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Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_quad_opt_set (d01zk)

▸▿ Contents

    1  Purpose
    2  Syntax
    3  Description
    4  References
▸▿ 5  Parameters
    6  Error Indicators and Warnings
    7  Accuracy
    8  Further Comments
    9  Example

Purpose

nag_quad_opt_set (d01zk) either initializes or resets the optional parameter arrays or sets a single optional parameter for supported problem solving functions in Chapter D01.

Syntax

[iopts, opts, ifail] = d01zk(optstr, iopts, opts, 'liopts', liopts, 'lopts', lopts)
[iopts, opts, ifail] = nag_quad_opt_set(optstr, iopts, opts, 'liopts', liopts, 'lopts', lopts)

Description

nag_quad_opt_set (d01zk) has three purposes: to initialize optional parameter arrays; to reset all optional parameters to their default values; or to set a single optional parameter to a user-supplied value.
Optional parameters and their values are, in general, presented as a character string, optstr, of the form ‘option =optval’; alphabetic characters can be supplied in either upper or lower case. Both option and optval may consist of one or more tokens separated by white space. The tokens that comprise optval will normally be either an integer, real or character value as defined in the description of the specific optional argument. In addition all optional parameters can take an optval DEFAULT which resets the optional parameter to its default value.
It is imperative that optional parameter arrays are initialized before any options are set, before the relevant problem solving function is called and before any options are queried using nag_quad_opt_get (d01zl). To initialize the optional parameter arrays iopts and opts for a specific problem solving function, the option Initialize is used with optval identifying the problem solving function to be called, via its short name. For example, to initialize the optional parameter arrays to be passed to nag_quad_1d_gen_vec_multi_rcomm (d01ra) and its associated function nag_quad_1d_gen_vec_multi_dimreq (d01rc), nag_quad_opt_set (d01zk) is called as follows: 
[iopts, opts, ifail] = d01zk('Initialize = d01ra', iopts, opts);
The available option names and their corresponding valid values are given in Optional Parameters in nag_quad_md_sgq_multi_vec (d01es) and nag_quad_1d_gen_vec_multi_rcomm (d01ra).

References

None.

Parameters

Compulsory Input Parameters

1:     optstr – string
A string identifying the option to be set.
Initialize=function name
Initialize the optional parameter arrays iopts and opts for use with function function name, where function name is the short name associated with the function of interest.
Defaults
Resets all options to their default values.
option=optval
See Optional Parameters in nag_quad_md_sgq_multi_vec (d01es) and nag_quad_1d_gen_vec_multi_rcomm (d01ra) for details of valid values for option and optval. The equals sign (=) delimiter must be used to separate the option from its optval value.
optstr is case insensitive. Each token in the option and optval component must be separated by at least one space.
2:     ioptsliopts – int64int32nag_int array
Optional parameter array.
If optstr has the form Initialize=function name, the contents of iopts need not be set.
Otherwise, iopts must not have been altered since the last call to nag_quad_opt_set (d01zk), nag_quad_opt_get (d01zl) or the selected problem solving function.
3:     optslopts – double array
Optional parameter array.
If optstr has the form Initialize=function name, the contents of opts need not be set.
Otherwise, opts must not have been altered since the last call to nag_quad_opt_set (d01zk), nag_quad_opt_get (d01zl) or the selected problem solving function.

Optional Input Parameters

1:     liopts – int64int32nag_int scalar
Default: the dimension of the array iopts.
The length of the array iopts.
Constraint: unless otherwise stated in the documentation for a specific, supported, problem solving function, liopts≥100.
2:     lopts – int64int32nag_int scalar
Default: the dimension of the array opts.
The length of the array opts.
Constraint: unless otherwise stated in the documentation for a specific, supported, problem solving function, lopts≥100.

