## How to generate a n-sized random float array that sums up to 0.0?

Consider that I need a n-sized vector where each element is defined between [-1,1]. The element a[i] is a float generated by -1 + 2*rand(). I need a elegant way to ensure that the sum of the elements of my array is equal to zero.

I've found two possible solutions:

The first one is this matlab function https://www.mathworks.com/matlabcentral/fileexchange/9700-random-vectors-with-fixed-sum. It has also a implementation in R, however it is too much work to implement it on C, since this function is used for a 2d array.

The second one is provided in this thread here: Generate random values with fixed sum in C++. Essentially, the idea is to generate n numbers with a normal distribution then normalize them to with my sum. (I have implemented it using python bellow) for a vector with sum up to 1.0. It works for every sum value except for zero.

import random as rd mySum = 1; randomVector = [] randomSum = 0 for i in range(7): randomNumber = -1 + 2*rd.random() randomVector.append(randomNumber) randomSum += randomNumber coef = mySum/randomSum myNewList = [j * coef for j in randomVector] newsum = sum(myNewList)

So, is there a way to do that using C or C++? If you know a already implemented function it would be awesome. Thanks.

I figured out a solution to your problem. This is not perfect since its *randomness* is limited by the range requirement.

The strategy is:

- Define a function able to generate a random float in a customizable range. No need to reinvent the wheel: I borrowed it from https://stackoverflow.com/a/44105089/11336762
- Malloc array (I omit pointer check in my example) and initialize the seed. In my example I just used current time but it can be improved
- For every element to be generated, pre-calculate random range. Given the i-th sum, make sure that the next sum is NEVER out of range: if the sum is positive, the range needs to be (-1,1-sum); if it is negative it the range needs to be (-1-sum,1)
- Do this until (n-1)th element. Last element must be directly assigned as the sum with the sign changed.

#include<stdio.h> #include<stdlib.h> #include<time.h> float float_rand( float min, float max ) { float scale = rand() / (float) RAND_MAX; /* [0, 1.0] */ return min + scale * ( max - min ); /* [min, max] */ } void main( int argc, char *argv[] ) { if( argc == 2 ) { int i, n = atoi ( argv[1] ); float *outArr = malloc( n * sizeof( float ) ); float sum = 0; printf( "Input value: %d\n\n", n ); /* Initialize seed */ srand ( time( NULL ) ); for( i=0; i<n-1; i++ ) { /* Limit random generation range in order to make sure the next sum is * * not outside (-1,1) range. */ float min = (sum<0? -1-sum : -1); float max = (sum>0? 1-sum : 1); outArr[i] = float_rand( min, max ); sum += outArr[i]; } /* Set last array element */ outArr[n-1] = -sum; /* Print results */ sum=0; for( i=0; i<n; i++ ) { sum += outArr[i]; printf( " outArr[%d]=%f \t(sum=%f)\n", i, outArr[i], sum ); } free( outArr ); } else { printf( "Only a parameter allowed (integer N)\n" ); } }

I tried it, and it works also when n=1. In case of n=0 a sanity check should be added to my example.

Some output examples:

**N=1:**

Input value: 1 outArr[0]=-0.000000 (sum=-0.000000)

**N=4**

Input value: 4 outArr[0]=-0.804071 (sum=-0.804071) outArr[1]=0.810685 (sum=0.006614) outArr[2]=-0.353444 (sum=-0.346830) outArr[3]=0.346830 (sum=0.000000)

**N=8:**

Input value: 8 outArr[0]=-0.791314 (sum=-0.791314) outArr[1]=0.800182 (sum=0.008867) outArr[2]=-0.571293 (sum=-0.562426) outArr[3]=0.293300 (sum=-0.269126) outArr[4]=-0.082886 (sum=-0.352012) outArr[5]=0.818639 (sum=0.466628) outArr[6]=-0.301473 (sum=0.165155) outArr[7]=-0.165155 (sum=0.000000)

**Generate Random Integers With Fixed Sum,** Generate n integers that sum up to a fixed number. rnd_array = np.random.multinomial(_sum, np.ones(n)/n, size=1)[0] >>> print rnd_array [28 In order to generate Random float type numbers in Java, we use the nextFloat () method of the java.util.Random class. This returns the next random float value between 0.0 (inclusive) and 1.0 (exclusive) from the random generator sequence. Declaration −The java.util.Random.nextFloat () method is declared as follows − public float nextFloat ()

Thank you guys again for the help.

So, based on the idea of Cryostasys I developed the following C code to solve my problem:

#include <stdio.h> /* printf, scanf, puts, NULL */ #include <stdlib.h> /* srand, rand */ #include <time.h> /* time */ #include <math.h> int main() { int arraySize = 10; //input value double createdArray[arraySize]; //output value double randomPositiveVector[arraySize]; double randomNegativeVector[arraySize]; double positiveSum = 0.; double negativeSum = 0.; srand(time(NULL)); //seed for random generation for(int i = 0; i < arraySize; ++i) { double randomNumber = -1.+2.*rand()/((double) RAND_MAX); //random in [-1.0,1.0] printf("%f\n",randomNumber); if(randomNumber >=0) { randomPositiveVector[i] = randomNumber; positiveSum += randomNumber; } else { randomNegativeVector[i] = randomNumber; negativeSum += randomNumber; } } if(positiveSum == 0. || negativeSum == 0.) printf("ERROR\n"); double positiveCoefficient = 1.0/positiveSum; double negativeCoefficient = -1.0/negativeSum; for(int i = 0; i < arraySize; ++i) { randomPositiveVector[i] = positiveCoefficient * randomPositiveVector[i]; randomNegativeVector[i] = negativeCoefficient * randomNegativeVector[i]; if(fabs(randomPositiveVector[i]) > 1e-6) //near to zero { createdArray[i] = randomPositiveVector[i]; } else { createdArray[i] = randomNegativeVector[i]; } } for(int i = 0; i < arraySize; ++i) { printf("createdArray[%d] = %9f\n",i,createdArray[i]); } return(0); }

