EqPerformance-multisys.ipynb

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    "import numpy as np\n",
    "from pycalphad import Model, Database, calculate, equilibrium\n",
    "import pycalphad.variables as v\n",
    "\n",
    "#dbf = Database('2016-08-10-AlGdMgand18RLPSO-for 3d plot.tdb')\n",
    "dbf = Database('alfe_sei.TDB')\n",
    "models = {key: Model(dbf, ['AL', 'FE', 'VA'], key) for key in dbf.phases.keys()}"
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      "/home/rotis/anaconda/envs/calphadpy3/lib/python3.5/site-packages/Cython/Distutils/old_build_ext.py:30: UserWarning: Cython.Distutils.old_build_ext does not properly handle dependencies and is deprecated.\n",
      "  \"Cython.Distutils.old_build_ext does not properly handle dependencies \"\n"
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       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">22</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=\"\">23</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-154\" onclick='toggleDiv(this)'>+<span class=\"\">24</span>: <span class=\"k\">def</span> <span class=\"nf\">_build_multiphase_system</span><span class=\"p\">(</span><span class=\"nb\">int</span><span class=\"p\">[:]</span> <span class=\"n\">phase_dof</span><span class=\"p\">,</span> <span class=\"n\">phases</span><span class=\"p\">,</span> <span class=\"n\">cur_conds</span><span class=\"p\">,</span> <span class=\"n\">double</span><span class=\"p\">[:]</span> <span class=\"n\">site_fracs</span><span class=\"p\">,</span> <span class=\"n\">double</span><span class=\"p\">[:]</span> <span class=\"n\">phase_fracs</span><span class=\"p\">,</span></pre>\n",
       "<pre class='cython code score-154 '>/* Python wrapper */\n",
       "static PyObject *__pyx_pw_46_cython_magic_c9e2ae6042f41ab910df839a817d1108_1_build_multiphase_system(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/\n",
       "static PyMethodDef __pyx_mdef_46_cython_magic_c9e2ae6042f41ab910df839a817d1108_1_build_multiphase_system = {\"_build_multiphase_system\", (PyCFunction)__pyx_pw_46_cython_magic_c9e2ae6042f41ab910df839a817d1108_1_build_multiphase_system, METH_VARARGS|METH_KEYWORDS, 0};\n",
       "static PyObject *__pyx_pw_46_cython_magic_c9e2ae6042f41ab910df839a817d1108_1_build_multiphase_system(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n",
       "  __Pyx_memviewslice __pyx_v_phase_dof = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
       "  PyObject *__pyx_v_phases = 0;\n",
       "  PyObject *__pyx_v_cur_conds = 0;\n",
       "  __Pyx_memviewslice __pyx_v_site_fracs = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
       "  __Pyx_memviewslice __pyx_v_phase_fracs = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
       "  CYTHON_UNUSED PyObject *__pyx_v_l_constraints = 0;\n",
       "  CYTHON_UNUSED PyObject *__pyx_v_constraint_jac = 0;\n",
       "  PyArrayObject *__pyx_v_constraint_hess = 0;\n",
       "  PyArrayObject *__pyx_v_l_multipliers = 0;\n",
       "  PyObject *__pyx_v_phase_records = 0;\n",
       "  PyObject *__pyx_r = 0;\n",
       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"_build_multiphase_system (wrapper)\", 0);\n",
       "  {\n",
       "    static PyObject **__pyx_pyargnames[] = {&amp;__pyx_n_s_phase_dof,&amp;__pyx_n_s_phases,&amp;__pyx_n_s_cur_conds,&amp;__pyx_n_s_site_fracs,&amp;__pyx_n_s_phase_fracs,&amp;__pyx_n_s_l_constraints,&amp;__pyx_n_s_constraint_jac,&amp;__pyx_n_s_constraint_hess,&amp;__pyx_n_s_l_multipliers,&amp;__pyx_n_s_phase_records,0};\n",
       "    PyObject* values[10] = {0,0,0,0,0,0,0,0,0,0};\n",
       "    if (unlikely(__pyx_kwds)) {\n",
       "      Py_ssize_t kw_args;\n",
       "      const Py_ssize_t pos_args = <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args);\n",
       "      switch (pos_args) {\n",
       "        case 10: values[9] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 9);\n",
       "        case  9: values[8] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 8);\n",
       "        case  8: values[7] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 7);\n",
