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%REL_ERR_FORMULA Compare two formulas for relative error. | |
n = 500; | |
a = 3; | |
x = a*ones(n,1,'single'); | |
y = zeros(size(x)); | |
d = eps(single(a)); | |
for i=1:n | |
i-n/2 |
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function F = funm_randomized(A,fun) | |
%FUNM_RANDOMIZED Evaluate general matrix function using | |
% randomized approximate diagonalization method of Davies (2007). | |
tol = 8*eps(A(1,1)); % Tolerance for single or double precision A. | |
E = randn(size(A)); | |
[V,D] = eig(A + (tol*norm(A,'fro')/norm(E,'fro'))*E); | |
F = V*diag(fun(diag(D)))/V; |
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%NCM_COMPARE | |
% M-file to carry out experiment in "Explicit Solutions to Correlation | |
% Matrix Completion Problems, with an Application to Risk Management and | |
% Insurance" by Dan I. Georgescu, Nicholas J. Higham and Gareth W. Peters. | |
C = [% | |
1 0.25 0.6 0.55 0.65 0 0.4 0.6 0.2 0.3 | |
0.25 1 0 0 0 0 NaN NaN NaN NaN | |
0.6 0 1 0.75 0.75 0 NaN NaN NaN NaN | |
0.55 0 0.75 1 0.5 0 NaN NaN NaN NaN |
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function A = edelman | |
%EDELMAN Alan Edelman's matrix for which det is computed as the wrong integer. | |
% A = EDELMAN is a 27-by-27 matrix of 1s and -1s for which the | |
% MATLAB det function returns an odd integer, though the exact | |
% determinant is an even integer. | |
A = [% | |
1 1 1 1 -1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 | |
1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 1 1 1 | |
-1 1 -1 -1 1 1 1 1 1 -1 1 -1 1 1 1 1 -1 -1 1 -1 -1 1 1 -1 1 1 -1 |
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function fd = complex_step(f,x,h) | |
%COMPLEX_STEP Complex step approximation to derivative. | |
% fd = COMPLEX_STEP(f,x,h) computes the complex step approximation | |
% fd to the derivative of f at x, using step h (default 1e-100). | |
if nargin < 3, h = 1e-100; end | |
fd = imag( f(x + sqrt(-1)*h) )/h; |
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(use-package hydra | |
:config | |
(global-set-key (kbd "C-x m") 'hydra-major/body) | |
(global-set-key (kbd "<f3>") 'hydra-bib-etc/body) | |
(global-set-key (kbd "C-<f3>") 'hydra-dired/body) | |
) | |
(defhydra hydra-major (:color blue :columns 4) | |
"major-mode" | |
("b" bibtex-mode "bibtex") |
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% Complex step example. Requires Symbolic Math Toolbox. | |
format long | |
syms x; f = atan(x)/(1+exp(-x^2)) | |
% Derivative at $a = 2$: | |
a = 2; fd = double(subs( diff(f), a)) | |
% Convert symbolic function to MATLAB function. | |
f = matlabFunction(f); |