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10,000 | ( ** mid-point and again |
10,001 | ** so change lower bound to give an interval of length / |
10,002 | one more iteration find the mid-point square it compare the square to do you change the lower or upper bound minutes please make sure that you understand the principle and do one more iteration by hand |
10,003 | apologies for spending so long on the maths but this is general situation you must understand the situation before you can program it |
10,004 | lower upper middle (lower+upper)/ so now let' start the implementation of this process in python we will do exactly the same mathsbut this time with python syntax first we set the end points for the interval of uncertainty and attach names to the two -values the names lower and upper are attached to the end pointslower... |
10,005 | middle** true lower middle print(lowerupper nextwe find the -value corresponding to the mid-point (by squaring the -value and ask if it is less than the number whose square root we are looking for middle** recall that this will return python boolean valuetrue or false the squared value is which is less than ( we get tr... |
10,006 | middle (lower+upper)/ print(middlemiddle** so we do it again we re-calculate the -value for the mid-point note that because we changed the value the name lower was attached to the python instruction is identical to the one we gave first time roundmiddle (lower+upper)/ we do some additional printing to track progress |
10,007 | middle** false upper middle print(lowerupper againwe ask if the mid-point' -value ( its -value squaredis above or below our target of middle** and this time get boolean false because the value is greater than (our test evaluates to falsewe change the value of the upper bound of the interval by attaching the name upper ... |
10,008 | middle (lower+upper)/ print(middlemiddle** we now do third iteration |
10,009 | middle** true lower middle print(lowerupper this time the test evaluates to true so we change lower |
10,010 | middle (lower+upper)/ print(middlemiddle** fourth iteration |
10,011 | middle** true lower middle print(lowerupper and another true so we change lower again and that' enough of stepping through it manually |
10,012 | lower upper middle (lower+upper)/ print(middlemiddle** middle** lower middle upper middle print(lowerupper let' look at the python code we have used we started by initializing our interval of uncertaintylower upper then we started the operations we would repeat by calculating the -value of the mid-pointmiddle (lower+up... |
10,013 | lower upper set up loop middle (lower+upper)/ print(middlemiddle** choice middle** lower middle upper middle print(lowerupper structurallywe need to be able to do two things beyond our current knowledge of python we need to be able to run certain instructions time and time again ("looping"and we need to be able to choo... |
10,014 | before loop test loop body should the loop run (again)what is run each loopafter we will address looping first loop has number of components strictly not part of the loop are the "beforeand "aftersections but these give context and may use values needed by the loop the loop itself must have some sort of test to indicat... |
10,015 | before number loop test number < loop body after print(numbernumber + print('done!' let' consider an example that' simpler than our square root loopcounting from to our "beforeblock initializes the attachment of name number to value number our test sees if number is attached to value less than or equal to (our final va... |
10,016 | number number while number < number < print(numbernumber + print('done!'print(numbernumber + print('done!' this is how we encode the structure in python we will examine it element by elementbut at first glance we observe "whilekeyword and colon on either wise of the test and the loop body being indented four spaces |
10,017 | number "whilekeyword loop test while number < colon print(numbernumber + print('done!' we will start by looking at what we have done to the test the test itself is number < which is python expression that evaluates to booleantrue or false we precede the test expression with the python keyword "whilethis is what tells p... |
10,018 | number while number < print(numbernumber + loop body indentation print('done!' the loop bodythe code that is repeatedappears on the lines following the "while lineboth its lines are indented by four spaces each note that the "aftersection is not indented |
10,019 | number while number < print(numbernumber + print('done!'while py python while py done first let' check that this really works in the file while py in your home directories you will find exactly the code shown in the slide run it and watch python count from to |
10,020 | number while number < four spacesindentation indicate "blockof code print(numbernumber + print('done!'the block forms the repeated lines the first unindented line marks the end of the block the four spaces of indentation are not cosmetic sequence of lines that have the same indentation form blocks in python and can be ... |
