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Initial model
# Proposed Initial Model xgb1 = xgb.XGBClassifier( learning_rate =0.1, n_estimators=200, max_depth=5, min_child_weight=1, gamma=0, subsample=0.6, colsample_bytree=0.6, reg_alpha=0, reg_lambda=1, objective='multi:softmax', nthread=4, scale_pos...
HouMath/Face_classification_HouMath_XGB_01.ipynb
esa-as/2016-ml-contest
apache-2.0
The typical range for learning rate is around 0.01~0.2, so we vary ther learning rate a bit and at the same time, scan over the number of boosted trees to fit. This will take a little bit of time to finish.
print("Parameter optimization") grid_search1 = GridSearchCV(xgb1,{'learning_rate':[0.05,0.01,0.1,0.2] , 'n_estimators':[200,400,600,800]}, scoring='accuracy' , n_jobs = 4) grid_search1.fit(X_train,Y_train) print("Best Set of Parameters") grid_search1.grid_scores_, grid_search1.best_pa...
HouMath/Face_classification_HouMath_XGB_01.ipynb
esa-as/2016-ml-contest
apache-2.0
It seems that we need to adjust the learning rate and make it smaller, which could help to reduce overfitting in my opinion. The number of boosted trees to fit also requires to be updated.
# Proposed Model with optimized learning rate and number of boosted trees to fit xgb2 = xgb.XGBClassifier( learning_rate =0.01, n_estimators=400, max_depth=5, min_child_weight=1, gamma=0, subsample=0.6, colsample_bytree=0.6, reg_alpha=0, reg_lambda=1, objective='multi...
HouMath/Face_classification_HouMath_XGB_01.ipynb
esa-as/2016-ml-contest
apache-2.0
Try it out
U = 4 * 10** -np.arange(11.) # generates values 4, 4e-1, 4e-2 .. 4e-10 print("{:>10s} {:>10s} {:>10s}".format('u ', 'W(u)','W1(u) ')) for u in U: print("{0:10.1e} {1:10.4e} {2:10.4e}".format(u, W(u), W1(u)))
exercises_notebooks/TheisWellFunction.ipynb
Olsthoorn/TransientGroundwaterFlow
gpl-3.0
Is seems that our numerical integration is a fair approximation to four significant digits, but not better, even when computed with 1000 steps as we did. So it is relatively easy to create one's own numerically computed value of an analytical expression like the exponential integral Theis well function as a power serie...
def W2(u): """Returns Theis well function computed as a power series""" tol = 1e-5 w = -0.5772 -np.log(u) + u a = u for n in range(1, 100): a = -a * u * n / (n+1)**2 # new term (next term) w += a if np.all(a) < tol: return w
exercises_notebooks/TheisWellFunction.ipynb
Olsthoorn/TransientGroundwaterFlow
gpl-3.0
Compare the three methods of computing the well function.
U = 4.0 * 10** -np.arange(11.) # generates values 4, 4e-1, 4e-2 .. 4e-10 print("{:>10s} {:>10s} {:>10s} {:>10s}".format('u ', 'W(u) ','W1(u) ', 'W2(u) ')) for u in U: print("{0:10.1e} {1:10.4e} {2:10.4e} {2:10.4e}".format(u, W(u), W1(u), W2(u)))
exercises_notebooks/TheisWellFunction.ipynb
Olsthoorn/TransientGroundwaterFlow
gpl-3.0
We see that all three methods yiedld the same results. Next we show the well function as it shown in groundwater hydrology books.
u = np.logspace(-7, 1, 71) import matplotlib.pylab as plt fig1= plt.figure() ax1 = fig1.add_subplot(111) ax1.set(xlabel='1/u', ylabel='W(u)', title='Theis type curve versus u', yscale='log', xscale='log') ax1.grid(True) ax1.plot(u, W(u), 'b', label='-expi(-u)') #ax1.plot(u, W1(u), 'rx', label='integal') # works only f...
exercises_notebooks/TheisWellFunction.ipynb
Olsthoorn/TransientGroundwaterFlow
gpl-3.0
The curve W(u) versus u runs counter intuitively which and is, therefore, confusing. Therefore, it generally presented as W(u) versus 1/u instead as shown below
fig2 = plt.figure() ax2 = fig2.add_subplot(111) ax2.set(xlabel='1/u', ylabel='W(u)', title='Theis type curve versus 1/u', yscale='log', xscale='log') ax2.grid(True) ax2.plot(1/u, W(u)) plt.show()
exercises_notebooks/TheisWellFunction.ipynb
Olsthoorn/TransientGroundwaterFlow
gpl-3.0
Now W(u) resembles the actual drawdown, which increases with time. The reason that this is so, becomes clear from the fact that $$ u = \frac {r^2 S} {4 kD t} $$ and that $$ \frac 1 u = \frac {4 kDt} {r^2 S} = \frac {4 kD} S \frac t {r^2} $$ which shows that $\frac 1 u$ increases with time, so that the values of $\frac ...
fig2 = plt.figure() ax2 = fig2.add_subplot(111) ax2.set(xlabel='1/u', ylabel='W(u)', title='Theis type curve versus 1/u', yscale='linear', xscale='log') ax2.grid(True) ax2.plot(1/u, W(u)) ax2.invert_yaxis() plt.show()
exercises_notebooks/TheisWellFunction.ipynb
Olsthoorn/TransientGroundwaterFlow
gpl-3.0
Logarithmic approximaion of the Theis type curve We see that after some time, the drawdown is linear when only the time-axis is logarithmic. This suggests that a logarithmic approximation of time-drawdown curve is accurate after some time. That this is indeed the case can be deduced from the power series description of...
