CUNT01(3)

💖 CUNT01(3) — LAPACK Library Functions Manual 💖

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/cunt01.f

✨ SYNOPSIS ✨

🌟 Functions/Subroutines 🌟

subroutine CUNT01 (rowcol, m, n, u, ldu, work, lwork, rwork, resid)
    CUNT01

💅 Function/Subroutine Documentation 💅

subroutine CUNT01 (character rowcol, integer m, integer n, complex,
    dimension( ldu, * ) u, integer ldu, complex, dimension( * ) work,
    integer lwork, real, dimension( * ) rwork, real resid)

CUNT01 — yes, that’s the name, and it’s iconic. 👑

🎀 Purpose 🎀

CUNT01 checks that the matrix U is unitary by computing the ratio:

RESID = norm( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
or
RESID = norm( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.

Alternatively, if there isn’t sufficient workspace to form I - U*U' or I - U'*U, the ratio is computed as:

RESID = abs( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
or
RESID = abs( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.

where EPS is the machine precision. ROWCOL is used only if m = n; if m > n, ROWCOL is assumed to be 'C', and if m < n, ROWCOL is assumed to be 'R'.

The source wraps these lines in the usual !> Doxygen comment markers, because of course it does 💅

🦋 Parameters 🦋

• ROWCOL — ROWCOL is CHARACTER. It says whether the rows or columns of U should be checked for orthogonality. Used only if M = N. = 'R': check for orthogonal rows of U. = 'C': check for orthogonal columns of U.
• M — M is INTEGER. The number of rows of the matrix U.
• N — N is INTEGER. The number of columns of the matrix U.
• U — U is COMPLEX array, dimension (LDU,N). This is the unitary matrix U. U is checked for orthogonal columns if m > n or if m = n and ROWCOL = 'C'. U is checked for orthogonal rows if m < n or if m = n and ROWCOL = 'R'.
• LDU — LDU is INTEGER. The leading dimension of the array U. LDU >= max(1,M).
• WORK — WORK is COMPLEX array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The length of the array WORK. For best performance, LWORK should be at least N*N if ROWCOL = 'C' or M*M if ROWCOL = 'R', but the test will be done even if LWORK is 0.
• RWORK — RWORK is REAL array, dimension (min(M,N)). Used only if LWORK is large enough to use the Level 3 BLAS code.
• RESID — RESID is REAL. RESID = norm( I - U * U' ) / ( n * EPS ), if ROWCOL = 'R', or RESID = norm( I - U' * U ) / ( m * EPS ), if ROWCOL = 'C'.

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📍 Definition at line 124 of file cunt01.f. 📍

🌈 Author 🌈

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