Postgres – Random IT Utensils https://blog.adamfurmanek.pl IT, operating systems, maths, and more. Tue, 26 Mar 2019 00:58:34 +0000 en-US hourly 1 https://wordpress.org/?v=6.6.2 Machine Learning Part 7 — Forward propagation in neural net in SQL https://blog.adamfurmanek.pl/2019/07/20/machine-learning-part-7/ https://blog.adamfurmanek.pl/2019/07/20/machine-learning-part-7/#respond Sat, 20 Jul 2019 08:00:35 +0000 https://blog.adamfurmanek.pl/?p=2997 Continue reading Machine Learning Part 7 — Forward propagation in neural net in SQL]]>

This is the seventh part of the ML series. For your convenience you can find other parts in the table of contents in Part 1 – Linear regression in MXNet

Today we are going to create a neural net and calculate forward propagation using PostgreSQL. Let’s go.

We start with definition of the network: we will have input layer, hidden layer, and output layer. Input layer will have 3 nodes, hidden layer will have 2, output layer will have 3. In input layer we don’t do any transformation on the input data, in hidden layer we use ReLU, in output layer we use linear activation function (so no transformation).

Let’s start with the following definitions:

DROP TABLE IF EXISTS inputs;
DROP TABLE IF EXISTS weights1;
DROP TABLE IF EXISTS weights2;
DROP TABLE IF EXISTS biases;

CREATE TABLE inputs (
  inputNode NUMERIC,
  inputValue NUMERIC
);

INSERT INTO inputs VALUES
    (1, 1)
   ,(2, 3)
   ,(3, 5)
;

CREATE TABLE weights1 (
  weight1InputNodeNumber NUMERIC,
  weight1OutputNodeNumber NUMERIC,
  weight1Value NUMERIC,
  weight1Bias NUMERIC
);

INSERT INTO weights1 VALUES
    (1, 1, 2, 1)
   ,(1, 2, 3, 1)
   ,(2, 1, 4, 2)
   ,(2, 2, 5, 2)
   ,(3, 1, 6, 3)
   ,(3, 2, 7, 3)
;

CREATE TABLE weights2 (
  weight2InputNodeNumber NUMERIC,
  weight2OutputNodeNumber NUMERIC,
  weight2Value NUMERIC,
  weight2Bias NUMERIC
);

INSERT INTO weights2 VALUES
    (1, 1, 1, 2)
   ,(1, 2, 2, 2)
   ,(1, 3, 3, 2)
   ,(2, 1, 4, 3)
   ,(2, 2, 5, 3)
   ,(2, 3, 6, 3)
;

We define some input values, weights and biases. Values are completely made up and do not make a difference.

Before we write SQL code, let’s calculate result manually.

We have the following variables:

    \begin{gather*} input = \left[\begin{array}{c} 1 \\ 3 \\ 5 \end{array}\right] \\ W^1 = \left[\begin{array}{cc} 2 & 3 \\ 4 & 5 \\ 6 & 7 \end{array}\right] \\ b^1 = \left[\begin{array}{cc} 1 & 1 \\ 2 & 2 \\ 3 & 3 \end{array}\right] \\ W^2 = \left[\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \end{array}\right] \\ b^2 = \left[\begin{array}{ccc} 2 & 2 & 2 \\ 3 & 3 & 3 \end{array}\right] \\ \end{gather*}

Now, let’s calculate input for hidden layer:

    \begin{gather*} h^{in} = \left[\begin{array}{c} W^1_{1, 1} \cdot input_1 + b^1_{1, 1} + W^1_{2, 1} \cdot input_2 + b^1_{2, 1} + W^1_{3, 1} \cdot input_3 + b^1_{3, 1} \\ W^1_{1, 2} \cdot input_1 + b^1_{1, 2} + W^1_{2, 2} \cdot input_2 + b^1_{2, 2} + W^1_{3, 2} \cdot input_3 + b^1_{3, 2} \end{array}\right] \end{gather*}

