This document discusses three ways to perform addition of two numbers using only one variable in C and C++ programming.
The first method uses a function that accepts user input for the variable and returns its value. This function is called twice in the main method to perform the addition.
The second method uses scope resolution to access a global variable. It accepts input, performs the addition, and prints the result.
The third method also uses a function but returns the variable value directly to perform the addition in the main method. It accepts input inside the function and returns the variable.
The bubble point is the temperature at which the first drop of a liquid mixture begins to vaporize. This occurs when either the temperature is increased or the pressure is decreased. The document provides an example of calculating the bubble point temperature using MATLAB by defining a nonlinear equation and solving it using a root-finding function (fzero).
The document discusses refactoring code to improve its structure and readability without changing its external behavior. It defines refactoring as restructuring software to make it easier to understand and modify. The goals of refactoring are to reduce technical debt by improving code quality. Examples show refactoring an Android app by extracting methods, renaming variables for clarity, and converting the architecture to MVP pattern to separate concerns. Lessons recommend writing unit tests first and using metrics as a guide rather than mandate when refactoring.
Actividad 1 taller de expresiones algoritmicasleikgm
The document contains 14 math or logic expressions with variables a, b, c, and d assigned values. Each expression is followed by "R/ta" which likely stands for the result or target answer of evaluating that expression. The expressions include operations like addition, subtraction, multiplication, division, exponents, modulo, Boolean logic, and comparisons using symbols like =, <, >, and, or, not.
The document compares a C program that calculates student GPAs in different ways to an equivalent Java program using object-oriented principles. The C program defines a struct and separate functions to calculate the GPA using different methods, while the Java program defines classes to encapsulate the GPA calculation logic and allow code reuse through inheritance. Object-oriented programming aims to maximize code reuse and minimize recoding. To start programming in OOP, a class is defined as a template, with main() as the entry point and javac/java to compile and run Java programs.
This document describes a script that simulates bit error rate (BER) performance for BPSK modulation over a Rayleigh fading channel with a 2 transmitter and 2 receiver (2x2) multiple-input multiple-output (MIMO) system using zero forcing equalization. The script generates transmitted bits, applies BPSK modulation, sends the signals over a Rayleigh fading channel with additive noise, uses zero forcing equalization at the receiver, and compares the estimated and transmitted bits to calculate the simulated BER over a range of signal-to-noise ratio (SNR) values. The simulated results are then plotted along with theoretical BER curves for 1x1 and 2x2 MIMO systems.
This document contains 10 experiments on numerical analysis and C programming. Each experiment includes the aim, C code implementation, and sample output for programs that calculate sphere volume and area, sum of digits in a number, triangle property classification, checking for Pythagorean triplets, printing prime numbers within a range, calculating digit sum using a function, reversing an integer using recursion, summing even numbers recursively, sorting an array using bubble sort, and finding the intersection of values in two arrays.
This document discusses representations of natural numbers in programming languages like Haskell, Scala, and Java. It presents natural numbers as a type with two constructors: Zero and Suc. It also presents an eliminator and computation rules for reducing terms, as well as a uniqueness principle for natural numbers. Examples are given of defining and proving properties of functions over natural numbers using a proof assistant called ProvingGround.
This document discusses three ways to perform addition of two numbers using only one variable in C and C++ programming.
The first method uses a function that accepts user input for the variable and returns its value. This function is called twice in the main method to perform the addition.
The second method uses scope resolution to access a global variable. It accepts input, performs the addition, and prints the result.
The third method also uses a function but returns the variable value directly to perform the addition in the main method. It accepts input inside the function and returns the variable.
The bubble point is the temperature at which the first drop of a liquid mixture begins to vaporize. This occurs when either the temperature is increased or the pressure is decreased. The document provides an example of calculating the bubble point temperature using MATLAB by defining a nonlinear equation and solving it using a root-finding function (fzero).
The document discusses refactoring code to improve its structure and readability without changing its external behavior. It defines refactoring as restructuring software to make it easier to understand and modify. The goals of refactoring are to reduce technical debt by improving code quality. Examples show refactoring an Android app by extracting methods, renaming variables for clarity, and converting the architecture to MVP pattern to separate concerns. Lessons recommend writing unit tests first and using metrics as a guide rather than mandate when refactoring.
