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In this article we will learn about the Jacobian matrix and how to calculate this matrix using different methods in PyTorch. We use Jacobian matrix in various machine learning applications. Jacobian Matrix We use Jacobian matrix to calculate relation between the input and output variable. Jacobian matrix has all the partial derivatives of vector valued function. We can use this matrix in various applications machine learning applications. Here are some of its usages − For analyzing the gradients and derivatives of functions in multivariable calculus. Solving differential equations of systems. Calculating inverse of vector-values functions. Analyzing stability of dynamic ... Read More
In this article we will learn about different methods to find the Summation of Random Numbers using Python language. In some scenarios we need to generate some random number and find its summation so we will see basic to improved versions of functions using which we can get this task done. Let’s see some methods to find the summation of random numbers. Method 1. Using Simple Loop Example import random n = 10 rand_nums = [] for _ in range(n): rand_nums.append(random.randint(1, 100)) total = sum(rand_nums) print("Random Numbers:", rand_nums) print("Summation of random numbers:", total) Output Random Numbers: ... Read More
The purpose of integration (definite) is to calculate the area under a curve of a function between two limits, a and b. The plot shown below will clear this concept further. Quadrature, which is also commonly called as numerical integration, is a method for evaluating the area under the curve of a given function. The process is very simple i.e. first we dividing the bounded area into several regions or strips. Thereafter, the areas is evaluated with the help of mathematical formula of simple rectangle. Then the area of all strips is added to obtain the gross area under ... Read More
Stirling Cycle Four processes—two reversible isochoric and two reversible isothermal—make up the Stirling cycle. In the same temperature range, the efficiency of the ideal regenerative Stirling cycle is equivalent to that of the Carnot cycle. Heat interaction takes place throughout the cycle, whereas work interaction only happens in processes 1-2 and 3–4. The figure shown below displays the cycle's schematic. Maximum pressure $\mathrm{(p_{max})}$, minimum pressure $\mathrm{(p_{min})}$, maximum volume $\mathrm{(v_{max})}$, compression ratio (r), and adiabatic exponent $\mathrm{(\gamma)}$ are the input variables taken into consideration when modelling the cycle. The following list includes the thermodynamic calculations of several processes involved in ... Read More
In this article, we will discuss different types of ICs (Integrated Circuits) in electronics. As we know, the integrated circuits (ICs) are one of the crucial parts of all electronic devices and systems. Without ICs, most of the hi tech electronic devices and gadgets that we use would cease to exist. Integrated circuits made the electronic devices and systems so small that they became an integral part of every field of human life. Therefore, integrated circuits or ICs are entirely responsible for miniaturization of electronic devices and circuits. Before discussing different types of ICs, let us first understand a ... Read More
SOP Form SOP form stands for Sum of Products form. SOP form is one in which a Boolean expression is expressed as a sum of product terms. For example, $$\mathrm{\mathit{f}\lgroup A, B, C\rgroup=AB+ABC+B\overline{C}}$$ This is a Boolean function expressed in SOP (Sum of Products) form. NAND Gate The NAND Gate is a type of universal logic gate. It is a logic gate one that can be used to realize any kind of logical function or any other type of logic gate. A NAND gate is basically a combination of two basic logic gates namely AND gate and NOT gate, i.e. ... Read More
In positional number systems, the radix is the total number of unique digits that are used to represent numbers in that number system. Radix is also called Base. For example, in decimal number system, we use total ten digits from 0 to 9 (i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) to represent any decimal number. Therefore, for the decimal number system, the radix or base is ten (10). Although we can easily convert a given number from one radix (i.e. number system) to any other radix (number system) by using radix conversion protocols. In this article, ... Read More
Otto Cycle An air standard cycle called the Otto Cycle is employed in spark ignition (SI) engines. It comprises of two reversible adiabatic processes and two isochoric processes (constant volume), totaling four processes. When the work interactions take place in reversible adiabatic processes, the heat addition (2-3) and rejection (4-1) occur isochorically (3-4 and 1-2). The Otto cycle's schematic is shown in Figure given below. To model the cycle in Python, the input variables considered are maximum pressure $\mathrm{(P_{max})}$, minimum pressure $\mathrm{(P_{min})}$, maximum volume $\mathrm{(V_{max})}$, compression ratio (r), and adiabatic exponent $\mathrm{(\gamma)}$. Table 2 explains the thermodynamic computations of ... Read More
Gauss Seidel Method is the iterative method to solve any system of linear equations. Though the method is very much similar to the Jacobi's method but the values of unknown (x) obtained in an iteration are used in the same iteration in Gauss Seidel whereas, in Jacobi's method they are used in the next iteration level. The updation of x in the same step speeds up the convergence rate. A system of liner equation can be written as − $$\mathrm{a_{1, 1}x_{1} \: + \: a_{1, 2}x_{2} \: + \: \dotso \: + \: a_{1, n}x_{n} \: = \: b_{1}}$$ $$\mathrm{a_{2, ... Read More
When an object at very high temperature is suddenly dropped in a cooler liquid and if it is assumed that the conductive resistance of the solid is very small in comparison to the surrounding convective resistance then the heat transfer analysis is called as lumped capacitance analysis (as shown in the figure given below). Here, we treat the system as a lump. In that case, we can assume that the rate of change of internal energy of lump will be equal to the heat interaction with the surrounding fluid. Mathematically, this can be written as − $$\mathrm{pcV\frac{\partial T}{\partial t} ... Read More