Output Parameters

1:     ioptsliopts – int64int32nag_int array
Dependent on the contents of optstr, either an initialized, reset or updated version of the optional parameter array.
2:     optslopts – double array
Dependent on the contents of optstr, either an initialized, reset or updated version of the optional parameter array.
3:     ifail – int64int32nag_int scalar
ifail=0 unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

W  ifail=11
On entry, the optional parameter in optstr was not recognized.
W  ifail=12
On entry, the expected delimiter ‘=’ was not found in optstr.
W  ifail=13
On entry, could not convert the specified optval to an integer.
On entry, could not convert the specified optval to a real.
   ifail=14
On entry, attempting to initialize the optional parameter arrays but specified function name was not valid.
W  ifail=15
On entry, the optval supplied for the integer optional parameter is not valid.
W  ifail=16
On entry, the optval supplied for the real optional parameter is not valid.
W  ifail=17
On entry, the optval supplied for the character optional parameter is not valid.
   ifail=21
On entry, either the option arrays have not been initialized or they have been corrupted.
   ifail=31
liopts is too small.
   ifail=51
lopts is too small.
   ifail=-99
An unexpected error has been triggered by this routine. Please contact NAG.
   ifail=-399
Your licence key may have expired or may not have been installed correctly.
   ifail=-999
Dynamic memory allocation failed.

Accuracy

Not applicable.

Further Comments

For suites of functions that share the same option arrays, the option arrays must be initialized using the primary (driver) function name. For example for functions nag_quad_1d_gen_vec_multi_rcomm (d01ra) and nag_quad_1d_gen_vec_multi_dimreq (d01rc), the option arrays must be initialized for nag_quad_1d_gen_vec_multi_rcomm (d01ra).
When encoding integer valued options in optstr, the integer optval must be written as an explicit integer. For example, "Maximum Subdivisions = 12" is acceptable, whereas "Maximum Subdivisions = 12.0" and "Maximum Subdivisions = 0.12E2" are not.
When encoding real valued options in optstr, the optval may be integral if appropriate. For example, "Absolute Tolerance = 10", "Absolute Tolerance = 10.0" and "Absolute Tolerance = 1.0E1" are all acceptable.

Example

See the example programs associated with the problem solving function you wish to use for a demonstration of how to use nag_quad_opt_set (d01zk) to initialize option arrays and set options.

Open in the MATLAB editor: d01zk_example

function d01zk_example


fprintf('d01zk example results\n\n');


  % Setup phase.

  % set problem parameters
  ni = int64(2);
  nx = int64(0);
  % lower (a) and upper (b) bounds
  a = 0;
  b = pi;
  iopts = zeros(100, 1, 'int64');
  opts  = zeros(100, 1);

  % initialize option arrays
  [iopts, opts, ifail] = d01zk('Initialize = d01ra', iopts, opts);

  % set any non-default options required
  [iopts, opts, ifail] = d01zk('Quadrature Rule = gk41', iopts, opts);
  [iopts, opts, ifail] = d01zk('Absolute Tolerance = 1.0e-7', iopts, opts);
  [iopts, opts, ifail] = d01zk('Relative Tolerance = 1.0e-7', iopts, opts);

  % determine maximum required array lengths
  [lenxrq, ldfmrq, sdfmrq, licmin, licmax, lcmin, lcmax, ifail] = ...
        d01rc(ni, iopts, opts);

  % allocate remaining arrays
  needi  = zeros(ni, 1, 'int64');
  comm   = zeros(lcmax, 1);
  icomm  = zeros(licmax, 1, 'int64');
  fm     = zeros(ldfmrq, sdfmrq);
  dinest = zeros(ni, 1);
  errest = zeros(ni, 1);
  x      = zeros(1, lenxrq);

  % Solve phase.

  % Use d01ra to evaluate the definate integrals of:
  %   f_1 = (x*sin(2*x))*cos(15*x)
  %   f_2 = (x*sin(2*x))*(x*cos(50*x))

  % set initial irevcm
  irevcm = int64(1);

  while irevcm ~= 0
    [irevcm, sid, needi, x, nx, dinest, errest, icomm, comm, ifail] = ...
      d01ra(irevcm, a, b, needi, x, nx, fm, dinest, errest, ...
            iopts, opts, icomm, comm);

    switch irevcm
      case 11
        % Initial returns.
        % These will occur during the non-adaptive phase.
        % All values must be supplied.
        % dinest and errest do not contain approximations
        % over the complete interval at this stage.

