TESTING/EIG/sort01.f(3)

TESTING/EIG/sort01.f(3) 🦋

Ok bestie, this page is from the Library Functions Manual, and it’s giving “let’s check if this matrix is orthogonal” energy. Every detail is staying, no cap. 💅

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NAME 🌸

TESTING/EIG/sort01.f

SYNOPSIS ✨

Functions/Subroutines 🎀

• subroutine sort01 (rowcol, m, n, u, ldu, work, lwork, resid) — SORT01

Function/Subroutine Documentation 💖

Here’s the whole signature, exactly as the page serves it:

subroutine sort01 (character rowcol, integer m, integer n, real, dimension(
     ldu, * ) u, integer ldu, real, dimension( * ) work, integer lwork, real
     resid)

SORT01

Purpose 🔥

SORT01 checks that the matrix U is orthogonal 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'. 🫶

Parameters 🧚

• ROWCOL — ROWCOL is CHARACTER. Specifies 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 REAL array, dimension (LDU,N). The orthogonal 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 REAL array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The length of the array WORK. For best performance, LWORK should be at least N*(N+1) if ROWCOL = 'C' or M*(M+1) if ROWCOL = 'R', but the test will be done even if LWORK is 0.
• 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 115 of file sort01.f.

Author 💀

Generated automatically by Doxygen for LAPACK from the source code.

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That’s the whole iconic page, bestie — LAPACK Version 3.12.0 energy for TESTING/EIG/sort01.f(3), straight from the footer vibe, and not a single formula or parameter got left behind 💖🫶