       "        case  7: values[6] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 6);\n",
       "        case  6: values[5] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 5);\n",
       "        case  5: values[4] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 4);\n",
       "        case  4: values[3] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 3);\n",
       "        case  3: values[2] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 2);\n",
       "        case  2: values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "        case  1: values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
       "        case  0: break;\n",
       "        default: goto __pyx_L5_argtuple_error;\n",
       "      }\n",
       "      kw_args = <span class='py_c_api'>PyDict_Size</span>(__pyx_kwds);\n",
       "      switch (pos_args) {\n",
       "        case  0:\n",
       "        if (likely((values[0] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_phase_dof)) != 0)) kw_args--;\n",
       "        else goto __pyx_L5_argtuple_error;\n",
       "        case  1:\n",
       "        if (likely((values[1] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_phases)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"_build_multiphase_system\", 1, 10, 10, 1); __PYX_ERR(0, 24, __pyx_L3_error)\n",
       "        }\n",
       "        case  2:\n",
       "        if (likely((values[2] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_cur_conds)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"_build_multiphase_system\", 1, 10, 10, 2); __PYX_ERR(0, 24, __pyx_L3_error)\n",
       "        }\n",
       "        case  3:\n",
       "        if (likely((values[3] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_site_fracs)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"_build_multiphase_system\", 1, 10, 10, 3); __PYX_ERR(0, 24, __pyx_L3_error)\n",
       "        }\n",
       "        case  4:\n",
       "        if (likely((values[4] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_phase_fracs)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"_build_multiphase_system\", 1, 10, 10, 4); __PYX_ERR(0, 24, __pyx_L3_error)\n",
       "        }\n",
       "        case  5:\n",
       "        if (likely((values[5] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_l_constraints)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"_build_multiphase_system\", 1, 10, 10, 5); __PYX_ERR(0, 24, __pyx_L3_error)\n",
       "        }\n",
       "        case  6:\n",
       "        if (likely((values[6] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_constraint_jac)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"_build_multiphase_system\", 1, 10, 10, 6); __PYX_ERR(0, 24, __pyx_L3_error)\n",
       "        }\n",
       "        case  7:\n",
       "        if (likely((values[7] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_constraint_hess)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"_build_multiphase_system\", 1, 10, 10, 7); __PYX_ERR(0, 24, __pyx_L3_error)\n",
       "        }\n",
       "        case  8:\n",
       "        if (likely((values[8] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_l_multipliers)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"_build_multiphase_system\", 1, 10, 10, 8); __PYX_ERR(0, 24, __pyx_L3_error)\n",
       "        }\n",
       "        case  9:\n",
       "        if (likely((values[9] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_phase_records)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"_build_multiphase_system\", 1, 10, 10, 9); __PYX_ERR(0, 24, __pyx_L3_error)\n",
       "        }\n",
       "      }\n",
       "      if (unlikely(kw_args &gt; 0)) {\n",
       "        if (unlikely(<span class='pyx_c_api'>__Pyx_ParseOptionalKeywords</span>(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, \"_build_multiphase_system\") &lt; 0)) __PYX_ERR(0, 24, __pyx_L3_error)\n",
       "      }\n",
       "    } else if (<span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args) != 10) {\n",
       "      goto __pyx_L5_argtuple_error;\n",
       "    } else {\n",