10,021 | ( ( ( )( ( )(ii ( )(iii ( if this seems little alien consider the "legaleseof complex documents they have paragraphssub-paragraphs and sub-sub-paragraphs etc each indented relative to the one containing them |
10,022 | shell while do done while do done syntax clarity syntax clarity marking blocks of code is one of the places where computing languages differ from one another some have special words that appear at the start and end of blocks like "doand "doneothers use various forms of brackets like "{and "}interestinglyprogrammers in ... |
10,023 | while test to keep looping code blocks before while test action action action afterwards indentation |
10,024 | for each scriptwhile py predict what it will do while py run the script while py were you rightwhile py while py to kill running scriptctrl minutes |
10,025 | uncertainty tolerance - / / what we want / / what we get now let' return to our square root example we have loop the body of which halves the length of the interval of uncertainty we need to put this into python loop so we need corresponding loop test one typical approach is to test to see if the interval is longer tha... |
10,026 | uncertainty tolerance while uncertainty tolerance do stuff we need python test for this recall that python needs test that evaluates to true for the loop body to run our test then is "is the current uncertainty larger than the acceptable tolerance?we will set nametoleranceto have the value - calculate an uncertainty ea... |
10,027 | tolerance - lower upper uncertainty upper lower while uncertainty tolerance set up loop middle (lower upper)/ choice print(lowerupperuncertainty upper lower soif we return to our basic structure we can now see how python' while syntax fits in we establish tolerance we establish an initial uncertainty we test for uncert... |
10,028 | choice middle** lower middle upper middle middle** true or false true lower middle false upper middle once again we have test followed by some actions this timehoweverthe test doesn' decide whether or not to run block of code againbut rather which of two blocks of code to run once our test - python expression that eval... |
10,029 | text input('number'number int(textif number = print('even number'elseprint('odd number'print('that was fun!'ifthenelse py python ifthenelse py number even number that was fun python ifthenelse py number odd number that was fun againwe will look at an example that demonstrates just the structure there is script in your ... |
10,030 | if keyword test if number = colon print('even number'else upper middle print('that was fun!' the first line of the test looks very similar to the while syntax we have already seen in this casehoweverit uses new keyword"ifthe if keyword is followed by the testa python expression that evaluates to boolean the line ends w... |
10,031 | if number = print('even number'else run if test is true indentation upper middle print('that was fun!' the test line is immediately followed by the block of code that is run if the test evaluates as true because it is block of code it is indented by four spaces to mark it as block this example has single linebut the bl... |
10,032 | if number = print('even number'else elsekeyword upper middle run if test is false print('that was fun!'indentation after the then-block comes another new keyword"else:this is not indented and is level with the "ifto indicate that it is not part of the thenblock it is then followed by second block of codeknow as the "el... |
10,033 | if number = print('even number'else upper middle print('that was fun!'run afterwards regardless of test after the else-block the script continues the print line is unindented so is not part of the else-block this line is run regardless of the result of the test |
10,034 | middle (lower upper)/ before if middle** lower middle else if block upper middle print(lowerupperafter let' return to our square root example here we have the creation of mid-point -value followed by an if-test on itmiddle (lower+upper)/ if middle** this switches between two single-line code blocks if the test evaluate... |
10,035 | if before elseif test action action elseaction choice of two code blocks indentation afterwards |
10,036 | for each scriptifthenelse py predict what it will do ifthenelse py run the script ifthenelse py were you right minutes |
10,037 | tolerance - lower upper uncertainty upper lower while uncertainty tolerance middle (lower upper)/ if middle** if starts indented lower middle else doubly indented upper middle print(lowerupperuncertainty upper lower so how do we embed an if-test with its two code blocks inside while-loop as the loop' bodythe body of th... |
10,038 | tolerance - lower upper uncertainty upper lower while uncertainty tolerance middle (lower upper)/ spaces if middle** lower middle spaces else upper middle print(lowerupperuncertainty upper lower so if our standard indentation is four spaces then the doubly indented sections are indented eight spaces this is simple exam... |