Actividad 1 taller de expresiones algoritmicasleikgm
The document contains 14 math or logic expressions with variables a, b, c, and d assigned values. Each expression is followed by "R/ta" which likely stands for the result or target answer of evaluating that expression. The expressions include operations like addition, subtraction, multiplication, division, exponents, modulo, Boolean logic, and comparisons using symbols like =, <, >, and, or, not.
The document compares a C program that calculates student GPAs in different ways to an equivalent Java program using object-oriented principles. The C program defines a struct and separate functions to calculate the GPA using different methods, while the Java program defines classes to encapsulate the GPA calculation logic and allow code reuse through inheritance. Object-oriented programming aims to maximize code reuse and minimize recoding. To start programming in OOP, a class is defined as a template, with main() as the entry point and javac/java to compile and run Java programs.
This document describes a script that simulates bit error rate (BER) performance for BPSK modulation over a Rayleigh fading channel with a 2 transmitter and 2 receiver (2x2) multiple-input multiple-output (MIMO) system using zero forcing equalization. The script generates transmitted bits, applies BPSK modulation, sends the signals over a Rayleigh fading channel with additive noise, uses zero forcing equalization at the receiver, and compares the estimated and transmitted bits to calculate the simulated BER over a range of signal-to-noise ratio (SNR) values. The simulated results are then plotted along with theoretical BER curves for 1x1 and 2x2 MIMO systems.
This document contains 10 experiments on numerical analysis and C programming. Each experiment includes the aim, C code implementation, and sample output for programs that calculate sphere volume and area, sum of digits in a number, triangle property classification, checking for Pythagorean triplets, printing prime numbers within a range, calculating digit sum using a function, reversing an integer using recursion, summing even numbers recursively, sorting an array using bubble sort, and finding the intersection of values in two arrays.
This document discusses representations of natural numbers in programming languages like Haskell, Scala, and Java. It presents natural numbers as a type with two constructors: Zero and Suc. It also presents an eliminator and computation rules for reducing terms, as well as a uniqueness principle for natural numbers. Examples are given of defining and proving properties of functions over natural numbers using a proof assistant called ProvingGround.
This document provides MatLab code examples for analyzing well log data, plotting seismic data, and performing a Fourier transform. It loads well log data, finds a specific formation within the well based on depth, and performs a regression to relate P-wave velocity and density using Gardner's equation. It also shows how to plot the well data, seismic data in different views, and discusses interfacing MatLab with other languages and Unix.
The document contains 10 programming experiments involving basic C programming concepts like functions, arrays, loops, conditional statements, etc. Each experiment has the aim, code implementation, and sample output for programs to calculate sphere volume and area, sum of digits in a number, triangle properties, Pythagorean triplets, prime numbers in a range, recursive functions to reverse a number, sum even numbers, bubble sort an array, and find common elements between two arrays.
This document discusses different loop structures in C programming including for, while, and do-while loops. It provides 4 code examples, the first using a for loop to print numbers 1-10, the second manually printing the same using printfs, the third calculating a sum using a while loop, and the fourth calculating a factorial using a do-while loop. The document covers the basic syntax of these common loop structures.
This program uses recursive functions to:
1. Calculate the standard deviation of an array of values by calculating the mean, summing the squared differences from the mean, and taking the square root.
2. Find the factorial of a number by multiplying it by the factorial of the previous number down to 1.
3. Find the sum of odd numbers between a range by recursively adding each odd number.
This Matlab code simulates OFDM channel estimation using a PN sequence as a cyclic prefix. It generates transmitted OFDM signals, adds channel effects using different multipath delay profiles, and estimates the channel using three methods: conventional correlation, correlation with two-tap filter estimation, and interpolation of periodically inserted PN sequences. It compares the bit error rates of the three channel estimation methods under varying signal-to-noise ratios.
