FortranCalculus (FC) Computer Language

[OptimalDesigns]

FortranCalculus (FC) language was developed in late 1980s to replace PROSE language that ran on Time-Sharing computers starting in 1974 on a CDC 6600 computer.  PROSE and now FortranCalculus help Engineers & Scientists solve their math problems, in minutes!

FC Compiler improves Math Modeling, Simulation & Optimization efforts by improving their productivity by 20 times!  Solutions are Faster, Improved Accuracy, & Cheaper.

The FC compiler simplifies solving math problems by minimizing code necessary to state & solve a problem.  Some new thinking is necessary for those wanting to get the most for their buck; convert from simulation to optimization thinking.

If you were a manager or CEO and had the choice of a simulation design versus an optimization design, which would you pick?

Teach Educators: Modeling & Simulation’s next step is (Mathematical) Optimizations.  Optimizations require a design Goal or Objective (function).  Today's Engineers & Scientists solve problems with a “Find X” mind-set.  With some Operational Research training they could expand their thinking to a “Find X to Optimize Y” mind-set.  Then they would be ready for Optimizations, Calculus-level programming and software.  (This would drop today’s design times that require months even man years to one or two days!  Manufacturing processes could be optimized to the days demand and thus maximize their profits.)

“Find X to Optimize Y” thinking among professors will cause most engineering & science textbooks to be rewritten with optimization examples and discussions.  This will be great stuff for industries and government; applied engineering and/or science not just theories.

A little history, in 1974 Calculus programming was introduced at a Society of Industrial & Applied Mathematicians (SIAM) conference.  Two professors heading the conference would -not- allow this paper to be printed since they realized what it would do to their (numerical methods) field of work. (Few, if any, professors are aware of what can be achieved thru Calculus Programming.)  Help, we need Engineering & Science professors to teach the “Find X to Optimize Y” mind-set.

Design Goal | Objective required for Optimization
• Engineers & Scientists need to move from a “Find X” mind-set to a “Find X to Optimize Y” mind-set teaching in schools.
• Industry/Company Leaders need to state their company objectives so ALL employees know it; Leadership by objectives.

[mouser]

Sounds like a very interesting project.

[OptimalDesigns]

Hi,

I have been seeking High School & College math teachers that may be interested in the following Curve Fitting problem.  This type problem would be of great help for many future engineering & science students in industry. Do you know of any HS teachers that might be interested in teaching such?  If so, please forward a copy of this file to them.

Thanks, Phil
--------------

Want to help solve world (math) problems?
=====================

    Here is a typical cycle ... Problem to Solution
    -------------------------------------------------------
  • Find a Math model for a -regular- or normal cycle; i.e. a Lorentzian, sinusoidal, or whatever series.  If your model has 'n' components and workers for both -regular- and -irregular- cycles you hit the jackpot!  Your 'n' value must always be the same.  Other values in a math model are called Parameters and their values will vary with each dataset.

  • Build Pulse train: add 'i' -regular- cycles together separated by Tmin and add 1, 2, or 'j' -irregular- cycles in order to build your problem.  Next, find or build a 'black box' that can detect when a cycle is -irregular-.

  • Find or develop a 'pill' or 'black box' that will stop these -irregular- cycles from occurring.

Learn Curve Fitting for Industrial Applications
------------------------------------------

  With the Lorentz (function) where y = 1/(1+x*x), one can fit data to a wide variety of data.  There is a Windows App called CurvFit that has an option of a Lorentzian or Modified Lorentzian series; visit fortranCalculus.info/apps/curvfit.html.  Please download, install, and run some of its demo files.

  If it looks okay to you, then find some example dataset to fit on the web.  For example, I used Google to search for "one-cycle heartbeat data -apple".  When you find a one-cycle dataset, build a math model using my CurvFit app.  A heart-beat math model may help other researchers discover what's wrong with a heart, or, other disease.

  Would your students like to help find solutions to medical diseases/problems?  Ask them to find a math model for one-cycle heart-beat dataset problem using my CurvFit app.  Suggest forwarding top 5 (or so) CurvFit input files with the files named after the creators; e.g. JimS (for Jim Smith) or ElsaB (for Elsa Brubaker).  Link all of them with the same fileType of YYY (?).  Be sure students add their 'notes' below the "20. >> Keep notes below" line.  They should also Point out any unusual things that happen during a CurvFit run with their input (file) problem.  Also a good place to put references; e.g. Dataset came from the Oil Refinery field; or, Bob Jones provided this dataset from the magnetic disc drive field.  (Adding the xxx field may help websites locate these problem-solutions, in the future.)

  Add a write-up of a paragraph or two, stating the names of students that were involved in this exercise?  I would then add your statement to my CurvFit app's manual file or ReadMe.txt files for future (free) downloads.  Hope this would encourage your students.

  How about asking your students to ask their parents, grandparents, & friends if they have a dataset that may help R & D folks solve their problems?  The more folks involved the more excitement for the students.

