FC Coding is
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History:
Power of FortranCalculus and PROSE:
A good example of Nesting is our Match n Freq (tm) App.
Some Apps were developed to show the power of FortranCalculus in solving math problems. They are:
Try one or more of these applications to get an understanding of the FortranCalculus Compiler power that is available. Some Apps have a source code file for viewing; see how short the coding can be. Some Optimization Demo problems Solved and included with FC Compiler are,
Next, I will attempt to guide you through the various routines in order to create a 'picture' for you to understand what's going on. First, the code required and then a sample of output summary. 1. Introduce the Find statement that is used to tweak variables until ones objective(s) are met. The variables may have bounds and constraints that restrick where the selected solver may search for an Optimal solution. ! Find statement is key to tweak variables AND obtain an Optimal
! (i.e., Maximum / Minimum) solutions.
FIND y0, ydot0; ! variable list of those to tweak!
in bvp; by Ajax; ! Ajax is the solver for this problem
TO MINIMIZE errSum ! objective Minimize errSum variable!
2. Introduce the Integration Process. ! Integration procedure involves two commands:
! INITIATE (for 'setup') and INTEGRATE (for doing the work).
INITIATE isis; for ODEknown; ! isis is the integration solver.
equations y2dot/ydot, ydot/y; ! states how variables are related
of x; step dx; to xfinal
ooo
integrate ODEknown; by isis
3. This is the complete code necessary to solve this problem, but hope it gives you an idea what is going on. Variables to tweak (e.g. y0) MUST always be on the rightside of an equal sign; so the solver can change a value when it wants too. Follow y0 variable throughout the code for seeing what is required. Plus, see y0 and other tweaked variables in output section. global all
problem xCos
dimension xdata(6), ydata(6), error(6)
data xdata/ .5, 1., 1.5, 2., 2.5, 3./
data ydata/ .439, .540, .106, -.832, -2.00, -2.97/
npoints = 6
write(6,*) ' '
write(6,*) ' searching for parameters to minimize |error|'
write(6,*) ' '
x = xdata(1): dx = .01: xfinal = 3 ! initialize var.s
y2dot0 = 1: ydot0 = 1: y0 = 1
Find y0, ydot0; in bvp; by AJAX( cntl1);
~ to match errsum
write(6, *) ' i x y error'
write(6, *) ' - ----- ----- -----'
do 20 i = 1, npoints
write(6, 11) i, xdata(i), ydata(i) + error(i), error(i)
20 continue
11 format(2x, i2, 3(2x,g11.4))
! @aplot('od-plt') ! see Example Plot code below
end
model bvp ! boundary value problem
initiate isis; for ODEknown;
~ equations y2dot/ydot, ydot/y;
~ of x; step dx; to xfinal
y = y0: ydot = ydot0: x = xdata(1)
error(1) = y - ydata( 1): errsum = error(1)**2
do 20 i = 2, npoints
xfinal = xdata( i)
integrate ODEknown; by isis
error(i) = y - ydata( i)
errsum = errsum + error(i)**2
20 continue
end
model ODEknown ! known solution
y2dot = (2 * x * ydot - (x**2 + 2) * y) / x**2
! sol'n: y = x cos( x)
g = eq * 10000
end
controller cntl1( AJAX)
remax = 60
end
4. The following block shows code for an XYplots, if desired. C =============== Example code for writing XYplots ===============
! Following stmt. MUST be in bottom of main routine
@aplot('od-plt') ! any 6 char.s or less for 'od-plt'
end
procedure aplot( plot77)
character*(*) plot77
@graph( plot77, '2dgraph')
@window( plot77,100,500,50,400,xmin,xmax,ymin,ymax, 0,0,0,1,1.5)
xstep = (xmax - xmin)/8
@xaxis( plot77, xmin, xmax, xstep, 0, 1, 1)
ystep = (ymax - ymin)/6
@yaxis( plot77, ymin, ymax, ystep, 0, 1, 1)
@xclabel( plot77, 6, 'X-axis', 11)
@yelabel( plot77, 7, 'Y-axis ', 11)
@setup( plot77, 'pp', 0, 0, ichar('*'), 14) ! profile points (yellow *'s)
@setup( plot77, 'cr', 0, 10, -2, 0) ! profile curve (light green)
C Available colors include ...
