I recently discovered from a thread at Chandoo’s Excel Forum that the VBA Evaluate function can be used as an array function. As a simple example:
Range(“A11:A16”).Value = Evaluate(“= B11:B16 + C11:C16”)
will add the values in columns B and C, and return to column A.
This should not have come as a surprise, since Charles Williams mentioned it in his Excel Blog: Evaluate Functions and Formulas fun: How to make Excel’s Evaluate method twice as fast. As a rather more useful example than the one above, I have looked at options for calculating the distance between lists of pairs of coordinates. The code below shows four subroutines that read X and Y coordinates from a specified 4 column range, and return the distance between the two points on each row to the right of the table.
A sample spreadsheet with full open source code and examples may be downloaded from:
Sub Distance() With Sheet1.Range("B12").CurrentRegion.Columns .Item(6).Value2 = .Parent.Evaluate("=((" & .Item(3).Address & " - " & .Item(1).Address & ")^2 + (" & .Item(4).Address & "-" & .Item(2).Address & ")^2)^0.5") End With End Sub Sub Distance2() Dim Col1 As String, Col2 As String, Col3 As String, Col4 As String With Sheet1.Range("B12").CurrentRegion.Columns Col1 = "sheet1!" & .Item(1).Address Col2 = "sheet1!" & .Item(2).Address Col3 = "sheet1!" & .Item(3).Address Col4 = "sheet1!" & .Item(4).Address .Item(6).Value2 = Evaluate("=((" & Col3 & " - " & Col1 & ")^2 + (" & Col4 & "-" & Col2 & ")^2)^0.5") End With End Sub Sub Distance3() Dim XYData As Range Dim Col1 As String, Col2 As String, Col3 As String, Col4 As String Set XYData = Range("sheet1!B12:B111") With XYData.Columns Col1 = .Item(1).Address Col2 = .Item(2).Address Col3 = .Item(3).Address Col4 = .Item(4).Address .Item(6).Value2 = .Parent.Evaluate("=((" & Col3 & " - " & Col1 & ")^2 + (" & Col4 & "-" & Col2 & ")^2)^0.5") End With End Sub Sub Distance4() Dim XYData As Range, Res As Variant Dim Col1 As String, Col2 As String, Col3 As String, Col4 As String Set XYData = Range("sheet1!B12:B111") With XYData.Columns Col1 = .Item(1).Address Col2 = .Item(2).Address Col3 = .Item(3).Address Col4 = .Item(4).Address Res = .Parent.Evaluate("=((" & Col3 & " - " & Col1 & ")^2 + (" & Col4 & "-" & Col2 & ")^2)^0.5") .Item(6).Value2 = Res End With End Sub
In the first and third routine the Evaluate function is preceded by .Parent, which ensures that the addresses are treated as being on the same sheet as the range specified in the “With” statement. If this is omitted the addresses will be treated as being on whatever sheet is active when the routine is called. An alternative is to specify the sheet name with each range (as in Distance2 above). The fourth function is as Distance3, but the Evaluate results were written to an array for each iteration, and only written back to the spreadsheet once, after the last iteration. Benchmark results are shown below for these four routines with a range of column lengths and iterations:
Evaluate can also be used in this way from a user defined function (UDF). The code below shows three alternatives.
Function DistF(XYData As Variant) Dim DistA() As Double, i As Long, NRows As Long, j As Long XYData = XYData.Value2 NRows = UBound(XYData) ReDim DistA(1 To NRows, 1 To 1) For j = 1 To NRows DistA(j, 1) = ((XYData(j, 3) - XYData(j, 1)) ^ 2 + (XYData(j, 4) - XYData(j, 2)) ^ 2) ^ 0.5 Next j DistF = DistA End Function Function DistF2(XYData As Range) Dim DistA As Variant Dim Col1 As String, Col2 As String, Col3 As String, Col4 As String With XYData.Columns Col1 = .Item(1).Address Col2 = .Item(2).Address Col3 = .Item(3).Address Col4 = .Item(4).Address DistA = .Parent.Evaluate("=((" & Col3 & " - " & Col1 & ")^2 + (" & Col4 & "-" & Col2 & ")^2)^0.5") End With DistF2 = DistA End Function Function DistF3(XY_1 As Range, XY_2 As Range) Dim DistA As Variant Dim Col1 As String, Col2 As String, Col3 As String, Col4 As String, EvalTxt As String With XY_1.Columns Col1 = .Item(1).Address Col2 = .Item(2).Address End With With XY_2.Columns Col3 = .Item(1).Address Col4 = .Item(2).Address EvalTxt = "=((" & Col3 & " - " & Col1 & ")^2 + (" & Col4 & "-" & Col2 & ")^2)^0.5" DistA = .Parent.Evaluate(EvalTxt) End With DistF3 = DistA End Function
The first does not use Evaluate, converting the input data to a variant array, then looping through each row, writing the results to an array which is returned to the spreadsheet at completion. The second is similar to Option 3 in the subroutines, except the results are written to an array, which is returned at completion. The third option has two separate input arrays, so the function can be used on lists of coordinates that are not in adjacent columns. It also creates the string to be evaluated in a separate operation, which makes checking of the text easier. Benchmark results for the three functions are shown below:
The two functions using evaluate had very similar performance, and were 2-3 times faster than the routine that looped through the coordinate arrays. They were also faster than the subroutines, probably because the time do not include the time to write the results to the spreadsheet.
I frequently use Evaluate (or [.]), often finding the result needs to be coerced to an array, e.g.
Sheet1.[+index(ABS(A1:A5-B1:B5),)]
Including ‘Sheet1.’ and ‘+’ apparently makes it runs roughly twice as fast as per Charles Williams’ link. Not sure why, maybe something related to not needing to handle the case that the result is a reference?
Within a udf one should really replace ‘Sheet1’ with ‘Application.ThisCell.Worksheet’ and make all range references explicit in function arguments otherwise the workbook may not recalculate as expected.
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Thanks for this one too.
I’m not sure how much I’ll use Evaluate on ranges in UDFs because I don’t find them very readable, but that may be just because I’m not familiar with it in that context (I do use it to evaluate a formula entered as text on the spreadsheet) . I’ll check they are recalculating properly, and I’m getting the 2xspeed up.
I will be posting a similar example using Python, Numpy and xlwings. The conclusion is the calculation is much faster, but this is totally swamped by the data transfer time, which is much slower.
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