1. Writing Programs in MathCAD
PH Numerical Methods
Writing Programs in MathCAD

2. Writing Programs in MathCAD
Can do much without programming
Some algorithms need programs
Iterative, repeat until solution
Can make other tasks simpler
Hide detail inside a program

3. The Golden Rule of Programming
Applies to all programming
K.I.S.S. principle
Keep It
Simple
Stupid

4. A MathCAD program All MathCAD programs are functions
Expression over multiple lines
Lines executed in order
Local Variables
Value of last line is result

5. A simple MathCAD program #1
Common subexpression calculated 3 times in function
 Can re-write using a program

6. fExample(a,b) as a 2 line program
1st line calculates sqrt & assigns to local variable ‘r’
2nd line calculates expression & returns answer

7. Watch selection box, carefully
MathCAD Programs #1
Programming Palette from toolbar
Select keywords from palette, DO NOT TYPE
Add Line to add lines to program
Watch selection box, carefully

8. MathCAD Programs #2 Assignments are local to program
Assignments in program use 
Can use full range of MathCAD functions in program
Last line is result of program
Use Vectors & Arrays to return multiple results

9. MathCAD Programs Online Help
Help|Resource Centre
Advanced Topics|Treasury Guide to Programming|Programming Within MathCAD
Tutorial
Quicksheets|Programming
Reference
Examples

10. Rectangular to Polar Conversion #1
Equations for r and q given x & y
Want 1 function to return both values
 Use a vector

11. Rectangular to Polar Conversion
Function returns 2 element vector
Element 0  r
Element 1  q
NB. Could use atan2(x,y) No error for x=0

12. MathCAD Programs Structures
if, otherwise, for, while
Indentation & vertical bars
Watch selection rectangle
<Space> to increase (more lines)
<Insert> to swap sides
No GOTO
Considered harmful

13. MathCAD programs if statement
Better than if() function for complicated cases.
otherwise statement to catch unhandled cases.

14. If statement in programs
Model rocket engine
Thrust = 0 for t<0
Thrust = 100 for t>0 and t<5
Thrust = 80 for t>5 and t<20
Thrust = 0 for t>20

15. Programmed if statement
Note:
Comparisons
use of otherwise to catch all cases

16. fThrust() function

17. MathCAD programs – The for loop
Loop extend shown by indent
‘Result’ array built up
Note syntax of ‘for’ line
Use when you know in advance how many iterations

18. Using fOnes() program

19. The while loop Execute statements while a condition is true
Used when you don’t know in advance how many times loop will be executed.
Loop while you are searching
Loop while error is too big
Loop while system is stable

20. A while loop example
Find first member of vector ‘Vec’ greater than threshold, ‘t’
Written as function
j is index
while loop
return index & value as vector

21. Using our Thresh function
Vv is test vector
Function returns index and value

22. Longer Loops Use ‘Add Line’ in body of loop to extend scope of loop.
Lines added at vertical bar
<Insert> key swaps sides of selection bar

23. Longer Loops

24. MathCAD Programs Histogram Example #1
Without programming
Calculate number & width of bins
Create Bin array
Create histogram
Need to write these steps for every
histogram

25. MathCAD Programs Histogram Example #2
As a program
Returns 2 element vector
Bin
Histogram
Min, Max, i local
Written as a function

26. MathCAD Programs Using the Hist() function
Same as any other function

27. Calculating the Fibbonaci series

28. Program Example Photon Scattering #1
Photon enters box
Travels random distance
Scatter through random angle
Repeat from step 2 until photon leaves box
Record walk for posterity

29. Photon Scattering Program to create Walk

30. Program Example Photon Scattering #2
Store x-y co-ordinates as 2 element vectors V
Write functions for
Pathlength()
ScatterAngle(q)
InBox(V)
NewPos(V,P,q)
Test these functions !!!

31. Photon Scattering PathLength function
s is related to 1/mean path
x placeholder is dummy
rnd(1) gives random number 0-1
See also rexp(NPts,1/s) function

32. Photon Scattering ScatterAngle(q)
Isotropic scatter - uniform
All angles between –p  p
Deal with anisotropy later

33. Photon Scattering InBox(V) function
Takes Vector as argument
‘Unpacks’ argument with subscripts
Uses multiplication to form AND
Returns 1 if in box, 0 otherwise

34. Photon Scattering NewPos(V,P,q)
Arguments
OldPosition V
Pathlength P
Angle q
Returns new position as vector

35. Photon Scattering Program to create Walk

36. Photon Scattering Using the program

37. Photon Scattering Conclusions
8 line program + functions
Records entire walk
Extract info from result vector
Easy to extend
3D scatter
Anisotropy
Change ScatterAngle(q)