** Population Density Rectangular City Calculator and eTCL Slot Calculator Demo Example **

This page is under development. Comments are welcome, but please load any comments in the comments section at the bottom of the page. Please include your wiki MONIKER  in your comment with the same courtesy that I will give you. Its very hard to reply intelligibly without some background of the correspondent. Thanks,[gold]
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<<TOC>>

[gold]  Here i
 
#Formula for population of rectangular city was similar to probability of two dimensional distribution density in x and y. The population density function was f(z) = A1*f(x,y)*dx*dy.  A1*f(x,y) was population density and dx*dy was area. The population density A1*f(x,y) was the product of exp(-k1*x) and exp(-k2*y), where A1 is the maximum population density in the center of the countryside or city. The constants -k2 and -k2 were exponential decay constants.  Here the f(x) and f(y) components were treated with same exponential decay constant (-.1), but the calculator constants can be changed internally in the program to different constants for exp(-k1*x) and exp(-k2*y). Different decay constants in x and y dimensions may appear where a city is backed up or extended along a coast, river, or road. 

#The eTCL calculator implemented formula correctly if constant A1 was supplied. A1 was the maximum expected density in inhabitants per square kilometer (ints/sq km), whether in the center of the countryside or city. The model was that the rate (ints/sq km) was maximum at city center and declined exponentially with distance from city center.  The "6 for 6" rule for substance farmers in countryside was family of  6 inhabitants for 6 hectares.  The "6 for 6" rule converted to 6 ints / 6 h. * (100 h / (1 sq km)), 100 ints per sq km. Various references cite ancient cities at 100  inhabitants per square hectare to medieval cities at 300  inhabitants per square hectare. Converting, ancient and medieval cities ranged from 10000 ints/sq km to 30000 ints/sq km. Calculator was primarily written for ancient and medieval cities. The research will have to gather some testcases for modern cities to see if calculator is useful for modern cities.

*** Pseudocode and Equations ***
====== 
  liters = [* volume_in_cubic_cm .001]
  price? = raw materials + labor  +  profit
  price? = raw materials + heat process
  price? = raw materials + labor 
  average price per unit  = revenue  / units sold
====== 
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***Testcases Section***

In planning any software, it is advisable to gather a number of testcases to check the results of the program. The math for the testcases can be checked by pasting statements in the TCL console. Aside from the TCL calculator display, when one presses the report button on the calculator, one will have console show access to the   capacity  functions (subroutines). 

**** Testcase 1 ****
%|table 1|printed in| tcl wiki format|% 
&| quantity| value| comment, if any|& 
&| testcase number:|1 | |&
&| 500.0 :|up to hours =<t1 only|   |&
&| 1000.0 :|interval minimum hours =>t2 | |& 
&| 1500.0 :|interval maximum hours =< t3| |& 
&| 0.0014 :| exponential density coefficient (optional) |  |&
&| 0.503  :| probability up to =<t1 only|  |&
&| 0.496  :|probability  =>t1|  |&
&| 0.124  :|probability interval =>t2 to =<t3  |  |&
&| 1.0  :|probability =<t1+=>t1   | approx unity |&

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**** Testcase 2 ****
%|table 2|printed in| tcl wiki format|% 
&| quantity| value| comment, if any|& 
&| testcase number:|2 | |&
&| 1000.0 :|up to hours =<t1 only|   |&
&| 1200.0 :|interval minimum hours =>t2 | |& 
&| 1500.0 :|interval maximum hours =< t3| |& 
&| 0.0014 :| exponential density coefficient (optional) |  |&
&| 0.753  :| probability up to =<t1 only|  |&
&| 0.246  :|probability  =>t1|  |&
&| 0.063  :|probability interval =>t2 to =<t3  |  |&
&| 1.0  :|probability =<t1+=>t1   | approx unity |&

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**** Testcase 3 ****
%|table 3|printed in| tcl wiki format|% 
&| quantity| value| comment, if any|& 
&| testcase number:|3 | |&
&| 1200.0 :|up to hours =<t1 only|   |&
&| 1500.0 :|interval minimum hours =>t2 | |& 
&| 2000.0 :|interval maximum hours =< t3| |& 
&| 0.0014 :| exponential density coefficient (optional) |  |&
&| 0.813  :| probability up to =<t1 only|  |&
&| 0.186  :|probability  =>t1|  |&
&| 0.0616  :|probability interval =>t2 to =<t3  |  |&
&| 1.0  :|probability =<t1+=>t1   | approx unity |&

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***Screenshots Section***
****figure 1.****
[http://s30.postimg.org/nsq8fcurl/product_liifetime_exponential_density_calculator.png]
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***References:***
   
   * On Dairy Productivity 
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**Appendix Code**

