[OctDev] formula2mat : fill a matrix with values of formula

[Etienne G. <et...@is...>]

  Hello,

what about a function like this (in main/miscellaneous)? For people
too lazy to call linspace() and meshgrid().

  Cheers,

  Etienne

======================================================================
## z = formula2mat (f, ...)    - Fill matrix 'z' with values of formula 'f'
##
## INPUT ------
## f    :string: A formula written in octave code.
##
## OPTIONS ----
## bndx : 2x1 : Boundary  of x in which f is evaluated (overrides bnd)
## bndy : 2x1 : Boundary  of y in which f is evaluated (overrides bnd)
## bnd  : 2x2 : bnd = [bndx; bndy] Boundary in which f is evaluated
##                                                     Default = [-1,1;-1,1]
##                                                             
## sz   : 2x1 : Number of x and y values at which f is evaluated
##                                                     Default =   [11,11]
## 
## x    : vec : Values of x at which f is evaluated (overrides bndX and szX)
## y    : vec : Values of y at which f is evaluated (overrides bndY and szY)
##
## vec  : bool: If true, assume that z can be obtained by evaluating f when
##              x and y are matrices, rather than scalars.
## 
## OUTPUT -----
## z    : sz-sized matrix containing the values of f.
##
## EXAMPLES ---
##                                ## Fills a matrix z containing the values
##                                ## "x^2 - y^2" for x and y varying in
##                                ## [-1,1] by intervals of 0.2.
## z = formula2mat ("x^2 - y^2");
## 
##                                ## Same thing, quicker.
## z = formula2mat ("x.^2 + y.^2","vec",1);
##
function zz = formula2mat (f, ...)

op1 = " x y bndx bndy bnd sz szx szy vec ";

default = struct ("x", nan,\
		  "y", nan,\
		  "bnd",[-1,1;-1,1],\
		  "bndx",nan,\
		  "bndy",nan,\
		  "sz",[11,11],\
		  "szx",nan,\
		  "szy",nan,\
		  "vec",0);

if nargin > 1,
  opts = read_options (list (all_va_args), "default", default, \
		       "op1", op1);
else opts = default;
end

[x,y,bnd, bndx, bndy, sz, szx, szy, vec] = \
    getfield (opts, "x","y","bnd" ,"bndx", "bndy", "sz", "szx", "szy", "vec");

## szx overwrites sz (same for szy)
if ! isnan (szx), sz(1) = szx; end
if ! isnan (szy), sz(2) = szy; end

if length (sz) != 2
  error ("length of sz should be 2, not %i\n", length (sz));
end
bnd
## bndx overwrites bnd
if ! isnan (bndx(1)), bnd(1,1) = bndx(1); end
if length (bndx)>1 && ! isnan (bndx(2)), bnd(1,2) = bndy(2); end
if ! isnan (bndy(1)), bnd(2,1) = bndy(1); end
if length (bndy)>1 && ! isnan (bndy(2)), bnd(2,2) = bndy(2); end
bnd
if any (size (bnd) != [2,2])
  error ("size of bnd should be [2,2], not [%i,%i]\n", size (bnd));
end

## If x or y are not def'd, define them now
if isnan (x), x = linspace (bnd(1,1),bnd(1,2),sz(1)); end
if isnan (y), y = linspace (bnd(2,1),bnd(2,2),sz(2)); end


[xx,yy] = meshgrid (x,y);


## x and y will become scalar variables below


if ! vec
  zz = zeros (sz);
  eval (sprintf (["for ii = 1:sz(1),\n",\
		  "  for jj = 1:sz(2),\n",\
		  "    x = xx(ii,jj); y = yy(ii,jj);\n",\
		  "    zz(ii,jj) = %s;\n",\
		  "  end;\n",\
		  "end;\n"],\
		 f));
else
  x = xx;
  y = yy;
  eval (["zz = ",f,";"]);
end

-- 
Etienne Grossmann ------ http://www.isr.ist.utl.pt/~etienne