U = np.logspace(-2, 0, 21) Wa = lambda u : -0.5772 - np.log(u) print("{:>12s} {:>12s} {:>12s} {:>12s}".format('u','W(u)','Wa(u)','1-Wa(u)/W(u)')) print("{:>12s} {:>12s} {:>12s} {:>12s}".format(' ',' ',' ','the error')) for u in U: print("{:12.3g} {:12.3g} {:12.3g} {:12.1%}".format(u, W(u), Wa(...
exercises_notebooks/TheisWellFunction.ipynb
Olsthoorn/TransientGroundwaterFlow
gpl-3.0
Hence, in any practical situation, the logarithmic approximation is accurate enough when $u<0.01$. The approximatin of the Theis type curve can no be elaborated: $$ Wa (u) \approx -0.5772 - \ln(u) = \ln(e^{-0.5772}) - \ln(u) = \ln(0.5615) - \ln(u) = \ln \frac {0.5615} {u} $$ Because $u = \frac {r^2 S} {4 kD t}$ we have...
U = np.logspace(-7, 1, 81) fig = plt.figure() ax = fig.add_subplot(111) ax.set(xlabel='u', ylabel='W(u)', title='Theis type curve and its logarithmic approximation', yscale='linear', xscale='log') ax.grid(True) ax.plot(U, W(U), 'b', linewidth = 2., label='Theis type curve') ax.plot(U, Wa(U), 'r', linewidth = 0.25, lab...
exercises_notebooks/TheisWellFunction.ipynb
Olsthoorn/TransientGroundwaterFlow
gpl-3.0
This shows that the radius of influence is limited. We can now approximate this radius of influence by saying that the radius is where the appoximated Theis curve, that is the straight red line in the graph intersects the zero drawdown, i.e. $W(u) = 0$. Hence, for the radius of influence, R, we have $$ \ln \frac {2.25 ...
# t[min], s[m] H30 = [ [0.0, 0.0], [0.1, 0.04], [0.25, 0.08], [0.50, 0.13], [0.70, 0.18], [1.00, 0.23], [1.40, 0.28], [1.90, 0.33], [2.33, 0.36], [2.80, 0.39], [3.36, 0.42], [4.00, 0.45], [5.35, 0.50], [6.80, ...
exercises_notebooks/TheisWellFunction.ipynb
Olsthoorn/TransientGroundwaterFlow
gpl-3.0
Configure GCP environment settings Update the following variables to reflect the values for your GCP environment: PROJECT_ID: The ID of the Google Cloud project you are using to implement this solution. PROJECT_NUMBER: The number of the Google Cloud project you are using to implement this solution. You can find this i...
PROJECT_ID = 'yourProject' # Change to your project. PROJECT_NUMBER = 'yourProjectNumber' # Change to your project number BUCKET = 'yourBucketName' # Change to the bucket you created. REGION = 'yourPredictionRegion' # Change to your AI Platform Prediction region. ARTIFACTS_REPOSITORY_NAME = 'ml-serving' EMBEDDNIG_LOOK...
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
Authenticate your GCP account This is required if you run the notebook in Colab. If you use an AI Platform notebook, you should already be authenticated.
try: from google.colab import auth auth.authenticate_user() print("Colab user is authenticated.") except: pass
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
Deploy the embedding lookup model to AI Platform Prediction Create the embedding lookup model resource in AI Platform:
!gcloud ai-platform models create {EMBEDDNIG_LOOKUP_MODEL_NAME} --region={REGION}
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
Next, deploy the model:
!gcloud ai-platform versions create {EMBEDDNIG_LOOKUP_MODEL_VERSION} \ --region={REGION} \ --model={EMBEDDNIG_LOOKUP_MODEL_NAME} \ --origin={EMBEDDNIG_LOOKUP_MODEL_OUTPUT_DIR} \ --runtime-version=2.2 \ --framework=TensorFlow \ --python-version=3.7 \ --machine-type=n1-standard-2 print("The model version i...
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
Once the model is deployed, you can verify it in the AI Platform console. Test the deployed embedding lookup AI Platform Prediction model Set the AI Platform Prediction API information:
import googleapiclient.discovery from google.api_core.client_options import ClientOptions api_endpoint = f'https://{REGION}-ml.googleapis.com' client_options = ClientOptions(api_endpoint=api_endpoint) service = googleapiclient.discovery.build( serviceName='ml', version='v1', client_options=client_options)
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
Run the caip_embedding_lookup method to retrieve item embeddings. This method accepts item IDs, calls the embedding lookup model in AI Platform Prediction, and returns the appropriate embedding vectors.
def caip_embedding_lookup(input_items): request_body = {'instances': input_items} service_name = f'projects/{PROJECT_ID}/models/{EMBEDDNIG_LOOKUP_MODEL_NAME}/versions/{EMBEDDNIG_LOOKUP_MODEL_VERSION}' print(f'Calling : {service_name}') response = service.projects().predict( name=service_name, body=request_b...
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
Test the caip_embedding_lookup method with three item IDs:
input_items = ['2114406', '2114402 2120788', 'abc123'] embeddings = caip_embedding_lookup(input_items) print(f'Embeddings retrieved: {len(embeddings)}') for idx, embedding in enumerate(embeddings): print(f'{input_items[idx]}: {embedding[:5]}')
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
ScaNN matching service The ScaNN matching service performs the following steps: Receives one or more item IDs from the client. Calls the embedding lookup model to fetch the embedding vectors of those item IDs. Uses these embedding vectors to query the ANN index to find approximate nearest neighbor embedding vectors. M...
