MLAB

MLAB was originally developed at the National Institute of Health in the late 1970s using Stanford's SAIL running on Digital Equipment Corporation (DEC) PDP-10 computers. The creators of MLAB founded Civilized Software, Inc. in 1985 and expanded MLAB in the late 1980s and early 1990s through the application of Small Business Innovation Research grants.

MLAB was first adopted by researchers and practitioners in biochemistry, but quickly spread to many other domains. It is now also used in education, in particular the teaching of linear algebra, numerical analysis, and is popular amongst scientists involved in chemical kinetics analysis and modeling[3] and compartmental modeling in pharmacological (including pharmacokinetics) and physiological research.

The MLAB application is built around the MLAB scripting language. Common usage of the MLAB application involves using the Command Window as an interactive mathematical or executing text (script) files containing MLAB code.

There are dozens of MLAB commands and hundreds of MLAB functions. In essence, MLAB is an interpreter for a high-level mathematical language with the ability to process re-runnable script files called do-files.

Example

In MLAB one can define a function and graph it as follows.

 function f(x) = a*cos(b*x)*exp(-k*x)
 a = 1; b=4; k =.5
 v=1:10!100
 m= points(f,v)
 draw m
 view

The result is a simple plot:

Note that 1:10!100 = 1:10:0.0909090909, which means that we are dealing with a column vector of values from 1 to 10 in steps of size 0.0909090909

Also, note that points(f,v) = v&'(f on v), and that v

One can read-in 110 data values from a file into a 2-column matrix as follows (the result is a 55 row by 2 column matrix.)

 d = read("filename",55,2)

Taking the rows of the matrix d as (x,y) data-points - with error in the y-values - where these data points are "modeled" by the function f, defined above, one can estimate the unknown parameters a,b,k as follows.

 fit(a,b,k), f to d

One can use estimated weights for the various data points in d based on a moving-variance estimation function ewt as follows.

 fit(a,b,k), f to d with wt ewt(d)

One can graph the data and the "fit" as follows.

 delete w  /* to discard any previous picture */
 draw d linetype none, pointtype circle
 draw points(f,d col 1) color green
 view

One can look at the symbolic derivative of f and graph it as follows.

 type f'x
 draw points(f'x, d col 1) color red
 view

Note that MLAB can use symbolic-derivatives when derivative values are needed during curve-fitting, or solving ODEs. Also, note that one can fit (or just solve) differential-equation-defined models in MLAB, so that chemical kinetics and physiological and compartmental models can be handled.

• Comparison of numerical-analysis software
• List of numerical-analysis software

• Official website