Convex Optimization page 154

given
f ∈ ℝ^(n)
p ∈ ℝ^(n)

∑_i f_i²p_i - (∑_i f_i p_i)²

/*
given
f ∈ ℝ^(n)
p ∈ ℝ^(n)

∑_i f_i²p_i - (∑_i f_i p_i)²
*/
#include <Eigen/Core>
#include <Eigen/Dense>
#include <Eigen/Sparse>
#include <iostream>
#include <set>

struct convex_optimization_154ResultType {
    double ret;
    convex_optimization_154ResultType(const double & ret)
    : ret(ret)
    {}
};

convex_optimization_154ResultType convex_optimization_154(
    const Eigen::VectorXd & f,
    const Eigen::VectorXd & p)
{
    const long n = f.size();
    assert( p.size() == n );

    double sum_0 = 0;
    for(int i=1; i<=p.size(); i++){
        sum_0 += pow(f[i-1], 2) * p[i-1];
    }
    double sum_1 = 0;
    for(int i=1; i<=p.size(); i++){
        sum_1 += f[i-1] * p[i-1];
    }
    double ret = sum_0 - pow((sum_1), 2);
    return convex_optimization_154ResultType(ret);
}


void generateRandomData(Eigen::VectorXd & f,
    Eigen::VectorXd & p)
{
    const int n = rand()%10;
    f = Eigen::VectorXd::Random(n);
    p = Eigen::VectorXd::Random(n);
}


int main(int argc, char *argv[])
{
    srand((int)time(NULL));
    Eigen::VectorXd f;
    Eigen::VectorXd p;
    generateRandomData(f, p);
    convex_optimization_154ResultType func_value = convex_optimization_154(f, p);
    std::cout<<"return value:\n"<<func_value.ret<<std::endl;
    return 0;
}

"""
given
f ∈ ℝ^(n)
p ∈ ℝ^(n)

∑_i f_i²p_i - (∑_i f_i p_i)²
"""
import numpy as np
import scipy
import scipy.linalg
from scipy import sparse
from scipy.integrate import quad
from scipy.optimize import minimize


class convex_optimization_154ResultType:
    def __init__( self, ret):
        self.ret = ret


def convex_optimization_154(f, p):
    f = np.asarray(f, dtype=np.float64)
    p = np.asarray(p, dtype=np.float64)

    n = f.shape[0]
    assert f.shape == (n,)
    assert p.shape == (n,)

    sum_0 = 0
    for i in range(1, len(p)+1):
        sum_0 += np.power(f[i-1], 2) * p[i-1]
    sum_1 = 0
    for i in range(1, len(p)+1):
        sum_1 += f[i-1] * p[i-1]
    ret = sum_0 - np.power((sum_1), 2)
    return convex_optimization_154ResultType(ret)


def generateRandomData():
    n = np.random.randint(10)
    f = np.random.randn(n)
    p = np.random.randn(n)
    return f, p


if __name__ == '__main__':
    f, p = generateRandomData()
    print("f:", f)
    print("p:", p)
    func_value = convex_optimization_154(f, p)
    print("return value: ", func_value.ret)

function output = convex_optimization_154(f, p)
% output = convex_optimization_154(f, p)
%
%    given
%    f ∈ ℝ^(n)
%    p ∈ ℝ^(n)
%    
%    ∑_i f_i²p_i - (∑_i f_i p_i)²
    if nargin==0
        warning('generating random input data');
        [f, p] = generateRandomData();
    end
    function [f, p] = generateRandomData()
        n = randi(10);
        f = randn(n,1);
        p = randn(n,1);
    end

    f = reshape(f,[],1);
    p = reshape(p,[],1);

    n = size(f, 1);
    assert( numel(f) == n );
    assert( numel(p) == n );

    sum_0 = 0;
    for i = 1:size(p,1)
        sum_0 = sum_0 + f(i).^2 * p(i);
    end
    sum_1 = 0;
    for i = 1:size(p,1)
        sum_1 = sum_1 + f(i) * p(i);
    end
    ret = sum_0 - (sum_1).^2;
    output.ret = ret;
end

\documentclass[12pt]{article}
\usepackage{mathdots}
\usepackage[bb=boondox]{mathalfa}
\usepackage{mathtools}
\usepackage{amssymb}
\usepackage{libertine}
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\argmin}{arg\,min}
\usepackage[paperheight=8in,paperwidth=4in,margin=.3in,heightrounded]{geometry}
\let\originalleft\left
\let\originalright\right
\renewcommand{\left}{\mathopen{}\mathclose\bgroup\originalleft}
\renewcommand{\right}{\aftergroup\egroup\originalright}
\begin{document}

\begin{center}
\resizebox{\textwidth}{!} 
{
\begin{minipage}[c]{\textwidth}
\begin{align*}
\intertext{given} 
\mathit{f} & \in \mathbb{R}^{ \mathit{n}} \\
\mathit{p} & \in \mathbb{R}^{ \mathit{n}} \\
\\
 \omit \span \sum_\mathit{i} {\mathit{f}_{ \mathit{i} }}^{2}\mathit{p}_{ \mathit{i} } - {\left( \sum_\mathit{i} \mathit{f}_{ \mathit{i} }\mathit{p}_{ \mathit{i} } \right)}^{2} \\
\end{align*}
\end{minipage}
}
\end{center}

\end{document}