TESTING/LIN/cpbt05.f(3)

💅 TESTING/LIN/cpbt05.f 💅

okay so this is the TESTING/LIN/cpbt05.f page from the Library Functions Manual — yes bestie, we're in the LAPACK testing zone and it's lowkey iconic here 🎀

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✨ NAME ✨

TESTING/LIN/cpbt05.f — that's literally the whole name, she's mysterious like that 🦋

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine cpbt05 (uplo, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts) — CPBT05, that's her 💅

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👑 Function/Subroutine Documentation 👑

subroutine cpbt05 (character uplo, integer n, integer kd, integer nrhs, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldx, * ) x, integer ldx, complex, dimension( ldxact, * ) xact, integer ldxact, real, dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * ) reslts)

CPBT05 ✨

🎀 Purpose:

!>
!> CPBT05 tests the error bounds from iterative refinement for the
!> computed solution to a system of equations A*X = B, where A is a
!> Hermitian band matrix.
!>
!> RESLTS(1) = test of the error bound
!>           = norm(X - XACT) / ( norm(X) * FERR )
!>
!> A large value is returned if this ratio is not less than one.
!>
!> RESLTS(2) = residual from the iterative refinement routine
!>           = the maximum of BERR / ( NZ*EPS + (*) ), where
!>             (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
!>             and NZ = max. number of nonzeros in any row of A, plus 1
!>

so basically: she's testing the error bounds from iterative refinement for the computed solution to A*X = B where A is a Hermitian band matrix. no cap, that's the whole job 🫶

RESLTS(1) is the error bound test, = norm(X - XACT) / ( norm(X) * FERR ). and if that ratio is not less than one? you get a large value back. 💀

RESLTS(2) is the residual from the iterative refinement routine, = the maximum of BERR / ( NZ*EPS + (*) ), where (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i ) and NZ = max. number of nonzeros in any row of A, plus 1.

💜 Parameters

• UPLO — UPLO is CHARACTER*1, and she specifies whether the upper or lower triangular part of the Hermitian matrix A is stored. = 'U': Upper triangular, = 'L': Lower triangular. pick your fighter ⭐
• N — N is INTEGER, the number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.
• KD — KD is INTEGER. it's the number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
• NRHS — NRHS is INTEGER, the number of columns of the matrices X, B, and XACT. NRHS >= 0.
• AB — AB is COMPLEX array, dimension (LDAB,N). it holds the upper or lower triangle of the Hermitian 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). yes the indexing is giving main character energy, copy it exactly bestie 🙈
• LDAB — LDAB is INTEGER, the leading dimension of the array AB. LDAB >= KD+1.
• 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).
• X — X is COMPLEX array, dimension (LDX,NRHS). the computed solution vectors. each vector is stored as a column of the matrix X.
• LDX — LDX is INTEGER, the leading dimension of the array X. LDX >= max(1,N).
• XACT — XACT is COMPLEX array, dimension (LDX,NRHS). the exact solution vectors. each vector is stored as a column of the matrix XACT ✨
• LDXACT — LDXACT is INTEGER, the leading dimension of the array XACT. LDXACT >= max(1,N).
• FERR — FERR is REAL array, dimension (NRHS). the estimated forward error bounds for each solution vector X. if XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X.
• BERR — BERR is REAL array, dimension (NRHS). the componentwise relative backward error of each solution vector (i.e., the smallest relative change in any entry of A or B that makes X an exact solution) 💖
• RESLTS — RESLTS is REAL array, dimension (2). the maximum over the NRHS solution vectors of the ratios: RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) and RESLTS(2) = BERR / ( NZ*EPS + (*) ) 🔥

🌈 Author

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

Definition at line 169 of file cpbt05.f. 📍

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⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. not a human, just a robot doing her thing 🤖💅

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so yeah, that's the whole page — every flag, every bound, every >=, all accounted for. go off bestie 🫶

LAPACK, Version 3.12.0 — mwah, that's the sign-off, ily, bye! 🎀💖✨