!gcloud beta artifacts repositories create {ARTIFACTS_REPOSITORY_NAME} \ --location={REGION} \ --repository-format=docker !gcloud beta auth configure-docker {REGION}-docker.pkg.dev --quiet
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
Use Cloud Build to build the Docker container image The container runs the gunicorn HTTP web server and executes the Flask app variable defined in the main.py module. The container image to deploy to AI Platform Prediction is defined in a Dockerfile, as shown in the following code snippet: ``` FROM python:3.8-slim COPY...
IMAGE_URL = f'{REGION}-docker.pkg.dev/{PROJECT_ID}/{ARTIFACTS_REPOSITORY_NAME}/{SCANN_MODEL_NAME}:{SCANN_MODEL_VERSION}' PORT=5001 SUBSTITUTIONS = '' SUBSTITUTIONS += f'_IMAGE_URL={IMAGE_URL},' SUBSTITUTIONS += f'_PORT={PORT}' !gcloud builds submit --config=index_server/cloudbuild.yaml \ --substitutions={SUBSTITUTI...
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
Run the following command to verify the container image has been built:
repository_id = f'{REGION}-docker.pkg.dev/{PROJECT_ID}/{ARTIFACTS_REPOSITORY_NAME}' !gcloud beta artifacts docker images list {repository_id}
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
Create a service account for AI Platform Prediction Create a service account to run the custom container. This is required in cases where you want to grant specific permissions to the service account.
SERVICE_ACCOUNT_NAME = 'caip-serving' SERVICE_ACCOUNT_EMAIL = f'{SERVICE_ACCOUNT_NAME}@{PROJECT_ID}.iam.gserviceaccount.com' !gcloud iam service-accounts create {SERVICE_ACCOUNT_NAME} \ --description="Service account for AI Platform Prediction to access cloud resources."
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
Grant the Cloud ML Engine (AI Platform) service account the iam.serviceAccountAdmin privilege, and grant the caip-serving service account the privileges required by the ScaNN matching service, which are storage.objectViewer and ml.developer.
!gcloud projects describe {PROJECT_ID} --format="value(projectNumber)" !gcloud projects add-iam-policy-binding {PROJECT_ID} \ --role=roles/iam.serviceAccountAdmin \ --member=serviceAccount:service-{PROJECT_NUMBER}@cloud-ml.google.com.iam.gserviceaccount.com !gcloud projects add-iam-policy-binding {PROJECT_ID} \ ...
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
Deploy the custom container to AI Platform Prediction Create the ANN index model resource in AI Platform:
!gcloud ai-platform models create {SCANN_MODEL_NAME} --region={REGION}
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
Deploy the custom container to AI Platform prediction. Note that you use the env-vars parameter to pass environmental variables to the Flask application in the container.
HEALTH_ROUTE=f'/v1/models/{SCANN_MODEL_NAME}/versions/{SCANN_MODEL_VERSION}' PREDICT_ROUTE=f'/v1/models/{SCANN_MODEL_NAME}/versions/{SCANN_MODEL_VERSION}:predict' ENV_VARIABLES = f'PROJECT_ID={PROJECT_ID},' ENV_VARIABLES += f'REGION={REGION},' ENV_VARIABLES += f'INDEX_DIR={INDEX_DIR},' ENV_VARIABLES += f'EMBEDDNIG_LOO...
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
Test the Deployed ScaNN Index Service After deploying the custom container, test it by running the caip_scann_match method. This method accepts the parameter query_items, whose value is converted into a space-separated string of item IDs and treated as a single query. That is, a single embedding vector is retrieved fro...
from google.cloud import datastore import requests client = datastore.Client(PROJECT_ID) def caip_scann_match(query_items, show=10): request_body = { 'instances': [{ 'query':' '.join(query_items), 'show':show }] } service_name = f'projects/{PROJECT_ID}/models/{SCANN_MODEL_NAM...
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
Call the caip_scann_match method with five item IDs and request five match items for each:
songs = { '2120788': 'Limp Bizkit: My Way', '1086322': 'Jacques Brel: Ne Me Quitte Pas', '833391': 'Ricky Martin: Livin\' la Vida Loca', '1579481': 'Dr. Dre: The Next Episode', '2954929': 'Black Sabbath: Iron Man' } for item_Id, desc in songs.items(): print(desc) print("==================") s...
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
(Optional) Deploy the matrix factorization model to AI Platform Prediction Optionally, you can deploy the matrix factorization model in order to perform exact item matching. The model takes Item1_Id as an input and outputs the top 50 recommended item2_Ids. Exact matching returns better results, but takes significantly ...
BQ_DATASET_NAME = 'recommendations' BQML_MODEL_NAME = 'item_matching_model' BQML_MODEL_VERSION = 'v1' BQML_MODEL_OUTPUT_DIR = f'gs://{BUCKET}/bqml/item_matching_model' !bq --quiet extract -m {BQ_DATASET_NAME}.{BQML_MODEL_NAME} {BQML_MODEL_OUTPUT_DIR} !saved_model_cli show --dir {BQML_MODEL_OUTPUT_DIR} --tag_set serv...
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
Deploy the exact matching model to AI Platform Prediction
!gcloud ai-platform models create {BQML_MODEL_NAME} --region={REGION} !gcloud ai-platform versions create {BQML_MODEL_VERSION} \ --region={REGION} \ --model={BQML_MODEL_NAME} \ --origin={BQML_MODEL_OUTPUT_DIR} \ --runtime-version=2.2 \ --framework=TensorFlow \ --python-version=3.7 \ --machine-type=n1-sta...
retail/recommendation-system/bqml-scann/05_deploy_lookup_and_scann_caip.ipynb
GoogleCloudPlatform/analytics-componentized-patterns
apache-2.0
Creating Series A Series can be created and initialised by passing either a scalar value, a NumPy nd array, a Python list or a Python Dict as the data parameter of the Series constructor.