       "      values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
       "      values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "      values[2] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 2);\n",
       "      values[3] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 3);\n",
       "      values[4] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 4);\n",
       "      values[5] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 5);\n",
       "      values[6] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 6);\n",
       "      values[7] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 7);\n",
       "      values[8] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 8);\n",
       "      values[9] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 9);\n",
       "    }\n",
       "    __pyx_v_phase_dof = <span class='pyx_c_api'>__Pyx_PyObject_to_MemoryviewSlice_ds_int</span>(values[0]); if (unlikely(!__pyx_v_phase_dof.memview)) __PYX_ERR(0, 24, __pyx_L3_error)\n",
       "    __pyx_v_phases = values[1];\n",
       "    __pyx_v_cur_conds = values[2];\n",
       "    __pyx_v_site_fracs = <span class='pyx_c_api'>__Pyx_PyObject_to_MemoryviewSlice_ds_double</span>(values[3]); if (unlikely(!__pyx_v_site_fracs.memview)) __PYX_ERR(0, 24, __pyx_L3_error)\n",
       "    __pyx_v_phase_fracs = <span class='pyx_c_api'>__Pyx_PyObject_to_MemoryviewSlice_ds_double</span>(values[4]); if (unlikely(!__pyx_v_phase_fracs.memview)) __PYX_ERR(0, 24, __pyx_L3_error)\n",
       "    __pyx_v_l_constraints = values[5];\n",
       "    __pyx_v_constraint_jac = values[6];\n",
       "    __pyx_v_constraint_hess = ((PyArrayObject *)values[7]);\n",
       "    __pyx_v_l_multipliers = ((PyArrayObject *)values[8]);\n",
       "    __pyx_v_phase_records = values[9];\n",
       "  }\n",
       "  goto __pyx_L4_argument_unpacking_done;\n",
       "  __pyx_L5_argtuple_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"_build_multiphase_system\", 1, 10, 10, <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args)); __PYX_ERR(0, 24, __pyx_L3_error)\n",
       "  __pyx_L3_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_c9e2ae6042f41ab910df839a817d1108._build_multiphase_system\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return NULL;\n",
       "  __pyx_L4_argument_unpacking_done:;\n",
       "  if (unlikely(!<span class='pyx_c_api'>__Pyx_ArgTypeTest</span>(((PyObject *)__pyx_v_constraint_hess), __pyx_ptype_5numpy_ndarray, 1, \"constraint_hess\", 0))) __PYX_ERR(0, 26, __pyx_L1_error)\n",
       "  if (unlikely(!<span class='pyx_c_api'>__Pyx_ArgTypeTest</span>(((PyObject *)__pyx_v_l_multipliers), __pyx_ptype_5numpy_ndarray, 1, \"l_multipliers\", 0))) __PYX_ERR(0, 27, __pyx_L1_error)\n",
       "  __pyx_r = __pyx_pf_46_cython_magic_c9e2ae6042f41ab910df839a817d1108__build_multiphase_system(__pyx_self, __pyx_v_phase_dof, __pyx_v_phases, __pyx_v_cur_conds, __pyx_v_site_fracs, __pyx_v_phase_fracs, __pyx_v_l_constraints, __pyx_v_constraint_jac, __pyx_v_constraint_hess, __pyx_v_l_multipliers, __pyx_v_phase_records);\n",
       "\n",
       "  /* function exit code */\n",
       "  goto __pyx_L0;\n",
       "  __pyx_L1_error:;\n",
       "  __pyx_r = NULL;\n",
       "  __pyx_L0:;\n",
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       "}\n",
       "\n",
       "static PyObject *__pyx_pf_46_cython_magic_c9e2ae6042f41ab910df839a817d1108__build_multiphase_system(CYTHON_UNUSED PyObject *__pyx_self, __Pyx_memviewslice __pyx_v_phase_dof, PyObject *__pyx_v_phases, PyObject *__pyx_v_cur_conds, __Pyx_memviewslice __pyx_v_site_fracs, __Pyx_memviewslice __pyx_v_phase_fracs, CYTHON_UNUSED PyObject *__pyx_v_l_constraints, CYTHON_UNUSED PyObject *__pyx_v_constraint_jac, PyArrayObject *__pyx_v_constraint_hess, PyArrayObject *__pyx_v_l_multipliers, PyObject *__pyx_v_phase_records) {\n",
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       "  __Pyx_memviewslice __pyx_v_obj_res = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
       "  int __pyx_v_max_phase_dof;\n",
       "  __Pyx_memviewslice __pyx_v_grad_res = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
