From eff88170b516f7490dc8840ad12454f4d95d9840 Mon Sep 17 00:00:00 2001 From: Victor Grau Serrat Date: Mon, 20 Nov 2017 09:15:18 -0700 Subject: [PATCH] DOC: mean_reversion_simple algo added --- _sources/example-algos.txt | 276 +++++++++++++++++++++++++++++++++++- appendix.html | 3 +- beginner-tutorial.html | 8 +- bundles.html | 8 +- development-guidelines.html | 8 +- example-algos.html | 269 ++++++++++++++++++++++++++++++++++- genindex.html | 3 +- index.html | 3 +- install.html | 8 +- jupyter.html | 8 +- live-trading.html | 8 +- naming-convention.html | 8 +- objects.inv | Bin 436 -> 502 bytes release-process.html | 8 +- releases.html | 8 +- resources.html | 8 +- search.html | 3 +- searchindex.js | 2 +- utilities.html | 3 +- videos.html | 12 +- welcome.html | 8 +- 21 files changed, 637 insertions(+), 25 deletions(-) diff --git a/_sources/example-algos.txt b/_sources/example-algos.txt index 7882208d..e341f331 100644 --- a/_sources/example-algos.txt +++ b/_sources/example-algos.txt @@ -6,8 +6,10 @@ This section documents a small number of example algorithms to complement the beginner tutorial, and show how other trading algorithms can be implemented using Catalyst: -Buy and Hodl -~~~~~~~~~~~~ +.. _buy_and_hodl: + +Buy and Hodl Algorithm +~~~~~~~~~~~~~~~~~~~~~~ source: `examples/buy_and_hodl.py `_ @@ -170,3 +172,273 @@ one day prior to the current date. plt.gcf().set_size_inches(18, 8) plt.show() +.. _mean_reversion: + +Mean Reversion Algorithm +~~~~~~~~~~~~~~~~~~~~~~~~ + +source: `examples/mean_reversion_simple.py `_ + +This algorithm is based on a simple momentum strategy. When the cryptoasset goes +up quickly, we're going to buy; when it goes down quickly, we're going to sell. +Hopefully, we'll ride the waves. + +We are choosing to run this trading algorithm with the ``neo_usd`` currency pair +on the ``Bitfinex`` exchange. Thus, first ingest the historical pricing data +that we need, with minute resolution: + +.. code-block:: bash + + catalyst ingest-exchange -x bitfinex -f minute -i neo_usd + +To run this algorithm, we are opting for the Python interpreter, instead of the +command line (CLI). All of the parameters for the simulation are specified in +lines 218-245, so in order to run the algorithm we just type: + +.. code-block:: bash + + python mean_reversion_simple.py + +.. code-block:: python + + import pandas as pd + import talib + from logbook import Logger + + from catalyst import run_algorithm + from catalyst.api import symbol, record, order_target_percent, get_open_orders + from catalyst.exchange.stats_utils import extract_transactions + + # We give a name to the algorithm which Catalyst will use to persist its state. + # In this example, Catalyst will create the `.catalyst/data/live_algos` + # directory. If we stop and start the algorithm, Catalyst will resume its + # state using the files included in the folder. + NAMESPACE = 'mean_reversion_simple' + log = Logger(NAMESPACE) + + # To run an algorithm in Catalyst, you need two functions: initialize and + # handle_data. + + def initialize(context): + # This initialize function sets any data or variables that you'll use in + # your algorithm. For instance, you'll want to define the trading pair (or + # trading pairs) you want to backtest. You'll also want to define any + # parameters or values you're going to use. + + # In our example, we're looking at Ether in USD Tether. + context.neo_usd = symbol('neo_usd') + context.base_price = None + context.current_day = None + + + def handle_data(context, data): + # This handle_data function is where the real work is done. Our data is + # minute-level tick data, and each minute