIN/dtbt02.f — that's the manual page, no cap. 💅

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

Here's the signature, bestie:

subroutine dtbt02 (uplo, trans, diag, n, kd, nrhs, ab, ldab, x, ldx, b,
     ldb, work, resid)

and the name is DTBT02 — iconic. 👑

💅 FUNCTION/SUBROUTINE DOCUMENTATION 💅

subroutine dtbt02 (character uplo, character trans, character diag, integer
     n, integer kd, integer nrhs, double precision, dimension( ldab, * ) ab,
     integer ldab, double precision, dimension( ldx, * ) x, integer ldx,
     double precision, dimension( ldb, * ) b, integer ldb, double precision,
     dimension( * ) work, double precision resid)

DTBT02 — the full documentation moment. 🫶

🎀 Purpose 🎀

okay so DTBT02 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. 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. slay. 🌈

🧚 Parameters 🧚

Every parameter, every constraint, every little detail — here we go, bestie:

• UPLO — CHARACTER*1. Specifies whether the matrix A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — 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 — CHARACTER*1. Specifies 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.
• KD — INTEGER. The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
• NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
• AB — DOUBLE PRECISION array, dimension (LDAB,N). 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 — INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• X — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 — DOUBLE PRECISION array, dimension (N).
• RESID — DOUBLE PRECISION. The maximum over the number of right hand sides of norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).

👑 Author 👑

the academic credits, periodt:

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

Definition at line 152 of file dtbt02.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

---

and that's the whole page, bestie. footer vibe: LAPACK Version 3.12.0, source TESTING/LIN/dtbt02.f(3). date? the footer doesn't give one, so I'm not making one up — no cap. 💅✨