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Syntax
values = fnval(f,x) values = fnval(x,f) values = fnval(f,x,'l')
Description
Both fnval(f,x) and fnval(x,f) provide the matrix f(x), with f the function whose description is contained in f. The output (and input) depends on whether f is univariate or multivariate.
If the function in f is univariate, then the output is a matrix of size [d*m,n], with [m,n] the size of x and d the dimension of f`s target (e.g., d = 2 if f maps into the plane).
If f has a jump discontinuity at x, then the value f(x+), i.e., the limit from the right, is returned, except when x equals the right end of f's basic interval; for it, the value f(x-), i.e., the limit from the left, is returned.
If the optional third input argument is present and is a string beginning with 'l', then, f is instead made to be continuous from the left. This means that if f has a jump discontinuity at x, then the value f(x-), i.e., the limit from the left, is returned, except when x equals the left end of the basic interval; for it, the value f(x+) is returned.
If the function is multivariate, then the above statements concerning continuity from the left and right apply coordinatewise. Further, if the function is, more precisely, m-variate for some m>1, then x must be either a list of m-vectors, i.e., of size [m,n], or a cell array {x1,...,xm} containing m vectors. In the first case, the output is of size [d*m,n] and contains the values of the function at the sites in x. In the second case, the output is of size [d,length(x1),...,length(xm)] (or of size [length(x1),...,length(xm)] in case d is 1), and contains the values of the function at the m-dimensional grid specified by x.
Examples
The statement fnval(csapi(x,y),xx) has the same effect as the statement csapi(x,y,xx).
Algorithm
For each entry of x, the relevant break- or knot-interval is determined and the relevant information assembled. Depending on whether f is in ppform or in B-form, nested multiplication or the B-spline recurrence (see, e.g., [PGS; X.(3)]) is then used vector-fashion for the simultaneous evaluation at all entries of x. Evaluation of a multivariate function takes full advantage of the tensor product structure.
See Also
| | fntlr | getcurve | |