TMB is an R package for statistical modeling that was developed by Kasper Kristensen. It implements template-based models in C++ and allows for automatic differentiation, sparse matrices, parallel computing, and Laplace approximations for random effects. The document provides an introduction and overview of TMB, examples of simple linear and state-space models coded in TMB, and a table comparing the computation times of TMB to another template modeling software called ADMB.
This document provides an introduction to AD Model Builder, a tool for developing and optimizing nonlinear models. It supports C++ programming with an automatic differentiation-aided quasi-Newton minimizer and libraries for parameters, data objects, uncertainty quantification, and random effects. AD Model Builder is used for complex, nonlinear models in fisheries science that should run quickly. A brief example fits a negative binomial distribution to data in just a few lines of code. A more complex fisheries catch-at-age model with over 100 parameters optimizes and runs output in 0.3 seconds. The document demonstrates how random effects can be easily incorporated.
This C++ program allows a user to input the coefficients a, b, and c of a quadratic equation ax^2 + bx + c. It then calculates the two roots of the equation and displays them, assigning both roots a value of 0 if the equation results in complex roots. The program was written by Wilson on February 5, 2015.
This function demodulates BPSK modulated signals. It takes in a signal, samples it based on the bit rate to extract individual bits. It uses the sampled signals and reference sine and cosine waves to calculate inphase and quadrature values to determine if each bit is a 1 or 0. It then plots the original signal, demodulated binary data and received binary values.
This document contains instructions for 4 programming problems. Each problem requires determining the number of inputs and outputs, writing an algorithm to convert inputs to outputs, and testing the algorithm using sample data when provided. The problems involve calculating distance from speed and time, exponential growth given an equation, displaying a name and address, and determining Ergies from Fergies and Lergies values.
This document discusses algorithmic complexity and developing theoretical models to quantitatively predict algorithm performance. It provides an example of modeling the runtime of a particle simulation algorithm. Key points:
- Algorithmic complexity analysis measures how an algorithm scales with input size using asymptotic Big O notation.
- A practical runtime model accounts for implementation-specific constants and is fitted to runtime data to solve for parameters.
- The example models simulation and processing times separately for a particle simulation algorithm running in parallel.
- The developed model closely matches actual runtimes and can be used to predict performance for different input sizes and processor counts.
This document discusses parallelizing the trapezoidal rule for numerical integration. It outlines four basic steps for designing a parallel program: 1) partition the problem into tasks, 2) identify communication between tasks, 3) aggregate tasks, and 4) map tasks to cores. For the trapezoidal rule, the tasks are calculating the area of individual trapezoids and summing the areas. The tasks are aggregated and mapped by distributing groups of trapezoids to different cores, with each core calculating a local integral and communicating the result to be summed. Pseudocode is provided for both the serial and parallel versions.
BIometrics- plotting DET and EER curve using MatlabShiv Koppad
This document describes analyzing biometric sample data to evaluate a system's performance. It includes:
1) Plotting score distributions to visualize genuine and imposter data.
2) Generating a DET curve to evaluate accuracy at different operating points and determine equal error rate.
3) Calculating an optimal operating point that minimizes total costs based on false accept and reject rates.
The analysis uses MATLAB to load sample data, calculate performance metrics, and plot the results. Key results include an equal error rate of 0.08611 and optimal operating point with 0.02333 false accept rate and 0.1092 false reject rate minimizing total cost to 1.6725.
This document discusses a programming problem involving calculating the area of a circle using scanf() and printf() functions in C programming language. It provides instructions on including header files, defining constants, getting user input with scanf(), calculating area using a defined constant pi and the radius, and outputting the result using printf(). It also includes some additional reading links about scanf() and printf() functions.
This document discusses integration in MATLAB. It describes how MATLAB can be used to find both indefinite integrals (anti-derivatives) and definite integrals. The int command is used to find indefinite integrals by calculating the primitive function of an expression. Definite integrals, which calculate the area under a curve between bounds, can also be found using int by specifying the limits of integration. Examples are provided to demonstrate calculating indefinite and definite integrals of common functions in MATLAB.
