jrus

function [Q, R] = qr(A, econ)
%QR   QR factorization of an array-valued CHEBFUN.
%   [Q, R] = QR(A) or QR(A, 0), where A is a column CHEBFUN with n columns,
%   produces a column CHEBFUN Q with n orthonormal columns and an n x n upper
%   triangular matrix R such that A = Q*R.
%
%   The algorithm used is described in L.N. Trefethen, "Householder
%   triangularization of a quasimatrix", IMA J. Numer. Anal. (30), 887-897
%   (2010).
%

jrus

% All lengths up to 16, plus an additional 8 random sizes for each power of two larger than that.
coeff_lengths = [
          1        2        3        4        5        6        7        8, ...
          9       10       11       12       13       14       15       16, ...
         17       20       23       25       26       29       30       32, ...
         34       37       42       43       49       52       59       64, ...
         65       66       67       71       76       89       97      128, ...
        129      146      165      171      176      203      233      256, ...
        267      276      292      331      378      413      482      512, ...
        522      536      709      754      784      909      921     1024, ...

jrus

function varargout = subsref(f, index)
%SUBSREF   CHEBFUN subsref.
% ( )
%   F(X) returns the values of the CHEBFUN F evaluated on the array X. If X
%   falls on a breakpoint of F, the corresponding value from F.POINTVALUES is
%   returned. F(X, 'left') or F(X, 'right') will evaluate F at breakpoints
%   using left- or right-hand limits, respectively. See CHEBFUN/FEVAL for
%   further details. F(:) returns F.
%
%   If F is an array-valued column CHEBFUN, and X is an array of arbitrary

jrus

function out = feval(F, x, varargin)
%FEVAL   Evaluate a CHEBFUN.
%   FEVAL(F, X) evaluates a CHEBFUN F at the points in X.  If F is a quasimatrix
%   with columns F1, ..., FN, then the result will be [F1(X), ..., FN(X)], the
%   horizontal concatenation of the results of evaluating each column at the
%   points in X.
%
%   FEVAL(F, 'left'), FEVAL(F, 'start'), and FEVAL(F, '-') return the value of F
%   at the left endpoint of its domain.  FEVAL(F, 'right'), FEVAL(F, 'end'), and
%   FEVAL(F, '+') do the same for the right endpoint.

jrus

function out = feval(F, x, varargin)
%FEVAL   Evaluate a CHEBFUN.
%   FEVAL(F, X) evaluates a CHEBFUN F at the points in X.  If F is a quasimatrix
%   with columns F1, ..., FN, then the result will be [F1(X), ..., FN(X)], the
%   horizontal concatenation of the results of evaluating each column at the
%   points in X.
%
%   FEVAL(F, 'left'), FEVAL(F, 'start'), and FEVAL(F, '-') return the value of F
%   at the left endpoint of its domain.  FEVAL(F, 'right'), FEVAL(F, 'end'), and
%   FEVAL(F, '+') do the same for the right endpoint.

jrus

local random = math.random
local function uuid()
    local template ='xxxxxxxx-xxxx-4xxx-yxxx-xxxxxxxxxxxx'
    return string.gsub(template, '[xy]', function (c)
        local v = (c == 'x') and random(0, 0xf) or random(8, 0xb)
        return string.format('%x', v)
    end)
end

jrus

decode_macroman = do ->
    high_chars_unicode = '''
        ÄÅÇÉÑÖÜáàâäãåçéèêëíìîïñóòôöõúùûü
        †°¢£§•¶ß®©™´¨≠ÆØ∞±≤≥¥µ∂∑∏π∫ªºΩæø
        ¿¡¬√ƒ≈∆«»… ÀÃÕŒœ–—“”‘’÷◊ÿŸ⁄€‹›fifl
        ‡·‚„‰ÂÊÁËÈÍÎÏÌÓÔÒÚÛÙıˆ˜¯˘˙˚¸˝˛ˇ
        '''.replace /\n/g, ''

    (mac_roman_bytestring) ->
        char_array = for idx in [0...mac_roman_bytestring.length]

jrus

# Accepts a list and a key function to apply to each item,
# and then uses a decorate-sort-undecorate pattern to actually
# do the sorting. Returns a new list. Keeps track of the index
# to make sure the sort is stable.
sort_by = (list, key) ->
    cmp = ({key: k_a, index: i_a}, {key: k_b, index: i_b}) ->
        if k_a == k_b then i_a - i_b else if k_a < k_b then -1 else 1
    decorated = ({item, index, key: key item} for item, index in list)
    item for {item} in decorated.sort cmp