SpectralExperiments.ipynb

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    "This experiment was done a long time ago for kaggle competition.\n",
    "\n",
    "We had a dataset of 400 features and 200,000 rows. We wanted to see what we can do by\n",
    "converting it to polar coordinates, constructing a 200,000 by 200,000 similarity matrix\n",
    "(Cosine similarity) and performing an SVD on it.\n",
    "\n",
    "Unfortunately it didn't have much success for the competition, but it helped us learn\n",
    "how to perform such a task.\n",
    "\n",
    "A 200,000 by 200,000 matrix cannot be performed directly using our puny computers due to\n",
    "insane memory requirements. Think 160GB just for materialising the initial matrix.\n",
    "\n",
    "The tricks we used to avoid this:\n",
    "* Split the matrix into 32 parts with 6250 columns each\n",
    "* Perform an SVD on each part and store the results\n",
    "* Merge the results together\n",
    "\n",
    "Although in reality, each part was generated on demand and merged on demand to reduce the\n",
    "total memory requirements.\n",
    "Also, we used the truncated SVD instead of the full SVD.\n",
    "\n",
    "In the end, the whole thing managed to run in 50 minutes!"
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   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.preprocessing import scale"
   ]
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     "text": [
      "/usr/local/anaconda3/lib/python3.7/site-packages/pyarrow/pandas_compat.py:752: FutureWarning: .labels was deprecated in version 0.24.0. Use .codes instead.\n",
      "  labels, = index.labels\n"
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   "source": [
    "df = pd.read_feather('../train.feather')"
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   "source": [
    "X = df.iloc[:, 2:].values.astype(np.float32)"
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       "<pre class='cython code score-2 '>  __pyx_t_7 = <span class='pyx_c_api'>__Pyx_PyObject_to_MemoryviewSlice_d_dc_float</span>(((PyObject *)__pyx_v_ret), PyBUF_WRITABLE);<span class='error_goto'> if (unlikely(!__pyx_t_7.memview)) __PYX_ERR(0, 18, __pyx_L1_error)</span>\n",
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       "<pre class=\"cython line score-4\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">20</span>:     <span class=\"k\">with</span> <span class=\"k\">nogil</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-4 '>  {\n",
       "      #ifdef WITH_THREAD\n",
       "      PyThreadState *_save;\n",
       "      Py_UNBLOCK_THREADS\n",
       "      <span class='pyx_c_api'>__Pyx_FastGIL_Remember</span>();\n",
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       "          <span class='pyx_c_api'>__Pyx_FastGIL_Forget</span>();\n",
       "          Py_BLOCK_THREADS\n",
       "          #endif\n",
       "          goto __pyx_L5;\n",
       "        }\n",
       "        __pyx_L5:;\n",
       "      }\n",
       "  }\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">21</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\">m</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>        __pyx_t_8 = __pyx_v_m;\n",
       "        __pyx_t_9 = __pyx_t_8;\n",
       "        for (__pyx_t_10 = 0; __pyx_t_10 &lt; __pyx_t_9; __pyx_t_10+=1) {\n",
       "          __pyx_v_i = __pyx_t_10;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">22</span>:             <span class=\"n\">x_tmp1</span> <span class=\"o\">=</span> <span class=\"n\">view</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">n</span> <span class=\"o\">-</span> <span class=\"mf\">1</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>          __pyx_t_11 = __pyx_v_i;\n",
       "          __pyx_t_12 = (__pyx_v_n - 1);\n",
       "          __pyx_v_x_tmp1 = (*((float *) ( /* dim=1 */ ((char *) (((float *) ( /* dim=0 */ (__pyx_v_view.data + __pyx_t_11 * __pyx_v_view.strides[0]) )) + __pyx_t_12)) )));\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">23</span>:             <span class=\"n\">x_tmp2</span> <span class=\"o\">=</span> <span class=\"n\">view</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">n</span> <span class=\"o\">-</span> <span class=\"mf\">2</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>          __pyx_t_13 = __pyx_v_i;\n",
       "          __pyx_t_14 = (__pyx_v_n - 2);\n",
       "          __pyx_v_x_tmp2 = (*((float *) ( /* dim=1 */ ((char *) (((float *) ( /* dim=0 */ (__pyx_v_view.data + __pyx_t_13 * __pyx_v_view.strides[0]) )) + __pyx_t_14)) )));\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">24</span>:             <span class=\"n\">r_tmp</span> <span class=\"o\">=</span> <span class=\"n\">x_tmp1</span> <span class=\"o\">*</span> <span class=\"n\">x_tmp1</span> <span class=\"o\">+</span> <span class=\"n\">x_tmp2</span> <span class=\"o\">*</span> <span class=\"n\">x_tmp2</span></pre>\n",
       "<pre class='cython code score-0 '>          __pyx_v_r_tmp = ((__pyx_v_x_tmp1 * __pyx_v_x_tmp1) + (__pyx_v_x_tmp2 * __pyx_v_x_tmp2));\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">25</span>:             <span class=\"n\">tmp</span> <span class=\"o\">=</span> <span class=\"n\">view</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"mf\">0</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>          __pyx_t_15 = __pyx_v_i;\n",