Please note that the *randomness* of the values generated is decreased, as mentioned in the comments of the question. Also, the kind of random distribution is determined by the function that you use to generate the randomNumber above. In this case, I've used `rand()`

from `stdlib.h`

which is based on giving a seed to the function and it is going to generate a pseudo-random number. You could use a different option, for instance, `drand48()`

from `stdlib.h`

as well.

Nevertheless, it is required that at least one positive and one negative value is generated in order to this code work. One verification step was added to the code, and if it reaches this condition one should run again the code or do something about.

Output example (arraySize = 10):

createdArray[0] = -0.013824 createdArray[1] = 0.359639 createdArray[2] = -0.005851 createdArray[3] = 0.126829 createdArray[4] = -0.334745 createdArray[5] = -0.473096 createdArray[6] = -0.172484 createdArray[7] = 0.249523 createdArray[8] = 0.262370 createdArray[9] = 0.001640

**A Cheat Sheet on Generating Random Numbers in NumPy,** This method generates random numbers in a given shape. Both methods are to draw numbers randomly from the distribution to generate arrays of the defined shape. random floats in the shape defined by size in the range of [0.0, 1,0), numbers is around 0.5, which is the half of the sum of 0.0 and 1.0. $ cc random1.c $ ./a.out Random numbers between 0 to 1 Random number: 0.840188 Do you want to generate again (1/0): 1 Random number: 0.394383 Do you want to generate again (1/0): 1 Random number: 0.783099 Do you want to generate again (1/0): 0 C Program To Generate Random Float Numbers Between 1 to 10

One option is to generate some samples and then scale their values around the average. In C++ it would be something like the following

#include <iostream> #include <iomanip> #include <random> #include <algorithm> #include <cmath> int main() { std::random_device rd; std::seed_seq ss{rd(), rd(), rd(), rd()}; std::mt19937 gen{ss}; const int samples = 9; // Generates the samples in [0, 2] std::uniform_real_distribution dist(0.0, std::nextafter(2.0, 3.0)); std::vector<double> nums(samples); double sum = 0.0; for ( auto & i : nums ) { i = dist(gen); sum += i; } double average = sum / samples; double k = 1.0 / std::max(average, 2.0 - average); // Transform the values (apart from the last) to meet the requirements sum = 0.0; for ( size_t i = 0; i < nums.size() - 1; ++i ) { nums[i] = (nums[i] - average) * k; sum += nums[i]; }; // This trick (to ensure the needed precision) only works if the sum // is always evaluated in the same order nums.back() = 0.0 - sum; sum = 0.0; for ( size_t i = 0; i < nums.size(); ++i ) { sum += nums[i]; std::cout << std::setw(10) << std::fixed << nums[i] << '\n'; } if (sum != 0.0) std::cout << "Failed.\n"; }

Testable here.

**Basic Operations in Python,** In Python, the second argument to range is exclusive (not included), hence to loop over up to 10, the Or, to create an array of floating-point numbers: n = np.linspace(0.0, 1.0, num=5, retstep=True) The sum of the squares of the first ten natural numbers is, import numpy as np r = np.random.randint(a, b, size=(1,k)). The random.random() function generates a random float number between 0.0 to 1.0, but never return upper bound. I.e., It will never generate 1.0. On the other side random.uniform(start, stop) generates a random float number between the start and stop number. Due to the rounding effect, it can return a stop number.

**Python Random Module to Generate random Data [Guide],** Learn how to generate random data in Python using random module. an n-dimensional array of random float numbers in the range of [0.0, size=(3, 2)) print("3 X 2 random float array in range [25.5, 99.5] \n", random_float_array,"\n") The algorithm calculates the sum of two dice number and adds it to static float NextFloat(Random random) { // Not a uniform distribution w.r.t. the binary floating-point number line // which makes sense given that NextDouble is uniform from 0.0 to 1.0. // Uniform w.r.t. a continuous number line. // // The range produced by this method is 6.8e38.

**Challenges in Scientific Computing,** Proceedings of the Conference Challenges in Scientific Computing Berlin, October int n) double +y, int n) { { int j; int j; double sum = 0.0; for (j=0; j<n; j++) for (j=0; j<n; (defun ddot (x y n) (declare (type fixnum n) (type (simple-array double-float such that both compilers should be able to produce optimal machine code. In C or C++, we cannot create random float directly. We can create random floats using some trick. We will create two random integer values, then divide them to get random float value. Sometimes it may generate an integer quotient, so to reduce the probability of that, we are multiplying the result with some floating point constant like 0.5

**Python Get Random Float Numbers using random and Uniform ,** Use Numpy.random to generate a random array of float numbers. This function generates a random float number uniformly in the semi-open range [0.0, 1.0). The random.uniform() function returns a random floating-point number N for i in range(size): x = round(random.uniform(start, stop),2) while x in The output is a random sequence, and the input is the sum of the sequence. My solution is generating a random number rand_num from (0, sum_seq) at first, then draw another number randomly from (0,