TESTING/LIN/ztbt02.f(3)

💖 TESTING/LIN/ztbt02.f(3) 💖

okay bestie, welcome to the Library Functions Manual page for TESTING/LIN/ztbt02.f — it’s giving LAPACK testing subroutine energy, and the main character is ZTBT02. ✨

🌸 NAME 🌸

TESTING/LIN/ztbt02.f — yes, that’s the file, and this whole page is about the ZTBT02 subroutine. 💅

✨ SYNOPSIS ✨

📚 Functions/Subroutines 📚

The synopsis is literally this:

subroutine ztbt02 (uplo, trans, diag, n, kd, nrhs, ab, ldab, x, ldx, b,
    ldb, work, rwork, resid)
    ZTBT02

👑 Function/Subroutine Documentation 👑

ZTBT02

Here’s the full signature, exact and unfiltered:

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

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. The test ratio is the maximum over this exact formula:

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. 🫶

🧚 Parameters 🧚

• UPLO — CHARACTER*1. Tells you 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*16 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).

• LDAB — INTEGER. The leading dimension of the array AB. LDAB >= max(1,KD+1).
• X — COMPLEX*16 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*16 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*16 array, dimension (N).
• RWORK — 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

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

Definition at line 157 of file ztbt02.f.

🌈 Author 🌈

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LAPACK Version 3.12.0 — source page TESTING/LIN/ztbt02.f(3) — that’s the footer, bestie. No cap, you ate. 💖✨