Now, we use ReLU activation function for hidden layer:

    \begin{gather*} h^{out} = \left[\begin{array}{c} \max(h^{in}_1, 0) \\ \max(h^{in}_2, 0) \end{array}\right] \end{gather*}

We carry on with calculating input for output layer:

    \begin{gather*} y^{in} = \left[\begin{array}{c} W^2_{1, 1} \cdot h^{out}_1 + b^2_{1, 1} + W^2_{2, 1} \cdot h^{out}_2 + b^2_{2, 1} \\ W^2_{1, 2} \cdot h^{out}_1 + b^2_{1, 2} + W^2_{2, 2} \cdot h^{out}_2 + b^2_{2, 2} \\ W^2_{1, 3} \cdot h^{out}_1 + b^2_{1, 3} + W^2_{2, 3} \cdot h^{out}_2 + b^2_{2, 3} \end{array}\right] \end{gather*}

Activation function for output layer is linear, so it is easy now:

    \begin{gather*} y^{out} = y^{in} \end{gather*}

We will calculate errors next time.

Now, let’s calculate the result:

WITH RECURSIVE currentPhase AS(
	SELECT CAST(0 AS NUMERIC) AS phase
),
oneRow AS(
	SELECT CAST(NULL AS NUMERIC) AS rowValue
),
solution AS (
	SELECT I.*, O1.rowValue AS inputLayerOutput, W1.*, I2.rowValue AS hiddenLayerInput, O2.rowValue AS hiddenLayerOutput, W2.*, I3.rowValue AS outputLayerInput, O3.rowValue AS outputLayerOutput, P.*
	FROM inputs AS I
	CROSS JOIN oneRow AS O1
	JOIN weights1 AS W1 ON W1.weight1InputNodeNumber = I.inputNode
	CROSS JOIN oneRow AS I2
	CROSS JOIN oneRow AS O2
	JOIN weights2 AS W2 ON W2.weight2InputNodeNumber = W1.weight1OutputNodeNumber
	CROSS JOIN oneRow AS I3
	CROSS JOIN oneRow AS O3
	CROSS JOIN currentPhase AS P

	UNION ALL
	
    SELECT
		inputNode,
		inputValue,

		CASE
			WHEN phase = 0 THEN inputValue
			ELSE inputLayerOutput
		END AS inputLayerOutput,

		weight1InputNodeNumber,
		weight1OutputNodeNumber,
		weight1Value,
		weight1Bias,

		CASE
			WHEN phase = 1 THEN SUM(weight1Value * inputLayerOutput + weight1Bias) OVER (PARTITION BY weight1OutputNodeNumber, phase) / 3
			ELSE hiddenLayerInput
		END AS hiddenLayerInput,

		CASE
			WHEN phase = 2 THEN CASE WHEN hiddenLayerInput > 0 THEN hiddenLayerInput ELSE 0 END
			ELSE hiddenLayerOutput
		END AS hiddenLayerOutput,

		weight2InputNodeNumber,
		weight2OutputNodeNumber,
		weight2Value,
		weight2Bias,

		CASE
			WHEN phase = 3 THEN SUM(weight2Value * hiddenLayerOutput + weight2Bias) OVER (PARTITION BY weight2OutputNodeNumber, phase) / 3
			ELSE outputLayerInput
		END AS outputLayerInput,

		CASE
			WHEN phase = 4 THEN outputLayerInput
			ELSE outputLayerOutput
		END AS outputLayerOutput,

		phase + 1 AS phase

	FROM solution
	WHERE phase <= 4
)
SELECT DISTINCT weight2OutputNodeNumber, outputLayerOutput
FROM solution WHERE phase = 5

This is actually very easy. We divide the process into multiple phases. Each row of CTE represents one complete path from some input node to some output node. Initially row carries some metadata and input value, in each phase we fill some next value using different case expressions.

In phase 0 we get the input and transform it into output, since input layer has no logic, we just copy the value.
In phase 1 we calculate inputs for next layer by multiplying weights and values.
In phase 2 we activate hidden layer. Since we use ReLU, we perform a very simple comparison.
In phase 3 we once again use weights and values to calculate input for next layer, this time we use different weights.
In phase 4 we activate output layer, which just copies values (since we use a linear activation function).

