{"text_format":"1","workbook":"xlsx","n_sheets":3,"sheets":["Describe","Parabola","2Dim Grad"],"not_rendered":{"charts":0,"images":1,"macros":1,"external_links":0,"defined_names":7,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Describe","index":0,"n_rows":9,"n_cols":2,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
["The purpose of this workbook is to assist the validation of Whittaker-Henderson graduation using whgrad.dll."]
["This workbook, the dll and associated documentation is available at http://www.howardfamily.ca/graduation."]
[]
["The worksheet \"Parabola\" shows a validation by deduction. It should give confidence, but it is not a solid check."]
["The worksheet \"2Dim Grad\" compares the graduation using whgrad.dll to a graduation using matrices in VBA code."]
[null,"Those who are familiar with the theory of WH graduation and with VBA programming can use this to"]
[null,"check that whgrad.dll is working correctly."]
[]
["You can use the VBA code to construct other tests if desired."]

{"sheet":"Parabola","index":1,"n_rows":12,"n_cols":8,"rows_kept":12,"cut":false,"hidden":false,"merged":[]}
[null,"parabola","weight","Graduated",null,null,null,"A graduation is done whenever the numbers in the yellow cells are changed."]
[40,{"$f":"0.00001*(A2-30)^2","v":1E-3},1,{"$f":"Gradrange(B2:B12,C2:C12,G2,G3)","v":1.0000000000000031E-3},null,"order",3,"If order is set to 3 or more, the graduated rates should be the same as the parabola (raw) for all values of smooth."]
[41,{"$f":"0.00001*(A3-30)^2","v":1.2100000000000001E-3},2,1.2100000000000075E-3,null,"smooth",10,"If order is set to less than 3, the graduated rates will be flatter than the parabola,"]
[42,1.4400000000000001E-3,3,1.4400000000000088E-3,null,null,null,"and the greater smooth, the flatter the graduated."]
[43,1.6900000000000001E-3,4,1.6900000000000068E-3]
[44,1.9600000000000004E-3,5,1.9600000000000025E-3]
[45,2.2500000000000003E-3,6,2.2499999999999968E-3]
[46,2.5600000000000002E-3,5,2.5599999999999907E-3]
[47,2.8900000000000002E-3,4,2.8899999999999855E-3]
[48,3.2400000000000003E-3,3,3.2399999999999825E-3]
[49,3.6100000000000004E-3,2,3.6099999999999817E-3]
[50,4.0000000000000001E-3,1,3.9999999999999836E-3]

{"sheet":"2Dim Grad","index":2,"n_rows":57,"n_cols":20,"rows_kept":57,"cut":false,"hidden":false,"merged":[]}
["Parameters","Order","Smooth","Rate",null,"Graduations statistics",null,null,null,null,null,"Raw rates"]
["Horizontal",2,300,0,null,null,"Combined","Fit","H Diff","V Diff",null,2.0971762235589459E-2,1.8997810992581146E-2,1.9153792404346174E-2,2.1080440606439901E-2,1.9235206905738371E-2,1.885357990681678E-2,1.9723553408055764E-2,2.0617250716536556E-2,1.8452173361656259E-2]
["Vertical",3,100,0,null,"whgrad",2.2647717038100807E-4,2.1593306623886861E-4,2.8686406132750986E-9,9.6835119581569395E-8,null,2.3159672852694262E-2,2.3103006712059518E-2,2.0423292887281914E-2,2.1974870179738197E-2,2.2102020966707527E-2,2.1867268282768141E-2,2.0865030416830566E-2,2.0661326740815993E-2,2.1507205918067644E-2]
[null,null,null,null,null,"VBGrad",2.2647717038100807E-4,2.1593306623888874E-4,2.8686406132905408E-9,9.6835119581321744E-8,null,2.341951388967815E-2,2.5654643561561077E-2,2.5396364655977149E-2,2.3591401239109369E-2,2.4213266420022625E-2,2.4807431069482827E-2,2.4115668268779547E-2,2.2621213319623509E-2,2.2613393234964942E-2]
["Grad by whgrad.dll",null,null,null,null,null,null,null,null,null,null,2.4846444155742834E-2,2.3943872101743178E-2,2.745584213334596E-2,2.8447530581243243E-2,2.549773499908926E-2,2.6659825754062616E-2,2.6938212583596164E-2,2.4916663827484375E-2,2.4381112688313524E-2]
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["Grad by VBGraduate",null,null,null,null,null,null,null,null,null,null,56002.7,57068.69,58266.03,59636.62,61252.92,62953.37,64858.21,66862.69,68875.929999999993]
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[]
["Differences",null,"Abs Max =",2.2912227670701668E-14]
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