content/doc/5.1/cassandra/_images/unified/shards_graph_lambda_1.svg

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<!--
  Licensed to the Apache Software Foundation (ASF) under one or more
  contributor license agreements.  See the NOTICE file distributed with
  this work for additional information regarding copyright ownership.
  The ASF licenses this file to You under the Apache License, Version 2.0
  (the "License"); you may not use this file except in compliance with
  the License.  You may obtain a copy of the License at

      http://www.apache.org/licenses/LICENSE-2.0

  Unless required by applicable law or agreed to in writing, software
  distributed under the License is distributed on an "AS IS" BASIS,
  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  See the License for the specific language governing permissions and
  limitations under the License.
-->
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<!-- 
Generated using the following python script:

import math
import numpy
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker


m = 100000000
t = 1000000000
b = 10
l = 1

def f(d):
    if (d < m):
        return 1;
    elif d < m * b:
        return min(2**math.floor(math.log2(d/m)), b & -b)
    elif d < t * b:
        return b
    else:
        return b*2**math.floor((1 - l) * math.log2(d/(t*b)) + 0.5)


e_values = list(range(1250, 2200))
x_values = [2**(x/50) for x in e_values]
fx_values = [f(x) for x in x_values]
x_f_ratio_values = [x / fx if fx > 0 else 0 for x, fx in zip(x_values, fx_values)]


# plt.plot(x_values, fx_values, 'b', label='shards')
# plt.plot(x_values, x_f_ratio_values, 'r', label='SSTable size MiB')
# plt.xscale('log')
# plt.yscale('log')
# plt.xlabel('density MiB')
# plt.ylabel('shards / MiB')
# plt.legend()
# plt.title('SSTable size and shard count')
# plt.grid()
# plt.show()


fig, (ax0, ax1) = plt.subplots(nrows=2)

formatter0 = ticker.EngFormatter(unit='B')
formatter1 = ticker.ScalarFormatter(useMathText=True)
#ax1.axis('equal')
ax0.set_xscale('log')
ax0.set_yscale('log', base=2)
ax1.set_xscale('log')
ax1.set_yscale('log')
ax0.xaxis.set_major_formatter(formatter0)
ax0.yaxis.set_major_locator(ticker.FixedLocator([1, 2, 4, 10]))
ax0.yaxis.set_major_formatter(formatter1)
ax1.xaxis.set_major_formatter(formatter0)
ax1.yaxis.set_major_formatter(formatter0)

ax0.plot(x_values, fx_values, 'b', label='shards')
ax0.set_xlabel('density')
ax0.set_ylabel('shards')
ax0.set_title('Shard count')
ax0.grid()

ax1.plot(x_values, x_f_ratio_values, 'r', label='SSTable size')
ax1.set_xlabel('density')
ax1.set_ylabel('SSTable size')
ax1.set_title('SSTable size')
ax1.grid()

plt.tight_layout()
plt.show()
-->

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