This document describes three methods for creating Bode plots of a transfer function in MATLAB:
1. Using the Control Toolbox with the tf and Bode functions
2. Creating arrays of the transfer function coefficients and using freqs to calculate the frequency response
3. Calculating the magnitude and phase directly from the transfer function and plotting the results
Ежегодное проведение конкурса «Таланты среди нас» давно стало в колледже доброй традицией. В новом учебном году мы, как всегда, ждем его с нетерпением. Дорогие первокурсники, ваш первый выход на сцену всегда волнительный. Мы с удовольствием придем вас поддержать! Успешного бенефиса!
This document provides MatLab code examples for analyzing well log data, plotting seismic data, and performing a Fourier transform. It loads well log data, finds a specific formation within the well based on depth, and performs a regression to relate P-wave velocity and density using Gardner's equation. It also shows how to plot the well data, seismic data in different views, and discusses interfacing MatLab with other languages and Unix.
The document contains 10 programming experiments involving basic C programming concepts like functions, arrays, loops, conditional statements, etc. Each experiment has the aim, code implementation, and sample output for programs to calculate sphere volume and area, sum of digits in a number, triangle properties, Pythagorean triplets, prime numbers in a range, recursive functions to reverse a number, sum even numbers, bubble sort an array, and find common elements between two arrays.
This document discusses different loop structures in C programming including for, while, and do-while loops. It provides 4 code examples, the first using a for loop to print numbers 1-10, the second manually printing the same using printfs, the third calculating a sum using a while loop, and the fourth calculating a factorial using a do-while loop. The document covers the basic syntax of these common loop structures.
This program uses recursive functions to:
1. Calculate the standard deviation of an array of values by calculating the mean, summing the squared differences from the mean, and taking the square root.
2. Find the factorial of a number by multiplying it by the factorial of the previous number down to 1.
3. Find the sum of odd numbers between a range by recursively adding each odd number.
This Matlab code simulates OFDM channel estimation using a PN sequence as a cyclic prefix. It generates transmitted OFDM signals, adds channel effects using different multipath delay profiles, and estimates the channel using three methods: conventional correlation, correlation with two-tap filter estimation, and interpolation of periodically inserted PN sequences. It compares the bit error rates of the three channel estimation methods under varying signal-to-noise ratios.
TMB is an R package for statistical modeling that was developed by Kasper Kristensen. It implements template-based models in C++ and allows for automatic differentiation, sparse matrices, parallel computing, and Laplace approximations for random effects. The document provides an introduction and overview of TMB, examples of simple linear and state-space models coded in TMB, and a table comparing the computation times of TMB to another template modeling software called ADMB.
This document provides an introduction to AD Model Builder, a tool for developing and optimizing nonlinear models. It supports C++ programming with an automatic differentiation-aided quasi-Newton minimizer and libraries for parameters, data objects, uncertainty quantification, and random effects. AD Model Builder is used for complex, nonlinear models in fisheries science that should run quickly. A brief example fits a negative binomial distribution to data in just a few lines of code. A more complex fisheries catch-at-age model with over 100 parameters optimizes and runs output in 0.3 seconds. The document demonstrates how random effects can be easily incorporated.
This C++ program allows a user to input the coefficients a, b, and c of a quadratic equation ax^2 + bx + c. It then calculates the two roots of the equation and displays them, assigning both roots a value of 0 if the equation results in complex roots. The program was written by Wilson on February 5, 2015.
This function demodulates BPSK modulated signals. It takes in a signal, samples it based on the bit rate to extract individual bits. It uses the sampled signals and reference sine and cosine waves to calculate inphase and quadrature values to determine if each bit is a 1 or 0. It then plots the original signal, demodulated binary data and received binary values.
This document contains instructions for 4 programming problems. Each problem requires determining the number of inputs and outputs, writing an algorithm to convert inputs to outputs, and testing the algorithm using sample data when provided. The problems involve calculating distance from speed and time, exponential growth given an equation, displaying a name and address, and determining Ergies from Fergies and Lergies values.
This document discusses algorithmic complexity and developing theoretical models to quantitatively predict algorithm performance. It provides an example of modeling the runtime of a particle simulation algorithm. Key points:
- Algorithmic complexity analysis measures how an algorithm scales with input size using asymptotic Big O notation.