       "          __pyx_t_16 = 0;\n",
       "          __pyx_v_tmp = (*((float *) ( /* dim=1 */ ((char *) (((float *) ( /* dim=0 */ (__pyx_v_view.data + __pyx_t_15 * __pyx_v_view.strides[0]) )) + __pyx_t_16)) )));\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">26</span>:             <span class=\"k\">if</span> <span class=\"n\">tmp</span> <span class=\"o\">&gt;=</span> <span class=\"mf\">0</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-0 '>          __pyx_t_17 = ((__pyx_v_tmp &gt;= 0.0) != 0);\n",
       "          if (__pyx_t_17) {\n",
       "/* … */\n",
       "            goto __pyx_L8;\n",
       "          }\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">27</span>:                 <span class=\"n\">ret_view</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">n</span> <span class=\"o\">-</span> <span class=\"mf\">1</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">acos</span><span class=\"p\">(</span><span class=\"n\">tmp</span> <span class=\"o\">/</span> <span class=\"n\">sqrt</span><span class=\"p\">(</span><span class=\"n\">r_tmp</span><span class=\"p\">))</span></pre>\n",
       "<pre class='cython code score-0 '>            __pyx_t_18 = __pyx_v_i;\n",
       "            __pyx_t_19 = (__pyx_v_n - 1);\n",
       "            *((float *) ( /* dim=1 */ ((char *) (((float *) ( /* dim=0 */ (__pyx_v_ret_view.data + __pyx_t_18 * __pyx_v_ret_view.strides[0]) )) + __pyx_t_19)) )) = acos((((double)__pyx_v_tmp) / sqrt(__pyx_v_r_tmp)));\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">28</span>:             <span class=\"k\">else</span><span class=\"p\">:</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">29</span>:                 <span class=\"n\">ret_view</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">n</span> <span class=\"o\">-</span> <span class=\"mf\">1</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"p\">(</span><span class=\"mf\">2</span> <span class=\"o\">*</span> <span class=\"n\">pi</span><span class=\"p\">)</span> <span class=\"o\">-</span> <span class=\"n\">acos</span><span class=\"p\">(</span><span class=\"n\">tmp</span> <span class=\"o\">/</span> <span class=\"n\">sqrt</span><span class=\"p\">(</span><span class=\"n\">r_tmp</span><span class=\"p\">))</span></pre>\n",
       "<pre class='cython code score-0 '>          /*else*/ {\n",
       "            __pyx_t_20 = __pyx_v_i;\n",
       "            __pyx_t_21 = (__pyx_v_n - 1);\n",
       "            *((float *) ( /* dim=1 */ ((char *) (((float *) ( /* dim=0 */ (__pyx_v_ret_view.data + __pyx_t_20 * __pyx_v_ret_view.strides[0]) )) + __pyx_t_21)) )) = ((2.0 * M_PI) - acos((((double)__pyx_v_tmp) / sqrt(__pyx_v_r_tmp))));\n",
       "          }\n",
       "          __pyx_L8:;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">30</span>: </pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">31</span>:             <span class=\"k\">for</span> <span class=\"n\">j</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">n</span> <span class=\"o\">-</span> <span class=\"mf\">2</span><span class=\"p\">,</span> <span class=\"mf\">0</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_22 = (__pyx_v_n - 2); __pyx_t_22 &gt; 0; __pyx_t_22-=1) {\n",
       "            __pyx_v_j = __pyx_t_22;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">32</span>:                 <span class=\"n\">x_tmp1</span> <span class=\"o\">=</span> <span class=\"n\">view</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">j</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>            __pyx_t_23 = __pyx_v_i;\n",
       "            __pyx_t_24 = __pyx_v_j;\n",
       "            __pyx_v_x_tmp1 = (*((float *) ( /* dim=1 */ ((char *) (((float *) ( /* dim=0 */ (__pyx_v_view.data + __pyx_t_23 * __pyx_v_view.strides[0]) )) + __pyx_t_24)) )));\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">33</span>:                 <span class=\"n\">r_tmp</span> <span class=\"o\">=</span> <span class=\"n\">r_tmp</span> <span class=\"o\">+</span> <span class=\"n\">x_tmp1</span> <span class=\"o\">*</span> <span class=\"n\">view</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">j</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>            __pyx_t_25 = __pyx_v_i;\n",
       "            __pyx_t_26 = __pyx_v_j;\n",
       "            __pyx_v_r_tmp = (__pyx_v_r_tmp + (__pyx_v_x_tmp1 * (*((float *) ( /* dim=1 */ ((char *) (((float *) ( /* dim=0 */ (__pyx_v_view.data + __pyx_t_25 * __pyx_v_view.strides[0]) )) + __pyx_t_26)) )))));\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">34</span>:                 <span class=\"n\">ret_view</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">j</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">acos</span><span class=\"p\">(</span><span class=\"n\">view</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">j</span><span class=\"p\">]</span> <span class=\"o\">/</span> <span class=\"n\">sqrt</span><span class=\"p\">(</span><span class=\"n\">r_tmp</span><span class=\"p\">))</span></pre>\n",
