dispel tutorial - verce.eu · 1 packagedispel.datamine f 2 usedispel.core.randomlistsplit; 3...
TRANSCRIPT
Virtual Earthquake and seismology Research Community e-science environment in Europe
Project 283543 – FP7-INFRASTRUCTURES-2011-2 – www.verce.eu – [email protected]
DISPEL Tutorial
Paul Martin
VERCE Training Programme
3rd September 2012
www.verce.eu
Workflow enactment
ComputeCluster
User Machine
DISPEL Tutorial 3rd September 2012 2 / 30
Workflow enactment
VERCE Gateway / Portal
ADMIRE Gateway
Data Store
Enactment Engine
Component Registry
Component Repository
DISPEL Tutorial 3rd September 2012 2 / 30
Workflow enactment
User Request
Dispel Request
DISPEL Tutorial 3rd September 2012 2 / 30
Workflow enactment
Delegation / Registry Lookup
DISPEL Tutorial 3rd September 2012 2 / 30
Workflow enactment
Instruction
DISPEL Tutorial 3rd September 2012 2 / 30
Workflow enactment
Data Request / Submission / Signalling
DISPEL Tutorial 3rd September 2012 2 / 30
Workflow enactment
Result Notification
DISPEL Tutorial 3rd September 2012 2 / 30
An example workflow
DISPEL Tutorial 3rd September 2012 3 / 30
A simple script
1 // Import PEs from the local registry.2 use dispel.db.SQLQuery;
3 use dispel.lang.Results;
4
5 // Create instances of PEs.6 SQLQuery query = new SQLQuery;
7 Results results = new Results;
8
9 // Construct workflow and feed in data.10 |-"SELECT * FROM littleblackbook WHERE id < 10"-| => query.expression;
11 |-"uk.org.UoE.dbA"-| => query.resource;
12 |-"10 entries from the little black book"-| => results.name;
13 query.data => results.input;
14
15 // Submit the entire workflow.16 submit;
DISPEL Tutorial 3rd September 2012 4 / 30
Demonstrating stream literals
1 // Import PEs from the local registry.2 use dispel.db.SQLQuery;
3
4 // Create instances of PEs.5 SQLQuery query = new SQLQuery;
6 Results results = new Results;
7
8 // Define a set of queries.9 String[] queries = new String[2];
10 queries[0] = "SELECT name FROM littleblackbook WHERE id < 10";
11 queries[1] = "SELECT name FROM littleblackbook WHERE id >= 10 AND id < 20";
12 queries[2] = "SELECT address FROM littleblackbook WHERE name = ’David Hume’";
13
14 // Construct workflow and feed in data.15 |-queries[0], queries[1], queries[2]-| => query.expression;
16 |-"uk.org.UoE.dbA", "uk.org.UoE.dbB", "uk.org.UoE.dbC"-| => query.resource;
17 |-"Results from the little black book"-| => results.name;
18 query.data => results.input;
19
20 // Submit the entire workflow.21 submit;
DISPEL Tutorial 3rd September 2012 5 / 30
Demonstrating stream literals
1 // Import PEs from the local registry.2 use dispel.db.SQLQuery;
3
4 // Create instances of PEs.5 SQLQuery query = new SQLQuery;
6 Results results = new Results;
7
8 // Define a set of queries.9 String[] queries = new String[2];
10 queries[0] = "SELECT name FROM littleblackbook WHERE id < 10";
11 queries[1] = "SELECT name FROM littleblackbook WHERE id >= 10 AND id < 20";
12 queries[2] = "SELECT address FROM littleblackbook WHERE name = ’David Hume’";
13
14 // Construct workflow and feed in data.15 |-queries[0], queries[1], queries[2]-| => query.expression;
16 |-repeat 3 of "uk.org.UoE.dbA"-| => query.resource;
17 |-"Results from the little black book"-| => results.name;
18 query.data => results.input;
19
20 // Submit the entire workflow.21 submit;
DISPEL Tutorial 3rd September 2012 6 / 30
A precocious script
1 // Import PEs from the local registry.2 use dispel.db.SQLQuery;
3 use dispel.tutorial.PrecociousChild;
4
5 // Create instances of PEs.6 PrecociousChild child = new PrecociousChild;