- A practical runtime model accounts for implementation-specific constants and is fitted to runtime data to solve for parameters.
- The example models simulation and processing times separately for a particle simulation algorithm running in parallel.
- The developed model closely matches actual runtimes and can be used to predict performance for different input sizes and processor counts.
This document discusses parallelizing the trapezoidal rule for numerical integration. It outlines four basic steps for designing a parallel program: 1) partition the problem into tasks, 2) identify communication between tasks, 3) aggregate tasks, and 4) map tasks to cores. For the trapezoidal rule, the tasks are calculating the area of individual trapezoids and summing the areas. The tasks are aggregated and mapped by distributing groups of trapezoids to different cores, with each core calculating a local integral and communicating the result to be summed. Pseudocode is provided for both the serial and parallel versions.
BIometrics- plotting DET and EER curve using MatlabShiv Koppad
This document describes analyzing biometric sample data to evaluate a system's performance. It includes:
1) Plotting score distributions to visualize genuine and imposter data.
2) Generating a DET curve to evaluate accuracy at different operating points and determine equal error rate.
3) Calculating an optimal operating point that minimizes total costs based on false accept and reject rates.
The analysis uses MATLAB to load sample data, calculate performance metrics, and plot the results. Key results include an equal error rate of 0.08611 and optimal operating point with 0.02333 false accept rate and 0.1092 false reject rate minimizing total cost to 1.6725.
This document discusses a programming problem involving calculating the area of a circle using scanf() and printf() functions in C programming language. It provides instructions on including header files, defining constants, getting user input with scanf(), calculating area using a defined constant pi and the radius, and outputting the result using printf(). It also includes some additional reading links about scanf() and printf() functions.
This document discusses integration in MATLAB. It describes how MATLAB can be used to find both indefinite integrals (anti-derivatives) and definite integrals. The int command is used to find indefinite integrals by calculating the primitive function of an expression. Definite integrals, which calculate the area under a curve between bounds, can also be found using int by specifying the limits of integration. Examples are provided to demonstrate calculating indefinite and definite integrals of common functions in MATLAB.
This document describes three methods for creating Bode plots of a transfer function in MATLAB:
1. Using the Control Toolbox with the tf and Bode functions
2. Creating arrays of the transfer function coefficients and using freqs to calculate the frequency response
3. Calculating the magnitude and phase directly from the transfer function and plotting the results
Ежегодное проведение конкурса «Таланты среди нас» давно стало в колледже доброй традицией. В новом учебном году мы, как всегда, ждем его с нетерпением. Дорогие первокурсники, ваш первый выход на сцену всегда волнительный. Мы с удовольствием придем вас поддержать! Успешного бенефиса!
Este documento discute el desarrollo regional y territorial en el estado de Sinaloa, México. Explora conceptos como región natural, funcional, cultural y territorio, y examina a Sinaloa como entorno regional y territorial, incluyendo sus fronteras productivas y regiones económicas y naturales. También analiza el paso del keynesianismo al neoliberalismo y las reformas asociadas, así como proyectos de desarrollo fallidos en Sinaloa. Plantea la necesidad de superar el neoliberalismo y propone nuevas ciudades medias y ruralidades
This document contains C programming code examples and exercises provided by Vikram Neerugatti, an assistant professor. It includes multiple code snippets demonstrating various programming concepts like data types, operators, control structures, functions, arrays, strings, pointers, structures and file handling. The document is divided into sections with labels like 1(A), 2(B) etc. and each section contains 1-3 code examples/exercises on different C programming topics.
The document contains code for several C programs that demonstrate different programming concepts like calculating the roots of a quadratic equation, converting between Fahrenheit and Celsius, finding the largest of three numbers, calculating the harmonic series, checking for a leap year, calculating the area of a circle, and calculating the factorial of a number. Each code sample is preceded by a brief description and followed by the output when the code is run.