# create one item series s1 = pd.Series(1) s1
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
'0' is the index and '1' is the value. The data type (dtype) is also shown. We can also retrieve the value using the associated index.
# get value with label 0 s1[0] # create from list s2 = pd.Series([1,2,3,4,5]) s2 # get the values in the series s2.values # get the index of the series s2.index
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
Creating Series with named index Pandas will create different index types based on the type of data identified in the index parameter. These different index types are optimized to perform indexing operations for that specific data type. To specify the index at the time of creation of the Series, use the index parameter...
# explicitly create an index # index is alpha, not an integer s3 = pd.Series([1,2,3], index=['a','b','c']) s3 s3.index
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
Please note the type of the index items. It is not string but 'object'.
# look up by label value and not object position s3['b'] # position also works s3[2] # create series from an existing index # scalar value will be copied at each index label s4 = pd.Series(2,index=s2.index) s4
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
It is a common practice to initialize the Series objects using NumPy ndarrays, and with various NumPy functions that create arrays. The following code creates a Series from five normally distributed values:
np.random.seed(123456) pd.Series(np.random.randn(5)) # 0 through 9 pd.Series(np.linspace(0,9,10)) # o through 8 pd.Series(np.arange(0,9))
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
A Series can also be created from a Python dictionary. The keys of the dictionary are used as the index lables for the Series:
s6 = pd.Series({'a':1,'b':2,'c':3,'d':4}) s6
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
Size, Shape, Count and Uniqueness of Values
# example series which also contains a NaN s = pd.Series([0,1,1,2,3,4,5,6,7,np.NaN]) s # length of the Series len(s) s.size # shape is a tuple with one value s.shape # number of values not part of NaN can be found using count() method s.count() # all unique values s.unique() # count of non-NaN values, returned ma...
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
Peeking at data with heads, tails and take pandas provides the .head() and .tail() methods to examine just the first few or last records in a Series. By default, these return the first five or last rows respectively, but you can use the n parameter or just pass an integer to specify the number of rows:
# first five s.head() # first three s.head(3) # last five s.tail() # last 2 s.tail(n=2) # equivalent to s.tail(2)
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
The .take() method will return the rows in a series that correspond to the zero-based positions specified in a list:
# only take specific items s.take([0,3,9])
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
Looking up values in Series Values in a Series object can be retrieved using the [] operator and passing either a single index label or a list of index labels.
# single item lookup s3['a'] # lookup by position since index is not an integer s3[2] # multiple items s3[['a','c']] # series with an integer index but not starting with 0 s5 = pd.Series([1,2,3], index =[11,12,13]) s5[12] # by value as value passed and index are both integer
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
To alleviate the potential confusion in determining the label-based lookups versus position-based lookups, index based lookup can be enforced using the .loc[] accessor:
# force lookup by index label s5.loc[12]
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
Lookup by position can be enforced using the iloc[] accessor:
# force lookup by position or location s5.iloc[1] # multiple items by index label s5.loc[[12,10]] # multiple items by position or location s5.iloc[[1,2]]
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
If a location / position passed to .iloc[] in a list is out of bounds, an exception will be thrown. This is different than with .loc[], which if passed a label that does not exist, will return NaN as the value for that label:
s5.loc[[12,-1,15]]
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
A Series also has a property .ix that can be used to look up items either by label or by zero-based array position.
s3 # label based lookup s3.ix[['a','b']] # position based lookup s3.ix[[1,2]]
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
This can become complicated if the indexes are integers and you pass a list of integers to ix. Since they are of the same type, the lookup will be by index label instead of position:
# this looks by label and not position # note that 1,2 have NaN as those labels do not exist in the index s5.ix[[1,2,10,11]]
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
Alignment via index labels A fundamental difference between a NumPy ndarray and a pandas Series is the ability of a Series to automatically align data from another Series based on label values before performing an operation.
s6 = pd.Series([1,2,3,4], index=['a','b','c','d']) s6 s7 = pd.Series([4,3,2,1], index=['d','c','b','a']) s7 s6 + s7
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
This is a very different result that what it would have been if it were two pure NumPy arrays being added. A NumPy ndarray would add the items in identical positions of each array resulting in different values.
a1 = np.array([1,2,3,4,5]) a2 = np.array([5,4,3,2,1]) a1 + a2
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
The process of adding two Series objects differs from the process of addition of arrays as it first aligns data based on index label values instead of simply applying the operation to elements in the same position. This becomes significantly powerful when using pandas Series to combine data based on labels instead of h...
# multiply all values in s3 by 2 s3 * 2 # scalar series using the s3's index # not efficient as it will no use vectorisation t = pd.Series(2,s3.index) s3 * t
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
To reinforce the point that alignment is being performed when applying arithmetic operations across two Series objects, look at the following two Series as examples:
# we will add this to s9 s8 = pd.Series({'a':1,'b':2,'c':3,'d':5}) s8 s9 = pd.Series({'b':6,'c':7,'d':9,'e':10}) s9 # NaN's result for a and e demonstrates alignment s8 + s9 s10 = pd.Series([1.0,2.0,3.0],index=['a','a','b']) s10 s11 = pd.Series([4.0,5.0,6.0], index=['a','a','c']) s11 # will result in four 'a' inde...