7 SQLQuery query = new SQLQuery;
8 Results results = new Results;
9
10 // Construct workflow and feed in data.11 child.output => query.expression;
12 |-repeat enough of "uk.org.UoE.dbA"-| => query.resource;
13 |-"Adult responses"-| => results.name;
14 query.data => results.input;
15
16 // Submit the entire workflow.17 submit;
DISPEL Tutorial 3rd September 2012 7 / 30
PE Specification
1 // Within the Dispel database package.2 package dispel.db {3 // Link to database ontology.4 namespace db "http://www.dispel-lang.org/resource/db";
5 // Type signature for the SQLQuery PE.6 Type SQLQuery is PE( <Connection:String::"db:SQLQuery" terminator expression; Connection:String::"db:URI" locator resource> =>
7 <Connection:[<rest>]::"db:TupleRowSet" data> );
8 // Register the PE.9 register SQLQuery;
10 }11
12 // Within the package of generically useful PEs.13 package dispel.core {14 // A generic interpolation PE with few restrictions.15 Type Interpolate is PE( Stype Element is Any; <Connection[]:Element inputs> => <Connection:Element output> );
16 // This PE evenly interpolates in order of input connections.17 Type OrderedInterpolate is Interpolate
18 with roundrobin inputs, @description = "Interpolates evenly by order of inputs.";
19
20 register Interpolate, OrderedInterpolate;
21 }22
23 // Within the Dispel filter package.24 package dispel.filter {25 Type AbstractFilter is PE( Stype Element is Any;
26 <Connection:Element inputs> => <Connection:Element filtered; Connection:Element unfiltered> )
27 with @description = "A filter splits input into filtered and unfiltered streams.";
28
29 Type HeadFilter is AbstractFilter
30 with filtered as head, unfiltered as tail, @description = "Diverts the head of a stream.";
31
32 Type ProgrammableIntegerFilter is PE( <Connection:Integer terminator input; Connection:String initiator expression;
33 Connection[]:Integer lockstep parameters> =>
34 <Connection:Integer filtered; Connection:Integer unfiltered> )
35 with @description = "Splits the input integer stream into ’filtered’ and ’unfiltered’ streams in" +
36 "accordance with the expression and parameters given.";
37
38 register AbstractFilter, HeadFilter, ProgrammableIntegerFilter;
39 }40
DISPEL Tutorial 3rd September 2012 8 / 30
Constructing new PEs
1 package tutorial.example {2 // Import existing PE from the registry.3 use dispel.db.SQLQuery;
4
5 // Define new PE type.6 Type SQLToTupleList is PE( <Connection expression> => <Connection data> );
7
8 // Define new PE constructor.9 PE<SQLToTupleList> lockSQLDataSource(String dataSource) {
10 SQLQuery query = new SQLQuery;
11 |-repeat enough of dataSource-| => query.resource;
12 return PE( <Connection expression = query.expression> =>
13 <Connection data = query.data> );
14 }15
16 // Create new PEs.17 PE<SQLToTupleList> TutorialQuery = lockSQLDataSource("uk.org.UoE.dbA");
18 PE<SQLToTupleList> MirrorQuery = lockSQLDataSource("uk.org.UoE.dbB");
19
20 // Register new entities.21 register TutorialQuery, MirrorQuery;
22 }
DISPEL Tutorial 3rd September 2012 9 / 30
Using the new PE
1 // Import PEs from the local registry.2 use tutorial.example.TutorialQuery;
3
4 // Create instances of PEs (no import necessary).5 TutorialQuery query = new TutorialQuery;
6 Results results = new Results;
7
8 // Connect PEI together to create workflow (no data source needed).9 |-"SELECT * FROM littleblackbook WHERE id <= 10"-| => query.expression;
10 |-"10 entries from the little black book"-| => results.name;
11 query.data => results.input;
12
13 // Submit workflow.14 submit results;