So in our query we start by defining a schema. We simply join all tables and cross join dummy table with one row which we use to define additional column. We fill these columns later throughout the process.

In recursive part of CTE we simply either rewrite values or do some logic depending on the phase number.

You can see results here.

Next time we will see how to backpropagate errors.

]]> https://blog.adamfurmanek.pl/2019/07/20/machine-learning-part-7/feed/ 0 Windowing functions in recursive CTE https://blog.adamfurmanek.pl/2019/07/13/windowing-functions-in-recursive-cte/ https://blog.adamfurmanek.pl/2019/07/13/windowing-functions-in-recursive-cte/#respond Sat, 13 Jul 2019 08:00:24 +0000 https://blog.adamfurmanek.pl/?p=2994 Continue reading Windowing functions in recursive CTE]]> Today we will see an interesting case of incompatibility between MS SQL Server 2017 and PostgreSQL 9.6 (and different versions as well). Let’s start with this code:

WITH dummy AS(
    SELECT 1 AS rowValue, 0 AS phase
    UNION ALL
    SELECT 2 AS rowValue, 0 AS phase
),
solution AS (
    SELECT * FROM dummy
),
solution2 AS(
    SELECT
        SUM(rowValue) OVER (PARTITION BY phase) AS rowValue,
        phase + 1 AS phase
    FROM solution
    WHERE phase = 0
)
SELECT *
FROM solution2
WHERE phase = 1

We emulate a recursive CTE. We have two columns in source dataset, we want to sum first column for rows partitioned by second column. This gives a very expected result:

rowValue    phase
----------- -----------
3           1
3           1

Now let’s use recursive CTE in MS SQL:

WITH dummy AS(
    SELECT 1 AS rowValue, 0 AS phase
    UNION ALL
    SELECT 2 AS rowValue, 0 AS phase
),
solution AS (
    SELECT * FROM dummy
    UNION ALL
        SELECT
        SUM(rowValue) OVER (PARTITION BY phase) AS rowValue,
        phase + 1 AS phase
    FROM solution
    WHERE phase = 0
)
SELECT * FROM solution WHERE phase = 1;

And result is:

rowValue    phase
----------- -----------
2           1
1           1

However, PostgreSQL gives correct values:

rowValue    phase
----------- -----------
3           1
3           1

Beware! Also, see this great post explaining row-based approach and set-based approach for implementing CTE.

]]> https://blog.adamfurmanek.pl/2019/07/13/windowing-functions-in-recursive-cte/feed/ 0 Machine Learning Part 3 — Linear regression in SQL revisited https://blog.adamfurmanek.pl/2018/11/03/machine-learning-part-3/ https://blog.adamfurmanek.pl/2018/11/03/machine-learning-part-3/#comments Sat, 03 Nov 2018 09:00:42 +0000 https://blog.adamfurmanek.pl/?p=2637 Continue reading Machine Learning Part 3 — Linear regression in SQL revisited]]>

This is the third part of the ML series. For your convenience you can find other parts in the table of contents in Part 1 – Linear regression in MXNet

Last time we saw how to calculate linear regression for the Iris dataset. However, we had to hardcode all the featuers. Today we are going to make our query much more flexible. Let’s begin.

We start with the same schema as before. Now, the query, this time for PostgreSQL 10:

WITH RECURSIVE constants AS (
	SELECT 1 AS column_1
	UNION
	SELECT 2 AS column_1
	UNION
	SELECT 3 AS column_1
	UNION
	SELECT 4 AS column_1
	UNION
	SELECT 5 AS column_1
),
extended AS (
	SELECT
		S.*, 
		CASE WHEN S.iris = 'setosa' THEN 1.0 ELSE 0.0 END AS is_setosa, 
		CASE WHEN S.iris = 'virginica' THEN 1.0 ELSE 0.0 END AS is_virginica
	FROM samples AS S order by random() 
),
training AS (
  SELECT * FROM extended LIMIT 100
),
test AS (
  SELECT * FROM extended EXCEPT SELECT * FROM training
),
numbered AS(
    SELECT 
		*, 
		ROW_NUMBER() OVER (ORDER BY (SELECT NULL)) AS row_number 
	FROM training
),
pivoted_training AS (
	SELECT
		N.row_number AS sample, C.column_1 AS feature,
		CAST(CASE
			WHEN C.column_1 = 1 THEN N.sepal_width
			WHEN C.column_1 = 2 THEN N.petal_length
			WHEN C.column_1 = 3 THEN N.petal_width
			WHEN C.column_1 = 4 THEN N.is_setosa
			ELSE N.is_virginica
		END AS float) AS value,
		N.sepal_length AS y
	FROM numbered AS N, constants AS C
),
 learning AS (
  SELECT 
		C.column_1 AS feature,
		CAST(0.0 AS float) as w,
		CAST(0.0 AS float) as b,
		CAST(0.0 AS float) as gw,
		CAST(0.0 AS float) as gb,
		1 as iteration,
		CAST(0.0 AS float) as mse,
		CAST(0.0 AS float) as distance,
		1 as dummy
  FROM constants AS C
	  
  UNION ALL
  
  SELECT R.feature, R.w, R.b, R.gw, R.gb, R.iteration, R.mse, R.distance, R.dummy
  FROM (
	  SELECT
		  CAST(Z.w AS float) AS w,
		  CAST(Z.b AS float) AS b,
		  CAST(AVG(Z.gw) OVER(PARTITION BY Z.feature) AS float) AS gw,
		  CAST(AVG(Z.gb) OVER(PARTITION BY Z.feature) AS float) AS gb, 
		  Z.iteration + 1 AS iteration,
		  Z.feature,
		  CAST(AVG(Z.squared_distance) OVER(PARTITION BY Z.dummy) AS float) AS mse,
		  Z.sample AS sample,
		  CAST(Z.distance AS FLOAT) AS distance,
		  Z.dummy
	  FROM (
		SELECT
		  X.*, 
		  X.distance * x.distance AS squared_distance,
		  X.distance * X.value AS gw,
		  X.distance AS gb
		FROM (
			SELECT 
				K.*,
				SUM(K.value * K.w + K.b) OVER(PARTITION BY K.sample) - K.y AS distance
			FROM (
			  SELECT
				T.*,
				L.w,
				L.b,
				L.iteration,
				L.dummy
			  FROM pivoted_training AS T INNER JOIN (
				SELECT
				  L.w - 0.01 * L.gw AS w,
				  L.b - 0.01 * L.gb AS b,
				  L.feature,
				  L.iteration,
				  MAX(L.iteration) OVER(PARTITION BY L.dummy) AS max_iteration,
				  L.dummy
				FROM learning AS L
			  ) AS L ON T.feature = L.feature AND L.iteration = max_iteration 
			  WHERE 
				L.iteration < 100
			) AS K
		) AS X
	  ) AS Z
  ) AS R
  WHERE R.sample = 1
)
SELECT * FROM learning

Uuu, terrible. Let’s go step by step.

First, constants is just a table with some numbers. We have 5 features so we have 5 rows there. This could be done much easier with recursive CTE or any other dynamic solution.

Next, extended: we just add two more features and randomize the rows.

training, test, and numbered are just tables for bookkeeping the samples.

pivoted_training: here comes some magic. We don’t want to have rows with all the features inside, we want to have one row for each sample’s feature. So we do the translation and emit rows with sample number, feature id, feature value, and target variable.

Next comes our recursive CTE for training. We start with some rows representing coefficients for each feature. We initialize w and b, as well as iteration and distances. We have dummy column again.

Next, we do the calculation. Let’s go from the middle.

We do the training in similar way as before. Assuming we have 100 samples, each has 5 features, the inner join target has 5\cdot i rows where i stands for iterations. We join this with samples (100 \cdot 5 rows) based on the feature id and maximum iteration. So finally, we should have 100 \cdot 5 rows per each iteration.

Next, we calculate the distance for each sample (this is the PARTITION BY K.sample part).

Next, we square the distance and calculate gradient coefficients for each sample.