       "  __Pyx_memviewslice __pyx_v_tmp_hess = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
       "  double *__pyx_v_tmp_hess_ptr;\n",
       "  __Pyx_memviewslice __pyx_v_dof = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
       "  __Pyx_memviewslice __pyx_v_dof_2d_view = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
       "  int __pyx_v_num_vars;\n",
       "  __Pyx_memviewslice __pyx_v_l_hessian = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
       "  __Pyx_memviewslice __pyx_v_gradient_term = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
       "  int __pyx_v_var_offset;\n",
       "  int __pyx_v_phase_idx;\n",
       "  int __pyx_v_cur_phase_dof;\n",
       "  int __pyx_v_dof_x_idx;\n",
       "  int __pyx_v_dof_y_idx;\n",
       "  double __pyx_v_phase_frac;\n",
       "  struct PhaseRecordObject *__pyx_v_prn = 0;\n",
       "  PyObject *__pyx_v_name = NULL;\n",
       "  __Pyx_LocalBuf_ND __pyx_pybuffernd_constraint_hess;\n",
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       "  __pyx_pybuffer_constraint_hess.refcount = 0;\n",
       "  __pyx_pybuffernd_constraint_hess.data = NULL;\n",
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       "  __pyx_pybuffer_l_multipliers.pybuffer.buf = NULL;\n",
       "  __pyx_pybuffer_l_multipliers.refcount = 0;\n",
       "  __pyx_pybuffernd_l_multipliers.data = NULL;\n",
       "  __pyx_pybuffernd_l_multipliers.rcbuffer = &amp;__pyx_pybuffer_l_multipliers;\n",
       "  {\n",
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       "  __pyx_pybuffernd_constraint_hess.diminfo[0].strides = __pyx_pybuffernd_constraint_hess.rcbuffer-&gt;pybuffer.strides[0]; __pyx_pybuffernd_constraint_hess.diminfo[0].shape = __pyx_pybuffernd_constraint_hess.rcbuffer-&gt;pybuffer.shape[0]; __pyx_pybuffernd_constraint_hess.diminfo[1].strides = __pyx_pybuffernd_constraint_hess.rcbuffer-&gt;pybuffer.strides[1]; __pyx_pybuffernd_constraint_hess.diminfo[1].shape = __pyx_pybuffernd_constraint_hess.rcbuffer-&gt;pybuffer.shape[1]; __pyx_pybuffernd_constraint_hess.diminfo[2].strides = __pyx_pybuffernd_constraint_hess.rcbuffer-&gt;pybuffer.strides[2]; __pyx_pybuffernd_constraint_hess.diminfo[2].shape = __pyx_pybuffernd_constraint_hess.rcbuffer-&gt;pybuffer.shape[2];\n",
       "  {\n",
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       "  __pyx_pybuffernd_l_multipliers.diminfo[0].strides = __pyx_pybuffernd_l_multipliers.rcbuffer-&gt;pybuffer.strides[0]; __pyx_pybuffernd_l_multipliers.diminfo[0].shape = __pyx_pybuffernd_l_multipliers.rcbuffer-&gt;pybuffer.shape[0];\n",
       "/* … */\n",
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       "  __pyx_L1_error:;\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_1);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_2);\n",
       "  __PYX_XDEC_MEMVIEW(&amp;__pyx_t_3, 1);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_5);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_6);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_7);\n",
       "  __PYX_XDEC_MEMVIEW(&amp;__pyx_t_8, 1);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(((PyObject *)__pyx_t_13));\n",
       "  __PYX_XDEC_MEMVIEW(&amp;__pyx_t_22, 1);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_42);\n",
       "  { PyObject *__pyx_type, *__pyx_value, *__pyx_tb;\n",
       "    __Pyx_PyThreadState_declare\n",
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       "    <span class='pyx_c_api'>__Pyx_ErrFetch</span>(&amp;__pyx_type, &amp;__pyx_value, &amp;__pyx_tb);\n",
       "    <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_constraint_hess.rcbuffer-&gt;pybuffer);\n",
       "    <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_l_multipliers.rcbuffer-&gt;pybuffer);\n",
       "  <span class='pyx_c_api'>__Pyx_ErrRestore</span>(__pyx_type, __pyx_value, __pyx_tb);}\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_c9e2ae6042f41ab910df839a817d1108._build_multiphase_system\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
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       "      index = 0; __pyx_t_5 = __pyx_t_20(__pyx_t_1); if (unlikely(!__pyx_t_5)) goto __pyx_L5_unpacking_failed;\n",