DISPEL Tutorial 3rd September 2012 10 / 30
Multicasting with composite PEs
MulticastQuery
QueryGenerator
"uk.org.UoE.dbA"
"uk.org.UoE.dbB"
"uk.org.UoE.dbC"
Results
DISPEL Tutorial 3rd September 2012 11 / 30
Multicasting with composite PEs
QueryGenerator
"uk.org.UoE.dbA"
"uk.org.UoE.dbB"
"uk.org.UoE.dbC"
SQLQuery
SQLQuery
SQLQuery
ListIntersect Results
DISPEL Tutorial 3rd September 2012 12 / 30
A PE constructor featuring iteration
1 package tutorial.example {2 use dispel.db.SQLQuery;
3 use dispel.list.ListIntersect;
4
5 // A PE type which queries multiple sources.6 Type MulticastQuery is PE( <Connection expression; Connection[] sources> => <Connection data> );
7
8 // Use parallel SQLQuery instances to corroborate results.9 PE<MulticastQuery> makeCorroboratedSQLQuery(Integer size) {
10 // Define aliases for workflow inputs in advance.11 Connection expr;
12 Connection[] srcs = new Connection[size];
13 // Create instances of internal PEs.14 SQLQuery[] queries = new SQLQuery[size];
15 ListIntersect intersect = new ListIntersect with inputs.length = size;
16
17 // Connect SQLQuery instances in parallel.18 for (Integer i = 0; i < size; i++) {19 queries[i] = new SQLQuery;
20 expr => queries[i].expression;
21 srcs[i] => queries[i].resource;
22 queries[i].data => intersect.inputs[i];
23 }24
25 // Return intersection of query results.26 return PE( <Connection expression = expr; Connection[] sources = srcs> =>
27 <Connection data = intersect.output> );
28 }29
30 register MulticastQuery, makeCorroboratedSQLQuery;
31 }
DISPEL Tutorial 3rd September 2012 13 / 30
Multicasting with composite PEs
QueryGenerator
"uk.org.UoE.dbA"
"uk.org.UoE.dbB"
"uk.org.UoE.dbC"
SQLQuery
SQLQuery
SQLQuery
ListMerge Results
QueryGenerator
"uk.org.UoE.dbD"
"uk.org.UoE.dbE"
"uk.org.UoE.dbF"
SQLQuery
SQLQuery
SQLQuery
ListUnion Results
DISPEL Tutorial 3rd September 2012 14 / 30
A PE constructor featuring selection
1 package tutorial.example {2 use dispel.db.SQLQuery;
3 use dispel.list.Combiner;
4 use dispel.list.ListUnion;
5 use dispel.list.ListMerge;
6 // Import abstract type defined earlier.7 use tutorial.example.MulticastQuery;
8
9 // Use parallel SQLQuery instances to collect results.10 PE<MulticastQuery> makeMassSQLQuery(Integer size, Boolean unique) {11 // Prepare components for connection.12 Connection expr;
13 Connection[] srcs = new Connection[size];
14 SQLQuery[] queries = new SQLQuery[size];
15 Combiner merge;
16 // Select combiner based on uniqueness condition.17 if (unique) merge = new ListUnion with inputs.length = size;
18 else merge = new ListMerge with inputs.length = size;
19
20 // Connect SQLQuery instances in parallel.21 for (Integer i = 0; i < size; i++) {22 queries[i] = new SQLQuery;
23 expr => queries[i].expression;
24 srcs[i] => queries[i].resource;
25 queries[i].data => merge.inputs[i];
26 }27
28 // Return merger of query results.29 return PE( <Connection expression = expr; Connection[] sources = srcs> =>
30 <Connection data = merge.output> );
31 }32
33 register makeMassSQLQuery;
34 }35
DISPEL Tutorial 3rd September 2012 15 / 30
k-fold cross validation
DataValidator
DataProducer
Results
DISPEL Tutorial 3rd September 2012 16 / 30
k-fold cross validation
1 package dispel.datamine {2 use dispel.core.DataPartition;
3 use dispel.list.ListMerge;
4
5 // Produces a k-fold cross validation workflow pattern.6 PE<Validator> makeCrossValidator(Integer k, PE<TrainClassifier> Train,
7 PE<ApplyClassifier> Classify, PE<ModelEvaluate> Evaluate) {8 Connection input;
9 // Data must be partitioned and re-combined for each fold.10 PE<DataPartitioner> FoldData = makeDataFold(k);