       "<pre class='cython code score-0 '>            __pyx_t_27 = __pyx_v_i;\n",
       "            __pyx_t_28 = __pyx_v_j;\n",
       "            __pyx_t_29 = __pyx_v_i;\n",
       "            __pyx_t_30 = __pyx_v_j;\n",
       "            *((float *) ( /* dim=1 */ ((char *) (((float *) ( /* dim=0 */ (__pyx_v_ret_view.data + __pyx_t_29 * __pyx_v_ret_view.strides[0]) )) + __pyx_t_30)) )) = acos((((double)(*((float *) ( /* dim=1 */ ((char *) (((float *) ( /* dim=0 */ (__pyx_v_view.data + __pyx_t_27 * __pyx_v_view.strides[0]) )) + __pyx_t_28)) )))) / sqrt(__pyx_v_r_tmp)));\n",
       "          }\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">35</span>: </pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">36</span>:             <span class=\"n\">ret_view</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"mf\">0</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">sqrt</span><span class=\"p\">(</span><span class=\"n\">r_tmp</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-0 '>          __pyx_t_31 = __pyx_v_i;\n",
       "          __pyx_t_32 = 0;\n",
       "          *((float *) ( /* dim=1 */ ((char *) (((float *) ( /* dim=0 */ (__pyx_v_ret_view.data + __pyx_t_31 * __pyx_v_ret_view.strides[0]) )) + __pyx_t_32)) )) = sqrt(__pyx_v_r_tmp);\n",
       "        }\n",
       "      }\n",
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       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">41</span>: <span class=\"nd\">@cython</span><span class=\"o\">.</span><span class=\"n\">boundscheck</span><span class=\"p\">(</span><span class=\"bp\">False</span><span class=\"p\">)</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">42</span>: <span class=\"nd\">@cython</span><span class=\"o\">.</span><span class=\"n\">wraparound</span><span class=\"p\">(</span><span class=\"bp\">False</span><span class=\"p\">)</span></pre>\n",
       "<pre class=\"cython line score-75\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">43</span>: <span class=\"k\">def</span> <span class=\"nf\">cy_distance_subset</span><span class=\"p\">(</span><span class=\"nb\">float</span><span class=\"p\">[:,</span> <span class=\"p\">::</span><span class=\"mf\">1</span><span class=\"p\">]</span> <span class=\"n\">A</span><span class=\"p\">,</span> <span class=\"nb\">int</span> <span class=\"n\">start</span><span class=\"p\">,</span> <span class=\"nb\">int</span> <span class=\"n\">end</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-75 '>/* Python wrapper */\n",
       "static PyObject *__pyx_pw_46_cython_magic_7a7b8833d1d849d183182dd4c87dfc96_3cy_distance_subset(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/\n",
       "static PyMethodDef __pyx_mdef_46_cython_magic_7a7b8833d1d849d183182dd4c87dfc96_3cy_distance_subset = {\"cy_distance_subset\", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_46_cython_magic_7a7b8833d1d849d183182dd4c87dfc96_3cy_distance_subset, METH_VARARGS|METH_KEYWORDS, 0};\n",
       "static PyObject *__pyx_pw_46_cython_magic_7a7b8833d1d849d183182dd4c87dfc96_3cy_distance_subset(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n",
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       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">44</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">m</span> <span class=\"o\">=</span> <span class=\"n\">A</span><span class=\"o\">.</span><span class=\"n\">shape</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_m = (__pyx_v_A.shape[0]);\n",
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       "<pre class='cython code score-0 '>  __pyx_v_n = (__pyx_v_A.shape[1]);\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">46</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">cols</span> <span class=\"o\">=</span> <span class=\"n\">end</span> <span class=\"o\">-</span> <span class=\"n\">start</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_cols = (__pyx_v_end - __pyx_v_start);\n",
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       "    }\n",
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       "  __pyx_v_ret = ((PyArrayObject *)__pyx_t_5);\n",
       "  __pyx_t_5 = 0;\n",
       "</pre><pre class=\"cython line score-2\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">52</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">float</span>[<span class=\"p\">:,</span> <span class=\"p\">::</span><span class=\"mf\">1</span><span class=\"p\">]</span> <span class=\"n\">data</span> <span class=\"o\">=</span> <span class=\"n\">ret</span></pre>\n",
       "<pre class='cython code score-2 '>  __pyx_t_7 = <span class='pyx_c_api'>__Pyx_PyObject_to_MemoryviewSlice_d_dc_float</span>(((PyObject *)__pyx_v_ret), PyBUF_WRITABLE);<span class='error_goto'> if (unlikely(!__pyx_t_7.memview)) __PYX_ERR(0, 52, __pyx_L1_error)</span>\n",
       "  __pyx_v_data = __pyx_t_7;\n",
       "  __pyx_t_7.memview = NULL;\n",