        % Calculate x*sin(2*x), storing the result in fm(2,1:nx) for re-use.
        fm(2, :) = x.*sin(2*x);

        % Calculate f_1
        fm(1, :) = fm(2, :).*cos(15*x);

        % Calculate f_2
        fm(2, :) = fm(2, :).*x.*cos(50*x);
      case 12
        % Intermediate returns.
        % These will occur during the adaptive phase.
        % All requested values must be supplied.
        % dinest and errest do not contain approximations
        % over the complete interval at this stage.

        % Calculate x*sin(2*x).
        fm(2, :) = x.*sin(2*x);

        % Calculate f_1 if required
        if needi(1) == 1
          fm(1, :) = fm(2, :).*cos(15*x);
        end

        % Complete f_2 calculation if required.
        if needi(2) == 1
          fm(2, :) = fm(2, :).*x.*cos(50*x);
        end
      case 0
        % Final return
    end
  end

  % query some currently set options and statistics.
  [ivalue, rvalue, cvalue, optype, ifail] = ...
     d01zl('Quadrature rule', iopts, opts);
  display_option('Quadrature rule',optype,ivalue,rvalue,cvalue);
  [ivalue, rvalue, cvalue, optype, ifail] = ...
     d01zl('Maximum Subdivisions', iopts, opts);
  display_option('Maximum Subdivisions',optype,ivalue,rvalue,cvalue);
  [ivalue, rvalue, cvalue, optype, ifail] = ...
     d01zl('Extrapolation', iopts, opts);
  display_option('Extrapolation',optype,ivalue,rvalue,cvalue);
  [ivalue, rvalue, cvalue, optype, ifail] = ...
     d01zl('Extrapolation Safeguard', iopts, opts);
  display_option('Extrapolation Safeguard',optype,ivalue,rvalue,cvalue);

  % print solution
  fprintf('\nIntegral |  needi  |   dinest   |   errest   \n');
  for j=1:ni
    fprintf('%9d %9d %12.4e %12.4e\n', j, needi(j), dinest(j), errest(j));
  end



function [dinest, errest, user] = monit(ni, ns, dinest, errest, fcount, ...
                                        sinfoi, evals, ldi, sinfor, fs, ...
                                        es, ldr, user)
  % Display information on individual segments
  fprintf('\nInformation on splitting and evaluations over subregions.\n');
  for k=1:ns
    sid = sinfoi(1,k);
    parent = sinfoi(2,k);
    child1 = sinfoi(3,k);
    child2 = sinfoi(4,k);
    level = sinfoi(5,k);
    lbnd = sinfor(1,k);
    ubnd = sinfor(2,k);
    fprintf('\nSegment %3d Sid = %3d', k, sid);
    fprintf(' Parent = %3d Level = %3d.\n', parent, level);
    if (child1>0)
      fprintf('Children = (%3d, %3d)\n', child1, child2);
    end
    fprintf('Bounds (%11.4e, %11.4e)\n', lbnd, ubnd);
    for j = 1:ni
      if (evals(j,k) ~= 0)
        fprintf('Integral %2d approximation %11.4e\n', j, fs(j,k));
        fprintf('Integral %2d error estimate %11.4e\n', j, es(j,k));
      end
      if (evals(j,k) ~= 1)
        fprintf('Integral %2d evaluation', j);
        fprintf(' has been superseded by descendants.\n');
      end
    end
  end

function display_option(optstr,optype,ivalue,rvalue,cvalue)
  % Query optype and print the appropriate option values

  switch optype
    case 1
      fprintf('%30s: %13d\n', optstr, ivalue);
    case 2
      fprintf('%30s: %13.4e\n', optstr, rvalue);
    case 3
      fprintf('%30s: %16s\n', optstr, cvalue);
    case 4
      fprintf('%30s: %3d  %16s\n', optstr, ivalue, cvalue);
    case 5
      fprintf('%30s: %14.4e  %16s\n', optstr, rvalue, cvalue);
  end

d01zk example results

               Quadrature rule: GK41                            
          Maximum Subdivisions:            50
                 Extrapolation: ON                              
       Extrapolation Safeguard:    1.0000e-12

Integral |  needi  |   dinest   |   errest   
        1         0  -2.8431e-02   1.1234e-14
        2         0   7.9083e-03   2.6600e-09
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