  Math folks
  Develop a math model of a regular one-cycle heartbeat.  Try using a Lorentzian or Modified Lorentzian series.  Download My (free) CurvFit app for more insight.

  R & D folks
  Build a pulse train of regular cycle heart-beats and 1 or 2 or ??? irregular cycles.  Build/develop a 'black box' what can detect irregular cycles.

  Chemistry folks
  Find/develop a 'pill' or 'black box' that will stop future irregular cycles.

 

Irregular cycle problem solved!
  ===============

[OptimalDesigns]

Sounds like a very interesting project.

Might you be interested in making some extra income by supporting FortranCalculus (Computer) language?  I'm retiring, closing my website, as of early Apr. 2024.  There are 5 (math) apps with source code for users to download and use for free.  One app, FC-Compiler, is a Calculus-level (math) compiler for the FortranCalculus (Computer) language.  FC was developed or funded by NASA during the 1960s.

FC has the power to increase ones income by a factor of ten!

If you or someone you know may be interested in pursuing FC, please let me know.

For an introduction to FC, download my 'CurvFit' app from goal-driven.net website.  Download it, Install it, and execute it.  Run some demos, look at the output files, and view the 'Fit4user.fc' file that is the source code the running in the DOS background.

Things you need to know in order to support FC:  Fortran (77) basics, I/O stmt.s; Batch programming basics; and Engineering or some science field (physics, chemistry, etc.).

There is allot that can be done with FC ... solving some Heart problems and Cancer are two that sound promising.

Just some ideas.

Phil

[OptimalDesigns]

I'm having numerical problems with a nested solver.  Any ideas how to solve this?

JOVE solver is a sequential unconstrained optimization technique applying Newton's second-order
gradient search;
JUPITER solver is a moving exterior truncations penalty-function method applying a Davidon-Fletcher-
Powell (DFP) variable-metric search;

        FIND Yzero, Zimag, Zreal;
    1      in flatDlay;  by Jove( contrl2);
    2      with lower zeroLow;
    3      TO MINIMIZE errDlay

This 'Find' stmt. eventually calls following (nested) 'Find' stmt.

              FIND gain, pReal, pImag;
    1          in transfer; by Jupiter( contrl1);
    2          with lower poleLow; and uppers poleHi;
    3          TO MINIMIZE errTran

This 'find' stmt. calls 'transfer' routine until 'errTran' parameter is minimized.
Then execution returns to the first 'find' stmt. where it changes it's parameters
(Yzero, Zimag, Zreal) in order to achieve its objective of minimizing 'errDlay'.
This loop may continue for 20+ iteration, but I'm getting an error msg. saying
"*** THE OBJECTIVE FUNCTION BEING OPTIMIZED IS NEITHER AN EXPLICIT NOR
    AN IMPLICIT FUNCTION OF THE INDEPENDENT VARIABLES."

But it just finished the 2nd 'find' stmt. summary #1 having tweaked parameters
gain, pReal, pImag on its 1st loop.  Here is part of the summay ..

LOOP NUMBER .........  [INITIAL]        7              8
UNKNOWNS
  GAIN                2.293703E-03  2.293707E-03  2.293697E-03
  PREAL  (    1)    6.259960E-02  6.259913E-02  6.259846E-02
  PREAL  (    2)    4.406212E-02  4.406053E-02  4.405971E-02
  PREAL  (    3)    5.736741E-02  5.753962E-02  5.743653E-02
  PIMAG  (    1)    2.148273E-01  2.148198E-01  2.148219E-01
  PIMAG  (    2)    3.752846E-01  3.752705E-01  3.752753E-01
  PIMAG  (    3)    9.999969E-01  9.999994E-01  9.999997E-01
OBJECTIVE
  ERRTRAN            2.881500E-03  2.881502E-03  2.881502E-03
---

Another time with different initial values ...

LOOP NUMBER .........  [INITIAL]        1
UNKNOWNS
  GAIN                2.141501E-05  2.199075E-03
  PREAL  (    1)    2.000000E-01  2.241059E-02
  PREAL  (    2)    2.000000E-01  5.400497E-02
  PREAL  (    3)    2.000000E-01  6.942999E-02
  PIMAG  (    1)    1.000000E-01  4.238228E-01
  PIMAG  (    2)    2.000000E-01  3.050316E-01
  PIMAG  (    3)    3.000000E-01  1.751917E-01
OBJECTIVE
  ERRTRAN            1.840880E-01  1.657471E-03


---END OF LOOP SUMMARY

"*** IMPROPER RANK IN REFERENCE TO A DYNAMIC ARRAY" at a different place
in my code ... hmmm

Same problem just different initial conditions ... better objective

I'm trying to fit to a dataset that has the shape of a mountain (right side of peak only). So after a few iterations it should be settling in on the 5th, 6th, 7th, etc. digits of accuracy; kind of a stiff equation at this point. I’ve done this before with sequential find stmt. in a loop and it works. But I learned why an engineer will want it in a nested find stmt.

I have tried multiplying the error function by 10,000 in order to magnify the last few digits. It help some but still ends with such error msg.s.

Ideas or comments?