is called a frame. This function + # runs on each frame of the data. + + # We flag the first period of each day. + # Since cryptocurrencies trade 24/7 the `before_trading_starts` handle + # would only execute once. This method works with minute and daily + # frequencies. + today = data.current_dt.floor('1D') + if today != context.current_day: + context.traded_today = False + context.current_day = today + + # We're computing the volume-weighted-average-price of the security + # defined above, in the context.neo_usd variable. For this example, we're + # using three bars on the 15 min bars. + + # The frequency attribute determine the bar size. We use this convention + # for the frequency alias: + # http://pandas.pydata.org/pandas-docs/stable/timeseries.html#offset-aliases + prices = data.history( + context.neo_usd, + fields='close', + bar_count=50, + frequency='15T' + ) + + # Ta-lib calculates various technical indicator based on price and + # volume arrays. + + # In this example, we are comp + rsi = talib.RSI(prices.values, timeperiod=14) + + # We need a variable for the current price of the security to compare to + # the average. Since we are requesting two fields, data.current() + # returns a DataFrame with + current = data.current(context.neo_usd, fields=['close', 'volume']) + price = current['close'] + + # If base_price is not set, we use the current value. This is the + # price at the first bar which we reference to calculate price_change. + if context.base_price is None: + context.base_price = price + + price_change = (price - context.base_price) / context.base_price + cash = context.portfolio.cash + + # Now that we've collected all current data for this frame, we use + # the record() method to save it. This data will be available as + # a parameter of the analyze() function for further analysis. + record( + price=price, + volume=current['volume'], + price_change=price_change, + rsi=rsi[-1], + cash=cash + ) + + # We are trying to avoid over-trading by limiting our trades to + # one per day. + if context.traded_today: + return + + # Since we are using limit orders, some orders may not execute immediately + # we wait until all orders are executed before considering more trades. + orders = get_open_orders(context.neo_usd) + if len(orders) > 0: + return + + # Exit if we cannot trade + if not data.can_trade(context.neo_usd): + return + + # Another powerful built-in feature of the Catalyst backtester is the + # portfolio object. The portfolio object tracks your positions, cash, + # cost basis of specific holdings, and more. In this line, we calculate + # how long or short our position is at this minute. + pos_amount = context.portfolio.positions[context.neo_usd].amount + + if rsi[-1] <= 30 and pos_amount == 0: + log.info( + '{}: buying - price: {}, rsi: {}'.format( + data.current_dt, price, rsi[-1] + ) + ) + order_target_percent(context.neo_usd, 1) + context.traded_today = True + + elif rsi[-1] >= 80 and pos_amount > 0: + log.info( + '{}: selling - price: {}, rsi: {}'.format( + data.current_dt, price, rsi[-1] + ) + ) + order_target_percent(context.neo_usd, 0) + context.traded_today = True + + + def analyze(context=None, perf=None): + import matplotlib.pyplot as plt + + # The base currency of the algo exchange + base_currency = context.exchanges.values()[0].base_currency.upper() + + # Plot the portfolio value over time. + ax1 = plt.subplot(611) + perf.loc[:, 'portfolio_value'].plot(ax=ax1) + ax1.set_ylabel('Portfolio Value ({})'.format(base_currency)) + + # Plot the price increase or decrease over time. + ax2 = plt.subplot(612, sharex=ax1) + perf.loc[:, 