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lagru/eval_select_by_peak_distance.ipynb

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eval_select_by_peak_distance.ipynb
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"%load_ext Cython\n",
"%load_ext line_profiler\n",
"\n",
"import timeit\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import line_profiler\n",
"from scipy.signal import find_peaks"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Vectorized NumPy solution"
]
},
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"source": [
"def select_by_peak_distance_py(peaks, priority, dmin):\n",
" \"\"\"\n",
" Evaluate which peaks fulfill the distance condition.\n",
"\n",
" Parameters\n",
" ----------\n",
" peaks : ndarray\n",
" Indices of peaks in `vector`.\n",
" priority : ndarray\n",
" An array with priorities matching `peaks` used to determine priority of\n",
" peaks. A peak with a higher priority value is kept over one with a lower\n",
" one.\n",
" dmin : number\n",
" Minimal distance that peaks must be spaced.\n",
"\n",
" Returns\n",
" -------\n",
" keep : ndarray[bool]\n",
" A boolean mask evaluating to true where `peaks` fulfill the distance\n",
" condition.\n",
"\n",
" Notes\n",
" -----\n",
"\n",
" .. versionadded:: 1.1.0\n",
" \"\"\"\n",
" # Peaks are evaluated by priority (larger first)\n",
" eval_peaks = peaks[np.argsort(priority)][::-1]\n",
"\n",
" # Flag peaks for deletion\n",
" del_flag = np.zeros(eval_peaks.size, dtype=bool)\n",
" for i in range(eval_peaks.size):\n",
" if not del_flag[i]:\n",
" # Flag peaks in intervall +-distance around current peak\n",
" del_flag |= (eval_peaks > eval_peaks[i] - dmin) \\\n",
" & (eval_peaks < eval_peaks[i] + dmin)\n",
" # Keep current peak\n",
" del_flag[i] = False\n",
"\n",
" keep = ~del_flag[np.argsort(eval_peaks)]\n",
"\n",
" return keep"
]
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"## Loop-based Cython solution"
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"<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">56</span>: <span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">peaks_size</span> <span class=\"o\">-</span> <span class=\"mf\">1</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">1</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">1</span><span class=\"p\">):</span></pre>\n",
"<pre class='cython code score-0 '> for (__pyx_t_8 = (__pyx_v_peaks_size - 1); __pyx_t_8 &gt; -1L; __pyx_t_8-=1) {\n",
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"<pre class='cython code score-0 '> __pyx_t_9 = __pyx_v_i;\n",
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"<pre class='cython code score-0 '> __pyx_t_10 = __pyx_v_j;\n",
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"<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">64</span>: <span class=\"n\">k</span> <span class=\"o\">=</span> <span class=\"n\">j</span> <span class=\"o\">-</span> <span class=\"mf\">1</span></pre>\n",
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" *((__pyx_t_5numpy_int8_t *) ( /* dim=0 */ ((char *) (((__pyx_t_5numpy_int8_t *) __pyx_v_keep.data) + __pyx_t_15)) )) = 0;\n",
"</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">68</span>: <span class=\"n\">k</span> <span class=\"o\">-=</span> <span class=\"mf\">1</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_v_k = (__pyx_v_k - 1);\n",
" }\n",
"</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">69</span>: </pre>\n",
"<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">70</span>: <span class=\"n\">k</span> <span class=\"o\">=</span> <span class=\"n\">j</span> <span class=\"o\">+</span> <span class=\"mf\">1</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_v_k = (__pyx_v_j + 1);\n",
"</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">71</span>: <span class=\"c\"># Flag &quot;later&quot; peaks for removal until minimal distance is exceeded</span></pre>\n",
"<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">72</span>: <span class=\"k\">while</span> <span class=\"n\">k</span> <span class=\"o\">&lt;</span> <span class=\"n\">peaks_size</span> <span class=\"ow\">and</span> <span class=\"n\">peaks</span><span class=\"p\">[</span><span class=\"n\">k</span><span class=\"p\">]</span> <span class=\"o\">-</span> <span class=\"n\">peaks</span><span class=\"p\">[</span><span class=\"n\">j</span><span class=\"p\">]</span> <span class=\"o\">&lt;</span> <span class=\"n\">distance_</span><span class=\"p\">:</span></pre>\n",
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" __pyx_t_12 = ((__pyx_v_k &lt; __pyx_v_peaks_size) != 0);\n",
" if (__pyx_t_12) {\n",
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" }\n",
" __pyx_t_16 = __pyx_v_k;\n",
" __pyx_t_17 = __pyx_v_j;\n",
" __pyx_t_12 = ((((*((__pyx_t_5numpy_intp_t *) ( /* dim=0 */ (__pyx_v_peaks.data + __pyx_t_16 * __pyx_v_peaks.strides[0]) ))) - (*((__pyx_t_5numpy_intp_t *) ( /* dim=0 */ (__pyx_v_peaks.data + __pyx_t_17 * __pyx_v_peaks.strides[0]) )))) &lt; __pyx_v_distance_) != 0);\n",