10,039 | tolerance - lower upper uncertainty upper lower while uncertainty tolerance middle (lower upper)/ if middle** lower middle elseupper middle print(lowerupperuncertainty upper lower sqrt py python sqrt py the file sqrt py in your home directories contains the code as described in the slide it produces very nice approxima... |
10,040 | tolerance - lower upper uncertainty upper lower while uncertainty tolerance middle (lower upper)/ if middle** lower middle else upper middle print(lowerupperuncertainty upper lower so now we have the script for the square root of the next thing to do is to generalize it to produce square roots of any number |
10,041 | text input('number'number float(textif middle** number obviously we have to input the number whose square root we want we have already seen how to do this and to convert it from string into floating point numbertext input('number'number float(textonce we have the number the test middle** is straightforwardly extended t... |
10,042 | lower upper if then else we have to set initial bounds for our interval of uncertainty this is where it is important that you think about the problem before coding if the number whose square root is sought is less than then the square root is bigger than the number and less than if it is larger than then its square roo... |
10,043 | if number lower number upper else lower upper number it looks like this |
10,044 | text input('number?'number float(textuser input if number lower number upper elselower upper number initialization tolerance - uncertainty upper lower while uncertainty tolerancemiddle (lower+upper)/ if middle** numberlower middle elseupper middle processing uncertainty upper lower print(lowerupper output sqrt py this ... |
10,045 | need to catch negative numbers if number print('number must be positive!'exit(quit immediately "elseis optional we can improve our code step missing from the previous script is "input validationwhere we check that the input makes sense we ought to check that we have not been asked to generate the square root of negativ... |
10,046 | text input('number?'number float(textuser input if number print('number must be positive!'exit(input validation if number lower number upper elselower upper number initialization the input validation phase comes straight after the input itself |
10,047 | text input('number?'number float(textif number print('number must be positive!'exit(elif number lower number upper elselower upper number elif"else if sqrt py howeverit can be integrated with the initialization phaseand often is after allif you can' initialize from the input then the input isn' valid this leads us to m... |
10,048 | text input('number?'number float(textif number print('number is negative 'elseif number print('number is between zero and one 'elseif number print('number is between one and two 'elseif number print('number is between two and three 'elseprint('number is three or more 'stacked clauses get unwieldy to take an extreme exa... |
10,049 | text input('number?'number float(textif number print('number is negative 'elif number print('number is between zero and one 'elif number print('number is between one and two 'elif number print('number is between two and three 'elseprint('number is three or more ' applying elif causes everything to slide back into place |
10,050 | nested structures while if chained tests if elif elif elsetesting inputs to scripts exit( |
10,051 | only attempt each part after you have the previous part workingexercise py edit the square root script to catch negative numbers edit the square root script to ask for the tolerance edit the square root script to catch negative tolerances minutes the minimum tolerance used in this example will work for target values up... |
10,052 | we have written our first real python script what did it dowhy did it do itneed to annotate the script sqrt py is real program now imagine you pass it to someone else or put it away for twelve months and come back to it forgetting how you wrote it in the first place chances are that the reader of your script might like... |
10,053 | the "hashcharacter "pound""number""sharplines starting with "#are ignored partial lines starting "#are ignored used for annotating scripts pythonin common with most other scripting languagesuses the hash character to introduce comments the hash character and everything beyond it on the line is ignored (strictly speakin... |
10,054 | script to calculate square roots by bisection (cbob dowling licensed under gpl text input('number?'number float(textneed real number test number for validityset initial bounds if ok if number print('number must be non-negative!'exit(elif number lower number upper elselower upper number this is what commented script loo... |
10,055 | #!/usr/bin/python script to calculate square roots by bisection (cbob dowling licensed under gpl text input('number?'number float(textneed real number magic line for executable files fubar py instead of python fubar py you may encounter "hash plingfirst line in many imported python scripts this is part of some "unix ma... |
10,056 | comments "#character |
10,057 | comment your square root script from exercise minutes |