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
The reason for the above result is that during alignment, pandas actually performs a cartesian product of the sets of all the unique index labels in both Series objects, and then applies the specified operation on all items in the products. To explain why there are four 'a' index values s10 contains two 'a' labels and ...
nda = np.array([1,2,3,4,5]) nda.mean() # mean of numpy array values with a NaN nda = np.array([1,2,3,4,np.NaN]) nda.mean() # Series object ignores NaN values - does not get factored s = pd.Series(nda) s.mean() # handle NaN values like Numpy s.mean(skipna=False)
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
Boolean selection Items in a Series can be selected, based on the value instead of index labels, via the utilization of a Boolean selection.
# which rows have values that are > 5 s = pd.Series(np.arange(0,10)) s > 5 # select rows where values are > 5 # overloading the Series object [] operator logicalResults = s > 5 s[logicalResults] # a little shorter version s[s > 5] # using & operator s[(s>5)&(s<9)] # using | operator s[(s > 3) | (s < 5)] # are all ...
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
The result of these logical expressions is a Boolean selection, a Series of True and False values. The .sum() method of a Series, when given a series of Boolean values, will treat True as 1 and False as 0. The following demonstrates using this to determine the number of items in a Series that satisfy a given expression...
(s < 2).sum()
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
Reindexing a Series Reindexing in pandas is a process that makes the data in a Series or DataFrame match a given set of labels. This process of performing a reindex includes the following steps: 1. Reordering existing data to match a set of labels. 2. Inserting NaN markers where no data exists for a label. 3. Possibly,...
# sample series of five items s = pd.Series(np.random.randn(5)) s # change the index s.index = ['a','b','c','d','e'] s # concat copies index values verbatim # potentially making duplicates np.random.seed(123456) s1 = pd.Series(np.random.randn(3)) s2 = pd.Series(np.random.randn(3)) combined = pd.concat([s1,s2]) combin...
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
Greater flexibility in creating a new index is provided using the .reindex() method. An example of the flexibility of .reindex() over assigning the .index property directly is that the list provided to .reindex() can be of a different length than the number of rows in the Series:
np.random.seed(123456) s1 = pd.Series(np.random.randn(4),['a','b','c','d']) # reindex with different number of labels # results in dropped rows and/or NaN's s2 = s1.reindex(['a','c','g']) s2
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
There are several things here that are important to point out about .reindex() method. First is that the result of .reindex() method is a new Series. This new Series has an index with labels that are provided as parameter to reindex(). For each item in the given parameter list, if the original Series contains that lab...
# s2 is a different series than s1 s2['a'] = 0 s2 # this did not modify s1 s1
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
Reindex is also useful when you want to align two Series to perform an operation on matching elements from each series; however, for some reason, the two Series has index labels that will not initially align.
# different types for the same values of labels causes big issue s1 = pd.Series([0,1,2],index=[0,1,2]) s2 = pd.Series([3,4,5],index=['0','1','2']) s1 + s2
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
The reason why this happens in pandas are as follows: pandas first tries to align by the indexes and finds no matches, so it copies the index labels from the first series and tries to append the indexes from the second Series. However, since they are different type, it defaults back to zero-based integer sequence that...
# reindex by casting the label types and we will get the desired result s2.index = s2.index.values.astype(int) s1 + s2
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
The default action of inserting NaN as a missing value during reindexing can be changed by using the fill_value parameter of the method.
# fill with 0 instead on NaN s2 = s.copy() s2.reindex(['a','f'],fill_value=0)
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
When performing a reindex on ordered data such as a time series, it is possible to perform interpolation or filling of values. The following example demonstrates forward filling, often referred to as "last known value".
# create example to demonstrate fills s3 = pd.Series(['red','green','blue'],index=[0,3,5]) s3 # forward fill using ffill method s3.reindex(np.arange(0,7), method='ffill') # backward fill using bfill method s3.reindex(np.arange(0,7),method='bfill')
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
Modifying a Series in-place There are several ways that an existing Series can be modified in-place having either its values changed or having rows added or deleted. A new item can be added to a Series by assigning a value to an index label that does not already exist.
np.random.seed(123456) s = pd.Series(np.random.randn(3),index=['a','b','c']) s # change a value in the Series # this done in-place # a new Series is not returned that has a modified value s['d'] = 100 s # value at a specific index label can be changed by assignment: s['d'] = -100 s
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
Items can be removed from a Series using the del() function and passing the index label(s) to be removed.
del(s['a']) s
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
Slicing a Series
# a series to use for slicing # using index labels not starting at 0 to demonstrate # position based slicing s = pd.Series(np.arange(100,110),index=np.arange(10,20)) s # items at position 0,2,4 s[0:6:2] # equivalent to s.iloc[[0,2,4]] # first five by slicing, same as .head(5) s[:5] # fourth position to the end s[4...
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
An important thing to keep in mind when using slicing, is that the result of the slice is actually a view into the original Series. Modification of values through the result of the slice will modify the original Series.
# preserve s # slice with first 2 rows copy = s.copy() slice = copy[:2] slice
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
Now the assignment of a value to an element of a slice will change the value in the original Series:
slice[11] = 1000 copy
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
Slicing can be performed on Series objects with a non-integer index.