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       "      <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
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       "    __pyx_t_5 = 0;\n",
       "    __pyx_v_phase_frac = __pyx_t_16;\n",
       "/* … */\n",
       "    <span class='trace'>__Pyx_TraceLine</span>(48,0,__PYX_ERR(0, 48, __pyx_L1_error))\n",
       "  }\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_6); __pyx_t_6 = 0;\n",
       "</pre><pre class=\"cython line score-8\" onclick='toggleDiv(this)'>+<span class=\"\">49</span>:         <span class=\"n\">prn</span> <span class=\"o\">=</span> <span class=\"n\">phase_records</span><span class=\"p\">[</span><span class=\"n\">name</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-8 '>    <span class='trace'>__Pyx_TraceLine</span>(49,0,__PYX_ERR(0, 49, __pyx_L1_error))\n",
       "    __pyx_t_7 = <span class='py_c_api'>PyObject_GetItem</span>(__pyx_v_phase_records, __pyx_v_name); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 49, __pyx_L1_error)\n",
       "    <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_7);\n",
       "    if (!(likely(((__pyx_t_7) == Py_None) || likely(<span class='pyx_c_api'>__Pyx_TypeTest</span>(__pyx_t_7, __pyx_ptype_9pycalphad_4core_9phase_rec_PhaseRecord))))) __PYX_ERR(0, 49, __pyx_L1_error)\n",
       "    <span class='pyx_macro_api'>__Pyx_XDECREF_SET</span>(__pyx_v_prn, ((struct PhaseRecordObject *)__pyx_t_7));\n",
       "    __pyx_t_7 = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">50</span>:         <span class=\"k\">with</span> <span class=\"k\">nogil</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-0 '>    <span class='trace'>__Pyx_TraceLine</span>(50,0,__PYX_ERR(0, 50, __pyx_L1_error))\n",
       "    {\n",
       "        #ifdef WITH_THREAD\n",
       "        PyThreadState *_save;\n",
       "        Py_UNBLOCK_THREADS\n",
       "        #endif\n",
       "        /*try:*/ {\n",
       "/* … */\n",
       "        <span class='trace'>__Pyx_TraceLine</span>(50,1,__PYX_ERR(0, 50, __pyx_L1_error))\n",
       "        /*finally:*/ {\n",
       "          /*normal exit:*/{\n",
       "            #ifdef WITH_THREAD\n",
       "            Py_BLOCK_THREADS\n",
       "            #endif\n",
       "            goto __pyx_L11;\n",
       "          }\n",
       "          __pyx_L10_error: {\n",
       "            #ifdef WITH_THREAD\n",
       "            Py_BLOCK_THREADS\n",
       "            #endif\n",
       "            goto __pyx_L1_error;\n",
       "          }\n",
       "          __pyx_L11:;\n",
       "        }\n",
       "    }\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">51</span>:             <span class=\"n\">cur_phase_dof</span> <span class=\"o\">=</span> <span class=\"p\">&lt;</span><span class=\"kt\">int</span><span class=\"p\">&gt;</span><span class=\"n\">phase_dof</span><span class=\"p\">[</span><span class=\"n\">phase_idx</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>          <span class='trace'>__Pyx_TraceLine</span>(51,1,__PYX_ERR(0, 51, __pyx_L10_error))\n",
       "          __pyx_t_21 = __pyx_v_phase_idx;\n",
       "          __pyx_v_cur_phase_dof = ((int)(*((int *) ( /* dim=0 */ (__pyx_v_phase_dof.data + __pyx_t_21 * __pyx_v_phase_dof.strides[0]) ))));\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">52</span>:             <span class=\"n\">dof</span><span class=\"p\">[</span><span class=\"mf\">2</span><span class=\"p\">:</span><span class=\"mf\">2</span><span class=\"o\">+</span><span class=\"n\">cur_phase_dof</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">site_fracs</span><span class=\"p\">[</span><span class=\"n\">var_offset</span><span class=\"p\">:</span><span class=\"n\">var_offset</span> <span class=\"o\">+</span> <span class=\"n\">cur_phase_dof</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>          <span class='trace'>__Pyx_TraceLine</span>(52,1,__PYX_ERR(0, 52, __pyx_L10_error))\n",
       "          __pyx_t_22.data = __pyx_v_site_fracs.data;\n",
       "          __pyx_t_22.memview = __pyx_v_site_fracs.memview;\n",