Finally, we cast variables and calculate the final gradients by taking averages over features. We also calculate mse and we are almost done.

The only tricky part is how to get exactly 5 rows representing new coefficients. This is done by WHERE R.sample = 1 as for each sample we have exactly the same results so we can just take any of them.

Finally, we get our training results with SELECT * FROM learning. You can see it here:

feature	w	b	gw	gb	iteration	mse	distance	dummy
3	0	0	0	0	1	0	0	1
2	0	0	0	0	1	0	0	1
1	0	0	0	0	1	0	0	1
5	0	0	0	0	1	0	0	1
4	0	0	0	0	1	0	0	1
1	0	0	-16.52	-5	2	25.01	-5.1	1
2	0	0	-7.245	-5	2	25.01	-5.1	1
3	0	0	-0.755	-5	2	25.01	-5.1	1
4	0	0	-5	-5	2	25.01	-5.1	1
5	0	0	0	-5	2	25.01	-5.1	1
1	0.1652	0.05	-13.3746025	-4.048655	3	16.39653605105	-4.11886	1
2	0.07245	0.05	-5.8670395	-4.048655	3	16.39653605105	-4.11886	1
3	0.00755	0.05	-0.6108085	-4.048655	3	16.39653605105	-4.11886	1
4	0.05	0.05	-4.048655	-4.048655	3	16.39653605105	-4.11886	1
5	0	0.05	0	-4.048655	3	16.39653605105	-4.11886	1
1	0.298946025	0.09048655	-10.8278890377	-3.278385532	4	10.7499354232339	-3.3244694425	1
2	0.131120395	0.09048655	-4.751354825875	-3.278385532	4	10.7499354232339	-3.3244694425	1
3	0.013658085	0.09048655	-0.494062025325	-3.278385532	4	10.7499354232339	-3.3244694425	1
4	0.09048655	0.09048655	-3.278385532	-3.278385532	4	10.7499354232339	-3.3244694425	1
5	0	0.09048655	0	-3.278385532	4	10.7499354232339	-3.3244694425	1
1	0.407224915377	0.12327040532	-8.76590822437997	-2.65472632382273	5	7.04827711689888	-2.6812831026476	1
2	0.17863394325875	0.12327040532	-3.84802533060171	-2.65472632382273	5	7.04827711689888	-2.6812831026476	1
3	0.01859870525325	0.12327040532	-0.399536787514652	-2.65472632382273	5	7.04827711689888	-2.6812831026476	1
4	0.12327040532	0.12327040532	-2.65472632382273	-2.65472632382273	5	7.04827711689888	-2.6812831026476	1
5	0	0.12327040532	0	-2.65472632382273	5	7.04827711689888	-2.6812831026476	1
1	0.4948839976208	0.149817668558227	-7.09639777302516	-2.14977210051383	6	4.62163562959118	-2.16052130716148	1
2	0.217114196564767	0.149817668558227	-3.11663208541266	-2.14977210051383	6	4.62163562959118	-2.16052130716148	1
3	0.0225940731283965	0.149817668558227	-0.323003275409457	-2.14977210051383	6	4.62163562959118	-2.16052130716148	1
4	0.149817668558227	0.149817668558227	-2.14977210051383	-2.14977210051383	6	4.62163562959118	-2.16052130716148	1
5	0	0.149817668558227	0	-2.14977210051383	6	4.62163562959118	-2.16052130716148	1
1	0.565847975351051	0.171315389563366	-5.7446562719125	-1.74092897782157	7	3.03083789510468	-1.73888220332818	1
2	0.248280517418894	0.171315389563366	-2.52444935656594	-1.74092897782157	7	3.03083789510468	-1.73888220332818	1
3	0.0258241058824911	0.171315389563366	-0.261037007948566	-1.74092897782157	7	3.03083789510468	-1.73888220332818	1
4	0.171315389563366	0.171315389563366	-1.74092897782157	-1.74092897782157	7	3.03083789510468	-1.73888220332818	1
5	0	0.171315389563366	0	-1.74092897782157	7	3.03083789510468	-1.73888220332818	1
1	0.623294538070176	0.188724679341581	-4.65020071011763	-1.40990351099703	8	1.98798177898635	-1.39749913013413	1
2	0.273525010984553	0.188724679341581	-2.04498030998884	-1.40990351099703	8	1.98798177898635	-1.39749913013413	1
