Division into Parts by Multiple Ratios and eTCL demo example calculator, numerical analysis

Division into Parts by Multiple Ratios and eTCL demo example calculator, numerical analysis

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 and date in your comment with the same courtesy that I will give you. Aside from your courtesy, your wiki MONIKER and date as a signature and minimal good faith of any internet post are the rules of this TCL-WIKI. Its very hard to reply reasonably without some background of the correspondent on his WIKI bio page. Thanks, gold 12Dec2018



Introduction

gold Here is some eTCL starter code for Division into Parts by Multiple Ratios in calculator shell. Additional console programs below are used to check or improve subroutines in calculator shell.


Pseudocode Section

            # using pseudocode
        proc test1 {   
               # possible problem instances,
               low vs high
               middle vs low
               high vs middle}
        proc test2 {
            initialize algorithm_result = 1.
            initialize terms 
       proc test6 {
             check algorithm
            f(solution) =? initial product
            check_sum = a+b+c+d+e
            set answers and printout with resulting values
            pseudocode: need test cases > small,medium, giant
            pseudocode: need testcases within range of expected operation.
            pseudocode: are there any cases too small or large to be solved?
            pseudocode: limit to size of eTCL list,   ref  versions.   }
                #end of file

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 1printed in tcl wiki format
quantity value comment, if any
1:testcase_number
84.0 :quantity
1.0 :ratio 1
2.0 :ratio 2
4.0 :ratio 3
0.0 :optional:
84.0 :answers: quantity
7.0 :sum of ratios
12.0 24.0 48.0 :list

Testcase 2

table 2printed in tcl wiki format
quantity value comment, if any
2:testcase_number
120.0 :quantity
1.0 :ratio 1
2.0 :ratio 2
3.0 :ratio 3
0.0 :optional:
120.0 :answers: quantity
6.0 :sum of ratios
20.0 40.0 60.0 :list

Testcase 3

table 3printed in tcl wiki format
quantity value comment, if any
3:testcase_number
360.0 :quantity
1.0 :ratio 1
2.0 :ratio 2
3.0 :ratio 3
0.0 :optional:
360.0 :answers: quantity
6.0 :sum of ratios
60.0 120.0 180.0 :list

Screenshots Section

figure 1.

Division into Parts by Multiple Ratios and eTCL demo example calculator screenshoot


References:

Appendix Code

appendix TCL programs and scripts

        # pretty print from autoindent and ased editor
        # Division into Parts by Ratios calculator
        # written on Windows XP on TCL
        # working under TCL version 8.6
        # gold on TCL Club, 12Dec2018
        package require Tk
        package require math::numtheory
        namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory }
        set tcl_precision 17
        frame .frame -relief flat -bg aquamarine4
        pack .frame -side top -fill y -anchor center
        set names {{} {quantity :} }
        lappend names {ratio 1:}
        lappend names {ratio 2: }
        lappend names {ratio 3: }
        lappend names {optional:}
        lappend names {answers: quantity : }
        lappend names {sum of ratios : }
        lappend names {list :}
        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 Division into Parts by Ratios V2
            from TCL,
            # gold on TCL Club, 12Dec2018 "
            tk_messageBox -title "About" -message $msg }
        proc self_help {} {
            set msg " Division into Parts by Ratios V2
            from TCL ,
            # self help listing
            # problem, Combined Availability V2
            # 3 givens follow.
            1) quantity
            2) ratio 1:
            3) ratio 2:
            4) ratio 3:
            # 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 to conventional texteditor.
            # For testcases, testcase number is internal
            # to the calculator and will not be printed
            # until the report button is pushed
            # for the current result numbers.
            # >>> copyright notice <<<
            # This posting, screenshots, and TCL source code is
            # copyrighted under the TCL/TK license terms.
            # Editorial rights and disclaimers
            # retained under the TCL/TK license terms
            # and will be defended as necessary in court.
            Conventional text editor formulas
            or  formulas grabbed from internet
            screens can be pasted into green console.
            # gold on  TCL Club, 12Dec2018 "
            tk_messageBox -title "Self_Help" -message $msg }
        # adapted from tcl-wiki Stats 2011-05-22, arithmetic mean  [RLE]
        #
        # ::math::quantity_into_ratios --
        #
        # Return the division of quantity by  two or more given ratios
        #
        # Arguments:
        #    val  first value is quantity
        #    args other values are two or more given ratios
        #
        # Results: parts of quantity divided  by ratios
        #
        proc ::math::quantity_into_ratios {quantity args} {
            set sum 0.
            set N [ expr { [ llength $args ] + 1 } ]
            if { $N == 1  } { return 0 }
            foreach val $args {
                set sum [ expr { $sum + $val } ]
            }
            foreach val $args {
                lappend answer [ expr { $quantity * ($val/$sum) } ]
            }
            set answer
        }
        #puts "  ::math::quantity_into_ratios ( 84 2 2 2  )  answer 12.0 24.0 48.0    "
        #puts " [ ::math::quantity_into_ratios 84 1 2 4  ]  "
        #puts " [ ::math::quantity_into_ratios 84 ] for (::math::quantity_into_ratios 84) returns zero "
        proc calculate {     } {
            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 side6 [* $side6 1. ]
            set side7 [* $side7 1. ]
            set side8 [* $side8 1. ]
            set answer2 [ ::math::quantity_into_ratios $side1 $side2 $side3 $side4 ]
            set sum_of_ratios [+ $side2 $side3 $side4  ]
            set side6 $side1
            set side7 $sum_of_ratios
            set side8 $answer2
        }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$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 eval {.console config -bg palegreen}
            console eval {.console config -font {fixed 20 bold}}
            console eval {wm geometry . 40x20}
            console eval {wm title . " Division into Parts Report, screen grab and paste from console 2 to texteditor"}
            console eval {. configure -background orange -highlightcolor brown -relief raised -border 30}
            console show;
            puts "%|table $testcase_number|printed in| tcl wiki format|% "
            puts "&| quantity| value| comment, if any|& "
            puts "&| $testcase_number:|testcase_number | |&"
            puts "&| $side1 :|quantity |   |&"
            puts "&| $side2 :|ratio 1   | |& "
            puts "&| $side3 :|ratio 2 | |& "
            puts "&| $side4 :|ratio 3 | |&"
            puts "&| $side5 :|optional:  | |&"
            puts "&| $side6 :|answers: quantity |  |&"
            puts "&| $side7 :|sum of ratios  |  |&"
            puts "&| $side8 :|list|  |&"
        }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { set side8 0 ; calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 84.0  1.  2.0 4.0  0.0  84.   7.0  12.0}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 120.0 1.0 2.0 3.0  0.0  120.0 6.0  20.0}
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 360.0 1.0 2.0 3.0  0.0  360.0 12.0 30.0}
        ::ttk::button .clearallx -text clear -command {clearx }
        ::ttk::button .about -text about -command {about}
        ::ttk::button .self_help -text self_help -command { self_help }
        ::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 .self_help .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 . "Division into Parts by Ratios Calculator V2"

