The theoretical relationship between deflection, \Delta y, and the applied load, P, for an end-loaded cantilever beam having an elastic modulus E is: load data for a cantilever beam and extraction from the elastic modulus from the slope of the line. The output argument is an array containing the coefficients of the polyomial.Īs a first example, consider a linear fit to a set of deflection vs. ![]() The input arguments are the x and y data arrays and the order, n, of the polynomial. MATLAB has a built-in function, polyfit(), to perform least-squares fitting with polynomial models. the coefficients of a polynomial) are chosen to minimize the sum of the squares of the differences between the theoretical curve and the experimental points. The standard approach is least-squares fitting, in which the model parameters (e.g. A basic technique for accomplishing that is to fit a curve describing a theoretical relationship to the data. solving an ordinary differential equationĮxtracting information from experimental data is a fundamental task in engineering analysis.This chapter covers some of MATLAB’s built-in functions for several kinds of fundamental engineering analysis: While writing a simulation from scratch using Euler’s method is a valuable educational exercise, it is not the best use of a practicing engineer’s time, when MATLAB has functions to perform the calculation with little or no programming. In reality, it is almost always smarter to use “canned” routines for performing complex computations, since many hours of development have gone into ensuring their accuracy and efficiency. The file ID is 8627.Since this book (and the course it is based on) focuses on programming, it has not emphasized MATLAB’s many built-in capabilities for performing mathematics. Note: After writing this function, I noticed Umberto Picchini's fast interpolation function, which provides up to a 4x speedup without the requirement of an evenly-spaced array. Note that, surprisingly, in the case of evenly-spaced x vectors, interp1q is slower than interp1 for most parameters, and interp1's nearest-neghbor interpolation is almost always slower than linear interpolation! The qinterp1 method came out ahead in all parameters tested. The same x, y, and xi vectors were used for each algorithm. The attached image shows the result of speed tests performed on a 2.4GHz, 2GB Windows XP machine. ![]() This should be backwards compatible for quite a few releases. Type "help qinterp1" for usage instructions. This function will return an error if the y and xi arrays are not both column or both row vectors. ![]() Per John D'Errico's suggestion, the nearest-lower-neighbor method has been changed to now use true nearest-neighbor interpolation (at a slight speed cost).Ī note on error checking: Because any error checking of the library array would destroy the flat scaling law, this function performs no error checking on the library (x and y) arrays. ![]() Like interp1, qinterp1 returns NaN for xi values that are out of bounds. qinterp1 requires an evenly spaced, monotonically increasing x array. In the limit of large library arrays, qinterp1 has a flat scaling, while interp1 has a linearly increasing scaling (see the image for this file). In the limit of small library and search arrays, it is ~5x faster. This function performs interpolation faster than MATLAB's "interp1" function.
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