The document contains summaries of several C programming examples:
1. Programs to calculate the area and circumference of a circle, find simple interest, convert temperatures between Celsius and Fahrenheit, calculate subject marks and percentages, and calculate gross salary.
2. Additional programs demonstrate swapping values with and without a third variable, finding the greatest of three numbers, determining if a year is a leap year, and identifying integers as odd or even, positive or negative.
3. Further programs check if an integer is divisible by 5 and 11, compare two integers for equality, use a switch statement to print days of the week, and perform arithmetic operations using a switch case.
The document describes several programs to solve problems related to quadratic equations, reversing integers, finding square roots, and determining if a year is a leap year. It includes algorithms and C code to:
1) Take coefficients of a quadratic equation as input and compute all possible roots, handling real, equal, and complex cases.
2) Reverse an integer number and check if it is a palindrome.
3) Find the square root of a number without using library functions.
4) Read a year and determine if it is a leap year, considering end of century rules.
This document contains C code examples for various programming concepts like functions, loops, arrays, structures, unions, file handling etc. There are a total of 30 code snippets showing how to use different data types, control structures and functions in C programming language. The code snippets range from simple Hello World program to more complex examples demonstrating concepts like recursion, structures, file handling etc.
This document contains C code examples for various programming concepts like functions, loops, arrays, structures, pointers etc. There are a total of 40 code snippets showing how to use different features in C like printing output, taking input, if-else conditions, switch case, loops (while, for, do-while), functions (call by value, call by reference), arrays (single, multi-dimensional), structures, pointers etc. Each code snippet is commented and labeled to explain the concept demonstrated in that section.
The document contains MATLAB scripts for simulating different digital modulation schemes:
1) A binary amplitude-shift keying (ASK) script that generates a random bit stream and maps 0s and 1s to different amplitude levels to create a modulated signal.
2) A binary frequency-shift keying (FSK) script that maps 0s and 1s to different frequency tones and sums the tones to create the modulated signal.
3) A binary phase-shift keying (PSK) script that maps 0s and 1s to different phase shifts, adds noise, and calculates the bit error rate for varying signal-to-noise ratios.
This document contains C program code snippets and explanations for various programming problems including:
1) Finding perfect, Armstrong, and prime numbers as well as reversing, summing digits, and checking palindromes of numbers.
2) Converting between decimal and binary, multiplying matrices, and calculating LCM and factorial.
3) Checking for leap years and strong, palindrome, and generic root of numbers.
This document contains C program code examples for various programming problems. It is divided into 5 weeks. Some of the programs included are: exchanging values between two variables with and without a temporary variable, finding the sum of digits of a positive integer, generating factors of numbers, calculating the factorial of a number, computing the sine function as a series, generating the Fibonacci sequence, reversing digits of an integer, converting decimal to binary, octal and hexadecimal, calculating terms of a series, and performing basic mathematical operations based on user input. The document provides the code and output for each problem.
This program defines floating point variables a and b and initializes them to 0.001 and 0.003 respectively. It also defines a floating point variable c and pointers pa and pb. Pa is initialized to point to a, and pb is initialized to point to b. The value of a is then doubled through pa. The question asks to complete the statement to calculate c based on the other variables.
The document contains 10 code snippets showing different C programming examples:
1) Swapping two numbers using a third variable and without a third variable.
2) Calculating power of a number.
3) Counting digits of a number using while and for loops.
4) Finding the largest number from user input.
5) Calculating sum of digits of a number using while, for, and recursion.
6) Finding LCM and sum of an infinite GP series.
The document contains C code to perform matrix addition and multiplication using functions. It includes functions to read and write matrices, take user input for matrix dimensions and elements, perform the operations, and output the results. The code provides a menu for the user to select addition or multiplication and handles different cases for valid and invalid inputs.
The document discusses the C programming language. It provides a brief history of C, describes its data types and operators. It then presents 26 sample C programs demonstrating basic concepts like input/output, conditional statements, loops, functions, arrays and strings. The programs cover calculations, pattern printing, factorial, Fibonacci series and other simple programming examples.