3	0.0284344759619768	0.188724679341581	-0.21086530760641	-1.40990351099703	8	1.98798177898635	-1.39749913013413	1
4	0.188724679341581	0.188724679341581	-1.40990351099703	-1.40990351099703	8	1.98798177898635	-1.39749913013413	1
5	0	0.188724679341581	0	-1.40990351099703	8	1.98798177898635	-1.39749913013413	1
1	0.669796545171352	0.202823714451552	-3.76406019771898	-1.14188416444708	9	1.30433157451662	-1.12109643966513	1
2	0.293974814084442	0.202823714451552	-1.65677142468737	-1.14188416444708	9	1.30433157451662	-1.12109643966513	1
3	0.0305431290380408	0.202823714451552	-0.170243238427965	-1.14188416444708	9	1.30433157451662	-1.12109643966513	1
4	0.202823714451552	0.202823714451552	-1.14188416444708	-1.14188416444708	9	1.30433157451662	-1.12109643966513	1
5	0	0.202823714451552	0	-1.14188416444708	9	1.30433157451662	-1.12109643966513	1
1	0.707437147148542	0.214242556096022	-3.04658478966489	-0.924878577539922	10	0.856160630419917	-0.897305996455662	1
2	0.310542528331315	0.214242556096022	-1.3424525664871	-0.924878577539922	10	0.856160630419917	-0.897305996455662	1
3	0.0322455614223205	0.214242556096022	-0.137353157576775	-0.924878577539922	10	0.856160630419917	-0.897305996455662	1
4	0.214242556096022	0.214242556096022	-0.924878577539922	-0.924878577539922	10	0.856160630419917	-0.897305996455662	1
5	0	0.214242556096022	0	-0.924878577539922	10	0.856160630419917	-0.897305996455662	1
1	0.737902995045191	0.223491341871422	-2.46567137030609	-0.749176972878157	11	0.562359311948542	-0.716113771919023	1
2	0.323967053996186	0.223491341871422	-1.08795977072128	-0.749176972878157	11	0.562359311948542	-0.716113771919023	1
3	0.0336190929980882	0.223491341871422	-0.110723385883767	-0.749176972878157	11	0.562359311948542	-0.716113771919023	1
4	0.223491341871422	0.223491341871422	-0.749176972878157	-0.749176972878157	11	0.562359311948542	-0.716113771919023	1
5	0	0.223491341871422	0	-0.749176972878157	11	0.562359311948542	-0.716113771919023	1
1	0.762559708748252	0.230983111600203	-1.99532721675111	-0.606917697531082	12	0.369755786024592	-0.569411772023755	1
2	0.334846651703399	0.230983111600203	-0.881905957695436	-0.606917697531082	12	0.369755786024592	-0.569411772023755	1
3	0.0347263268569259	0.230983111600203	-0.089162358354296	-0.606917697531082	12	0.369755786024592	-0.569411772023755	1
4	0.230983111600203	0.230983111600203	-0.606917697531082	-0.606917697531082	12	0.369755786024592	-0.569411772023755	1
5	0	0.230983111600203	0	-0.606917697531082	12	0.369755786024592	-0.569411772023755	1
1	0.782512980915763	0.237052288575514	-1.61450696845941	-0.491735457602315	13	0.243492987372605	-0.450635249461157	1
2	0.343665711280353	0.237052288575514	-0.715071423930415	-0.491735457602315	13	0.243492987372605	-0.450635249461157	1
3	0.0356179504404689	0.237052288575514	-0.0717053082332894	-0.491735457602315	13	0.243492987372605	-0.450635249461157	1
4	0.237052288575514	0.237052288575514	-0.491735457602315	-0.491735457602315	13	0.243492987372605	-0.450635249461157	1
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4	0.264125600603971	0.264125600603971	-0.00173389777249344	-0.00173389777249344	89	0.00306479045172715	0.0535994922397016	1
5	0	0.264125600603971	0	-0.00173389777249344	89	0.00306479045172715	0.0535994922397016	1