# used to demonstrate the next two slices s = pd.Series(np.arange(0,5),index=['a','b','c','d','e']) s # slicing with integer values will extract items based on position: s[1:3] # with non-integer index, it is also possible to slice with values in the same type of the index: s['b':'d']
pandas/01.Pandas - Series Object.ipynb
vravishankar/Jupyter-Books
mit
Load in the SIF file for Pathway Commons, using pandas.read_csv and specifying the three column names species1, interaction_type, and species2:
sif_data = pandas.read_csv("shared/pathway_commons.sif", sep="\t", names=["species1","interaction_type","species2"])
class10_closeness_python3_template.ipynb
ramseylab/networkscompbio
apache-2.0
Subset the data frame to include only rows for which the interaction_type column contains the string controls-expression-of; subset columns to include only columns species1 and species2 using the [ operator and the list ["species1","species2"]; and eliminate redundant edges in the edge-list using the drop_duplicates me...
interac_grn = sif_data[sif_data.interaction_type == "controls-expression-of"] interac_grn_unique = interac_grn[["species1","species2"]].drop_duplicates()
class10_closeness_python3_template.ipynb
ramseylab/networkscompbio
apache-2.0
Create an undirected graph in igraph, from the dataframe edge-list, using Graph.TupleList and specifying directed=False. Print out the graph summary using the summary instance method.
grn_igraph = igraph.Graph.TupleList(interac_grn_unique.values.tolist(), directed=False) grn_igraph.summary()
class10_closeness_python3_template.ipynb
ramseylab/networkscompbio
apache-2.0
For one vertex at a time (iterating over the vertex sequence grn_igraph.vs), compute that vertex's harmonic mean closeness centrality using Eq. 7.30 from Newman's book. Don't forget to eliminate the "0" distance between a vertex and itself, in the results you get back from calling the shortest_paths method on the Verte...
N = len(grn_igraph.vs) # allocate a vector to contain the vertex closeness centralities; initialize to zeroes # (so if a vertex is a singleton we don't have to update its closeness centrality) closeness_centralities = numpy.zeros(N) # initialize a counter ctr = 0 # start the timer start_time = timeit.default_timer()...
class10_closeness_python3_template.ipynb
ramseylab/networkscompbio
apache-2.0
Histogram the harmonic-mean closeness centralities. Do they have a large dynamic range?
import matplotlib.pyplot matplotlib.pyplot.hist(closeness_centralities) matplotlib.pyplot.xlabel("Ci") matplotlib.pyplot.ylabel("Frequency") matplotlib.pyplot.show()
class10_closeness_python3_template.ipynb
ramseylab/networkscompbio
apache-2.0
Scatter plot the harmonic-mean closeness centralities vs. the log10 degree. Is there any kind of relationship?
ax = matplotlib.pyplot.gca() ax.scatter(grn_igraph.degree(), closeness_centralities) ax.set_xscale("log") matplotlib.pyplot.xlabel("degree") matplotlib.pyplot.ylabel("closeness") matplotlib.pyplot.show()
class10_closeness_python3_template.ipynb
ramseylab/networkscompbio
apache-2.0
Which protein has the highest harmonic-mean closeness centrality in the network, and what is its centrality value? use numpy.argmax
print(numpy.max(closeness_centralities)) grn_igraph.vs[numpy.argmax(closeness_centralities)]["name"]
class10_closeness_python3_template.ipynb
ramseylab/networkscompbio
apache-2.0
Print names of the top 10 proteins in the network, by harmonic-mean closeness centrality:, using numpy.argsort:
grn_igraph.vs[numpy.argsort(closeness_centralities)[::-1][0:9].tolist()]["name"]
class10_closeness_python3_template.ipynb
ramseylab/networkscompbio
apache-2.0
Будем совсем неразумно обучаться на всем train'е, так как тогда мы переобучимся, то есть наш алгоритм "подгониться" под закономерности, присущие только train'у, а на реальных данных будет неистово лажать. Так что train разделим на две части: на 75% будем обучаться, а на 25% проверять, что мы лажаем не неистово. Если во...
# Выделяем outdoor'ы и indoor'ы. sample_out = sample[result[:, 0] == 1] sample_in = sample[result[:, 1] == 1] result_out = result[result[:, 0] == 1] result_in = result[result[:, 1] == 1] # Считаем размер indoor- и outdoor-частей в train'е. train_size_in = int(sample_in.shape[0] * 0.75) train_size_out = int(sample_out....
optimizaion/kaggle/eshlykov-kaggle.ipynb
eshlykov/mipt-day-after-day
unlicense
Для каждой картинки мы хотим найти вектор $(p_0, p_1)$, вероятностей такой, что $p_i$ - вероятность того, что картинка принадлежит классу $i$ ($0$ — outdoor, $1$ — indoor). Реализуя логистическую регрессию, мы хотим приближать вероятности к их настоящему распределению. Выражение выдает ответ вида $$ W x + b, $$ где $...
def softmax(W, x): # Функция logsumexp более стабтильно вычисляет функцию экспонент, почти # избавляя нас от проблемы переполнения. p = np.dot(x, W.T) return np.exp(p - scm.logsumexp(p, axis=1).reshape(-1, 1)) def loss(y, softmax, W, l): # Формула из Википедии по ссылке выше c добавленным регуляриз...
optimizaion/kaggle/eshlykov-kaggle.ipynb
eshlykov/mipt-day-after-day
unlicense
Посчитаем среднюю квадратичную ошибку на тесте, чтобы прикинуть, что будет на Kaggle.
# Добавляем 1 к выборке. nx_test = np.hstack([x_test, np.ones(x_test.shape[0]).reshape(x_test.shape[0], 1)]) probabilities = softmax(W, nx_test) # Считаем вероятности. recognized = np.argmax(probabilities, axis=1) # Что распознано. answers = np.argmax(y_test, axis=1) # Правильные ответы. np.sqrt(np.mean((recognized...
optimizaion/kaggle/eshlykov-kaggle.ipynb
eshlykov/mipt-day-after-day
unlicense
Теперь применяем найденную матрицу к исследумемым данным.