'price'].plot(ax=ax2, label='Price') + + ax2.set_ylabel('{asset} ({base})'.format( + asset=context.neo_usd.symbol, base=base_currency + )) + + transaction_df = extract_transactions(perf) + if not transaction_df.empty: + buy_df = transaction_df[transaction_df['amount'] > 0] + sell_df = transaction_df[transaction_df['amount'] < 0] + ax2.scatter( + buy_df.index.to_pydatetime(), + perf.loc[buy_df.index, 'price'], + marker='^', + s=100, + c='green', + label='' + ) + ax2.scatter( + sell_df.index.to_pydatetime(), + perf.loc[sell_df.index, 'price'], + marker='v', + s=100, + c='red', + label='' + ) + + ax4 = plt.subplot(613, sharex=ax1) + perf.loc[:, 'cash'].plot( + ax=ax4, label='Base Currency ({})'.format(base_currency) + ) + ax4.set_ylabel('Cash ({})'.format(base_currency)) + + perf['algorithm'] = perf.loc[:, 'algorithm_period_return'] + + ax5 = plt.subplot(614, sharex=ax1) + perf.loc[:, ['algorithm', 'price_change']].plot(ax=ax5) + ax5.set_ylabel('Percent Change') + + ax6 = plt.subplot(615, sharex=ax1) + perf.loc[:, 'rsi'].plot(ax=ax6, label='RSI') + ax6.axhline(70, color='darkgoldenrod') + ax6.axhline(30, color='darkgoldenrod') + + if not transaction_df.empty: + ax6.scatter( + buy_df.index.to_pydatetime(), + perf.loc[buy_df.index, 'rsi'], + marker='^', + s=100, + c='green', + label='' + ) + ax6.scatter( + sell_df.index.to_pydatetime(), + perf.loc[sell_df.index, 'rsi'], + marker='v', + s=100, + c='red', + label='' + ) + plt.legend(loc=3) + + # Show the plot. + plt.gcf().set_size_inches(18, 8) + plt.show() + pass + + + if __name__ == '__main__': + # The execution mode: backtest or live + MODE = 'backtest' + + if MODE == 'backtest': + # catalyst run -f catalyst/examples/mean_reversion_simple.py -x poloniex -s 2017-10-1 -e 2017-11-10 -c usdt -n mean-reversion --data-frequency minute --capital-base 10000 + run_algorithm( + capital_base=10000, + data_frequency='minute', + initialize=initialize, + handle_data=handle_data, + analyze=analyze, + exchange_name='bitfinex', + algo_namespace=NAMESPACE, + base_currency='usd', + start=pd.to_datetime('2017-10-1', utc=True), + end=pd.to_datetime('2017-11-10', utc=True), + ) + + elif MODE == 'live': + run_algorithm( + initialize=initialize, + handle_data=handle_data, + analyze=analyze, + exchange_name='bitfinex', + live=True, + algo_namespace=NAMESPACE, + base_currency='usd', + live_graph=True + ) diff --git a/appendix.html b/appendix.html index 2d65e21e..363d4202 100644 --- a/appendix.html +++ b/appendix.html @@ -120,7 +120,8 @@
  • Naming Convention
  • Example Algorithms
  • Utilities
      diff --git a/beginner-tutorial.html b/beginner-tutorial.html index 76660c21..78c806c9 100644 --- a/beginner-tutorial.html +++ b/beginner-tutorial.html @@ -122,7 +122,13 @@
    • Naming Convention
    • Example Algorithms +
      • +
    • Utilities
    • Videos
        diff --git a/bundles.html b/bundles.html index 1ff7bc11..eb870616 100644 --- a/bundles.html +++ b/bundles.html @@ -120,7 +120,13 @@
      • Naming Convention
      • Example Algorithms +
        • +
      • Utilities
      • Videos
          diff --git a/development-guidelines.html b/development-guidelines.html index a600071e..8ebb4dc3 100644 --- a/development-guidelines.html +++ b/development-guidelines.html @@ -122,7 +122,13 @@
        • Naming Convention
        • Example Algorithms +
          • +
        • Utilities
        • Videos
            diff --git a/example-algos.html b/example-algos.html index f94a8dde..6067eb19 100644 --- a/example-algos.html +++ b/example-algos.html @@ -122,7 +122,8 @@
          • Naming Convention
          • Example Algorithms
          • Utilities
              @@ -242,8 +243,8 @@

