ENGG1811 Computing for Engineers Week 7 Iteration; Sequential Algorithms; Strings and Built-in Functions

Transcription

1 ENGG1811 Computing for Engineers Week 7 Iteration; Sequential Algorithms; Strings and Built-in Functions ENGG1811 UNSW, CRICOS Provider No: 00098G1 W7 slide 1

2 References Chapra (Part 2 of ENGG1811 Text) Topic 19 (chapter 12) Loops Topic 17 (section 10.1) Strings Topic 16 (section 9.2) Built-in Functions ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 2

3 Iteration (Repetition) Very often need to execute statements repeatedly Loops are statements that can do this Process is called iteration Kinds of loop: For (iterate a fixed number of times) While (iterate as long as something is True) Do-Loop (general iteration) ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 3

4 A motivating example (1) Let us say you want to use VBA to compute the sum Two cumbersome programs: sum1() and sum2() Sub Sum1() 'A cumbersome program to compute the sum 'This is to motivate for loop Dim sum As Integer sum = Debug.Print "(Sum1) Sum of 1 to 10 is "; sum End Sub ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 4

5 A motivating example (2) Sum2() is also cumbersome but helps you to see the repetition and to progress to Sum3() Sub Sum2() Dim sum As Integer sum = 0 sum initialised to zero sum = sum + 1 sum is 1 after this line sum = sum + 2 sum is after this line sum = sum + 3 sum is after this line sum = sum + 4 sum = sum + 5 sum = sum + 6 sum = sum + 7 sum = sum + 8 sum = sum + 9 sum = sum + 10 VBA (as well as many other computer languages) has a number of constructions to deal with repetitions Sum3() (to be developed in the lecture) uses for-loop Debug.Print "(Sum2) Sum of 1 to 10 is "; sum End Sub ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 5

6 Iteration For For statement sets a loop variable to each value in a range and executes statements forming the loop body for each value: optional For intvar = start To finish Step amount statements Next intvar Loop body start and finish are expressions, evaluated once Step amount is optional (default 1) statements may use (but not change) the value of the loop variable loop must terminate (VBA checks consistency of start, finish and amount) ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 6

7 For loop examples ' 1. factorial (assume n is set beforehand) fact = 1 For i = 1 To n fact = fact * i Next i ' fact = n! ' 2. sum = sum of the first n squares (reverse order!) sum = 0 For k = n To 1 Step - 1 sum = sum + k*k Next k ' 3. Compound interest without exponentiation ' (principal P, interest rate r (%), n years) balance = P For y = 1 To n balance = balance * (1.0 + r*0.01) Next y ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 7

8 Iteration While While statement continues to execute statements as long as a Boolean expression is True While boolean-expression statements Wend* Loop guard is evaluated If it is True execute the loop body and go back to start of loop to re-test the guard Otherwise (i.e., it is False) exit loop and continue with rest of program Loop body must change state so that loop guard can eventually become False (else infinite loop) * Why not End While? Beats me. Loop body Loop guard ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 8

9 While loop examples (1) ' 1. Print all powers of 2 less than LIMIT Sub DemoWhile() Const LIMIT = 12 Dim x As Integer End Sub x = 1 While x < LIMIT Debug.Print (x), x = 2 * x Wend Question: What is the output of the following program? Sub QuestionWhile() Const LIMIT = 8 Dim x As Integer End Sub x = 1 While x < LIMIT x = 2 * x Debug.Print (x), Wend (a) (b) 2 4 (c) (d) ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 9

10 Iterative algorithms For-loops and While-loops (iterations) are extensively used in computation Excel Goal-Seek and Solver use iterations We will use iterations to find the square root of a real number k x = k Initialise x to k If you repeat the following calculation many times, you will find that x will eventually equal to the square root of k x = x - (x ^ 2 k) / (2 * x) x = x - (x ^ 2 k) / (2 * x) x = x - (x ^ 2 k) / (2 * x) x = x - (x ^ 2 k) / (2 * x) x = x - (x ^ 2 k) / (2 * x) Implementation with for numiter specifies the number of iterations Function SquareRootFor x = k For i = 1 To numiter x = x - (x ^ 2 - k) / (2 * x) Next i SquareRootFor = x ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 10

11 While loop examples Problem: You need to specify the number of iterations in the for-loop. Need trial and error. Better method: Specify an acceptable error and terminate the calculations when error is small enough ' 2. approximation to square root: k for any k >= 0 ' Algorithm: Newton- Raphson. For theory see Wikipedia or ' x 1 = x 0 - f (x 0 ) / f '(x 0 ), where f (x) = x 2 - k and thus f '(x) = 2x Dim x As Double Dim lastx As Double ' current estimate ' previous estimate x = k: lastx = 0 ' guesses While Abs(x lastx) > EPSILON lastx = x x = x - (x ^ 2 k) / (2 * x) Wend ' x k Constant: tiny value representing acceptable error ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 11

