TESTING/LIN/ctbt02.f(3)

🌸 NAME 🌸

TESTING/LIN/ctbt02.f — that's the manual-page main character, bestie 💖 and yes, this is the TESTING/LIN/ctbt02.f(3) page from the Library Functions Manual.

✨ SYNOPSIS ✨

okay so the synopsis is giving "Functions/Subroutines" energy, periodt:

   Functions/Subroutines
       subroutine ctbt02 (uplo, trans, diag, n, kd, nrhs, ab, ldab, x, ldx, b,
           ldb, work, rwork, resid)
           CTBT02

💖 Function/Subroutine Documentation 💖

the declaration is right here, no cap:

   subroutine ctbt02 (character uplo, character trans, character diag, integer
       n, integer kd, integer nrhs, complex, dimension( ldab, * ) ab, integer
       ldab, complex, dimension( ldx, * ) x, integer ldx, complex, dimension(
       ldb, * ) b, integer ldb, complex, dimension( * ) work, real, dimension(
       * ) rwork, real resid)
       CTBT02

🎯 Purpose 🎯

CTBT02 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, A**T, or A**H, b is the column of B, x is the solution vector, and EPS is the machine epsilon. slay, math bestie 💅

🎛️ Parameters 🎛️

• 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)
• 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 — COMPLEX array, dimension (LDA,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). Keeping that LDA,N exactly as the source says, bestie 😭
• LDAB — INTEGER. The leading dimension of the array AB. LDAB >= max(1,KD+1).
• X — COMPLEX 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 — COMPLEX 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 — COMPLEX array, dimension (N).
• RWORK — REAL array, dimension (N).
• RESID — REAL. The maximum over the number of right hand sides of norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).

👑 Author 👑

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

Definition at line 157 of file ctbt02.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the page, bestie 🫶💖 — source/version sign-off: LAPACK Version 3.12.0, page TESTING/LIN/ctbt02.f(3), from the Library Functions Manual. The footer doesn't show a date on this one, so no date to report, periodt 💀✨