1. Introduction to PV-WAVE Welcome to IT’s seminar on statistical packages Sam Gordji, ccsam@olemiss.educcsam@olemiss.edu Weir 107

2. List of Statistical Packages SPSS SAS Mathematica MathWorks IMSL

3. Statistical Package: SAS/PC (cont.) 50 copies are available for faculty use For each copy purchased, a faculty member can get a free copy (to be installed on a student PC) The cost is $100 per copy per year To obtain a copy of SAS please email –ccsam@olemiss.educcsam@olemiss.edu –assist@mcsr.olemiss.eduassist@mcsr.olemiss.edu

4. List of Statistical Packages Mathematica  Mathematica (free copy for faculty, staff, and students). To obtain a copy of Mathematica please visit: http://www.mcsr.olemiss.edu/appssubpage.php?pagena me=mathematica.inc

5. List of Statistical Packages Matlab  Matlab is available on willow and sweetgum  Other packages such as Fortran, IMSL, etc. will be mentioned briefly

6. List of Statistical Packages IMSL  IMSL is a comprehensive package containing math, stat., and special functions  IMSL is available only on sweetgum  IMSL is a set of subroutines called by a Fortran program  PV-WAVE is a set of subroutines and is available only on willow and sweetgum

7. General Information  Email contact –Email your questions to ccsam@olemiss.educcsam@olemiss.edu  To download this and other materials visit: http://www.mcsr.olemiss.edu/appssubpage.http://www.mcsr.olemiss.edu/appssubpage php?pagename=mathcamp.inc  Please fill out the performance report and leave your email address so we may contact you for follow up questions

8. General Information  SAS performs statistical analysis  SPSS performs statistical analysis and is similar to SAS  Mathematica’s main function is to perform mathematical operations including statistics  MathWorks is similar to Mathematica and is available on willow and sweetgum

9. General Information  IT staff will assist users to access these packages. We also assist users to find the proper procedure to analyze their data. If you need assistance please send an email to Sam Gordji at ccsam@olemiss.edu, assist@mcsr.olemiss.eduassist@mcsr.olemiss.edu, or mathadm@olemiss.edu

10. Using PV To Solve Real Life Example Analytical Approach to Evaporation Problem Using Linearized Richards’ Equation and the Application of Green Function

14. PV-WAVE at UM/MCSR PV-WAVE is a comprehensive package for obtaining solutions for linear and non-linear equations and has a powerful graphics feature that is capable of graphing complex functions. Most if not all the famous mathematical and statistical functions such as Error Function, Gamma Function, FFT, etc, are programmed in PV-WAVE and are available without much effort. Instructions on how to run PV-WAVE is on this web page for PV8.5: http://www.mcsr.olemiss.edu/appssubpage.php?pagename=pvwave.inc And the following web page for PV9.0: http://www.mcsr.olemiss.edu/appssubpage.php?pagename=pvwave9.inc

15. The following two examples graph and solve equations 13 and 15 obtained by J. M. Chen et al. The t-axis on the graph represents the time in seconds and f(t) represents the rain fall intensity q(T), the rate at which the rainfall piles up on a certain soil (silt loam).

16. chen5_ex.pro ; *** This graphs, eq. 13 on pg. 1092 of Ap. 2001 of WRR paper by J.M. Chen. **** ; ** This is for the case when gama=5 & n=0, F(T)=5 *** ; Next 3 lines defines the problem. FUNCTION f,t RETURN,.0018455*(SQRT(t/3.14)+1.)*exp(-0.25*t) END ; pro or procedure tell the compiler that a user prog. module follows PRO chen5_ex ; activate the Math toolkit MATH_INIT t= INTERPOL([0,100],400000) ; plot statement plots f, f(t) with the range of 0 to 2 and.0018 to.0023 plot, t, f(t), xrange=[0,2], yrange=[.0018,.0023] ; zero=zerovect(f(t),t) ; print, zero ; oplot, plots the second plot in our case it plots over the original plot oplot, [zero], [f(zero)], psym=6 END

18. Program Zerovec_ex.pro Solves Equation 14 or 15 to obtain time for surface saturation ;;;;;;;;;zerovec_ex.pro, As before the three lines are to define the problem;;;;;;;;;;;;;; FUNCTION f,t RETURN, 2.18*SQRT((1/3.14)*t)*exp(-0.25*t) - 0.216 END PRO zerovec_ex ; pro = procedure zerovec_ex MATH_INIT ; call Mathematical Tool Kit from IMSL/PV t= INTERPOL([0,14],10000) ; Interpolate the above function from 0 to 14 with n=10000 ; choosing smaller number for n may yield a curve that is not smooth ; or may yeild bad answers plot, t, f(t) ; plot t and f(t) zero=zerovect(f(t),t) ; call zerovect and find zeros of the above function print, zero ;print the results oplot, [zero], [f(zero)], psym=6 xyouts,.2,.5, ' Computed zero is at x=' +STRING(zero(0))+' and x='+STRING(zero(1)) ; print the answers on the graph as well END ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;

19. Note that the below equation has 2 solution t=0.03131, 11.914

20. Web Pages Link below gets you to IMSL main site: http://www.imsl.com/ http://www.imsl.com/products/imsl/fortran/overview.php http://www.imsl.com/products/imsl/fortran/whatsNe w.php