       "  __pyx_t_7.data = NULL;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">53</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">i</span><span class=\"p\">,</span> <span class=\"nf\">j</span><span class=\"p\">,</span> <span class=\"nf\">k</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">54</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">float</span> <span class=\"nf\">val</span><span class=\"p\">,</span> <span class=\"nf\">denom1</span><span class=\"p\">,</span> <span class=\"nf\">denom2</span><span class=\"p\">,</span> <span class=\"nf\">numer</span><span class=\"p\">,</span> <span class=\"nf\">a</span><span class=\"p\">,</span> <span class=\"nf\">b</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">55</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">_start</span> <span class=\"o\">=</span> <span class=\"n\">start</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v__start = __pyx_v_start;\n",
       "</pre><pre class=\"cython line score-4\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">56</span>:     <span class=\"k\">with</span> <span class=\"k\">nogil</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-4 '>  {\n",
       "      #ifdef WITH_THREAD\n",
       "      PyThreadState *_save;\n",
       "      Py_UNBLOCK_THREADS\n",
       "      <span class='pyx_c_api'>__Pyx_FastGIL_Remember</span>();\n",
       "      #endif\n",
       "      /*try:*/ {\n",
       "/* … */\n",
       "      /*finally:*/ {\n",
       "        /*normal exit:*/{\n",
       "          #ifdef WITH_THREAD\n",
       "          <span class='pyx_c_api'>__Pyx_FastGIL_Forget</span>();\n",
       "          Py_BLOCK_THREADS\n",
       "          #endif\n",
       "          goto __pyx_L5;\n",
       "        }\n",
       "        __pyx_L5:;\n",
       "      }\n",
       "  }\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">57</span>:         <span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"n\">prange</span><span class=\"p\">(</span><span class=\"n\">m</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>        __pyx_t_8 = __pyx_v_m;\n",
       "        if (1 == 0) abort();\n",
       "        {\n",
       "            #if ((defined(__APPLE__) || defined(__OSX__)) &amp;&amp; (defined(__GNUC__) &amp;&amp; (__GNUC__ &gt; 2 || (__GNUC__ == 2 &amp;&amp; (__GNUC_MINOR__ &gt; 95)))))\n",
       "                #undef likely\n",
       "                #undef unlikely\n",
       "                #define likely(x)   (x)\n",
       "                #define unlikely(x) (x)\n",
       "            #endif\n",
       "            __pyx_t_10 = (__pyx_t_8 - 0 + 1 - 1/abs(1)) / 1;\n",
       "            if (__pyx_t_10 &gt; 0)\n",
       "            {\n",
       "                #ifdef _OPENMP\n",
       "                #pragma omp parallel\n",
       "                #endif /* _OPENMP */\n",
       "                {\n",
       "                    #ifdef _OPENMP\n",
       "                    #pragma omp for lastprivate(__pyx_v_a) lastprivate(__pyx_v_b) lastprivate(__pyx_v_denom1) lastprivate(__pyx_v_denom2) firstprivate(__pyx_v_i) lastprivate(__pyx_v_i) lastprivate(__pyx_v_j) lastprivate(__pyx_v_k) lastprivate(__pyx_v_numer) lastprivate(__pyx_v_val)\n",
       "                    #endif /* _OPENMP */\n",
       "                    for (__pyx_t_9 = 0; __pyx_t_9 &lt; __pyx_t_10; __pyx_t_9++){\n",
       "                        {\n",
       "                            __pyx_v_i = (int)(0 + 1 * __pyx_t_9);\n",
       "                            /* Initialize private variables to invalid values */\n",
       "                            __pyx_v_a = ((float)__PYX_NAN());\n",
       "                            __pyx_v_b = ((float)__PYX_NAN());\n",
       "                            __pyx_v_denom1 = ((float)__PYX_NAN());\n",
       "                            __pyx_v_denom2 = ((float)__PYX_NAN());\n",
       "                            __pyx_v_j = ((int)0xbad0bad0);\n",
       "                            __pyx_v_k = ((int)0xbad0bad0);\n",
       "                            __pyx_v_numer = ((float)__PYX_NAN());\n",
       "                            __pyx_v_val = ((float)__PYX_NAN());\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">58</span>:             <span class=\"k\">for</span> <span class=\"n\">j</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">cols</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>                            __pyx_t_11 = __pyx_v_cols;\n",
       "                            __pyx_t_12 = __pyx_t_11;\n",
       "                            for (__pyx_t_13 = 0; __pyx_t_13 &lt; __pyx_t_12; __pyx_t_13+=1) {\n",
       "                              __pyx_v_j = __pyx_t_13;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">59</span>:                 <span class=\"k\">if</span> <span class=\"n\">i</span> <span class=\"o\">==</span> <span class=\"n\">j</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-0 '>                              __pyx_t_14 = ((__pyx_v_i == __pyx_v_j) != 0);\n",
       "                              if (__pyx_t_14) {\n",
       "/* … */\n",
       "                                goto __pyx_L12;\n",
       "                              }\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">60</span>:                     <span class=\"n\">val</span> <span class=\"o\">=</span> <span class=\"mf\">1</span></pre>\n",