12 Pseudocode and refinement How did we come up with the square root solution? Initial version is statement of purpose set x to within EPSILON of k using Newton-Raphson algorithm Express algorithm using English statements and VB control structures (If, While etc): pseudocode Indent subsidiary statements Refine to subprograms and VB statements set initial guess and last guess to suitable starting values While current guess and last guess are too far apart Wend recalculate guess using N-R formula ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 12

13 Pseudocode and refinement Refined pseudocode: remember to update the variable holding the last guess before updating the current guess; Also choose a safe value for the initial guesses set current guess (x) to k [or 1, k/100, any > EPSILON] set last guess (lastx) to 0 While the abs val of the difference is > EPSILON update lastx update x using the formula Wend (when loop exits, x is an excellent approximation to k) Demo: use this loop in a subprogram to show convergence ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 13

14 Other kinds of loop Do-Loop statement is similar to While, but the loop body is always executed at least once: Do statements Loop body Loop While boolean-expression Alternative form uses complemented guard: Do statements Loop Until boolean-expression Can terminate the loop early with the statement Exit Do (also Exit While and Exit For) Loop guard ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 14

15 Excel object model (simplified) VBA programs can interact with the data on a worksheet, create new sheets etc. Workbook, sheets, cells form a hierarchy of objects, manipulated like ordinary variables (can use and/or change) Simplest reference to cells is via top-level Application object: Application.ActiveCell Application.ActiveSheet.Cells(row,col) any integer expression for row and col row counts from 1 to 65535* col counts from 1 (= A) to 255* Can omit Application. Prefix * Excel accepts a wider range than this ENGG1811 UNSW, CRICOS Provider No: 00098G W5 slide 15

16 Excel object model, cont. Each cell has a large number of attributes or properties, recording its contents and appearance. Most can be changed. Most important properties from our viewpoint are Value and Formula, the two attributes easily changed by the user Value is a variant (untyped value) Formula is a string (as it would appear in the formula bar) both can be assigned ENGG1811 UNSW, CRICOS Provider No: 00098G W5 slide 16

17 Worksheet Programming We can use values on the active worksheet as inputs to a program, and overwrite cells to show output and calculated values We can iterate over rows or columns of data We can detect empty cells to stop the iteration Example: running sum to the right of a column (defective subprogram over, to be corrected in the lecture) Developer Macros AddRunningSum ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 17

18 Example: Running sum ' WARNING: contains a deliberate error Sub AddRunningSum() Dim row As Integer ' index always integral Dim col As Integer Dim sum As Double ' numeric values normally real row = 2: col = 1: sum = 0 ' FYI, the : symbol separates multiple simple statements While ActiveSheet.Cells(row, col).value <> "" Wend End Sub sum = sum + ActiveSheet.Cells(row, col).value ActiveSheet.Cells(row, col+1).value = sum ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 18

19 Debugging Loops If a program fails to terminate, press Ctrl-Alt-Break (Break may be labelled Pause), or Esc in the labs VBA interpreter pauses, shows program state: current execution point Hover mouse over variable to show current value Is there a general principle you can apply to all loops? ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 19

20 Iteration termination Loop body must change state so that loop guard can eventually become False (else we have produced an infinite loop) MC Escher (1948) Handteckning [Drawing Hands]; lithograph ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 20

21 Procedures Functions and Subprograms are together called procedures Functions return a single value, should not change program state Subprograms can change state by altering variables outside the procedure altering files outside the application communicating with other applications changing the values of arguments passed by reference (next slide) ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 21

22 Calling sub Assuming that you have a sub: Sub SampleSub(x1 as integer, x2 as integer) You can call this sub in another program using either one of the following two methods SampleSub 3 5 Call SampleSub(3,5) ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 22

23 Parameters revisited Values passed to procedures are called arguments Variables defined to hold these values are called parameters Parameters are local variables, like ones declared using Dim Data can be passed in two different ways: by value (argument is expression, only value transferred) by reference (argument is variable, parameter acts as a temporary alias) keywords ByVal and ByRef specify which (ByRef is assumed if omitted) ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 23

