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+% Copyright The Numerical Algorithms Group Limited 1992-94. All rights reserved.
+% !! DO NOT MODIFY THIS FILE BY HAND !! Created by ht.awk.
+\newcommand{\MakeFunctionXmpTitle}{MakeFunction}
+\newcommand{\MakeFunctionXmpNumber}{9.50}
+%
+% =====================================================================
+\begin{page}{MakeFunctionXmpPage}{9.50 MakeFunction}
+% =====================================================================
+\beginscroll
+It is sometimes useful to be able to define a function given by
+the result of a calculation.
+%
+\xtc{
+Suppose that you have obtained the following expression
+after several computations
+and that you now want to tabulate the numerical values of \spad{f}
+for \spad{x} between \spad{-1} and \spad{+1} with increment
+\spad{0.1}.
+}{
+\spadpaste{expr := (x - exp x + 1)**2 * (sin(x**2) * x + 1)**3 \bound{expr}}
+}
+%
+You could, of course, use the function
+\spadfunFrom{eval}{Expression} within a loop and evaluate
+\spad{expr} twenty-one times, but this would be quite slow.
+A better way is to create a numerical function \spad{f} such that
+\spad{f(x)} is defined by the expression \spad{expr} above,
+but without retyping \spad{expr}!
+The package \spadtype{MakeFunction} provides the operation
+\spadfunFrom{function}{MakeFunction} which does exactly this.
+%
+\xtc{
+Issue this to create the function \spad{f(x)} given by \spad{expr}.
+}{
+\spadpaste{function(expr, f, x) \bound{f}\free{expr}}
+}
+\xtc{
+To tabulate \spad{expr}, we can now quickly evaluate \spad{f} 21 times.
+}{
+\spadpaste{tbl := [f(0.1 * i - 1) for i in 0..20]; \free{f}\bound{tbl}}
+}
+%
+%
+\xtc{
+Use the list \spad{[x1,...,xn]} as the
+third argument to \spadfunFrom{function}{MakeFunction}
+to create a multivariate function \spad{f(x1,...,xn)}.
+}{
+\spadpaste{e := (x - y + 1)**2 * (x**2 * y + 1)**2 \bound{e}}
+}
+\xtc{
+}{
+\spadpaste{function(e, g, [x, y]) \free{e}}
+}
+%
+%
+\xtc{
+In the case of just two
+variables, they can be given as arguments without making them into a list.
+}{
+\spadpaste{function(e, h, x, y) \free{e}\bound{h}}
+}
+%
+%
+\xtc{
+Note that the functions created by \spadfunFrom{function}{MakeFunction}
+are not limited to floating point numbers, but can be applied to any type
+for which they are defined.
+}{
+\spadpaste{m1 := squareMatrix [[1, 2], [3, 4]] \bound{m1}}
+}
+\xtc{
+}{
+\spadpaste{m2 := squareMatrix [[1, 0], [-1, 1]] \bound{m2}}
+}
+\xtc{
+}{
+\spadpaste{h(m1, m2) \free{h m1 m2}}
+}
+%
+For more information, see \downlink{``\ugUserMakeTitle''}{ugUserMakePage} in Section \ugUserMakeNumber\ignore{ugUserMake}.
+\showBlurb{MakeFunction}
+\endscroll
+\autobuttons
+\end{page}
+%