# Добавляем 1 к выборке. ntest = np.hstack([test, np.ones(test.shape[0]).reshape(test.shape[0], 1)]) probabilities = softmax(W, ntest) # Считаем вероятности. ress = np.argmax(probabilities, axis=1).reshape(-1, 1) # Что распознано. # Осталось загнать все в табличку, чтобы ее записать в csv. ids = np.arange(ress.size)...
optimizaion/kaggle/eshlykov-kaggle.ipynb
eshlykov/mipt-day-after-day
unlicense
Write a function derivs for usage with scipy.integrate.odeint that computes the derivatives for the damped, driven harmonic oscillator. The solution vector at each time will be $\vec{y}(t) = (\theta(t),\omega(t))$.
def derivs(y, t, a, b, omega0): """Compute the derivatives of the damped, driven pendulum. Parameters ---------- y : ndarray The solution vector at the current time t[i]: [theta[i],omega[i]]. t : float The current time t[i]. a, b, omega0: float The parameters in the ...
assignments/assignment10/ODEsEx03.ipynb
Jackporter415/phys202-2015-work
mit
Simple pendulum Use the above functions to integrate the simple pendulum for the case where it starts at rest pointing vertically upwards. In this case, it should remain at rest with constant energy. Integrate the equations of motion. Plot $E/m$ versus time. Plot $\theta(t)$ and $\omega(t)$ versus time. Tune the atol ...
# YOUR CODE HERE raise NotImplementedError() # YOUR CODE HERE raise NotImplementedError() # YOUR CODE HERE raise NotImplementedError() assert True # leave this to grade the two plots and their tuning of atol, rtol.
assignments/assignment10/ODEsEx03.ipynb
Jackporter415/phys202-2015-work
mit
Damped pendulum Write a plot_pendulum function that integrates the damped, driven pendulum differential equation for a particular set of parameters $[a,b,\omega_0]$. Use the initial conditions $\theta(0)=-\pi + 0.1$ and $\omega=0$. Decrease your atol and rtol even futher and make sure your solutions have converged. Ma...
def plot_pendulum(a=0.0, b=0.0, omega0=0.0): """Integrate the damped, driven pendulum and make a phase plot of the solution.""" # YOUR CODE HERE raise NotImplementedError()
assignments/assignment10/ODEsEx03.ipynb
Jackporter415/phys202-2015-work
mit
Use interact to explore the plot_pendulum function with: a: a float slider over the interval $[0.0,1.0]$ with steps of $0.1$. b: a float slider over the interval $[0.0,10.0]$ with steps of $0.1$. omega0: a float slider over the interval $[0.0,10.0]$ with steps of $0.1$.
# YOUR CODE HERE raise NotImplementedError()
assignments/assignment10/ODEsEx03.ipynb
Jackporter415/phys202-2015-work
mit
BEM method
#Q = 2000/3 #strength of the source-sheet,stb/d h=25.26 #thickness of local gridblock,ft phi=0.2 #porosity kx=200 #pemerability in x direction,md ky=200 #pemerability in y direction,md kr=kx/ky #pemerability ratio miu=1 #viscosity,cp Nw=1 #Number of well Qwell...
BEM_problem.ipynb
BradHub/SL-SPH
mit
Boundary Discretization we will create a discretization of the body geometry into panels (line segments in 2D). A panel's attributes are: its starting point, end point and mid-point, its length and its orientation. See the following figure for the nomenclature used in the code and equations below. <img src="./resources...
class Panel: """Contains information related to a panel.""" def __init__(self, xa, ya, xb, yb): """Creates a panel. Arguments --------- xa, ya -- Cartesian coordinates of the first end-point. xb, yb -- Cartesian coordinates of the second end-point. """ ...
BEM_problem.ipynb
BradHub/SL-SPH
mit
We create a node distribution on the boundary that is refined near the corner with cosspace function
def cosspace(st,ed,N): N=N+1 AngleInc=numpy.pi/(N-1) CurAngle = AngleInc space=numpy.linspace(0,1,N) space[0]=st for i in range(N-1): space[i+1] = 0.5*numpy.abs(ed-st)*(1 - math.cos(CurAngle)); CurAngle += AngleInc if ed<st: space[0]=ed space=space[::-1] r...
BEM_problem.ipynb
BradHub/SL-SPH
mit
Discretize boundary element along the boundary Here we implement BEM in a squre grid
N=80 #Number of boundary element Nbd=20 #Number of boundary element in each boundary Dx=1. #Grid block length in X direction Dy=1. #Gird block lenght in Y direction #Create the array x_ends = numpy.linspace(0, Dx, N) # computes a 1D-array for x y_ends = numpy.linspace(0, Dy, N) # computes a 1D-array ...
BEM_problem.ipynb
BradHub/SL-SPH
mit
Plot boundary elements and wells
#Plot the panel %matplotlib inline val_x, val_y = 0.3, 0.3 x_min, x_max = min(panel.xa for panel in panels), max(panel.xa for panel in panels) y_min, y_max = min(panel.ya for panel in panels), max(panel.ya for panel in panels) x_start, x_end = x_min-val_x*(x_max-x_min), x_max+val_x*(x_max-x_min) y_start, y_end = y_min...
BEM_problem.ipynb
BradHub/SL-SPH
mit
Boundary element implementation <img src="./resources/BEMscheme2.png" width="400"> <center>Figure 2. Representation of a local gridblock with boundary elements</center> Generally, the influence of all the j panels on the i BE node can be expressed as follows: \begin{matrix} {{c}{ij}}{{p}{i}}+{{p}{i}}\int{{{s}{j}}}{{{H}...