24 Reference Parameters ByRefDemo1 in The workbook Sub halve1(byval x As Double) x = x / 2 End Sub Sub halve2(byref x As Double) x = x / 2 End Sub y = 6.4: z = 6.4 halve1 y ' what is the value of y? halve2 z ' what is the value of z? The keyword ByRef (or none) passes a reference to the argument rather than its value. x becomes an alias for z and changes to x also affect z immediately. With ByVal, or if the argument is not a variable, x is an independent local variable initialised by the argument (6.4). Changing it has no effect outside the procedure. ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 24

25 Example: Swapping values ByRefDemo2 in The workbook Sub Swap(ByRef x1 As Variant, ByRef x2 As Variant) Dim tmp As Variant End Sub tmp = x1 x1 = x2 x2 = tmp Motivation: imagine exchanging the positions of an apple and an orange on the table in front of you. Now do it again using just one hand! y = : z = 6 Swap y, z ' what are the values of y and z? We used the Variant type so the procedure can be used to exchange the contents of variables any type. This is the only recommended use for Variants. Unfortunately, the following does NOT work Swap ActiveSheet.Cells(1,1), ActiveCell ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 25

26 Named Arguments For procedures with long argument lists (especially built-in procedures), arguments can be specified in any order using the notation paramname:=argument Example (see MsgBox Function in VBA Help) Example: ByRefDemo3 in the workbook ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 26

27 Sequential Algorithms VBA is particularly useful for tasks such as Processing rows or columns on one pass Locating cells with particular characteristics Identifying extreme values (max/min) These are called sequential tasks, because they treat the data as a sequence of items, usually stored in cells Standard sequential algorithms can be adapted to solve these kinds of problems ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 27

28 Simple Scans The simplest cases just process each element of a sequence in order (for convenience) Elements are independent End of sequence normally marked by empty cell Pseudocode: column scan set col to the required column number set row to the row where the sequence starts While ActiveSheet.Cells(row, col) is not empty Wend apply required step to this cell move row one cell down ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 28

29 State-based Scans Other cases accumulate history in variables during the scan Element order may or may not matter Variables need to be correctly initialised Examples: AddRunningSum, maximum or minimum calculation, run of equal values, merging ordered sequences, mode of an ordered sequence (you are not likely to need the last few). ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 29

30 Maximum/minimum FindMax in The workbook Max/min calculations maintain a best so far variable May also need to know the position of the (first or last occurrence of) the maximum Pseudocode for maximum of a column: Only works if the column is NOT EMPTY set col to the required column number set row to the row where the sequence starts set max to the value in that cell While ActiveSheet.Cells(row,col) is not empty Wend If cell value is greater than max Then set max to cell value End If move row one cell down ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 30

31 Maximum/minimum, continued If the problem is to highlight all extreme (max or min) values, need two passes First pass finds the extreme value (prev slide) Second pass processes each cell whose value matches the extreme value Next week we will see how cell appearance can be altered (more general than conditional formatting) Macro Recorder used to capture relevant code ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 31

32 Maximum/minimum, continued If the problem is to find min/max for only some cells, can t initialise from the first cell as usual use a Boolean variable to record whether a min/max has been found after the loop the variable tells you whether there was a min/max at all If you need to find out more than one piece of info about a list of values, consider whether you can perform multiple actions on a single pass example: min + max, or min/max + count etc ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 32

33 Example: min of positive values only Problem: Find where the smallest positive value (if any) is in the column containing the active cell Pseudocode, first attempt may or may not work set col to the column containing the active cell set row to the starting row set rowmin to zero ' = undefined minimum position While the cell at (row, col) contains a number If the cell value is positive Then If rowmin = 0 Or cell value < value at (rowmin, col) Then set rowmin to row ' now valid End If End If move row one cell down Wend (Solution developed in lecture) ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 33

34 Strings A string is a sequence of characters Strings in VBA can be of virtually any length (including zero, of course) Components are characters represented internally as codes with numeric value from 0 to 255 each code is interpreted by an output device as a graphic character or special action functions Chr and Asc convert between character and numeric code ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 34

35 Literal Strings String constants are enclosed in double-quote characters " " (not single quotes) How to include a double-quote as a member of the string (the delimiter-as-data problem)? Write it twice, as in "Reference: ""Excel for Experts""" Empty string is denoted by "" ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 35

36 String Operators & concatenates (joins) two strings "c" & "at" (= "cat") "cat" & "ch" & "-22" relational (comparison) operators compare individual characters, so "cat" < "dog" (because "c" < "d") "cat" < "cave" (because "t" < "v") "cat" < "catastrophe" (prefix) "Cat" < "cat" (case sensitive) can change to case-insensitive comparison (to make "Cat" = "cat") by placing Option Compare Text at the top of the module ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 36

