Re: plot data from multiple arguments

[Etienne Grossmann]

From: "D. Stimits" <address@hidden>

#  Everyone's replies got me a lot further along, I was able to figure out
#  more closely what the problem is. My "non-test" version of function that
#  fails requires the square of a scalar, the "x" that I am essentially
#  trying to iterate through from 0.0 to 1.0 in steps of 0.1. I'm used to
#  "strongly typed" languages, and failed to see that:
#  x = (0.0:0.1:1.0)';
#  data = [x, MyFunc(x, 3, 2)];

#  ...does not pass a scalar through multiple passes to the "x" of
#  MyFunc...instead it is passing a matrix one time. I was making a bad
#  assumption that MyFunc would be passed one array element at a time from
#  x, iterating throug it until each element, in order, had been passed,
#  and accumulate a return value of each pass. So when I expected "x ** 2"
#  to square a single value of x from a single index, it instead was dying
#  with:
#  error: operator *: nonconformant arguments (op1 is 11x1, op2 is 11x1)
#  error: evaluating binary operator `*' near line 21, column 17
#  error: evaluating assignment expression near line 21, column 13

#  Now I fear that to build "data" I won't be able to use a simple one-line
#  formula unless I modify MyFunc to handle "x" as a matrix...is this
#  correct? At which point I wonder what else might break. Btw, "MyFunc"

  Right. Octave provides operators for that, such as c = a .* b
(c(i,j)=a(i,j)*b(i,j)), or ./ (term by term division), .^
(exponentiation).

#  returns a single float between 0 and 1, much like sin(x) would. I'm
                    ^^^^
                  In octave, it's all doubles.

#  interested only in the input value of "x" (also between 0 and 1) and
#  associated value that MyFunc returns as pairs of xy coordinates on a
#  simple graph (MyFunc is a smooth polynomial curve). Can anyone suggest
#  my options? Here is some code, where "MyFunc" is actually
#  "BernsteinPoly":

  I am not sure I get your question right. But the func below could
  illustrate the usage of these operators.

     ## x : column vector of "input values"
     ## c : column vector of coefficients of poly (degree 0, 1, etc)
     function y = poly_foo (x, c)
       x = x(:);                  ## Make sure x and c are columns
       c = c(:);
       d = length (c);            ## Degree of poly + 1
       l = length (x);
       y = sum (((ones(d,1)*x') .^ ([0:d-1]'*ones(1,l))) .* (c*ones(1,l)));
     endfunction

     Here,

      a = ones(d,1)*x'       is a (d x l) matrix, each row is equal
                             to x'. 

      b = [0:d-1]'*ones(1,l) is also (d x l), the first row is zeros,
                             second is ones, third is twos, etc
 
      e = a .^ b             (d x l) : e(i,j) = x(j)^i
         
      f = c .* (c*ones(1,l)) (d x l) : f(i,j) = c(i) * x(j)^i

      g = sum (f)            (1 x l). "sum" does the sum of each
                             column. So g(j) = sum (i=1 to d, f(i,j)) =
                               = c(1)*x(j)^0 + ... + c(d)*x(j)^(d-1).
                            
                             (warn: sum (row_vector) returns sum of
                              elements of row_vector)

    Hth,

  Etienne


ps : You will probably save a lot of time by studying a little bit the
     octave docs, for basic functions and polynomial functions.


#  ####################################
#  function retval = BinomialCoefficient( degree, instance )
#      retval = prod( 1:degree );
#      retval = retval / ( prod(1:instance) * prod(1:(degree - instance))
#  );
#  endfunction

#  # x between 0.0 and 1.0. degree and instance whole numbers. degree
#  # between 1 and n, instance betwee 0 and n-1.
#  function retval = BernsteinPoly( x, degree, instance )
#     coefficient = BinomialCoefficient( degree, instance );
#  #   printf( "x, degree, instance: %1.1f, %d, %d\n", \
#  #      [x'; [degree;instance]*ones(1,rows(x))] );
#     left_weight = x ** instance;
#     right_weight = (( 1 - x ) ^ ( degree - instance ));
#     blend = left_weight * right_weight;
#     retval = coefficient * blend;
#  endfunction
#  ####################################

#  You'll see that "left_weight" of BernsteinPoly uses "x ** instance".
#  This is where I'm messing up by causing "x" to be a matrix instead of a
#  scalar passed multiple times. Since I might be mixing functions later
#  and looking at piecewise construction of a larger curve from multiple
#  segments, with each segment using a different forumula, I'm worried that
#  adding direct matrix handling abilities inside of BernsteinPoly (versus
#  expecting "x" to be scalar) might cause other troubles in the future.
#  Any advice?



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