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   |&"  

Console program for quantity_into_ratios

        # pretty print from autoindent and ased editor
        # quantity_into_ratios for math::stats? package
        # working under TCL version 8.5.6 and eTCL 1.0.1
        # console program written on Windows XP on eTCL
        # gold on TCL WIKI, 2Mar2017
        package require Tk
        console show
        package require math::numtheory
        namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory }
        set tcl_precision 17
        # adapted from tcl-wiki Stats 2011-05-22, arithmetic mean  [RLE]
        #
        # ::math::quantity_into_ratios --
        #
        # Return the division of quantity by  two or more given ratios
        #
        # Arguments:
        #    val  first value is quantity
        #    args other values are two or more given ratios
        #
        # Results: parts of quantity divided  by ratios
        #    
        proc ::math::quantity_into_ratios {quantity args} {
            set sum 0.
            set N [ expr { [ llength $args ] + 1 } ]
            if { $N == 1  } { return 0 }
            foreach val $args {
                set sum [ expr { $sum + $val } ]
            }
            foreach val $args {
                lappend answer [ expr { $quantity * ($val/$sum) } ]
            }
            set answer
        }
        puts "  ::math::quantity_into_ratios ( 84 2 2 2  )  answer 12.0 24.0 48.0    "
        puts " [ ::math::quantity_into_ratios 84 1 2 4  ]  "   
        puts " [ ::math::quantity_into_ratios 84 ] for (::math::quantity_into_ratios 84) returns zero "      
            #end of deck

Console program for geometric_mean

        # pretty print from autoindent and ased editor
        # geometric_mean for math::stats? package
        # working under TCL version 8.5.6 and eTCL 1.0.1
        # console program written on Windows XP on eTCL
        # gold on TCL WIKI, 2Mar2017
        package require Tk
        console show
        package require math::numtheory
        namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory }
        set tcl_precision 17
        # adapted from tcl-wiki Stats 2011-05-22, arithmetic mean  [RLE]
        console show
        # ::math::geometric_mean --
        #
        # Return the geometric_mean of two or more values
        #
        # Arguments:
        #    val  first value
        #    args other values
        #
        # Results:
        #    geometric_mean  arithmetic geometric_mean value
        proc ::math::geometric_mean { args } {
            set product 1.
            set N [ expr { [ llength $args ] } ]
            foreach val $args {
                set product [ expr { $product*$val } ]
            }
            set exponent [ expr { 1./$N } ]
            set geometric_mean [ expr { $product**$exponent } ]
            #puts " $N   $exponent $product  $args "
            set geometric_mean
        }
        puts "  ::math::geometric_mean ( 1 2 3 4  )  answer  2.2133638  "
        puts " [ ::math::geometric_mean 1 2 3 4  ]   answer  2.2133638  "
        
           #end of deck

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Comments Section

Please place any comments here with your wiki MONIKER and date, Thanks, gold 12Dec2018