       "<pre class='cython code score-0 '>                                __pyx_v_val = 1.0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">61</span>:                 <span class=\"k\">else</span><span class=\"p\">:</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">62</span>:                     <span class=\"c\"># Cosine similarity</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">63</span>:                     <span class=\"n\">numer</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>                              /*else*/ {\n",
       "                                __pyx_v_numer = 0.0;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">64</span>:                     <span class=\"n\">denom1</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>                                __pyx_v_denom1 = 0.0;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">65</span>:                     <span class=\"n\">denom2</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>                                __pyx_v_denom2 = 0.0;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">66</span>:                     <span class=\"k\">for</span> <span class=\"n\">k</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">n</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>                                __pyx_t_15 = __pyx_v_n;\n",
       "                                __pyx_t_16 = __pyx_t_15;\n",
       "                                for (__pyx_t_17 = 0; __pyx_t_17 &lt; __pyx_t_16; __pyx_t_17+=1) {\n",
       "                                  __pyx_v_k = __pyx_t_17;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">67</span>:                         <span class=\"n\">a</span> <span class=\"o\">=</span> <span class=\"n\">A</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">k</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>                                  __pyx_t_18 = __pyx_v_i;\n",
       "                                  __pyx_t_19 = __pyx_v_k;\n",
       "                                  __pyx_v_a = (*((float *) ( /* dim=1 */ ((char *) (((float *) ( /* dim=0 */ (__pyx_v_A.data + __pyx_t_18 * __pyx_v_A.strides[0]) )) + __pyx_t_19)) )));\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">68</span>:                         <span class=\"n\">b</span> <span class=\"o\">=</span> <span class=\"n\">A</span><span class=\"p\">[</span><span class=\"n\">start</span> <span class=\"o\">+</span> <span class=\"n\">j</span><span class=\"p\">,</span> <span class=\"n\">k</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>                                  __pyx_t_20 = (__pyx_v_start + __pyx_v_j);\n",
       "                                  __pyx_t_21 = __pyx_v_k;\n",
       "                                  __pyx_v_b = (*((float *) ( /* dim=1 */ ((char *) (((float *) ( /* dim=0 */ (__pyx_v_A.data + __pyx_t_20 * __pyx_v_A.strides[0]) )) + __pyx_t_21)) )));\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">69</span>:                         <span class=\"n\">numer</span> <span class=\"o\">=</span> <span class=\"n\">numer</span> <span class=\"o\">+</span> <span class=\"n\">a</span> <span class=\"o\">*</span> <span class=\"n\">b</span></pre>\n",
       "<pre class='cython code score-0 '>                                  __pyx_v_numer = (__pyx_v_numer + (__pyx_v_a * __pyx_v_b));\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">70</span>:                         <span class=\"n\">denom1</span> <span class=\"o\">=</span> <span class=\"n\">denom1</span> <span class=\"o\">+</span> <span class=\"n\">a</span> <span class=\"o\">*</span> <span class=\"n\">a</span></pre>\n",
       "<pre class='cython code score-0 '>                                  __pyx_v_denom1 = (__pyx_v_denom1 + (__pyx_v_a * __pyx_v_a));\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">71</span>:                         <span class=\"n\">denom2</span> <span class=\"o\">=</span> <span class=\"n\">denom2</span> <span class=\"o\">+</span> <span class=\"n\">b</span> <span class=\"o\">*</span> <span class=\"n\">b</span></pre>\n",
       "<pre class='cython code score-0 '>                                  __pyx_v_denom2 = (__pyx_v_denom2 + (__pyx_v_b * __pyx_v_b));\n",
       "                                }\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">72</span>:                     <span class=\"n\">val</span> <span class=\"o\">=</span> <span class=\"n\">numer</span> <span class=\"o\">/</span> <span class=\"p\">(</span><span class=\"n\">sqrt</span><span class=\"p\">(</span><span class=\"n\">denom1</span><span class=\"p\">)</span> <span class=\"o\">*</span> <span class=\"n\">sqrt</span><span class=\"p\">(</span><span class=\"n\">denom2</span><span class=\"p\">))</span></pre>\n",
       "<pre class='cython code score-0 '>                                __pyx_v_val = (((double)__pyx_v_numer) / (sqrt(__pyx_v_denom1) * sqrt(__pyx_v_denom2)));\n",
       "                              }\n",
       "                              __pyx_L12:;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">73</span>: </pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">74</span>:                 <span class=\"n\">data</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">j</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">val</span></pre>\n",