10,058 | whole numbers - floating point numbers complex numbers ( jtext 'the cat sat on the mat booleans true false we are about to introduce new python typeso we will take moment to remind ourseoves of the various python types we have met already |
10,059 | 'hydrogen''helium''lithium''beryllium''boron''thorium''protactinium''uranium- - the new python type we are going to meet is called "list |
10,060 | hydrogenheliumlithiumberylliumprotactiniumuranium sequence of values the names of the elements values stored in order atomic number order individual value identified by position in the sequence "heliumis the name of the second element so what is lista list is simply sequence of values stored in specific order with each... |
10,061 | sequence of values the prime numbers less than sixty values stored in order numerical order individual value identified by position in the sequence is the fourth prime or the list of primes up to note that list must be finite |
10,062 | primes literal list primes [ the whole list type(primesa python type so how might we do this in pythonwe will create list in python of the primes less than we can do this in single line as shown list in python is single python objectalbeit with multiple contentsand has its own typeunsurprisingly called "list |
10,063 | square brackets at the ends [ commas between items python presents (and acceptslists as series of values separated by commassurrounded by square brackets |
10,064 | primes [ literal list we are going to meet square brackets used fr lot of things so will build up summary slide of their various uses here is use |
10,065 | "index "value[ we still need to get at individual items in the list each is identified by its position in the list pythonin common with many programming languages (but not allstarts its count from zero the leading element in the list is "item number zerothe one that follows it is "item number oneand so on this numberth... |
10,066 | primes [ index primes[ square brackets primes[ sohow do we get "item number from listwe can follow the list (ormore usuallya name attached to the listwith the index in square brackets |
10,067 | primes [ literal list primes[ index into list and this is the second use of square brackets |
10,068 | primes [ - - - - - - - - getting at the last item primes[- python has trick for getting at the last element of the list negative indices are also valid and count backwards from the end of the list typically the only case of this that is used in paractice is that the index - gets the last element of the list |
10,069 | list int primes[ int primes[ primes int primes[ int primes[ we've seen these box diagrams for simple python types already the structures for lists are little more complicated but only little the list type records how long it is and an ordered set of references to the actual objects it contains |
10,070 | list len(primes len(functionlength of list primes maximum index is note that the length of list is the number of items it contains the largest legitimate index is one less than that because indices count from zero |
10,071 | data ['alpha''beta''gamma'the list data[ initial value 'gammadata[ 'gchange value data[ check change 'gdata changed list ['alpha''beta'' ' so far we have created lists all in one go by quoting literal list we can use the indexing notation (square bracketsto change items in list too |
10,072 | right to left data ['alpha''beta''gamma'list str str str we can track what happens in that example in some detail we will start with the first linedefining the initial list as everpython assignment is done right to left the right hand side is evaluated as list of three itemsall of themstrings |
10,073 | right to left data ['alpha''beta''gamma'list str str str data this then has the name "dataattached to it |
10,074 | right to left data[ 'glist str str str str data new value now we come to the second line which changes one of these list items the right hand side is evaluated as string containing single characters that object gets created |
10,075 | right to left data[ 'glist str str str str data no longer referenced the assignment causes the reference within the string to be changed to refer to the new string and to stop referring to the previous one"gammain this case there are now no references to the "gammastring |
10,076 | right to left data[ 'glist str str str data python then clears out the memory used for that old string so that it can reuse it for something else this process is called "garbage collectionin computing |
10,077 | del data[ list str data[ str data[ str data[ data we can remove entries from the list too with the "delkeywordjust as we removed names the del keyword removes the reference from the list |
10,078 | del data[ list str data[ str no longer referenced str data[ data this leaves the string "betano longer referenced by anything |
10,079 | del data[ list str data[ str data[ data and garbage collection kicks in again |
10,080 | list int int primes int int primes[ we have remarked on couple of occasions that the largest valid index is number one less than the length of the list so what happens if you ask for an index greater than the largest legal value |
