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x1 = np.linspace(-0.5, 1.25, num=100)
x2 = np.linspace(0, 2, num=100)

def y1(x):
    y = -2 * x**3 + 1.5 * x ** 2 + x
    return y[np.argmax(y <0):]

def y2(x):
    return 1 / (1 + np.exp(-5 * x + 4))

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-- Python function template to simulate the effects of a split test 
-- Returns string with expected uplift and probability of Alt being better than Orig
-- as these are the values used to support decision making for UIUX testing
create function f_simulate_split_test(completions_orig INTEGER, sessions_orig INTEGER,
                                      completions_alt INTEGER, sessions_alt INTEGER) 
;

create function f_simulate_split_test(completions_orig INTEGER, sessions_orig INTEGER,
                                      completions_alt INTEGER, sessions_alt INTEGER) 
returns varchar(2000)

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# http://stackoverflow.com/questions/17490444/import-matplotlib-pyplot-hangs#
cd ~/.matplotlib/
fc-list

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# http://stackoverflow.com/questions/33112020/how-do-i-install-jupyter-ipython-on-dataproc

PROJECT_ID=<project_id>
CLUSTER_NAME=<cluster_name>
# This should be ipython.sh 
# https://github.com/GoogleCloudPlatform/dataproc-initialization-actions/blob/master/ipython-notebook/ipython.sh 
INIT_GCS_SCRIPT=<init_gcs_script>
CHROME="/Applications/Google\ Chrome.app/Contents/MacOS/Google\ Chrome"

gcloud beta dataproc clusters create $CLUSTER_NAME --zone europe-west1-b \

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create function f_extract_query_param(query_string VARCHAR, param VARCHAR) 
returns varchar 
STABLE
AS $$

    # Split on ampersand and then on =, ensuring every param has a pair
    params = query_string.split("&")
    # split(.., 1) because there might be multiple '=' in the param 
    kp = [p.split("=", 1) for p in params]
    # create dict, with "" for missing values where the key is not an empty string

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# Based on
# http://stackoverflow.com/questions/2720014/upgrading-all-packages-with-pip
# pip freeze --local | grep -v '^\-e' | cut -d = -f 1  | xargs -n1 pip install -U 
pip3 list -o |  cut -d ' ' -f 1 | xargs -n1 pip3 install -U

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brew install proj
brew install geos

# Assuming normal scipy stack is installed
pip3 install Pillow
pip3 install cartopy