       "<pre class='cython code score-0 '>                              __pyx_t_22 = __pyx_v_i;\n",
       "                              __pyx_t_23 = __pyx_v_j;\n",
       "                              *((float *) ( /* dim=1 */ ((char *) (((float *) ( /* dim=0 */ (__pyx_v_data.data + __pyx_t_22 * __pyx_v_data.strides[0]) )) + __pyx_t_23)) )) = __pyx_v_val;\n",
       "                            }\n",
       "                        }\n",
       "                    }\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "        #if ((defined(__APPLE__) || defined(__OSX__)) &amp;&amp; (defined(__GNUC__) &amp;&amp; (__GNUC__ &gt; 2 || (__GNUC__ == 2 &amp;&amp; (__GNUC_MINOR__ &gt; 95)))))\n",
       "            #undef likely\n",
       "            #undef unlikely\n",
       "            #define likely(x)   __builtin_expect(!!(x), 1)\n",
       "            #define unlikely(x) __builtin_expect(!!(x), 0)\n",
       "        #endif\n",
       "      }\n",
       "</pre><pre class=\"cython line score-2\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">75</span>:     <span class=\"k\">return</span> <span class=\"n\">ret</span></pre>\n",
       "<pre class='cython code score-2 '>  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_r);\n",
       "  <span class='pyx_macro_api'>__Pyx_INCREF</span>(((PyObject *)__pyx_v_ret));\n",
       "  __pyx_r = ((PyObject *)__pyx_v_ret);\n",
       "  goto __pyx_L0;\n",
       "</pre></div></body></html>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%cython -a --compile-args=-Xpreprocessor --compile-args=-fopenmp --link-args=-lomp\n",
    "import numpy as np\n",
    "cimport numpy as np\n",
    "cimport cython\n",
    "from libc.math cimport sqrt, acos, pi\n",
    "from cython.parallel import prange\n",
    "\n",
    "@cython.cdivision(True)\n",
    "@cython.boundscheck(False)\n",
    "@cython.wraparound(False)\n",
    "def polar(float[:, ::1] A):\n",
    "    \"\"\"Convert cartesian to polar coordinates.\"\"\"\n",
    "    cdef int m = A.shape[0]\n",
    "    cdef int n = A.shape[1]\n",
    "    \n",
    "    cdef float r_tmp, denom, tmp, x_tmp1, x_tmp2\n",
    "    cdef float[:, ::1] view = A\n",
    "    cdef np.ndarray[np.float32_t, ndim=2] ret = np.empty((m, n), dtype=np.float32)\n",
    "    cdef float[:, ::1] ret_view = ret\n",
    "    \n",
    "    with nogil:\n",
    "        for i in range(m):\n",
    "            x_tmp1 = view[i, n - 1]\n",
    "            x_tmp2 = view[i, n - 2]\n",
    "            r_tmp = x_tmp1 * x_tmp1 + x_tmp2 * x_tmp2\n",
    "            tmp = view[i, 0]\n",
    "            if tmp >= 0:\n",
    "                ret_view[i, n - 1] = acos(tmp / sqrt(r_tmp))\n",
    "            else:\n",
    "                ret_view[i, n - 1] = (2 * pi) - acos(tmp / sqrt(r_tmp))\n",
    "\n",
    "            for j in range(n - 2, 0, -1):\n",
    "                x_tmp1 = view[i, j]\n",
    "                r_tmp = r_tmp + x_tmp1 * view[i, j]\n",
    "                ret_view[i, j] = acos(view[i, j] / sqrt(r_tmp))\n",
    "\n",
    "            ret_view[i, 0] = sqrt(r_tmp)  \n",
    "    np.nan_to_num(ret, copy=False)\n",
    "    return ret\n",
    "\n",
    "@cython.cdivision(True)\n",
    "@cython.boundscheck(False)\n",
    "@cython.wraparound(False)\n",
    "def cy_distance_subset(float[:, ::1] A, int start, int end):\n",
    "    cdef int m = A.shape[0]\n",
    "    cdef int n = A.shape[1]\n",
    "    cdef int cols = end - start\n",
    "    \n",
    "    assert start <= end\n",
    "    assert start >= 0\n",
    "    assert end <= m\n",
    "    cdef np.ndarray[np.float32_t, ndim=2] ret = np.empty((m, cols), dtype=np.float32)\n",
    "    cdef float[:, ::1] data = ret\n",
    "    cdef int i, j, k\n",
    "    cdef float val, denom1, denom2, numer, a, b\n",
    "    cdef int _start = start\n",
    "    with nogil:        \n",
    "        for i in prange(m):\n",
    "            for j in range(cols):\n",
    "                if i == j:\n",
    "                    val = 1\n",
    "                else:\n",
    "                    # Cosine similarity\n",
    "                    numer = 0\n",
    "                    denom1 = 0\n",
    "                    denom2 = 0\n",
    "                    for k in range(n):\n",
    "                        a = A[i, k]\n",
    "                        b = A[start + j, k]\n",
    "                        numer = numer + a * b\n",
    "                        denom1 = denom1 + a * a\n",
    "                        denom2 = denom2 + b * b\n",
    "                    val = numer / (sqrt(denom1) * sqrt(denom2))\n",
    "                    \n",
    "                data[i, j] = val\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.       , 0.       ],\n",
       "       [6.4031243, 0.8960554]], dtype=float32)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([[0, 0], [4, 5]], dtype=np.float32)\n",
    "polar(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((0.0, 0.0), (6.4031242374328485, 0.8960553845713439))"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import cmath\n",
    "t1 = complex(0, 0)\n",
    "t2 = complex(4, 5)\n",