              This section documents a small number of example algorithms to complement the beginner tutorial, and show how other trading algorithms can be implemented using Catalyst:

              -
              -

              Buy and Hodl

              +
              +

              Buy and Hodl Algorithm

              source: examples/buy_and_hodl.py

              First ingest the historical pricing data needed to run this algorithm:

              catalyst ingest-exchange -x poloniex -f daily -i btc_usdt
@@ -398,6 +399,268 @@ one day prior to the current date.
              +
              +

              Mean Reversion Algorithm

              +

              source: examples/mean_reversion_simple.py

              +

              This algorithm is based on a simple momentum strategy. When the cryptoasset goes +up quickly, we’re going to buy; when it goes down quickly, we’re going to sell. +Hopefully, we’ll ride the waves.

              +

              We are choosing to run this trading algorithm with the neo_usd currency pair +on the Bitfinex exchange. Thus, first ingest the historical pricing data +that we need, with minute resolution:

              +
              catalyst ingest-exchange -x bitfinex -f minute -i neo_usd
+
              +
              +

              To run this algorithm, we are opting for the Python interpreter, instead of the +command line (CLI). All of the parameters for the simulation are specified in +lines 218-245, so in order to run the algorithm we just type:

              +
              python mean_reversion_simple.py
+
              +
              +
              import pandas as pd
+import talib
+from logbook import Logger
+
+from catalyst import run_algorithm
+from catalyst.api import symbol, record, order_target_percent, get_open_orders
+from catalyst.exchange.stats_utils import extract_transactions
+
+# We give a name to the algorithm which Catalyst will use to persist its state.
+# In this example, Catalyst will create the `.catalyst/data/live_algos`
+# directory. If we stop and start the algorithm, Catalyst will resume its
+# state using the files included in the folder.
+NAMESPACE = 'mean_reversion_simple'
+log = Logger(NAMESPACE)
+
+# To run an algorithm in Catalyst, you need two functions: initialize and
+# handle_data.
+
+def initialize(context):
+    # This initialize function sets any data or variables that you'll use in
+    # your algorithm.  For instance, you'll want to define the trading pair (or
+    # trading pairs) you want to backtest.  You'll also want to define any
+    # parameters or values you're going to use.
+
+    # In our example, we're looking at Ether in USD Tether.
+    context.neo_usd = symbol('neo_usd')
+    context.base_price = None
+    context.current_day = None
+
+
+def handle_data(context, data):
+    # This handle_data function is where the real work is done.  Our data is
+    # minute-level tick data, and each minute is called a frame.  This function
+    # runs on each frame of the data.
+
+    # We flag the first period of each day.
+    # Since cryptocurrencies trade 24/7 the `before_trading_starts` handle
+    # would only execute once. This method works with minute and daily
+    # frequencies.
+    today = data.current_dt.floor('1D')
+    if today != context.current_day:
+        context.traded_today = False
+        context.current_day = today
+
+    # We're computing the volume-weighted-average-price of the security
+    # defined above, in the context.neo_usd variable.  For this example, we're
+    # using three bars on the 15 min bars.
+
+    # The frequency attribute determine the bar size. We use this convention
+    # for the frequency alias:
+    # http://pandas.pydata.org/pandas-docs/stable/timeseries.html#offset-aliases
+    prices = data.history(
+        context.neo_usd,
+        fields='close',
+        bar_count=50,
+        frequency='15T'
+    )
+
+    # Ta-lib calculates various technical indicator based on price and
+    # volume arrays.
+
+    # In this example, we are comp
+    rsi = talib.RSI(prices.values, timeperiod=14)
+
+    # We need a variable for the current price of the security to compare to
+    # the average. Since we are requesting two fields, data.current()
+    # returns a DataFrame with
+    current = data.current(context.neo_usd, fields=['close', 'volume'])
+    price = current['close']
+
+    # If base_price is not set, we use the current value. This is the
+    # price at the first bar which we reference to calculate price_change.
+    if context.base_price is None:
+        context.base_price = price
+
+    price_change = (price - context.base_price) / context.base_price
+    cash = context.portfolio.cash
+
+    # Now that we've collected all current data for this frame, we use