The document describes 5 common mathematical functions in C programming - atan(), cos(), div(), modf(), and sin(). It provides the purpose, syntax, parameters, and examples of how to use each function. The atan() function computes the inverse tangent of a value. The cos() function computes the cosine of an angle in radians. The div() function performs integer division and returns the quotient and remainder. The sin() function computes the sine of an angle in radians.
This document contains review questions and solutions regarding decision making and branching concepts in C programming from Chapter 5. It includes questions on if/else statements, switch statements, logical operators, and evaluating expressions. Sample programs test various branching logic and output values of variables based on conditional expressions.
The document contains 18 code snippets demonstrating solutions to common programming problems. The code snippets include programs to: 1) convert temperature between Celsius and Fahrenheit, 2) find the larger of two numbers, 3) determine if a number is even or odd, and 4) calculate the square of a number. The programs demonstrate a variety of programming concepts like if/else statements, for loops, functions, and more.
Critical buckling load geometric nonlinearity analysis of springs with rigid ...Salar Delavar Qashqai
This C program performs a geometric nonlinearity analysis of springs with rigid elements under displacement-controlled large deformations. It imports input data, analyzes the system over multiple increments of applied displacement, and outputs the results to Excel and HTML files. The analysis calculates forces, displacements, base shear, and critical buckling load at each increment. When the ultimate displacement is reached, the program terminates and displays completion messages.
Computer Architecture and Organization lab with matlabShankar Gangaju
This document contains Matlab code to perform arithmetic operations on 4-bit binary numbers, including addition, subtraction, multiplication, and division. It includes main programs to input numbers, perform the operations, and output or plot the results. Functions are also defined to perform basic logic operations like AND, OR, and XOR that are used in the arithmetic operations.
Incorporate the SOR method in the multigridTest-m and apply the multig.pdfaartechindia
Incorporate the SOR method in the multigridTest.m and apply the multigridTest.m, to
determine the effects of changes in
Pre-smoothing iterations
Post-smoothing iterations
Multigrid cycle type
Iterative method
Number of grids (or grid hierarchy)
% SOR (Successive Over-Relaxation)
n = input('Enter number of equations, n: ');
A = zeros(n,n+1);
x1 = zeros(1,n);
A=[5 -2 3 -1;-3 9 1 2;2 -1 -7 3];
x1 = [0 0 0];
tol = input('Enter tolerance, tol: ');
m = input('Enter maximum number of iterations, m: ');
w = input('Enter the parameter w (omega): ');
k = 1;
while k <= m
err = 0;
for i = 1 : n
s = 0;
for j = 1 : n
s = s-A(i,j)*x1(j);
end
s = w*(s+A(i,n+1))/A(i,i);
if abs(s) > err
err = abs(s);
end
x1(i) = x1(i)+s;
end
if err <= tol
break;
else
k = k+1;
end
end
fprintf('The solution vector after %d iterations is :\n', k);
for i = 1 : n
fprintf(' %11.8f \n', x1(i));
end
%% Multigrid test case with visulization
% Author: Ben Beaudry
clc; clear; close all
load A_b.mat;
A = full(A); % Unsparce matrix to show full power of Multigrid
