By Darren Redfern
How to exploit This guide The MATLAB guide is a whole reference instrument for the MATLAB computation language, and is written for all MATLAB clients, despite their self-discipline or field(s) of curiosity. the entire integrated mathematical, photograph, and system-based instructions avail capable in MATLAB fifty one are particular herein. total association one of many major premises of The MATLAB guide is that almost all MATLAB clients ap proach the method to unravel a selected challenge (or set of difficulties) in a particular topic zone. as a result, all instructions are geared up in logical subsets that mirror those various different types (e.g., linear equations, usual differential equations, sur face and quantity portraits, etc.) and the instructions inside a subset are defined in an identical language, making a software that enables you speedy and assured entry to the data essential to whole the matter you have got delivered to the procedure. moreover, simply because there's a lot information regarding MATLAB that's very tough to specific on a merely command-by-command foundation, each one topic is prefaced with an introductory part. the following, exact examples are given, profiling the most universal functions of the instructions in that specific part. there's additionally an introductory consultation, titled MATLAB fast begin, that is meant to get these readers now not already acquainted with MATLAB off to a flying start.
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Extra info for The Matlab ® 5 Handbook
Example text
LlThese times are in seconds of CPU time, and were obtained on a Sun SPARCstation 10. Sparse Matrices 44 2S 20 10 = S 0 • 0 0 0 400 200 600 800 1000 n FIGURE 6. Comparison of CPU time to solve Ax storage modes, for various sizes of n . 1200 1400 1600 1800 2000 = b (for tridiagonal A) in full versus sparse The sparse data structure represents a matrix in space proportional to the number of nonzero entries, and most of the operations compute sparse results in time proportional to the number of arithmetic operations on nonzeros.
Using load. spdiags(A, d, m, n): In cases like this where the data is defined along the main diagonal and subdiagonals, spdiags is very convenient to use. For example: A = [1 -2 1 -2 1 -2 1 -2 1 -2 1 1 1 1 1] ; S = spdiags(A, [ -1 0 1]. 5, 5) ; full(S) converts S to full storage mode so that we can display it in traditional format: full (S) ans -2 1 0 0 0 1 0 1 1 0 0 -2 -2 1 0 0 0 1 -2 1 0 0 0 1 -2 The second argument of spdiags: [-1, 0, 1], specifies the diagonals. -1 refers to the first subdiagonal (immediately below the main diagonal), 0 refers to the main diagonal, and 1 refers to the first superdiagonal.
Mnew = triu(M, -n) to extract the upper matrix elements starting with the nth subdiagonal of M. Linear Equations 41 Additional information: All matrices returned are of equal dimensions to M. See also: tril. diag M = vander(V) Creates the Vandermonde matrix whose columns are defined by the elements of vector V. Output: A square matrix with dimension equal to the length of V is assigned to M. Additional information: The columns of a Vandermonde matrix contain powers of the various elements in V.