+    # the record() method to save it. This data will be available as
+    # a parameter of the analyze() function for further analysis.
+    record(
+        price=price,
+        volume=current['volume'],
+        price_change=price_change,
+        rsi=rsi[-1],
+        cash=cash
+    )
+
+    # We are trying to avoid over-trading by limiting our trades to
+    # one per day.
+    if context.traded_today:
+        return
+
+    # Since we are using limit orders, some orders may not execute immediately
+    # we wait until all orders are executed before considering more trades.
+    orders = get_open_orders(context.neo_usd)
+    if len(orders) > 0:
+        return
+
+    # Exit if we cannot trade
+    if not data.can_trade(context.neo_usd):
+        return
+
+    # Another powerful built-in feature of the Catalyst backtester is the
+    # portfolio object.  The portfolio object tracks your positions, cash,
+    # cost basis of specific holdings, and more.  In this line, we calculate
+    # how long or short our position is at this minute.
+    pos_amount = context.portfolio.positions[context.neo_usd].amount
+
+    if rsi[-1] <= 30 and pos_amount == 0:
+        log.info(
+            '{}: buying - price: {}, rsi: {}'.format(
+                data.current_dt, price, rsi[-1]
+            )
+        )
+        order_target_percent(context.neo_usd, 1)
+        context.traded_today = True
+
+    elif rsi[-1] >= 80 and pos_amount > 0:
+        log.info(
+            '{}: selling - price: {}, rsi: {}'.format(
+                data.current_dt, price, rsi[-1]
+            )
+        )
+        order_target_percent(context.neo_usd, 0)
+        context.traded_today = True
+
+
+def analyze(context=None, perf=None):
+    import matplotlib.pyplot as plt
+
+    # The base currency of the algo exchange
+    base_currency = context.exchanges.values()[0].base_currency.upper()
+
+    # Plot the portfolio value over time.
+    ax1 = plt.subplot(611)
+    perf.loc[:, 'portfolio_value'].plot(ax=ax1)
+    ax1.set_ylabel('Portfolio Value ({})'.format(base_currency))
+
+    # Plot the price increase or decrease over time.
+    ax2 = plt.subplot(612, sharex=ax1)
+    perf.loc[:, 'price'].plot(ax=ax2, label='Price')
+
+    ax2.set_ylabel('{asset} ({base})'.format(
+        asset=context.neo_usd.symbol, base=base_currency
+    ))
+
+    transaction_df = extract_transactions(perf)
+    if not transaction_df.empty:
+        buy_df = transaction_df[transaction_df['amount'] > 0]
+        sell_df = transaction_df[transaction_df['amount'] < 0]
+        ax2.scatter(
+            buy_df.index.to_pydatetime(),
+            perf.loc[buy_df.index, 'price'],
+            marker='^',
+            s=100,
+            c='green',
+            label=''
+        )
+        ax2.scatter(
+            sell_df.index.to_pydatetime(),
+            perf.loc[sell_df.index, 'price'],
+            marker='v',
+            s=100,
+            c='red',
+            label=''
+        )
+
+    ax4 = plt.subplot(613, sharex=ax1)
+    perf.loc[:, 'cash'].plot(
+        ax=ax4, label='Base Currency ({})'.format(base_currency)
+    )
+    ax4.set_ylabel('Cash ({})'.format(base_currency))
+
+    perf['algorithm'] = perf.loc[:, 'algorithm_period_return']
+
+    ax5 = plt.subplot(614, sharex=ax1)
+    perf.loc[:, ['algorithm', 'price_change']].plot(ax=ax5)
+    ax5.set_ylabel('Percent Change')
+
+    ax6 = plt.subplot(615, sharex=ax1)
+    perf.loc[:, 'rsi'].plot(ax=ax6, label='RSI')
+    ax6.axhline(70, color='darkgoldenrod')
+    ax6.axhline(30, color='darkgoldenrod')
+
+    if not transaction_df.empty:
+        ax6.scatter(
+            buy_df.index.to_pydatetime(),
+            perf.loc[buy_df.index, 'rsi'],
+            marker='^',
+            s=100,
+            c='green',
+            label=''
+        )
+        ax6.scatter(
+            sell_df.index.to_pydatetime(),
+            perf.loc[sell_df.index, 'rsi'],
+            marker='v',
+            s=100,
+            c='red',
+            label=''
+        )
+    plt.legend(loc=3)
+
+    # Show the plot.
+    plt.gcf().set_size_inches(18, 8)
+    plt.show()
+    pass
+
+
+if __name__ == '__main__':
+    # The execution mode: backtest or live
+    MODE = 'backtest'
+
+    if MODE == 'backtest':
+        # catalyst run -f catalyst/examples/mean_reversion_simple.py -x poloniex -s 2017-10-1 -e 2017-11-10 -c usdt -n mean-reversion --data-frequency minute --capital-base 10000
+        run_algorithm(
+            capital_base=10000,
+            data_frequency='minute',
+            initialize=initialize,
+            handle_data=handle_data,
+            analyze=analyze,
+            exchange_name='bitfinex',
+            algo_namespace=NAMESPACE,
+            base_currency='usd',
+            start=pd.to_datetime('2017-10-1', utc=True),