pre = 2; % Number of presmoothing iterations
post = 2; % Number of postsmoothing iterations
% cycle = 1; % Type of multigrid cycle (1=V-cycle, 2=W-cycle, 3=F-cycle)
smooth = 1; % Smoother type (1=Jacobi, 2=Gauss-Seidel)
grids = 5; % Max grids in cycle
maxit = 10; % Max iterations of solver
tol = 1e-02; % Tolerance of solver
%% Solvers
% solve directly
t=cputime;
x_D = A\b;
fprintf('Direct Solve Time: %g Seconds\n',cputime-t)
% V-Cycle
t=cputime;
[x_V,res_V,it_V] = multigrid(A,b,pre,post,1,smooth,grids,maxit,tol);
fprintf('V-Cycle Solve Time: %g Seconds\n',cputime-t)
% W-Cycle
t=cputime;
[x_W,res_W,it_W] = multigrid(A,b,pre,post,2,smooth,grids,maxit,tol);
fprintf('W-Cycle Solve Time: %g Seconds\n',cputime-t)
% F-Cycle
t=cputime;
[x_F,res_F,it_F] = multigrid(A,b,pre,post,3,smooth,grids,maxit,tol);
fprintf('F-Cycle Solve Time: %g Seconds\n',cputime-t)
% max it for iterative methods
it = 100;
% Gauss-Siedel
t=cputime;
L = tril(A);
U = triu(A,1);
x_G = zeros(length(b),1);
res_G= zeros(it,1);
for g = 1:it
x_G = L\(b-U*x_G);
r = b - A * x_G;
res_G(g) = norm(r);
if res_G(g) < tol
break;
end
end
fprintf('Gauss-Seidel Solve Time: %g Seconds\n',cputime-t)
% Jacobi
t=cputime;
d = diag(A);
dinv = 1./d;
LU = tril(A,-1)+triu(A,1);
U = triu(A,1);
x_J = zeros(length(b),1);
res_J= zeros(it,1);
for j = 1:it
x_J = dinv.*(b-(LU*x_J));
r = b - A * x_J;
res_J(j) = norm(r);
if res_J(j) < tol
break;
end
end
fprintf('Jacobi Solve Time: %g Seconds\n',cputime-t)
%% Plotting
figure;
hold on
plot(1:g,res_G(1:g),'o-','DisplayName','Guass-Seidel')
plot(1:j,res_J(1:j),'o-','DisplayName','Jacobi')
plot(1:it_V,res_V(1:it_V),'o-','DisplayName','V-Cycle Multigrid')
plot(1:it_F,res_F(1:it_F),'o-','DisplayName','F-Cycle Multigrid')
plot(1:it_W,res_W(1:it_W),'o-','DisplayName','W-Cycle Multigrid')
set(gca,'XLim',[0 100]);
grid on
legend('location','best')
ylabel('Relative Convergance')
xlabel('Iterations')
title('Convergance of Numerical System')
hold off
MULTIGRID FUNC.
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1. %consts
vtransverse=590;
%origin
gamma=1;
%experimental data
load('C:Program FilesMatlabdatadata1Bb.dat');
load('C:Program FilesMatlabdatadata1rb.dat');
load('C:Program FilesMatlabdatadata1R.dat');
time=clock;starttime=(60*time(5)+time(6));
dr=0.001;%new advanced bracket
r = 0:dr:R;
n=(R/dr)+1;
root1=zeros(1,n);
root2=zeros(1,n);
M=10; %max degree of fitted polynom B
Bint=interp1(rb,Bb,r,'spline');
B=polyfit(r,Bint,M); %It ain't a simple MASSIVE
A=zeros(1,M+2);
for i=1:1:M+1
A(i)=B(i)/(M-i+3);
end
A(M+2)=0;
C=zeros(1,M+3);
for i=1:1:M+1
C(i)=gamma*A(i);
end
C(M+2)=-1;
%Solving the first kind equation (root1)
for i=1:1:n
rcur=r(i);
Acur=polyval(A,rcur);
const=rcur*(gamma*Acur+1);
C(M+3)=-const;
preroot=roots(C);
for j=1:1:numel(preroot)
if ((real(preroot(j))>0) && (real(preroot(j))<R) &&
(imag(preroot(j))==0))
root1(i)=preroot(j);
end
end
if (root1(i)==0)
root1(i)=R;
end
end
%Solving the second kind equation (root2)
for i=1:1:n
rcur=r(i);
Acur=polyval(A,rcur);
const=rcur*(gamma*Acur-1);
C(M+3)=-const;
preroot=roots(C);
2. for j=1:1:numel(preroot)
if ((real(preroot(j))>0) && (real(preroot(j))<R) &&
(imag(preroot(j))==0) && (real(preroot(j))>r(i)))
if (root2(i)<real(preroot(j)))
root2(i)=preroot(j);
end
end
end
if (root2(i)==0)
root2(i)=r(i);
end
end
time=clock;endtime=60*time(5)+time(6);
figure(5);plot(r,root1,'bluex',r,root2,'redx');grid on;title(num2str(endtime-
starttime));