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"source": [
"%%cython -a\n",
"\n",
"import numpy as np\n",
"import cython\n",
"\n",
"cimport numpy as np\n",
"from libc.math cimport ceil\n",
"\n",
"\n",
"@cython.wraparound(False)\n",
"@cython.boundscheck(False)\n",
"def select_by_peak_distance_cy(np.intp_t[:] peaks not None,\n",
" np.float64_t[:] priority not None,\n",
" np.float64_t distance):\n",
" \"\"\"\n",
" Evaluate which peaks fulfill the distance condition.\n",
"\n",
" Parameters\n",
" ----------\n",
" peaks : ndarray\n",
" Indices of peaks in `vector`.\n",
" priority : ndarray\n",
" An array matching `peaks` used to determine priority of each peak. A peak\n",
" with a higher priority value is kept over one with a lower one.\n",
" dmin : number\n",
" Minimal distance that peaks must be spaced.\n",
"\n",
" Returns\n",
" -------\n",
" keep : ndarray[bool]\n",
" A boolean mask evaluating to true where `peaks` fulfill the distance\n",
" condition.\n",
"\n",
" Notes\n",
" -----\n",
"\n",
" .. versionadded:: 1.1.0\n",
" \"\"\"\n",
" cdef:\n",
" np.intp_t[::1] priority_to_position\n",
" np.int8_t[::1] keep\n",
" np.intp_t i, j, k, peaks_size, distance_\n",
"\n",
" peaks_size = peaks.shape[0]\n",
" # Round up because actual peak distance can only be natural number\n",
" distance_ = <np.intp_t>ceil(distance)\n",
" keep = np.ones(peaks_size, dtype=np.int8) # Prepare array of flags\n",
"\n",
" # Create map from `i` (index for `peaks` sorted by `priority`) to `j` (index\n",
" # for `peaks` sorted by position). This allows to iterate `peaks` and `keep`\n",
" # with `j` by order of `priority` while still maintaining the ability to\n",
" # step to neighbouring peaks with (`j` + 1) or (`j` - 1).\n",
" priority_to_position = np.argsort(priority)\n",
"\n",
" with nogil:\n",
" # Highest priority first -> iterate in reverse order (decreasing)\n",
" for i in range(peaks_size - 1, -1, -1):\n",
" # \"Translate\" `i` to `j` which points to current peak whose\n",
" # neighbours are to be evaluated\n",
" j = priority_to_position[i]\n",
" if keep[j] == 0:\n",
" # Skip evaluation for peak already marked as \"don't keep\"\n",
" continue\n",
"\n",
" k = j - 1\n",
" # Flag \"earlier\" peaks for removal until minimal distance is exceeded\n",
" while 0 <= k and peaks[j] - peaks[k] < distance_:\n",
" keep[k] = 0\n",
" k -= 1\n",
"\n",
" k = j + 1\n",
" # Flag \"later\" peaks for removal until minimal distance is exceeded\n",
" while k < peaks_size and peaks[k] - peaks[j] < distance_:\n",
" keep[k] = 0\n",
" k += 1\n",
"\n",
" return keep.base.view(dtype=np.bool) # Return as boolean array"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Perfomance evaluation"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"10923\n"
]
}
],
"source": [
"peaks = np.arange(1, 2 ** 15, 3)\n",
"print(peaks.size)\n",
"priority = peaks.copy().astype(np.float64)\n",
"\n",
"np.random.seed(20180313)\n",
"np.random.shuffle(priority)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"188 ms ± 7.36 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
"951 µs ± 3.68 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
]
}
],
"source": [
"%timeit select_by_peak_distance_py(peaks, priority, 4.5)\n",
"%timeit select_by_peak_distance_cy(peaks, priority, 4.5)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"25 ms ± 411 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
"909 µs ± 2.3 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
]
}
],
"source": [
"%timeit select_by_peak_distance_py(peaks, priority, 32)\n",
"%timeit select_by_peak_distance_cy(peaks, priority, 32)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3.42 ms ± 55.7 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
"900 µs ± 2.67 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
]
}
],
"source": [
"%timeit select_by_peak_distance_py(peaks, priority, 1024)\n",
"%timeit select_by_peak_distance_cy(peaks, priority, 1024)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2.69 ms ± 43.2 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
"893 µs ± 1.86 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
]
}
],
"source": [
"%timeit select_by_peak_distance_py(peaks, priority, 2 ** 15)\n",
"%timeit select_by_peak_distance_cy(peaks, priority, 2 ** 15)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2.69 ms ± 35.9 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
"894 µs ± 2.98 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
]
}
],
"source": [
"%timeit select_by_peak_distance_py(peaks, priority, 2 ** 17)\n",
"%timeit select_by_peak_distance_cy(peaks, priority, 2 ** 17)"
]
}
],
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"kernelspec": {
"display_name": "Python 3",
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"file_extension": ".py",
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