    "cmath.polar(t1), cmath.polar(t2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "from sklearn.utils.extmath import randomized_svd\n",
    "from scipy.linalg import qr\n",
    "\n",
    "\n",
    "def fullsvd(A, k):\n",
    "    u, s, v = np.linalg.svd(A, full_matrices=False)\n",
    "    return u[:, :k], s[:k], v[:, :k]\n",
    "\n",
    "def merge(us1, us2, k):\n",
    "    u1, s1 = us1\n",
    "    u2, s2 = us2\n",
    "    \n",
    "    k1 = s1.shape[0]\n",
    "    k2 = s2.shape[0]\n",
    "    \n",
    "    Z = u1.T @ u2\n",
    "    u_, r = qr(u2 - u1 @ Z, mode='economic')\n",
    "    X = np.zeros((k1 + k2, k1 + k2))\n",
    "    X[:k1, :k1] = np.diag(s1)\n",
    "    X[:k1, k1:] = Z @ np.diag(s2)\n",
    "    X[k1:, k1:] = r @ np.diag(s2)\n",
    "    \n",
    "    ur, sr, _ = fullsvd(X, k)\n",
    "    r1 = ur[:k1, :]\n",
    "    r2 = ur[k2:, :]\n",
    "    urr = (u1 @ r1 + u_ @ r2)[:, :k]\n",
    "    return urr, sr\n",
    "\n",
    "def tsvd_dm(A, k=20, splits=2, randomized=False, split_k=None):\n",
    "    if split_k is None:\n",
    "        split_k = k\n",
    "        \n",
    "    m, n = A.shape\n",
    "    split_size = m // splits\n",
    "    results = []\n",
    "    \n",
    "    for i in range(splits):\n",
    "        A_sub = cy_distance_subset(A, i * split_size, (i + 1) * split_size)\n",
    "        print(A_sub.shape, split_size)\n",
    "        print(f'Subset {i} generated')\n",
    "        if randomized:\n",
    "            *us, _ = randomized_svd(A_sub, split_k)\n",
    "        else:\n",
    "            *us, _ = fullsvd(A_sub, split_k)\n",
    "        print(f'TSVD completed')\n",
    "        results.append(us)\n",
    "    \n",
    "    if len(results) % 2 == 1:\n",
    "        results.extend([None])\n",
    "    \n",
    "    while len(results) > 1:\n",
    "        work_stack = []\n",
    "        pairs = zip(results[::2], results[1::2])\n",
    "        for us1, us2 in pairs:\n",
    "            if us2 is None:\n",
    "                work_stack.append(us1)\n",
    "            else:\n",
    "                merged = merge(us1, us2, k=k)\n",
    "                work_stack.append(merged)\n",
    "                \n",
    "        if len(results) > 1 and len(results) % 2 == 1:\n",
    "            work_stack.extend([None])\n",
    "        results = work_stack\n",
    "        \n",
    "    return work_stack[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda3/lib/python3.7/site-packages/sklearn/preprocessing/data.py:176: UserWarning: Numerical issues were encountered when centering the data and might not be solved. Dataset may contain too large values. You may need to prescale your features.\n",
      "  warnings.warn(\"Numerical issues were encountered \"\n",
      "/usr/local/anaconda3/lib/python3.7/site-packages/sklearn/preprocessing/data.py:193: UserWarning: Numerical issues were encountered when scaling the data and might not be solved. The standard deviation of the data is probably very close to 0. \n",
      "  warnings.warn(\"Numerical issues were encountered \"\n"
     ]
    }
   ],
   "source": [
    "scaledX = polar(np.ascontiguousarray(scale(X)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(200000, 6250) 6250\n",
      "Subset 0 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 1 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 2 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 3 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 4 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 5 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 6 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 7 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 8 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 9 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 10 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 11 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 12 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 13 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 14 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 15 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 16 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 17 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 18 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 19 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 20 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 21 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 22 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 23 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 24 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 25 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 26 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 27 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 28 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 29 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 30 generated\n",
      "TSVD completed\n",
      "(200000, 6250) 6250\n",
      "Subset 31 generated\n",
      "TSVD completed\n",
      "CPU times: user 2h 54min 7s, sys: 3min 54s, total: 2h 58min 1s\n",