1	0.863466178963271	0.264142939581695	0.00534343975631799	-0.00173343078162702	90	0.00306317515460085	0.0535853758968088	1
2	0.385058642807539	0.264142939581695	-0.00527941496728097	-0.00173343078162702	90	0.00306317515460085	0.0535853758968088	1
3	0.0375700605231734	0.264142939581695	0.00250592571667774	-0.00173343078162702	90	0.00306317515460085	0.0535853758968088	1
4	0.264142939581695	0.264142939581695	-0.00173343078162702	-0.00173343078162702	90	0.00306317515460085	0.0535853758968088	1
5	0	0.264142939581695	0	-0.00173343078162702	90	0.00306317515460085	0.0535853758968088	1
1	0.863412744565707	0.264160273889512	0.00534205822553266	-0.00173296581823745	91	0.00306156070881689	0.0535712613103438	1
2	0.385111436957212	0.264160273889512	-0.00527801179287338	-0.00173296581823745	91	0.00306156070881689	0.0535712613103438	1
3	0.0375450012660066	0.264160273889512	0.00250526648369345	-0.00173296581823745	91	0.00306156070881689	0.0535712613103438	1
4	0.264160273889512	0.264160273889512	-0.00173296581823745	-0.00173296581823745	91	0.00306156070881689	0.0535712613103438	1
5	0	0.264160273889512	0	-0.00173296581823745	91	0.00306156070881689	0.0535712613103438	1
1	0.863359323983452	0.264177603547694	0.00534067196086156	-0.00173250251931423	92	0.00305994711392649	0.0535571488536783	1
2	0.385164217075141	0.264177603547694	-0.00527661122165526	-0.00173250251931423	92	0.00305994711392649	0.0535571488536783	1
3	0.0375199486011697	0.264177603547694	0.0025046071907525	-0.00173250251931423	92	0.00305994711392649	0.0535571488536783	1
4	0.264177603547694	0.264177603547694	-0.00173250251931423	-0.00173250251931423	92	0.00305994711392649	0.0535571488536783	1
5	0	0.264177603547694	0	-0.00173250251931423	92	0.00305994711392649	0.0535571488536783	1
1	0.863305917263843	0.264194928572887	0.00533928193388257	-0.00173204059093646	93	0.00305833436948097	0.053543038828928	1
2	0.385216983187357	0.264194928572887	-0.00527521282785109	-0.00173204059093646	93	0.00305833436948097	0.053543038828928	1
3	0.0374949025292622	0.264194928572887	0.00250394788235275	-0.00173204059093646	93	0.00305833436948097	0.053543038828928	1
4	0.264194928572887	0.264194928572887	-0.00173204059093646	-0.00173204059093646	93	0.00305833436948097	0.053543038828928	1
5	0	0.264194928572887	0	-0.00173204059093646	93	0.00305833436948097	0.053543038828928	1
1	0.863252524444505	0.264212248978797	0.00533788893123721	-0.00173157979511851	94	0.00305672247503216	0.053528931480523	1
2	0.385269735315636	0.264212248978797	-0.00527381626670392	-0.00173157979511851	94	0.00305672247503216	0.053528931480523	1
3	0.0374698630504386	0.264212248978797	0.0025032885945143	-0.00173157979511851	94	0.00305672247503216	0.053528931480523	1
4	0.264212248978797	0.264212248978797	-0.00173157979511851	-0.00173157979511851	94	0.00305672247503216	0.053528931480523	1
5	0	0.264212248978797	0	-0.00173157979511851	94	0.00305672247503216	0.053528931480523	1
1	0.863199145555192	0.264229564776748	0.00533649358982165	-0.00173111993916608	95	0.00305511143013205	0.0535148270061825	1
2	0.385322473478303	0.264229564776748	-0.00527242125905825	-0.00173111993916608	95	0.00305511143013205	0.0535148270061825	1
3	0.0374448301644935	0.264229564776748	0.00250262935639252	-0.00173111993916608	95	0.00305511143013205	0.0535148270061825	1
