CTBT02(3)

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/ctbt02.f

okay so bestie, welcome to CTBT02(3) — that's the manual name right there — and the manual family is Library Functions Manual. The header/footer path is /home/abui...IN/ctbt02.f(3) and it literally shows up in both places. iconic. 💅

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✨ SYNOPSIS ✨

🐚 Functions/Subroutines

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

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🎀 Function/Subroutine Documentation 🎀

CTBT02 is the subroutine, and here's the full signature, exactly as the page has it:

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)

🌸 Purpose 🌸

okay so 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. periodt.

🔥 Parameters 🔥

💅 UPLO

UPLO is CHARACTER*1. It specifies whether the matrix A is upper or lower triangular.

• = 'U': Upper triangular
• = 'L': Lower triangular

💅 TRANS

TRANS is CHARACTER*1. It 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

DIAG is CHARACTER*1. It specifies whether or not the matrix A is unit triangular.

• = 'N': Non-unit triangular
• = 'U': Unit triangular

💅 N

N is INTEGER. The order of the matrix A. N >= 0.

💅 KD

KD is INTEGER. The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.

💅 NRHS

NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.

💅 AB

AB is 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).

💅 LDAB

LDAB is INTEGER. The leading dimension of the array AB. LDAB >= max(1,KD+1).

💅 X

X is COMPLEX array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations.

💅 LDX

LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N).

💅 B

B is COMPLEX array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.

💅 LDB

LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).

💅 WORK

WORK is COMPLEX array, dimension (N).

💅 RWORK

RWORK is REAL array, dimension (N).

💅 RESID

RESID is 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.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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that's the whole CTBT02(3) vibe, bestie. The footer is LAPACK Version 3.12.0 plus the path /home/abui...IN/ctbt02.f(3) — no date on this one, just so you know. Generated automatically by Doxygen for LAPACK from the source code. 🫶✨