***appendix TCL programs and scripts ***

====== 
   
        # pretty print from autoindent and ased editor
        # Product lifetime exponential density calculator
        # written on Windows XP on eTCL
        # working under TCL version 8.5.6 and eTCL 1.0.1
        # gold on TCL WIKI, 15oct2014
        package require Tk
        namespace path {::tcl::mathop ::tcl::mathfunc}
        frame .frame -relief flat -bg aquamarine4
        pack .frame -side top -fill y -anchor center
        set names {{} {time up to hours =<t1:} }
        lappend names {time interval hours =>t2:}
        lappend names {time interval hours =<t3: }
        lappend names {exponential density coefficient (optional) :}
        lappend names {answers : probability =< t1 only:}
        lappend names {probability => t1 only : }
        lappend names {probability interval =>t2 to =<t3): }
        lappend names {probability =< t1 + =>t1 only , ~ unity :}
        foreach i {1 2 3 4 5 6 7 8} {
            label .frame.label$i -text [lindex $names $i] -anchor e
            entry .frame.entry$i -width 35 -textvariable side$i
            grid .frame.label$i .frame.entry$i -sticky ew -pady 2 -padx 1 }
        proc about {} {
            set msg "Calculator for Product lifetime exponential density
            from TCL WIKI,
            written on eTCL "
            tk_messageBox -title "About" -message $msg }       
        proc calculate {     } {
            global answer2
            global side1 side2 side3 side4 side5
            global side6 side7 side8
            global testcase_number
            incr testcase_number 
            set side1 [* $side1 1. ]
            set side2 [* $side2 1. ]
            set side3 [* $side3 1. ]
            set side4 [* $side4 1. ]
            set side5 [* $side5 1. ]
            set uptohours $side1
            set expcoeff $side4
            set excoef  [* $uptohours $expcoeff -1.]
            set probability [- 1. [exp  $excoef ]]
            set probability_gt_t1 [exp  $excoef ]
            set excoef1  [* $side2 $expcoeff -1.]
            set excoef2  [* $side3 $expcoeff -1.]
            set term1 [- 1. [exp  $excoef1 ]]
            set term2 [- 1. [exp  $excoef2 ]]
            set probability_interval [- $term2 $term1 ]
            set side5 [* $probability 1. ]
            set side6 [* $probability_gt_t1 1. ]
            set side7 [* $probability_interval 1. ]
            set side8 [+  $probability  $probability_gt_t1 ] }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$aa"
            .frame.entry2 insert 0 "$bb"
            .frame.entry3 insert 0 "$cc"
            .frame.entry4 insert 0 "$dd"
            .frame.entry5 insert 0 "$ee"
            .frame.entry6 insert 0 "$ff" 
            .frame.entry7 insert 0 "$gg"
            .frame.entry8 insert 0 "$hh" 
             }
        proc clearx {} {
            foreach i {1 2 3 4 5 6 7 8 } {
                .frame.entry$i delete 0 end } }
        proc reportx {} {
            global side1 side2 side3 side4 side5
            global side6 side7 side8 
            global testcase_number
            console show;
            puts "%|table $testcase_number|printed in| tcl wiki format|% "
            puts "&| quantity| value| comment, if any|& "
            puts "&| testcase number:|$testcase_number | |&"
            puts "&| $side1 :|up to hours =<t1 only|   |&"
            puts "&| $side2 :|interval minimum hours =>t2 | |& "
            puts "&| $side3 :|interval maximum hours =< t3| |& "
            puts "&| $side4 :| exponential density coefficient (optional) |  |&"
            puts "&| $side5  :| probability up to =<t1 only|  |&"
            puts "&| $side6  :|probability  =>t1|  |&"
            puts "&| $side7  :|probability interval =>t2 to =<t3  |  |&"
            puts "&| $side8  :|probability =<t1+=>t1   | approx unity |&"
         }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 500.0 1000.0 1500.0 0.0014  0.50 0.49 0.124 1.}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 1000.0 1200.0 1500.0 0.0014  0.75 0.24 0.064 1. }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 1200.00 1500.0 2000.0 0.0014 0.813 0.18 0.0616 1. }
        ::ttk::button .clearallx -text clear -command {clearx }
        ::ttk::button .about -text about -command about
        ::ttk::button .cons -text report -command { reportx }
        ::ttk::button .exit -text exit -command {exit}
        pack .calculator  -in .buttons -side top -padx 10 -pady 5
        pack  .clearallx .cons .about .exit .test4 .test3 .test2   -side bottom -in .buttons
        grid .frame .buttons -sticky ns -pady {0 10}
        . configure -background aquamarine4 -highlightcolor brown -relief raised -border 30
        wm title . "Product Lifetime and Exponential Density Calculator "
======

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*** Pushbutton Operation***

For the push buttons, the recommended procedure is push testcase and fill frame, change first three entries etc, push solve, and then push report. Report allows copy and paste from console. 

For  testcases in a computer session, the eTCL calculator increments a new testcase number internally, eg. TC(1), TC(2) , TC(3) , TC(N). The testcase number is internal to the calculator and will not be printed until the report button is pushed for the current result numbers. The current result numbers will be cleared on the next solve button.   The command { calculate; reportx  } or { calculate ; reportx; clearx  } can be added or changed to report automatically. Another wrinkle would be to print out the current text,  delimiters,  and numbers in a TCL wiki style table as

======
  puts " %| testcase $testcase_number | value| units |comment |%"
  puts " &| volume| $volume| cubic meters |based on length $side1 and width $side2   |&"  
======

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[gold] This page is copyrighted under the TCL/TK license terms, [http://tcl.tk/software/tcltk/license.html%|%this license]. 

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