#Panel infuence factor Bij def InflueceP(x, y, panel): """Evaluates the contribution of a panel at one point. Arguments --------- x, y -- Cartesian coordinates of the point. panel -- panel which contribution is evaluated. Returns ------- Integral over the panel of the influence...
BEM_problem.ipynb
BradHub/SL-SPH
mit
Well source function Line source solution for pressure and velocity (Datta-Gupta, 2007) \begin{equation} P(x,y)=B{{Q}{w}}=-\frac{70.60\mu }{h\sqrt{{{k}{x}}{{k}{y}}}}\ln \left{ {{(x-{{x}{w}})}^{2}}+\frac{{{k}{x}}}{{{k}{y}}}{{(y-{{y}{w}})}^{2}} \right}{{Q}{w}}+{{P}_{avg}} \end{equation} \begin{equation} \frac{\partial P}...
#Well influence factor def InflueceP_W(x, y, well): """Evaluates the contribution of a panel at one point. Arguments --------- x, y -- Cartesian coordinates of the point. panel -- panel which contribution is evaluated. Returns ------- Integral over the panel of the influence at...
BEM_problem.ipynb
BradHub/SL-SPH
mit
BEM function solution Generally, the influence of all the j panels on the i BE node can be expressed as follows: \begin{matrix} {{c}{ij}}{{p}{i}}+{{p}{i}}\int{{{s}{j}}}{{{H}{ij}}d{{s}{j}}}=({{v}{i}}\cdot \mathbf{n})\int_{{{s}{j}}}{{{G}{ij}}}d{{s}_{j}} \end{matrix} Applying boundary condition along the boundary on above...
def build_matrix(panels): """Builds the source matrix. Arguments --------- panels -- array of panels. Returns ------- A -- NxN matrix (N is the number of panels). """ N = len(panels) A = numpy.empty((N, N), dtype=float) #numpy.fill_diagonal(A, 0.5) for i, p...
BEM_problem.ipynb
BradHub/SL-SPH
mit
Plot results
#Visulize the pressure and velocity field #Define meshgrid Nx, Ny = 50, 50 # number of points in the x and y directions x_start, x_end = -0.01, 1.01 # x-direction boundaries y_start, y_end = -0.01, 1.01 # y-direction boundaries x = numpy.linspace(x_start, x_end, Nx) # computes...
BEM_problem.ipynb
BradHub/SL-SPH
mit
Create a graph and pass it to the VersionedGraph wrapper that will take care of the version control.
graph_obj = NXGraph() g = VersionedGraph(graph_obj)
examples/Tutorial_graph_audit.ipynb
Kappa-Dev/ReGraph
mit
Now let's create a rule that adds to the graph two nodes connected with an edge and apply it. If we want the changes to be commited to the version control we rewrite through the rewrite method of a VersioneGraph object.
rule = Rule.from_transform(NXGraph()) rule.inject_add_node("a") rule.inject_add_node("b") rule.inject_add_edge("a", "b") rhs_instance, _ = g.rewrite(rule, {}, message="Add a -> b") plot_graph(g.graph)
examples/Tutorial_graph_audit.ipynb
Kappa-Dev/ReGraph
mit
We create a new branch called "branch"
branch_commit = g.branch("branch") print("Branches: ", g.branches()) print("Current branch '{}'".format(g.current_branch()))
examples/Tutorial_graph_audit.ipynb
Kappa-Dev/ReGraph
mit
Apply a rule that clones the node 'b' to the current vesion of the graph (branch 'branch')
pattern = NXGraph() pattern.add_node("b") rule = Rule.from_transform(pattern) rule.inject_clone_node("b") plot_rule(rule) rhs_instance, commit_id = g.rewrite(rule, {"b": rhs_instance["b"]}, message="Clone b") plot_graph(g.graph)
examples/Tutorial_graph_audit.ipynb
Kappa-Dev/ReGraph
mit
The rewrite method of VersionedGraph returns the RHS instance of the applied and the id of the newly created commit corresponding to this rewrite.
print("RHS instance", rhs_instance) print("Commit ID: ", commit_id)
examples/Tutorial_graph_audit.ipynb
Kappa-Dev/ReGraph
mit
Switch back to the 'master' branch
g.switch_branch("master") print(g.current_branch())
examples/Tutorial_graph_audit.ipynb
Kappa-Dev/ReGraph
mit
Apply a rule that adds a loop form 'a' to itself, a new node 'c' and connects it with 'a'
pattern = NXGraph() pattern.add_node("a") rule = Rule.from_transform(pattern) rule.inject_add_node("c") rule.inject_add_edge("c", "a") rule.inject_add_edge("a", "a") rhs_instance, _ = g.rewrite(rule, {"a": "a"}, message="Add c and c->a") plot_graph(g.graph)
examples/Tutorial_graph_audit.ipynb
Kappa-Dev/ReGraph
mit
Create a new branch 'dev'
g.branch("dev")
examples/Tutorial_graph_audit.ipynb
Kappa-Dev/ReGraph
mit
In this branch remove an edge from 'c' to 'a' and merge two nodes together
pattern = NXGraph() pattern.add_node("c") pattern.add_node("a") pattern.add_edge("c", "a") rule = Rule.from_transform(pattern) rule.inject_remove_edge("c", "a") rule.inject_merge_nodes(["c", "a"]) plot_rule(rule) g.rewrite(rule, {"a": rhs_instance["a"], "c": rhs_instance["c"]}, message="Merge c and a") plot_graph(g.gr...
examples/Tutorial_graph_audit.ipynb
Kappa-Dev/ReGraph
mit
Switch back to the 'master' branch.
g.switch_branch("master")
examples/Tutorial_graph_audit.ipynb
Kappa-Dev/ReGraph
mit