       "          __PYX_INC_MEMVIEW(&amp;__pyx_t_22, 0);\n",
       "          __pyx_t_4 = -1;\n",
       "          if (unlikely(__pyx_memoryview_slice_memviewslice(\n",
       "    &amp;__pyx_t_22,\n",
       "    __pyx_v_site_fracs.shape[0], __pyx_v_site_fracs.strides[0], __pyx_v_site_fracs.suboffsets[0],\n",
       "    0,\n",
       "    0,\n",
       "    &amp;__pyx_t_4,\n",
       "    __pyx_v_var_offset,\n",
       "    (__pyx_v_var_offset + __pyx_v_cur_phase_dof),\n",
       "    0,\n",
       "    1,\n",
       "    1,\n",
       "    0,\n",
       "    1) &lt; 0))\n",
       "{\n",
       "    __PYX_ERR(0, 52, __pyx_L10_error)\n",
       "}\n",
       "\n",
       "__pyx_t_3.data = __pyx_v_dof.data;\n",
       "          __pyx_t_3.memview = __pyx_v_dof.memview;\n",
       "          __PYX_INC_MEMVIEW(&amp;__pyx_t_3, 0);\n",
       "          __pyx_t_4 = -1;\n",
       "          if (unlikely(__pyx_memoryview_slice_memviewslice(\n",
       "    &amp;__pyx_t_3,\n",
       "    __pyx_v_dof.shape[0], __pyx_v_dof.strides[0], __pyx_v_dof.suboffsets[0],\n",
       "    0,\n",
       "    0,\n",
       "    &amp;__pyx_t_4,\n",
       "    2,\n",
       "    (2 + __pyx_v_cur_phase_dof),\n",
       "    0,\n",
       "    1,\n",
       "    1,\n",
       "    0,\n",
       "    1) &lt; 0))\n",
       "{\n",
       "    __PYX_ERR(0, 52, __pyx_L10_error)\n",
       "}\n",
       "\n",
       "if (unlikely(__pyx_memoryview_copy_contents(__pyx_t_22, __pyx_t_3, 1, 1, 0) &lt; 0)) __PYX_ERR(0, 52, __pyx_L10_error)\n",
       "          __PYX_XDEC_MEMVIEW(&amp;__pyx_t_3, 0);\n",
       "          __pyx_t_3.memview = NULL;\n",
       "          __pyx_t_3.data = NULL;\n",
       "          __PYX_XDEC_MEMVIEW(&amp;__pyx_t_22, 0);\n",
       "          __pyx_t_22.memview = NULL;\n",
       "          __pyx_t_22.data = NULL;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">53</span>:             <span class=\"n\">obj</span><span class=\"p\">(</span><span class=\"n\">prn</span><span class=\"p\">,</span> <span class=\"n\">obj_res</span><span class=\"p\">,</span> <span class=\"n\">dof_2d_view</span><span class=\"p\">,</span> <span class=\"mf\">1</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-0 '>          <span class='trace'>__Pyx_TraceLine</span>(53,1,__PYX_ERR(0, 53, __pyx_L10_error))\n",
       "          __pyx_f_9pycalphad_4core_9phase_rec_obj(__pyx_v_prn, __pyx_v_obj_res, __pyx_v_dof_2d_view, 1);\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">54</span>:             <span class=\"n\">grad</span><span class=\"p\">(</span><span class=\"n\">prn</span><span class=\"p\">,</span> <span class=\"n\">grad_res</span><span class=\"p\">,</span> <span class=\"n\">dof</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-0 '>          <span class='trace'>__Pyx_TraceLine</span>(54,1,__PYX_ERR(0, 54, __pyx_L10_error))\n",
       "          __pyx_f_9pycalphad_4core_9phase_rec_grad(__pyx_v_prn, __pyx_v_grad_res, __pyx_v_dof);\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">55</span>:             <span class=\"n\">hess</span><span class=\"p\">(</span><span class=\"n\">prn</span><span class=\"p\">,</span> <span class=\"n\">tmp_hess</span><span class=\"p\">,</span> <span class=\"n\">dof</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-0 '>          <span class='trace'>__Pyx_TraceLine</span>(55,1,__PYX_ERR(0, 55, __pyx_L10_error))\n",
       "          __pyx_f_9pycalphad_4core_9phase_rec_hess(__pyx_v_prn, __pyx_v_tmp_hess, __pyx_v_dof);\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">56</span>:             <span class=\"k\">for</span> <span class=\"n\">dof_x_idx</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">cur_phase_dof</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>          <span class='trace'>__Pyx_TraceLine</span>(56,1,__PYX_ERR(0, 56, __pyx_L10_error))\n",
       "          __pyx_t_4 = __pyx_v_cur_phase_dof;\n",
       "          for (__pyx_t_23 = 0; __pyx_t_23 &lt; __pyx_t_4; __pyx_t_23+=1) {\n",