11 FoldData fold = new FoldData;
12 ListMerge union = new ListMerge with inputs.length = k;
13
14 // For each fold, train a classifier then evaluate it.15 input => fold.data;
16 for (Integer i = 0; i < k; i++) {17 Train train = new Train;
18 Classify classify = new Classify;
19 Evaluate evaluate = new Evaluate;
20
21 fold.training[i] => train.data;
22 train.classifier => classify.classifier;
23 fold.test[i] => classify.data;
24 classify.result => evaluate.predicted;
25 fold.test[i] => evaluate.expected;
26 evaluate.score => union.inputs[i];
27 }28
29 // Return cross validation pattern.30 return PE( <Connection data = input> => <Connection results = union.output> );
31 }32
33 register makeCrossValidator;
34 }
DISPEL Tutorial 3rd September 2012 17 / 30
k-fold cross validation
DataPartitioner
TrainClassifier
ApplyClassifier
ModelEvaluator
TrainClassifier
TrainClassifier
ApplyClassifier
ApplyClassifier
ModelEvaluator
ModelEvaluator
ListMerge
DataProducer
Results
DISPEL Tutorial 3rd September 2012 18 / 30
k-fold cross validation
1 package dispel.datamine {2 use dispel.core.RandomListSplit;
3 use dispel.list.ListMerge;
4
5 // Produces a PE capable of splitting data for k-fold cross validation.6 PE<DataPartitioner> makeDataFold(Integer k) {7 Connection input;
8 Connection[] trainingData = new Connection[k];
9 Connection[] testData = new Connection[k];
10 // Create instance of PEs for randomly splitting and recombining data.11 RandomListSplit sample = new RandomListSplit with results.length = k;
12 ListMerge[] union = new ListMerge[k];
13
14 // After partitioning data, form training and test sets.15 input => sample.input;
16 for (Integer i = 0; i < k; i++) {17 union[i] = new TupleUnionAll with inputs.length = k - 1;
18 for (Integer j = 0; j < i; j++) sample.outputs[j] => union[i].inputs[j];
19 sample.outputs[i] => testData[i];
20 for (Integer j = i + 1; j < k; j++) sample.outputs[j] => union[i].inputs[j - 1];
21 union[i].output => trainingData[i];
22 }23
24 // Return data folding pattern.25 return PE( <Connection data = input> =>
26 <Connection[] training = trainingData; Connection[] test = testData> );
27 }28
29 register makeDataFold;
30 }
DISPEL Tutorial 3rd September 2012 19 / 30
k-fold cross validation
ListMerge
ListMerge
ListMerge
RandomListSplit
TrainClassifier
ApplyClassifier
ModelEvaluator
TrainClassifier
TrainClassifier
ApplyClassifier
ApplyClassifier
ModelEvaluator
ModelEvaluator
ListMerge
DataProducer
Results
DISPEL Tutorial 3rd September 2012 20 / 30
k-fold cross validation
1 package dispel.datamine {2 // Import test PEs.3 use dispel.tutorial.DataProducer;
4 use dispel.tutorial.TrainingAlgorithmA;
5 use dispel.tutorial.BasicClassifier;
6 use dispel.tutorial.MeanEvaluator;
7
8 // Create a cross validator PE.9 PE<Validator> CrossValidator
10 = makeCrossValidator(12, TrainingAlgorithmA, BasicClassifier, MeanEvaluator);
11 // Make instances of PEs for workflows.12 DataProducer producer = new DataProducer;
13 CrossValidator validator = new CrossValidator;
14 Results results = new Results;
15
16 // Connect workflow.17 |- "uk.org.UoE.data.corpus11" -| => producer.source;
18 producer.data => validator.data;
19 validator.results => results.input;
20 |- "Classifier Scores" -| => results.name;
21
22 submit;
23 }
DISPEL Tutorial 3rd September 2012 21 / 30
k-fold cross validation
expression resource
queryTestuk.org.ogsadai.SQLQuery
data
expression data
uk.org.ogsadai.TupleArithmeticSample
result[0] result[2] result[1] result[3]
MySQLResourceselect outlook, temp...
