function s = traprl(f, a, b, m)
%
% trapezoidal rule.

h  = (b - a)/m;
s = 0;

for k=1:(m-1),
  x = a + h*k;
  s = s + feval(f,x);
end

s = h*(feval(f,a)+feval(f,b))/2;
s = s + h*s;
        
        

        

traprl(f, a, b, m)
{
  // trapezoidal rule

  h  = (b - a)/m;
  s = 0;

  for (k = 1; k < m; k++) {
    x = a + h*k;
    s = s + feval(f,x);
  }

  s = h*(feval(f,a)+feval(f,b))/2;
  s = s + h*s;
  return(s);
}
        
        

Similar..

Besides non-functional formatting differences, it is clear that the examples above are quite similar. The main differences here are the single line comment character (// verses % ) and the "for" loop syntax. SPL uses C/C++ style initialization and increment constructs where MATLAB employs a specialized vector-like syntax. Like C/C++, the SPL function uses the return statement to return a value. By comparison, the return value is part of the function declaration in MATLAB. Although one could argue which language is "better" or clearer overall, the SPL routine is understood very easily by those familiar with C/C++.

An example that illustrates further differences between SPL and MATLAB, consider a routine to remove a linear trend from a series or table as found in the MATLAB M file toolbox:

      

function y = detrend(x,o)
%DETREND Remove a linear trend from a vector, usually for
%        FFT processing.
%   Y = DETREND(X) removes the best straight-line fit from
%   the data in vector X and returns it in vector Y.  If X
%   is a matrix, DETREND removes the trend from each column
%   of the matrix.
%   Y = DETREND(X,0) removes just the mean value from vector
%   X, or the mean value from each column, if X is a matrix.

%   J.N. Little 6-08-86
%   Revised 2-29-88 JNL
%   Copyright (c) 1986-88 by the MathWorks, Inc.

if nargin == 1
    o = 1;
end
[m,n] = size(x);
if m == 1    % If a row, turn into column vector
    x = x(:);
end
[mp,np] = size(x);
if o == 0    % Remove just mean from each column
    y = x - ones(mp,1)*mean(x);
else        % Remove straight-line fit from each column
    a = [(1:mp)'/mp ones(mp,1)];
    y = x - a*(a\x);
end
if m == 1
    y = y.';
end
      
      

      

      
/*************************************************************
*                                                            *
* DETREND.SPL Copyright (C) 2005 DSP Development Corporation *
*                       All Rights Reserved                  *
*                                                            *
* Author:     Randy Race                                     *
*                                                            *
* Synopsis:   Remove a linear trend from a series or array   *
*                                                            *
* Revisions:  12 May 2005  RRR  Creation - from DETREND.M    *
*                               Copyright (c) 1986-88 by     *
*                               the MathWorks, Inc.          *
*                                                            *
*************************************************************/


#if @HELP_DETREND

DETREND

Purpose: Removes a linear trend from a series or array

Format:  DETREND(X, OPT)

           X - input series or array

         OPT - optional integer,
                0: remove mean
                1: do not remove mean (default)

Returns: A series or array

Example:  W1: gline(100, .01, 1, 0)
          W2: detrend(W1)

          W2 consists of a 100 point line with slope
          and intercept of 0.0.

See Also: Gline
          Linreg

#endif


// remove a linear trend
detrend(x, opt)
{
    
    local y;

    // if opt not specified, default to 1

    if (argc == 1) {
        opt = 1;
    }

    if (opt == 0) {
        // remove the mean from each column
        y = x - colmean(x);
    }
    else {
        // remove a linear trend from each column
        y = x - linreg(x);
    }

    return(y);
}
      

      

Yet Different

Both SPL and MATLAB are free-form and the examples above show the typical formatting styles of each language. The comment block after the function declaration in a M file is displayed when the user types help detrend. SPL displays the free-form text between the #if @HELP_DETREND and #endif block. This block can be placed anywhere within the SPL file.

detrend removes the least squares line from a series or table. The function also has an optional argument to specify that only the mean value should be removed. This optional argument is detected in MATLAB by counting the number of input arguments with nargin. SPL uses the C/C++ like argc to indicate the number of input parameters.