4	0.264229564776748	0.264229564776748	-0.00173111993916608	-0.00173111993916608	95	0.00305511143013205	0.0535148270061825	1
5	0	0.264229564776748	0	-0.00173111993916608	95	0.00305511143013205	0.0535148270061825	1
1	0.863145780619294	0.264246875976139	0.00533509642527563	-0.00173066086705953	96	0.00305350123433273	0.0535007255658009	1
2	0.385375197690893	0.264246875976139	-0.00527102757887934	-0.00173066086705953	96	0.00305350123433273	0.0535007255658009	1
3	0.0374198038709296	0.264246875976139	0.00250197019158409	-0.00173066086705953	96	0.00305350123433273	0.0535007255658009	1
4	0.264246875976139	0.264246875976139	-0.00173066086705953	-0.00173066086705953	96	0.00305350123433273	0.0535007255658009	1
5	0	0.264246875976139	0	-0.00173066086705953	96	0.00305350123433273	0.0535007255658009	1
1	0.863092429655041	0.26426418258481	0.00533369785509552	-0.00173020245246347	97	0.00305189188718688	0.0534866272886614	1
2	0.385427907966682	0.26426418258481	-0.00526963504312827	-0.00173020245246347	97	0.00305189188718688	0.0534866272886614	1
3	0.0373947841690137	0.26426418258481	0.00250131111918672	-0.00173020245246347	97	0.00305189188718688	0.0534866272886614	1
4	0.26426418258481	0.26426418258481	-0.00173020245246347	-0.00173020245246347	97	0.00305189188718688	0.0534866272886614	1
5	0	0.26426418258481	0	-0.00173020245246347	97	0.00305189188718688	0.0534866272886614	1
1	0.86303909267649	0.264281484609335	0.00533229821728032	-0.00172974459308683	98	0.00305028338824717	0.0534725322792475	1
2	0.385480604317113	0.264281484609335	-0.00526824350359263	-0.00172974459308683	98	0.00305028338824717	0.0534725322792475	1
3	0.0373697710578219	0.264281484609335	0.00250065215465369	-0.00172974459308683	98	0.00305028338824717	0.0534725322792475	1
4	0.264281484609335	0.264281484609335	-0.00172974459308683	-0.00172974459308683	98	0.00305028338824717	0.0534725322792475	1
5	0	0.264281484609335	0	-0.00172974459308683	98	0.00305028338824717	0.0534725322792475	1
1	0.862985769694318	0.264298782055265	0.00533089778548161	-0.00172928720610077	99	0.0030486757370664	0.05345844062197	1
2	0.385533286752149	0.264298782055265	-0.00526685284024966	-0.00172928720610077	99	0.0030486757370664	0.05345844062197	1
3	0.0373447645362753	0.264298782055265	0.00249999331048842	-0.00172928720610077	99	0.0030486757370664	0.05345844062197	1
4	0.264298782055265	0.264298782055265	-0.00172928720610077	-0.00172928720610077	99	0.0030486757370664	0.05345844062197	1
5	0	0.264298782055265	0	-0.00172928720610077	99	0.0030486757370664	0.05345844062197	1
1	0.862932460716463	0.264316074927326	0.00532949678123926	-0.00172883022443804	100	0.00304706893319777	0.0534443523849859	1
2	0.385585955280552	0.264316074927326	-0.00526546295590635	-0.00172883022443804	100	0.00304706893319777	0.0534443523849859	1
3	0.0373197646031704	0.264316074927326	0.00249933459680549	-0.00172883022443804	100	0.00304706893319777	0.0534443523849859	1
4	0.264316074927326	0.264316074927326	-0.00172883022443804	-0.00172883022443804	100	0.00304706893319777	0.0534443523849859	1
5	0	0.264316074927326	0	-0.00172883022443804	100	0.00304706893319777	0.0534443523849859	1

Now you can evaluate the model.

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