10,081 | len(primes primes[ primes[ traceback (most recent call last)file ""line in indexerrorlist index out of range type of error description of error you get an error unsurprisingly the type of the error is an "indexerror-something went wrong with an index the error message specifies that the index asked for was outside the ... |
10,082 | primes[ traceback (most recent call last)file ""line in indexerrorlist assignment index out of range same type of error similar description of error but with "assignment note that we can' use indicies beyond the limit to extend list either |
10,083 | lists [ index primes[ count from zero primes[ deletion del primes[ length len(primesover-running primes[ |
10,084 | track what the value of numbers is at each stage of this sequence of instructions numbers [ numbers[ del numbers[ numbers[ numbers[ numbers[ minutes do this by hand after each linework out what you think numbers will be and then print it to see if you were right to find outlaunch an interactive python and run each line... |
10,085 | list same list list new length int int int int int int extra item int sohow can we extend list |
10,086 | primes [ function built into list primes append( primes the list is now updated [ this is the python syntax for appending an item to the end of list you won' recognise the syntaxit is something new |
10,087 | the list connecting dot primes append( append(the value to append all lists have this function built in so we need to look at this new construction we have the list"primes"followed by dot which acts as connector this is followed by the name of function"appendthis function is not standard python function like print(or l... |
10,088 | behaves just like function object function function that has special access to the object' data (arguments these built in functions are called "methodsormore precisely"methods of the objectare used all over python and are general concept across an entire type of programming called "object oriented programming |
10,089 | print(primes[ primes append( primes append( the function doesn' return any value primes append( primes append( it modifies the list itself print(primes[ we can use the append(method repeatedly to extend the list as far as we want |
10,090 | numbers [ numbers reverse(the function doesn' return any value print(numbers[ it modifies the list itself append(is not the only method built into lists for example reverse(takes the list and reverses its contents note that it doesn' return reversed list as valuet doesn' return anything at all it silently reverses the ... |
10,091 | numbers [ numbers sort(the function does not return the sorted list print(numbers[ it sorts the list itself numerical order similarlythe sort(method doesn' return sorted list but silently sorts the list internally |
10,092 | greek ['alpha''beta''gamma''delta'greek sort(print(greek['alpha''beta''delta''gamma'alphabetical order of the words more or less any type can be sorted text sorting carries all the cautions about the complexities of collation that we covered under comparisons |
10,093 | greek ['alpha''gamma''delta'greek insert( 'betawhere to insert what to insert greek ['alpha''beta''gamma''delta' displaced the append(method sticks an item on the end of list if you want to insert an item elsewhere in the list we have the insert(method the insert(method takes two argumentsthe first is the item to be in... |
10,094 | numbers [ numbers remove( value to remove print(numbers[ del numbers[ index to remove there is remove(method this is passed value to remove from the list it then removes that value from the listwherever it is in the list contrast with with del where you had to know the index to remove |
10,095 | print(numbers[ there are two instances of numbers remove( print(numbers[ only the first instance is removed if the value appears more than once in list then only the first instance is removed trying to remove something that isn' there will lead to an error |
10,096 | help(numbershelp on list objectclass list(objectappendl append(object-append object to end paginationnext page back one page quit that' lot of methodsand it' only some of them how can we know all of themyou can always ask for help on any python object and you will be told all about the methods it possesses it is very f... |
10,097 | help(numbers appendhelp on built-in function appendappendl append(object-append object to end you can also get help on single method which is often simpler to deal with |
10,098 | greek ['alpha''beta''gamma''delta'greek sort(recallgreek sort(sorts the list "in placeprint(greek['alpha''beta''delta''gamma' we noted that the sort(method sorts the list itself experience shows that sorting is one of those operations where people want sorted copy of the list quite often |
10,099 | greek ['alpha''beta''gamma''delta'sorted(function returns sorted list ['alpha''beta''delta''gamma'print(sorted(greek)and leaves the list alone ['alpha''beta''gamma''delta'print(greek to assist with thispython offers standalone function called sorted(which makes copy of the list and sorts that copyleaving the original u... |
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