      "Wall time: 50min 19s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "u_, s_ = tsvd_dm(scaledX, k=256, splits=32, randomized=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.23329996e-03, -4.50305762e-05, -1.63995031e-05, ...,\n",
       "         9.23384342e-03, -7.32435296e-03, -2.06722987e-02],\n",
       "       [ 2.23904303e-03, -4.37589266e-05, -1.50274995e-05, ...,\n",
       "        -1.42078221e-03,  2.90455183e-03, -2.20233713e-03],\n",
       "       [ 2.22991245e-03, -4.34418987e-05, -1.43318189e-05, ...,\n",
       "         9.84443870e-03,  1.92597491e-02, -2.83856845e-02],\n",
       "       ...,\n",
       "       [ 2.23981194e-03, -4.38488438e-05, -1.45968639e-05, ...,\n",
       "        -2.50437212e-04, -3.68999544e-04,  9.19217300e-05],\n",
       "       [ 2.23113970e-03, -4.42691674e-05, -1.53046902e-05, ...,\n",
       "        -4.86012248e-04, -1.35428186e-03, -1.86371828e-04],\n",
       "       [ 2.23968731e-03, -4.39190640e-05, -1.47362449e-05, ...,\n",
       "        -1.07455434e-03,  8.36278454e-04, -7.07521603e-04]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "test = np.random.random((1000, 5)).astype(np.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1000, 125) 125\n",
      "Subset 0 generated\n",
      "TSVD completed\n",
      "(1000, 125) 125\n",
      "Subset 1 generated\n",
      "TSVD completed\n",
      "(1000, 125) 125\n",
      "Subset 2 generated\n",
      "TSVD completed\n",
      "(1000, 125) 125\n",
      "Subset 3 generated\n",
      "TSVD completed\n",
      "(1000, 125) 125\n",
      "Subset 4 generated\n",
      "TSVD completed\n",
      "(1000, 125) 125\n",
      "Subset 5 generated\n",
      "TSVD completed\n",
      "(1000, 125) 125\n",
      "Subset 6 generated\n",
      "TSVD completed\n",
      "(1000, 125) 125\n",
      "Subset 7 generated\n",
      "TSVD completed\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([[ 0.03317, -0.03126, -0.02837, ..., -0.00103,  0.01143,  0.01308],\n",
       "        [ 0.03459,  0.00192,  0.01074, ...,  0.00211,  0.00297,  0.00072],\n",
       "        [ 0.02829,  0.04725, -0.05226, ..., -0.00672, -0.00184, -0.02342],\n",
       "        ...,\n",
       "        [ 0.03288, -0.01295, -0.00853, ..., -0.00197, -0.00193, -0.0004 ],\n",
       "        [ 0.0343 , -0.03534, -0.00767, ..., -0.00128,  0.00025, -0.00113],\n",
       "        [ 0.02793, -0.00138,  0.07975, ...,  0.00331,  0.00012,  0.00473]]),\n",
       " array([7.78096e+02, 5.91851e+01, 5.67800e+01, 5.49997e+01, 5.09420e+01,\n",
       "        1.25378e+00, 1.08586e+00, 9.88866e-01, 8.50822e-01, 8.33857e-01,\n",
       "        8.03733e-01, 7.68136e-01, 7.56264e-01, 7.52898e-01, 7.45135e-01,\n",
       "        7.34743e-01, 7.32305e-01, 7.27463e-01, 7.14419e-01, 6.97193e-01]))"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.set_printoptions(suppress=False, precision=5)\n",
    "tsvd_dm(test, k=20, split_k=100, splits=8, randomized=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[-0.03313,  0.03175, -0.02861, ...,  0.03129,  0.01088,  0.02663],\n",
       "        [-0.03457, -0.00177,  0.01075, ...,  0.00825,  0.00216, -0.04409],\n",
       "        [-0.0282 , -0.0474 , -0.0529 , ...,  0.00046, -0.01445,  0.03134],\n",
       "        ...,\n",
       "        [-0.03289,  0.01285, -0.00872, ...,  0.02405, -0.02098, -0.00832],\n",
       "        [-0.03431,  0.03528, -0.00776, ..., -0.00929, -0.01536,  0.0145 ],\n",
       "        [-0.02793,  0.00163,  0.07973, ..., -0.02279,  0.03107, -0.03795]],\n",
       "       dtype=float32),\n",
       " array([7.77901e+02, 5.92396e+01, 5.68290e+01, 5.50381e+01, 5.09926e+01,\n",
       "        2.40677e-06, 2.38656e-06, 2.36640e-06, 2.36152e-06, 2.34998e-06,\n",
       "        2.33300e-06, 2.33038e-06, 2.31951e-06, 2.30577e-06, 2.30026e-06,\n",
       "        2.29809e-06, 2.29331e-06, 2.28218e-06, 2.27821e-06, 2.27747e-06],\n",
       "       dtype=float32))"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u, s, v = fullsvd(cy_distance_subset(test, 0, 1000), 20)\n",
    "u, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.     , 0.63343, 0.52882, 0.8548 , 0.85561, 0.50162, 0.73045],\n",
       "       [0.63343, 1.     , 0.88059, 0.83249, 0.88845, 0.77294, 0.94409],\n",
       "       [0.52882, 0.88059, 1.     , 0.83658, 0.87299, 0.70342, 0.88753],\n",
       "       [0.8548 , 0.83249, 0.83658, 1.     , 0.94649, 0.57287, 0.90613],\n",
       "       [0.85561, 0.88845, 0.87299, 0.94649, 1.     , 0.78465, 0.9623 ],\n",
       "       [0.50162, 0.77294, 0.70342, 0.57287, 0.78465, 1.     , 0.84579],\n",
       "       [0.73045, 0.94409, 0.88753, 0.90613, 0.9623 , 0.84579, 1.     ]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cy_distance_subset(test[:7], 0, 7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.     , 0.63343, 0.52882],\n",
       "       [0.63343, 1.     , 0.88059],\n",
       "       [0.52882, 0.88059, 1.     ],\n",
       "       [0.8548 , 0.83249, 0.83658],\n",
       "       [0.85561, 0.88845, 0.87299],\n",
       "       [0.50162, 0.77294, 0.70342],\n",
       "       [0.73045, 0.94409, 0.88753]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cy_distance_subset(test, 0, 3)[:7]"
   ]
  }
 ],
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