refraction-ray/eigh-issue.ipynb

## eigh-issue.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "% matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import sys\n",
    "import platform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No LSB modules are available.\r\n",
      "Distributor ID:\tUbuntu\r\n",
      "Description:\tUbuntu 18.04.2 LTS\r\n",
      "Release:\t18.04\r\n",
      "Codename:\tbionic\r\n"
     ]
    }
   ],
   "source": [
    "!lsb_release -a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              total        used        free      shared  buff/cache   available\r\n",
      "Mem:      263780292    51500748    55727464        2136   156552080   210428488\r\n",
      "Swap:       8388604      718096     7670508\r\n"
     ]
    }
   ],
   "source": [
    "!free"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Architecture:        x86_64\r\n",
      "CPU op-mode(s):      32-bit, 64-bit\r\n",
      "Byte Order:          Little Endian\r\n",
      "CPU(s):              56\r\n",
      "On-line CPU(s) list: 0-55\r\n",
      "Thread(s) per core:  2\r\n",
      "Core(s) per socket:  14\r\n",
      "Socket(s):           2\r\n",
      "NUMA node(s):        2\r\n",
      "Vendor ID:           GenuineIntel\r\n",
      "CPU family:          6\r\n",
      "Model:               85\r\n",
      "Model name:          Intel(R) Xeon(R) Gold 5120 CPU @ 2.20GHz\r\n",
      "Stepping:            4\r\n",
      "CPU MHz:             999.999\r\n",
      "CPU max MHz:         3200.0000\r\n",
      "CPU min MHz:         1000.0000\r\n",
      "BogoMIPS:            4400.00\r\n",
      "Virtualization:      VT-x\r\n",
      "L1d cache:           32K\r\n",
      "L1i cache:           32K\r\n",
      "L2 cache:            1024K\r\n",
      "L3 cache:            19712K\r\n",
      "NUMA node0 CPU(s):   0-13,28-41\r\n",
      "NUMA node1 CPU(s):   14-27,42-55\r\n",
      "Flags:               fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx pdpe1gb rdtscp lm constant_tsc art arch_perfmon pebs bts rep_good nopl xtopology nonstop_tsc cpuid aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 sdbg fma cx16 xtpr pdcm pcid dca sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave avx f16c rdrand lahf_lm abm 3dnowprefetch cpuid_fault epb cat_l3 cdp_l3 invpcid_single pti intel_ppin ssbd mba ibrs ibpb stibp tpr_shadow vnmi flexpriority ept vpid fsgsbase tsc_adjust bmi1 hle avx2 smep bmi2 erms invpcid rtm cqm mpx rdt_a avx512f avx512dq rdseed adx smap clflushopt clwb intel_pt avx512cd avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local dtherm ida arat pln pts hwp hwp_act_window hwp_epp hwp_pkg_req pku ospke md_clear flush_l1d\r\n"
     ]
    }
   ],
   "source": [
    "!lscpu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('1.16.1',\n",
       " '3.6.8 |Intel Corporation| (default, Mar  1 2019, 00:10:45) \\n[GCC 4.8.2 20140120 (Red Hat 4.8.2-15)]',\n",
       " 'Linux-4.15.0-50-generic-x86_64-with-debian-buster-sid')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.__version__, sys.version, platform.platform()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# python shipped with intel parallel studio xe 2019.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mkl_info:\n",
      "    libraries = ['mkl_rt', 'pthread']\n",
      "    library_dirs = ['/home/z/.conda/envs/test/lib']\n",
      "    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]\n",
      "    include_dirs = ['/home/z/.conda/envs/test/include']\n",
      "blas_mkl_info:\n",
      "    libraries = ['mkl_rt', 'pthread']\n",
      "    library_dirs = ['/home/z/.conda/envs/test/lib']\n",
      "    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]\n",
      "    include_dirs = ['/home/z/.conda/envs/test/include']\n",
      "blas_opt_info:\n",
      "    libraries = ['mkl_rt', 'pthread']\n",
      "    library_dirs = ['/home/z/.conda/envs/test/lib']\n",
      "    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]\n",
      "    include_dirs = ['/home/z/.conda/envs/test/include']\n",
      "lapack_mkl_info:\n",
      "    libraries = ['mkl_rt', 'pthread']\n",
      "    library_dirs = ['/home/z/.conda/envs/test/lib']\n",
      "    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]\n",
      "    include_dirs = ['/home/z/.conda/envs/test/include']\n",
      "lapack_opt_info:\n",
      "    libraries = ['mkl_rt', 'pthread']\n",
      "    library_dirs = ['/home/z/.conda/envs/test/lib']\n",
      "    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]\n",
      "    include_dirs = ['/home/z/.conda/envs/test/include']\n"
     ]
    }
   ],
   "source": [
    "np.__config__.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "n=32766\n",
    "a=np.random.rand(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(32766, 32766)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_32766=np.diag(a)\n",
    "m_32766.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 6h 6min 5s, sys: 15min 47s, total: 6h 21min 53s\n",
      "Wall time: 14min 5s\n"
     ]
    }
   ],
   "source": [
    "%time E_32766, V_32766 = np.linalg.eigh(m_32766) ## normal results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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XCbWFC0k/rhH9vhnG+1xCXVYwnDt56RWdCSPHjoZlREIlK4sXT3+Q3usf5kROoQP/YTod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\n4S4iEoP+Dw6gQDbF/uskAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(E_32766,\"b.\", sorted(a),\"r-\", markersize=0.5,)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(32767, 32767)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n=32767\n",
    "b=np.random.rand(n)\n",
    "m_32767=np.diag(b)\n",
    "m_32767.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 624 µs, sys: 0 ns, total: 624 µs\n",
      "Wall time: 508 µs\n"
     ]
    }
   ],
   "source": [
    "%time E_32767, V_32767=np.linalg.eigh(m_32767)  ## wierd results with very short time of computation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.91634688e-310, 6.91634712e-310, 6.91634712e-310, ...,\n",
       "       6.91634764e-310, 6.91634764e-310, 6.91634813e-310])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E_32767 ### totally wrong"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yhr/BTs1xn5cbpuCYJ1mT5F7gUYYl+q1F9vdsxrb9yZZvtf2sHpVjpRhGnTddLX+O9aqq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\nSUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(V_32767[:,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1h 31min 43s, sys: 54.5 s, total: 1h 32min 38s\n",
      "Wall time: 3min 22s\n"
     ]
    }
   ],
   "source": [
    "%time nE_32767 = np.linalg.eigvalsh(m_32767) ## normal results for only eigenvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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d6FuX7RjnXBrwJ1AqEAUeZ8IEkirXpA5L6MVYopn3V7cuIiIZ/An37DrwrFHq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\nRK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nE_32767,\"b.\", sorted(b),\"r-\", markersize=0.5,)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%time nnE_32767 = np.linalg.eig(m_32767) # seems correct for the compute time, though no patience to wait for the result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0b111111111111111'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bin(32767) # issue with related with int16?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len('111111111111111')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}