37 String Matching The Like operator allows a string expression to be tested against a pattern that includes wildcards strdata Like "pattern" The pattern consists of? any single character # any digit character * zero or more characters [list] any character in list [!list] any character not in list Important notation! Same notation as Access query partial match ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 37

38 String Matching Examples Assume the following values str1 = "cat": str2 = "Route66": str3 = "2*3" Expression Value Reason str1 Like "cat" True ordinary chars OK str1 Like "c?t" True? matches the character a str1 Like "c" False must match whole of string str2 Like "*##" True ends in two digits str2 Like "[A- Z]*" True [A- Z] matches any capital str2 Like "*[!6]" False can't match non-6 at end str2 Like "*[!6]*" True (you work it out!) str3 Like "*3" True * matches 2* str3 Like "#[*]?" True to match special chars * [? literally, enclose in [ ] ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 38

39 Select Case Multiway selection with a common expression: VBA has a simpler way than many If statements any number of each of these can occur Select Case expression Case value statements Case value 1, value 2 statements Case value 1 To value 2 statements Case Is > value statements Case Else statements End Select evaluated first, then matched against each label single value multiple values grouped inclusive range of values open range of values all unmatched values ENGG1811 UNSW, CRICOS Provider No: 00098G W5 slide 39

40 Select Case example Classify a single-character string c Select Case UCase(c) Case "A","E","I","O","U" sym = "vowel" Case "0" To "9" sym = "digit" Case "A" To "Z" sym = "consonant" Case "" sym = "empty Case Else sym = "punctuation" End Select use of UCase saves repeating upper and lower case letter rules ' or Case Like "[A- Z]" ENGG1811 UNSW, CRICOS Provider No: 00098G W5 slide 40

41 Built-in Functions VBA includes a range of mathematical, string and conversion functions Accept one argument (sometimes more than one) and return exactly one value Mathematical functions include Sin, Cos, Tan, Atn (arctangent), all in radians Abs, Sgn, Int (largest int ), Fix (truncate towards 0), Round (to any number of decimal places, including neg) Sqr ( ), Exp (e x ), Log (ln x) Rnd (pseudo-random number) Look up Math Functions in VBE's Help ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 41

42 Built-in Functions, cont. Can also use any* function available to worksheet formulas, using Application.WorksheetFunction.name(args ) Examples (Application. can be omitted): angle = WorksheetFunction.Radians(- 90) payment = WorksheetFunction.PMT(rate, numperiods, _ curvalue) code = WorksheetFunction.Replace(text, start, 3, _ "***") Some expect Range objects (described in a later lecture) as their data sources Look up Worksheet Functions in VBE's Help * except if there s a direct equivalent in VBA, like sin ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 42

43 String and Character Functions Function call Len(str) Mid(str,start,len) Asc(str) Chr(code) LCase(str) Trim(str) Returns number of characters in str len-char substring of str, start; also Left(str,len) and Right(str,len) char code for first char in str Unit string containing char with code str with all upper-case chars converted to lower case (also UCase) str with spaces removed from both ends (also LTrim, RTrim) InStr(str,match) first position in str where match occurs, or 0 Replace(str,match,r epl) String(str,n) str with all occurrences of match replaced by repl (other args possible) n copies of first char of str ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 43

44 Type Conversion Functions Can mix up numeric types (angle + intoffset is evaluated as Double) When explicit conversion is needed, use function: Function name Accepts as argument Returns CStr number String (also Format next slide) CLng number or string Long Integer (rounded if from Double) CDbl number or string Double Val string Integer or Double, ignores trailing junk Round(v,d) number v Rounded to d decimal places Hex integer Hexadecimal string form ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 44

45 Format Function Specialised formatting of numbers and dates Format(expr, fmt) returns a formatted string fmt mixes ordinary characters and formatting codes: Predefined code Displays 0 digit or zero # digit or nothing % percentage placeholder ( 100, show %) e+ e- E+ E- scientific single char or space < > force lower-case or upper-case ddd mmm yy hh nn date/time components (see text) Can also use predefined formats such as Scientific, Percent, Long Date etc. See VBE Help for details ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 45

46 Summary Reference parameters allow a subprogram to change the value of variables declared outside Use pseudocode to express algorithm prior to coding in VB Active sheet and its cells can be addressed directly Sequential algorithms process a row or column of data systematically Some algorithms accumulate values, others process cells locally and order-independently Strings store simple character sequences Built-in functions evaluate commonly-required quantities (string and numeric) Relatively complex tasks can usually be subdivided into easily managed subtasks and solutions combined ENGG1811 UNSW, CRICOS Provider No: 00098G W7 slide 46