       "            __pyx_v_dof_x_idx = __pyx_t_23;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">57</span>:                 <span class=\"n\">gradient_term</span><span class=\"p\">[</span><span class=\"n\">var_offset</span> <span class=\"o\">+</span> <span class=\"n\">dof_x_idx</span><span class=\"p\">]</span> <span class=\"o\">=</span> \\</pre>\n",
       "<pre class='cython code score-0 '>            <span class='trace'>__Pyx_TraceLine</span>(57,1,__PYX_ERR(0, 57, __pyx_L10_error))\n",
       "            __pyx_t_25 = (__pyx_v_var_offset + __pyx_v_dof_x_idx);\n",
       "            *((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_gradient_term.data) + __pyx_t_25)) )) = (__pyx_v_phase_frac * (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_grad_res.data) + __pyx_t_24)) ))));\n",
       "          }\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">58</span>:                     <span class=\"n\">phase_frac</span> <span class=\"o\">*</span> <span class=\"n\">grad_res</span><span class=\"p\">[</span><span class=\"mf\">2</span><span class=\"o\">+</span><span class=\"n\">dof_x_idx</span><span class=\"p\">]</span>  <span class=\"c\"># Remove P,T grad part</span></pre>\n",
       "<pre class='cython code score-0 '>            <span class='trace'>__Pyx_TraceLine</span>(58,1,__PYX_ERR(0, 58, __pyx_L10_error))\n",
       "            __pyx_t_24 = (2 + __pyx_v_dof_x_idx);\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">59</span>:             <span class=\"n\">gradient_term</span><span class=\"p\">[</span><span class=\"n\">site_fracs</span><span class=\"o\">.</span><span class=\"n\">shape</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">phase_idx</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">obj_res</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>          <span class='trace'>__Pyx_TraceLine</span>(59,1,__PYX_ERR(0, 59, __pyx_L10_error))\n",
       "          __pyx_t_26 = 0;\n",
       "          __pyx_t_27 = ((__pyx_v_site_fracs.shape[0]) + __pyx_v_phase_idx);\n",
       "          *((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_gradient_term.data) + __pyx_t_27)) )) = (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_obj_res.data) + __pyx_t_26)) )));\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">60</span>: </pre>\n",
       "<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">61</span>:             <span class=\"k\">for</span> <span class=\"n\">dof_x_idx</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">cur_phase_dof</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>          <span class='trace'>__Pyx_TraceLine</span>(61,1,__PYX_ERR(0, 61, __pyx_L10_error))\n",
       "          __pyx_t_4 = __pyx_v_cur_phase_dof;\n",
       "          for (__pyx_t_23 = 0; __pyx_t_23 &lt; __pyx_t_4; __pyx_t_23+=1) {\n",
       "            __pyx_v_dof_x_idx = __pyx_t_23;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">62</span>:                 <span class=\"k\">for</span> <span class=\"n\">dof_y_idx</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">dof_x_idx</span><span class=\"p\">,</span><span class=\"n\">cur_phase_dof</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>            <span class='trace'>__Pyx_TraceLine</span>(62,1,__PYX_ERR(0, 62, __pyx_L10_error))\n",
       "            __pyx_t_28 = __pyx_v_cur_phase_dof;\n",
       "            for (__pyx_t_29 = __pyx_v_dof_x_idx; __pyx_t_29 &lt; __pyx_t_28; __pyx_t_29+=1) {\n",
       "              __pyx_v_dof_y_idx = __pyx_t_29;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">63</span>:                     <span class=\"n\">l_hessian</span><span class=\"p\">[</span><span class=\"n\">var_offset</span><span class=\"o\">+</span><span class=\"n\">dof_x_idx</span><span class=\"p\">,</span> <span class=\"n\">var_offset</span><span class=\"o\">+</span><span class=\"n\">dof_y_idx</span><span class=\"p\">]</span> <span class=\"o\">=</span> \\</pre>\n",
       "<pre class='cython code score-0 '>              <span class='trace'>__Pyx_TraceLine</span>(63,1,__PYX_ERR(0, 63, __pyx_L10_error))\n",
       "              __pyx_t_30 = (__pyx_v_var_offset + __pyx_v_dof_x_idx);\n",
       "              __pyx_t_31 = (__pyx_v_var_offset + __pyx_v_dof_y_idx);\n",
