error-measurement

Calculation of Variance of a Function

This code allows you to calculate the variance of a mathematical function. Variance is a measure of the variability of values assumed by a function.

How it works:

The user needs to input the following information:

• The number of variables of the function
• The mathematical function
• The values of the variables
• The variances of the variables
• The covariances of the variables
• The code then calculates the variance of the function using the following formula: var = Σ(xi * xj * cov_mat[i,j])

where:

• xi is the first derivative of f() of variable i

• xj is the first derivative of f() of variable j

• cov_mat[i,j] is the covariance between variables i and j

• The first derivative of f() of each variable is calculated using the SymPy module

• The covariance between two variables is calculated as the average of the squared products of the variable values.

Output

The code prints the following results:

• The mathematical function entered by the user
• The values of the variables entered by the user
• The variances entered by the user
• The covariances entered by the user
• The calculated variance of the function
• The standard deviation of the function

Data Download

The code also provides an option to download the user-entered data. To do this, the user must click the "Download Data" button. The code creates a text file with the user-entered data and downloads it into the user's computer.

Requirements

The code requires the following prerequisites:

Python 3.6 or higher NumPy module SymPy module

Example

Here's an example of using the code in a web page with the prompts:

• Inserisci numero incognite (max 10): 2

• Inserisci funzione: a + b

• Valore incognita "a" ==> 1

• Valore incognita "b" ==> 2

• Sicuro di aver messo le varianze? (Rispondi si per continuare, altrimenti ricarica la pagina per ricominciare): si

• Varianza "a" ==> 1

• Varianza "b" ==> 4

• Covarianza "a-b" ==> 3

• Funzione: a + b

• Valori delle incognite:

• a: 1

• b: 2

• Varianze:

• a: 1

• b: 4

• Covarianze:

• a-b: 3

• Varianza = 10

• Deviazione standard = 3.162277660168379