result
name input
resultseu.admire.Results
select outlook, temp...
expression resource
queryTrainuk.org.ogsadai.SQLQuery
data
MySQLResource
columnIds aggregates data resultColumnNames
uk.org.ogsadai.GroupBy
result
data[0] data[2] data[1] data[3]
uk.org.ogsadai.TupleUnionAll
data
play
nominalValues columnIndices data classIndex
eu.admire.BuildClassifier
classifier
[, [, sunny, rainy, overcast, ], [, true, false, ], [, yes, no, ], ]
nominalValues columnIndices data classIndex
eu.admire.BuildClassifier
classifier
[, expected, actual, count, ]
columnIds aggregates data resultColumnNames
uk.org.ogsadai.GroupBy
result
play[, [, sunny, rainy, overcast, ], [, true, false, ], [, yes, no, ], ]
columnIds aggregates data resultColumnNames
uk.org.ogsadai.GroupBy
result
data[0] data[1]
uk.org.ogsadai.TupleSimpleMerge
result
[, expected, actual, count, ]
predicted
resultColumnName classifier data
eu.admire.datamine.Classify
result
[, COUNT(*), ]
predicted
resultColumnName classifier data
eu.admire.datamine.Classify
result
[, SUM(count), ]
columnIds aggregates data resultColumnNames
uk.org.ogsadai.GroupBy
result
resultColumnName classifier data
eu.admire.datamine.Classify
result
[, expected, actual, ]
data[0] data[1]
uk.org.ogsadai.TupleSimpleMerge
result
[, expected, actual, count, ][, play, predicted, ]
data[0] data[2] data[1]
uk.org.ogsadai.TupleUnionAll
data
nominalValues columnIndices data classIndex
eu.admire.BuildClassifier
classifier
[, outlook, windy, play, ]
[, COUNT(*), ]
data[0] data[1]
uk.org.ogsadai.TupleSimpleMerge
result
columnIds aggregates data resultColumnNames
uk.org.ogsadai.GroupBy
result
[, [, sunny, rainy, overcast, ], [, true, false, ], [, yes, no, ], ]
nominalValues columnIndices data classIndex
eu.admire.BuildClassifier
classifier
data[0] data[2] data[1]
uk.org.ogsadai.TupleUnionAll
data
data[0] data[1]
uk.org.ogsadai.TupleSimpleMerge
result
resultColumnName classifier data
eu.admire.datamine.Classify
result
play Floor(Rand(54783) * ...
