The Design of The NAG Toolbox for MATLAB

Structure of the Toolbox

• D01 – Quadrature

All documented routines in the Toolbox have five-character names, beginning with the characters of the chapter name, e.g.,

• d01aj

All routines have an alternative longer name beginning nag_ for example d01aj may be called via the name nag_quad_1d_fin_bad.

The documentation of the Toolbox follows the same chapter structure as the Library, so each chapter of routines has a corresponding chapter in the documentation, consisting of the following documents:

• Chapter Contents, e.g., Chapter D01;
• Chapter Introduction, e.g., the D01 Chapter Introduction;
• Routine Documents, one for each documented routine in the chapter.

Comparison with the Fortran Library

Optional Parameters

1. A sensible default value exists which applies to many problems.
2. The parameter only applies to some cases which the routine is designed to solve.
3. The value of the parameter can normally be determined from that of other parameters at runtime.

Parameters Omitted from the Toolbox Interface

1. Dimensions of arrays.
2. Workspace whose size depends entirely on the problem data.
3. Parameters whose value depends entirely on that of other input data.

User Workspace

x = [0.5; 1; 1.5];
y =
[0.14,0.18,0.22,0.25,0.29,0.32,0.35,0.39,0.37,0.58,0.73,0.96,1.34,2.10,4.39];
t = [[1.0, 15.0, 1.0],
     [2.0, 14.0, 2.0],
     [3.0, 13.0, 3.0],
     [4.0, 12.0, 4.0],
     [5.0, 11.0, 5.0],
     [6.0, 10.0, 6.0],
     [7.0, 9.0, 7.0],
     [8.0, 8.0, 8.0],
     [9.0, 7.0, 7.0],
     [10.0, 6.0, 6.0],
     [11.0, 5.0, 5.0],
     [12.0, 4.0, 4.0],
     [13.0, 3.0, 3.0],
     [14.0, 2.0, 2.0],
     [15.0, 1.0, 1.0]];
user = {y, t, 3};

[xOut, fsumsq] = e04fy(nag_int(15), 'e04fy_lsfun1', x, 'user', user);

function [fvecc, user] = lsfun1(m, n, xc, user)
  fvecc=zeros(m,1);

  % y is in user{1} and t is in user{2}
  for i = 1:m
    fvecc(i) = xc(1) + user{2}(i,1)/(xc(2)*user{2}(i,2)+xc(3)*user{2}(i,3))-...
                user{1}(i);
  end

Input/Output Parameters

Routines Omitted from the Toolbox

References

ACM (1960–1976) Collected algorithms from ACM index by subject to algorithms