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Chapter 18: Matrix Manipulation 14918 Matrix ManipulationThere are a number of functions available for checking to see if the elements of a matrixmeet some condition, and for rearranging the elements of a matrix. For example, Octavecan easily tell you if all the elements of a matrix are finite, or are less than some specifiedvalue. Octave can also rotate the elements, extract the upper- or lower-triangular parts, orsort the columns of a matrix.18.1 Finding Elements and Checking ConditionsThe functions any and all are useful for determining whether any or all of the elementsof a matrix satisfy some condition. The find function is also useful in determining whichelements of a matrix meet a specified condition.any (x, dim)Built-in FunctionFor a vector argument, return 1 if any element of the vector is nonzero.For a matrix argument, return a row vector of ones and zeros with each elementindicating whether any of the elements of the corresponding column of the matrix arenonzero. For example,any (eye (2, 4))⇒ [ 1, 1, 0, 0 ]If the optional argument dim is supplied, work along dimension dim. For example,any (eye (2, 4), 2)⇒ [ 1; 1 ]all (x, dim)Built-in FunctionThe function all behaves like the function any, except that it returns true only ifall the elements of a vector, or all the elements along dimension dim of a matrix, arenonzero.Since the comparison operators (see Section 10.4 [Comparison Ops], page 70) returnmatrices of ones and zeros, it is easy to test a matrix for many things, not just whether theelements are nonzero. For example,all (all (rand (5) < 0.9))⇒ 0tests a random 5 by 5 matrix to see if all of its elements are less than 0.9.Note that in conditional contexts (like the test clause of if and while statements) Octavetreats the test as if you had typed all (all (condition)).xor (x, y)Mapping FunctionReturn the ‘exclusive or’ of the entries of x and y. For boolean expressions x and y,xor (x, y) is true if and only if x or y is true, but not if both x and y are true.is duplicate entry (x)Return non-zero if any entries in x are duplicates of one another.Function File