[, play, predicted, ]
data[0] data[2] data[1]
uk.org.ogsadai.TupleUnionAll
data
[, outlook, windy, play, ][, outlook, windy, play, ]
[, expected, actual, count, ]
[, [, sunny, rainy, overcast, ], [, true, false, ], [, yes, no, ], ]
[, COUNT(*), ]
play
Floor(Rand(54783) * ...
expression data
uk.org.ogsadai.TupleArithmeticSample
result[0] result[2] result[1] result[3]
[, play, predicted, ] [, play, predicted, ]
data[0] data[2] data[1]
uk.org.ogsadai.TupleUnionAll
data
predicted
[, expected, actual, count, ]
[, outlook, windy, play, ]
predicted
[, COUNT(*), ]
DISPEL Tutorial 3rd September 2012 22 / 30
Sieve of Eratosthenes
PrimeGenerator
DISPEL Tutorial 3rd September 2012 23 / 30
Sieve of Eratosthenes
DISPEL Tutorial 3rd September 2012 24 / 30
Sieve of Eratosthenes
1 package tutorial.example {2 use dispel.filter.AbstractFilter;
3 use dispel.filter.HeadFilter;
4 use dispel.filter.ProgrammableIntegerFilter;
5
6 // Define sieve element constructor.7 PE<AbstractFilter> makeSieveFilter() {8 // Create reference to input connection.9 Connection:Integer input;
10 // Instantiate internal components.11 HeadFilter split = new HeadFilter;
12 ProgrammableIntegerFilter divide = new ProgrammableIntegerFilter with parameters.length = 1;
13
14 // Construct internal workflow.15 |-"x if (x % $0) == 0"-| => divide.expression;
16 input => split.input;
17 split.head => divide.parameter[0];
18 split.tail => divide.input;
19 divide.unfiltered => discard;
20
21 // Output first integer received and all indivisible integers.22 return PE( <Connection input = input> =>
23 <Connection filtered = split.head; Connection unfiltered = divide.filtered> );
24 }25
26 // Create the sieve element PE.27 PE<AbstractFilter> SieveFilter = makeSieveFilter();
28
29 register SieveFilter;
30 }31
DISPEL Tutorial 3rd September 2012 25 / 30
Sieve of Eratosthenes
1 package tutorial.example {2 use dispel.core.Interpolate;
3 use tutorial.example.SieveFilter;
4 use dispel.math.PrimeGenerator;
5
6 // Define sieve constructor.7 PE<PrimeGenerator> makeSieveOfEratosthenes(Integer count) {8 // Instantiate internal components.9 SieveFilter filter = new SieveFilter[count];
10 Interpolate interpolate = new Interpolate with roundrobin inputs, input.length = count;
11
12 // Initialise sieve elements.13 for (Integer i = 0; i < count - 1; i++) filter[i] = new SieveFilter with terminator output;
14 filter[count - 1] = new SieveFilter with terminator prime;
15
16 // Construct internal workflow.17 |-x for x in 2..-| => filter[0].input;
18 for (Integer i = 0; i < count - 1; i++) {19 filter[i].unfiltered => filter[i + 1].input;
20 filter[i].filtered => interpolate.inputs[i];
21 }22 filter[count - 1].unfiltered => discard;
23 filter[count - 1].filtered => interpolate.input[count - 1];
24 filter[count - 1].filtered => stop;
25
26 // Return all primes generated.27 return PE( <> => <Connection primes = interpolate.output> );
28 }29
30 register makeSieveOfEratosthenes;
31 }
DISPEL Tutorial 3rd September 2012 26 / 30
Sieve of Eratosthenes
1 package tutorial.example {2 // Import abstract PE type and constructor.3 use dispel.math.PrimeGenerator;
4
5 // Construct the sieve.6 PE <PrimeGenerator> SoE100 = makeSieveOfEratosthenes(100);
7 SoE100 sieve100 = new SoE100;
8 Results results = new Results;
9
10 // Construct the top-level workflow.11 |-"100 prime numbers"-| => results.name;
12 sieve100.primes => results.input;
13
14 // Submit the workflow.15 submit;
16 }
DISPEL Tutorial 3rd September 2012 27 / 30
Sieve of Eratosthenes
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DISPEL Tutorial 3rd September 2012 28 / 30
Sieve of Eratosthenes
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nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
eu.a
dm
ire.
mat
h.N
umbe
rGen
erat
or
out
put
DISPEL Tutorial 3rd September 2012 29 / 30
Sieve of Eratosthenes
The
fir
st 1
00
pri
me
...
nam
ein
put
resu
lts
eu.a
dm
ire.