Matrix vs Series Based Solution

Because MATLAB is matrix-based and series are stored in row form, row vectors must be transposed into columns. In fact, operators such as * and / actually perform matrix multiplication and inversion. Because SPL is series-based, row transpositions are not required and mathematical operators work in the way you would expect. SPL includes the explicit operators *^ and \^ to multiply and solve matrices.

If the optional argument is set to 1, the mean value of each column is removed by forming a table of the mean values and subtracting it from the data. MATLAB forms the table by creating a matrix of all ones and performing a matrix multiply. SPL simply subtracts the mean value of each column from the corresponding column.

The linear trend is removed by forming a least squares line. Again, MATLAB resorts to matrix operations where SPL uses the linreg function.

Although both routines accomplish the same goal, MATLAB approaches the problem from a matrix point of view, where SPL offers a series-based solution. Each approach has its advantages, but for problems that involve single or multi-column data series, SPL can result in clearer, more direct code.

M File Memory Limitations

All arrays in MATLAB are limited by the amount of physical memory. Because MATLAB relies on the operating system's general purpose implementation of virtual memory, if an array size exceeds the available memory, calculations produce errors or grind to a halt if a memory page is swapped to disk.

Virtual Series Management

SPL employs a optimized method called virtual series management. Each series and each column of an array is limited only by available disk space. If the series size exceeds available memory, SPL automatically uses hard disk storage. Because virtual series management is optimized for series processing, this method is much faster and more robust than general purpose operating system page swapping. The size of a series kept in memory is adjustible, allowing users to optimize processing based on system memory. With SPL, the memory footprint of large data series is small enough to bypass slow operating system page swapping, but computation is fast due to virtual data handling designed specifically for series processing. Thus, SPL is ideally suited for manipulating any number of very large data series.

More M File Issues

Because of the mixed heritage of the MATLAB language, several potentially confusing ambiguities persist. For example, the MATLAB * operator actually performs a matrix multiply. A common expression like:

a * b

would perform matrix multiplication if a and b are arrays or a standard multiply if either variable is a scalar. A careful reading of the code is required to establish the specific meaning of this simple expression.

SPL preserves the standard meaning of * and introduces the *^ operator for explicit matrix multiplication. Thus,

a * b

is always a standard multiplication whereas

a *^ b

is always a matrix multiplication. The intent of either expression is immediately obvious.

Further, the MATLAB expression:

b = f(x)

could refer to element x of array f or function f called with argument x. Again, a careful reading of the code is required to disambiguate the two possible meanings.

In SPL as well as C/C++,

b = f(x)

is always a function call and

b = f[x]

is always an array reference. The intent is immediately clear and consistent with the C/C++ family of modern programming languages.

C/C++ Style Syntax

In fact, SPL borrows so much of its syntax from C/C++ that many C/C++ programs can be loaded directly as SPL routines! For example, SPL supports C/C++ operators such as ++, --, +=, -=, /=, *= %=, ==, !=, >>, <<, >>=, <<=, ||, && and scalar pointers. Looping and iteration constructs such as for, while, do while, if, else, switch, goto work exactly as they do in C/C++. Array construction also mimics the C/C++ syntax. SPL also includes a full C/C++ like preprocessor: #if, #ifdef, #elif, #endif, #include, #define, #undef.

Useful Constructs

But SPL also borrows some good ideas from MATLAB. Matrix operators such as matrix multiply *^, divide \^ and transpose ' are supported. Powerful array addressing constructs such range specifiers 1..10, array assignments A[1..10] = 5, multiple return values (a, b) = f(x), automatic loading of SPL routines and built-in help syntax are provided.

A simple table gives a brief summary of the operators and syntax supported by MATLAB, C/C++ and SPL.

Convert M Files to SPL

Finally, if you need to convert your M files into SPL routines, the MathWorks offers a MATLAB-to-C conversion utility. Because SPL is so similar to C/C++, you can also use this utility as a great shortcut for converting M files into SPL functions for use in DADiSP.