- #MATLAB 2NORM OF VECTOR CODE SOFTWARE#
- #MATLAB 2NORM OF VECTOR CODE CODE#
- #MATLAB 2NORM OF VECTOR CODE LICENSE#
Romberg - Integrate func using Romberg integration Quadrature - Integrate with given tolerance using Gaussian quadrature Nquad - General purpose n-dimensional integrationįixed_quad - Integrate func(x) using Gaussian quadrature of order n Tplquad - General purpose triple integration Integrating functions, given function objectĭblquad - General purpose double integration
Integration and ODEs (:mod:`scipy.integrate`) All functionality from numpy seems to be available in scipy as well. You can use the help function for each numerical method to find out more about the source of the implementation.
#MATLAB 2NORM OF VECTOR CODE CODE#
As a rule of thumb, we expect compiled code to be two orders of magnitude faster than pure Python code. They will thus execute much faster than pure Python code (which is interpreted). Many of the numerical algorithms available through scipy and numpy are provided by established compiled libraries which are often written in Fortran or C. Scipy package (SCIentific PYthon) which provides a multitude of numerical algorithms and which is introduced in this chapter. The matplotlib package (also knows as pylab) provides plotting and visualisation capabilities (see 15-visualising-data.ipynb) and the The numpy module provides a data type specialised for “number crunching” of vectors and matrices (this is the array type provided by “ numpy” as introduced in 14-numpy.ipynb), and linear algebra tools. We list three such modules in particular: Provide numerical tools for frequently occurring tasksĪnd are more efficient in terms of CPU time and memory requirements than using the code Python functionality alone. However, there are dedicated (third-party) Python libraries that provide extended functionality which The core Python language (including the standard libraries) provide enough functionality to carry out computational research tasks. Numerical Methods using Python (scipy) ¶ Overview ¶ * normX2 ) else % group of different size n21 = 0 indice = 0 X = x (:) X = X ( g_d ) W2 = w2 W2 = W2 ( g_d ) for i = 1 : l n21 = n21 + w1 ( i ) * norm ( W2 ( indice + 1 : indice + g_t ( i )). w2 (:, ii ), w1 (:, ii )) end else % non overlapping groups l = length ( g_t ) % Compute the norm if max ( g_t ) = min ( g_t ) % group of the same size X = transpose ( x ) X = X ( g_d ) X = transpose ( reshape ( X, numel ( x ) / l, l )) W2 = transpose ( reshape ( w2 ( g_d ), numel ( x ) / l, l )) normX2 = sqrt ( sum (( abs ( W2. % Author: Nathanael Perraudin % Date: October 2011 % Testing: test_mixed_sparsity % Optional input arguments if nargin 1 n21 = 0 for ii = 1 : size ( g_d, 1 ) n21 = n21 + norm_l21 ( x, g_d ( ii ,:), g_t ( ii ,:).
#MATLAB 2NORM OF VECTOR CODE LICENSE#
% % You should have received a copy of the GNU General Public License % along with this program. See the % GNU General Public License for more details. % % This program is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
#MATLAB 2NORM OF VECTOR CODE SOFTWARE#
% This file is part of UNLOCBOX version 1.7.4 % % This program is free software: you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation, either version 3 of the License, or % (at your option) any later version. % % See also: norm_linf1 norm_tv % % Url: % Copyright (C) 2012-2016 Nathanael Perraudin. % % Example: % x= % Group 1: % Group 2: % % Leads to % % => g_d= and g_t= % Or this is also possible % => g_d= and g_t= % % This function works also for overlapping groups. g_d contain the indices of the % element to be group and g_t the size of different groups. % % 'norm_l21(x)' with x a row vector is equivalent to norm(x,1) and % 'norm_l21(x)' with x a line vector is equivalent to norm(x) % % For fancy group, please provide the groups vectors. If x is a % matrix the 2 norm will be computed as follow: % % n21 = || x ||_21 = sum_j ( sum_i |x(i,j)|^2 )^(1/2) % % In this case, all other argument are not necessary. Function n21 = norm_l21 (x, g_d,g_t, w2,w1 ) %NORM_L21 L21 mixed norm % Usage: n21 = norm_l21(x) % n21 = norm_l21(x, g_d,g_t) % n21 = norm_l21(x, g_d,g_t, w2,w1) % % Input parameters: % x : Input data % g_d : group vector 1 % g_t : group vector 2 % w2 : weights for the two norm (default 1) % w1 : weights for the one norm (default 1) % Output parameters: % y : Norm % % NORM_L21(x, g_d,g_t, w2,w1) returns the norm L21 of x.
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