Res
ults
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
r
inpu
t[4
0]
inpu
t[22
]in
put[
95
]in
put[
67]
inpu
t[4
9]
inpu
t[12
]in
put[
31]
inpu
t[20
]in
put[
6]
inpu
t[75
]in
put[
27]
inpu
t[5
5]
inpu
t[9
6]
inpu
t[89
]in
put[
68]
inpu
t[6
2]in
put[
19]
inpu
t[34
]in
put[
83]
inpu
t[13
]in
put[
41]
inpu
t[4
8]in
put[
5]
inpu
t[28
]in
put[
69
]in
put[
33]
inpu
t[9
7]in
put[
18]
inpu
t[6
1]in
put[
88]
inpu
t[74
]in
put[
42]
inpu
t[25
]in
put[
47]
inpu
t[5
6]
inpu
t[84
]in
put[
70]
inpu
t[7]
inpu
t[9
1]in
put[
81]
inpu
t[0
]in
put[
46
]in
put[
98]
inpu
t[73
]in
put[
53]
inpu
t[9
0]
inpu
t[9
9]
inpu
t[26
]in
put[
36]
inpu
t[8]
inpu
t[4
5]
inpu
t[35
]in
put[
63]
inpu
t[72
]in
put[
54
]in
put[
82]
inpu
t[17
]in
put[
2]in
put[
9]
inpu
t[5
1]in
put[
86]
inpu
t[4
4]
inpu
t[37
]in
put[
58]
inpu
t[6
4]
inpu
t[9
2]in
put[
16]
inpu
t[71
]in
put[
10]
inpu
t[5
2]in
put[
78]
inpu
t[4
3]in
put[
30]
inpu
t[23
]in
put[
15]
inpu
t[38
]in
put[
85]
inpu
t[29
]in
put[
1]in
put[
80]
inpu
t[5
7]in
put[
65
]in
put[
24]
inpu
t[79
]in
put[
93]
inpu
t[14
]in
put[
21]
inpu
t[6
0]
inpu
t[77
]in
put[
3]in
put[
94
]in
put[
66
]in
put[
32]
inpu
t[39
]in
put[
11]
inpu
t[4
]in
put[
50
]in
put[
87]
inpu
t[5
9]
inpu
t[76
]
eu.a
dm
ire.
mat
h.C
om
bine
r
out
put
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
eu.a
dm
ire.
mat
h.N
umbe
rGen
erat
or
out
put
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
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r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
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r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
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r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
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r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
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r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
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r
div
iso
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mai
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inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
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r
div
iso
rre
mai
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inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
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r
div
iso
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mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
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r
div
iso
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mai
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inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
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t
eu.a
dm
ire.
mat
h.D
ivis
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r
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iso
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mai
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inpu
t
eu.a
dm
ire.
mat
h.D
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r
div
iso
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t
eu.a
dm
ire.
mat
h.D
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t
eu.a
dm
ire.
mat
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t
eu.a
dm
ire.
mat
h.D
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r
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t
eu.a
dm
ire.
mat
h.D
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t
eu.a
dm
ire.
mat
h.D
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r
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t
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dm
ire.
mat
h.D
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div
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t
eu.a
dm
ire.
mat
h.D
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t
eu.a
dm
ire.
mat
h.D
ivis
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r
div
iso
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mai
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inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
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r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
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r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
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r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
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r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
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r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
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r
div
iso
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mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
inpu
t
eu.a
dm
ire.
mat
h.D
ivis
ionF
ilte
r
div
iso
rre
mai
nder
DISPEL Tutorial 3rd September 2012 30 / 30