C @setup( plot77, 'cr', 0, 1,-2,0) ! profile curve (blue)
C @setup( plot77, 'cr', 0, 2,-2,0) ! profile curve (green)
C @setup( plot77, 'cr', 0, 3,-2,0) ! profile curve (cyan)
C @setup( plot77, 'cr', 0, 4,-2,0) ! profile curve (red)
C @setup( plot77, 'cr', 0, 5,-2,0) ! profile curve (magenta)
C @setup( plot77, 'cr', 0, 6,-2,0) ! profile curve (orange)
C @setup( plot77, 'cr', 0, 7,-2,0) ! profile curve (white)
C @setup( plot77, 'cr', 0, 9,-2,0) ! profile curve (light blue)
C @setup( plot77, 'cr', 0, 10,-2,0) ! profile curve (light green)
C @setup( plot77, 'cr', 0, 12,-2,0) ! profile curve (light red)
C 2nd 'label' parameter is length of 3rd parm.; e.g., 14 is 2nd param. below
@label( plot77, 14, 'Plot title ...', 13, 150, 420, 0)
do 10 j=1, npoints
@point( plot77, 'pp', x(j), y(j))
@curve( plot77, 'cr', x(j), y(j))
10 continue
@show( plot77)
end
5. The following block shows a sample of output from the AJAX solver. The first column lists the variables being tweaked. The next column, INITIAL, shows initial values for variables that gets things rolling. The next columns are the values for that iteration. This problem required 60 iterations to solve for an optimal solution. Solution time was less than 8 seconds on a 5-year old PC. --- AJAX SUMMARY, INVOKED AT X8COS[16] FOR MODEL BVP ----
CONVERGENCE CONDITION AFTER 60 ITERATIONS
UNKNOWNS NOT CONVERGED
CONSTRAINTS UNSATISFIED
MAXIMUM ITERATIONS PERFORMED
SPECIFIED CRITERIA UNSATISFIED
LOOP NUMBER ......... [INITIAL] 1 2
UNKNOWNS
Y0 1.000000E+00 8.161676E-01 7.211046E-01
YDOT0 1.000000E+00 1.069793E+00 1.104053E+00
OBJECTIVE
||G|| @MIN ||X|| 5.760534E+01 1.394653E+01 3.849952E+00
ooo
LOOP NUMBER ......... [INITIAL] 59 60
UNKNOWNS
Y0 1.000000E+00 4.978819E-01 4.936162E-01
YDOT0 1.000000E+00 7.678495E-01 7.673392E-01
OBJECTIVE
||G|| @MIN ||X|| 5.760534E+01 7.865099E-02 7.412294E-02
! always decreasing ^^^ ?
---END OF LOOP SUMMARY
Are you ready to give it a try? First step is to download our free Calculus (Level) Compiler (i.e., FC-Compiler), install it, and run some Demo (example) files. Next, copy another (Demo) file and save it under another name in your 'user' folder. Edit this file with your equations and (math) models, then save it. Next, try executing it and see how it goes. Enjoy!
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(Here is a 'picture' of time-savings from FortranCalculus usage.) Rapid Prototyping for Adaptive Engineering
Basic, Fortran, MACSYMA, etc. vs. FortranCalculus
Engineering: Quickly Frozen Adaptive Source Code: Large Small Cost: High Low Delay: Long Short HTML code for linking to this page: <a href="https://goal-driven.net/apps/fc-compiler.html"><img style="float:left; width:100px" src="https://goal-driven.net/image/readrit-pic2.png"/> <strong>FortranCalculus Compiler</strong> </a>: Solves Algebraic Equations through Ordinary Differential Equations. Problem-Solving Applications include:
Industry Problem-Solving Descriptions include:
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