+            end=pd.to_datetime('2017-11-10', utc=True),
+        )
+
+    elif MODE == 'live':
+        run_algorithm(
+            initialize=initialize,
+            handle_data=handle_data,
+            analyze=analyze,
+            exchange_name='bitfinex',
+            live=True,
+            algo_namespace=NAMESPACE,
+            base_currency='usd',
+            live_graph=True
+        )
+
              +
              +
              diff --git a/genindex.html b/genindex.html index 9d946af5..5d75cbaa 100644 --- a/genindex.html +++ b/genindex.html @@ -121,7 +121,8 @@
            • Naming Convention
            • Example Algorithms
            • Utilities
                diff --git a/index.html b/index.html index 36df5f51..2b4c7458 100644 --- a/index.html +++ b/index.html @@ -121,7 +121,8 @@
              • Naming Convention
              • Example Algorithms
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                  diff --git a/install.html b/install.html index 0839388b..736be3db 100644 --- a/install.html +++ b/install.html @@ -122,7 +122,13 @@
                • Naming Convention
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                    diff --git a/jupyter.html b/jupyter.html index 24c75699..50730c58 100644 --- a/jupyter.html +++ b/jupyter.html @@ -122,7 +122,13 @@
                  • Naming Convention
                  • Example Algorithms +
                    • +
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                      diff --git a/live-trading.html b/live-trading.html index 3e1c012d..eb08a6b7 100644 --- a/live-trading.html +++ b/live-trading.html @@ -122,7 +122,13 @@
                    • Naming Convention
                    • Example Algorithms +
                      • +
                    • Utilities
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                        diff --git a/naming-convention.html b/naming-convention.html index 24fa1e98..acaba445 100644 --- a/naming-convention.html +++ b/naming-convention.html @@ -122,7 +122,13 @@
                      • Naming Convention
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                        • +
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                          diff --git a/objects.inv b/objects.inv index bb1747001f0dcd2a07bfb42fc3dec307899ef7f9..ded63fcdf3207ffd49ce64b905ec738b546cb3f6 100644 GIT binary patch delta 393 zcmV;40e1eh1NH-ucYl*jPs1<_hVS_mk>HvkuDfkQf(iLiV? zxl&_6NgsxKPAH*KK?JWk8%m$Q4}xFi7ht3j&`uTOX)nQq_)ah%_!^%qq?%2UjA%?o zu+*lVz0&>j`^{6N-r&&43N)D76U}q$XN4)xU$#F)z|Fn_oS2u^T%1Y3*%?nUM87dS z&qZ7DN2grJ#(xh(vr;P>+>gFzPP%`M68WG3Ji#KJoQk<~V1#T(^=2UHYLk#dgUh7Y zw>6j@(QCx%E_qCbWrz;7brSnAm}yy6wz}xkizb$7R1y!o%FC%ie>QY$+XEY306AeB n?P-4AyMdWZ{6o6XhDEshVytic6cYl)0PQx$|Mfd&+OR#kj+wO{xPy~TOg}R=`qjn_6c4Maxz8=R9 zL;wYK6FK%hb3J#w>9thoL}S_(wB*jqxq=NUE^hfI9nN;XRae*io?K%N*pc4y#Q`Yj z6!N36`7T_&4M2~ zAHHI+nzX2jG@7w+)&4Zu(!=xn%~Mpp;l8I1Th!jM78>Iw!5W&E)ep$XKU%V9Q4Vrf zwUK?uJvC>^UX*#z4-AGK6kur#gSDt7oeI6oO1@ZDY~P0mqQtj(O=kHT<$PT|R(Wc% zf;W~xi(IUwu0J!~zjYEcDp^O8IfSm+jSHl`oYpD{mas*33^AJH^kCLmGaAhY*&&A6 Y(EF_1ue@1%p2vsvJ3hfa0ZF_sBO@lFWdHyG diff --git a/release-process.html b/release-process.html index 47cd58dd..5d3c25fc 100644 --- a/release-process.html +++ b/release-process.html @@ -120,7 +120,13 @@
                        • Naming Convention
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                            diff --git a/releases.html b/releases.html index 4da2f8e1..9a28466b 100644 --- a/releases.html +++ b/releases.html @@ -121,7 +121,13 @@
                          • Naming Convention
                          • Example Algorithms +
                            • +
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                              diff --git a/resources.html b/resources.html index 454d4b87..9f5cd777 100644 --- a/resources.html +++ b/resources.html @@ -122,7 +122,13 @@
                            • Naming Convention
                            • Example Algorithms +
                              • +
                            • Utilities
                            • Videos
                                diff --git a/search.html b/search.html index 63f1071d..3c16a603 100644 --- a/search.html +++ b/search.html @@ -120,7 +120,8 @@
                              • Naming Convention
                              • Example Algorithms
                              • Utilities
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\ No newline at end of file diff --git a/utilities.html b/utilities.html index 987750a2..29889adf 100644 --- a/utilities.html +++ b/utilities.html @@ -122,7 +122,8 @@
                                • Naming Convention
                                • Example Algorithms
                                • Utilities