       "              *((double *) ( /* dim=1 */ (( /* dim=0 */ ((char *) (((double *) __pyx_v_l_hessian.data) + __pyx_t_30)) ) + __pyx_t_31 * __pyx_v_l_hessian.strides[1]) )) = (__pyx_v_phase_frac * (__pyx_v_tmp_hess_ptr[((2 + __pyx_v_dof_x_idx) + ((2 + __pyx_v_cur_phase_dof) * (2 + __pyx_v_dof_y_idx)))]));\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">64</span>:                       <span class=\"n\">phase_frac</span> <span class=\"o\">*</span> <span class=\"n\">tmp_hess_ptr</span><span class=\"p\">[</span><span class=\"mf\">2</span><span class=\"o\">+</span><span class=\"n\">dof_x_idx</span> <span class=\"o\">+</span> <span class=\"p\">(</span><span class=\"mf\">2</span><span class=\"o\">+</span><span class=\"n\">cur_phase_dof</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\">dof_y_idx</span><span class=\"p\">)]</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">65</span>:                     <span class=\"n\">l_hessian</span><span class=\"p\">[</span><span class=\"n\">var_offset</span><span class=\"o\">+</span><span class=\"n\">dof_y_idx</span><span class=\"p\">,</span> <span class=\"n\">var_offset</span><span class=\"o\">+</span><span class=\"n\">dof_x_idx</span><span class=\"p\">]</span> <span class=\"o\">=</span> \\</pre>\n",
       "<pre class='cython code score-0 '>              <span class='trace'>__Pyx_TraceLine</span>(65,1,__PYX_ERR(0, 65, __pyx_L10_error))\n",
       "              __pyx_t_34 = (__pyx_v_var_offset + __pyx_v_dof_y_idx);\n",
       "              __pyx_t_35 = (__pyx_v_var_offset + __pyx_v_dof_x_idx);\n",
       "              *((double *) ( /* dim=1 */ (( /* dim=0 */ ((char *) (((double *) __pyx_v_l_hessian.data) + __pyx_t_34)) ) + __pyx_t_35 * __pyx_v_l_hessian.strides[1]) )) = (*((double *) ( /* dim=1 */ (( /* dim=0 */ ((char *) (((double *) __pyx_v_l_hessian.data) + __pyx_t_32)) ) + __pyx_t_33 * __pyx_v_l_hessian.strides[1]) )));\n",
       "            }\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">66</span>:                       <span class=\"n\">l_hessian</span><span class=\"p\">[</span><span class=\"n\">var_offset</span><span class=\"o\">+</span><span class=\"n\">dof_x_idx</span><span class=\"p\">,</span> <span class=\"n\">var_offset</span><span class=\"o\">+</span><span class=\"n\">dof_y_idx</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>              <span class='trace'>__Pyx_TraceLine</span>(66,1,__PYX_ERR(0, 66, __pyx_L10_error))\n",
       "              __pyx_t_32 = (__pyx_v_var_offset + __pyx_v_dof_x_idx);\n",
       "              __pyx_t_33 = (__pyx_v_var_offset + __pyx_v_dof_y_idx);\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">67</span>:                 <span class=\"c\"># Phase fraction / site fraction cross derivative</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">68</span>:                 <span class=\"n\">l_hessian</span><span class=\"p\">[</span><span class=\"n\">site_fracs</span><span class=\"o\">.</span><span class=\"n\">shape</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">phase_idx</span><span class=\"p\">,</span> <span class=\"n\">var_offset</span> <span class=\"o\">+</span> <span class=\"n\">dof_x_idx</span><span class=\"p\">]</span> <span class=\"o\">=</span> \\</pre>\n",
       "<pre class='cython code score-0 '>            <span class='trace'>__Pyx_TraceLine</span>(68,1,__PYX_ERR(0, 68, __pyx_L10_error))\n",
       "            __pyx_t_37 = ((__pyx_v_site_fracs.shape[0]) + __pyx_v_phase_idx);\n",
       "            __pyx_t_38 = (__pyx_v_var_offset + __pyx_v_dof_x_idx);\n",
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       "  __pyx_r = __pyx_t_1;\n",
       "  __pyx_t_1 = 0;\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 -f --compile-args=-DCYTHON_TRACE=1\n",
    "import pycalphad.variables as v\n",
    "from pycalphad.core.utils import unpack_kwarg\n",
    "from pycalphad.core.utils import unpack_condition, unpack_phases\n",
    "from pycalphad import calculate, Model\n",
    "from pycalphad.constraints import mole_fraction\n",
    "from pycalphad.core.lower_convex_hull import lower_convex_hull\n",
    "from pycalphad.core.sympydiff_utils import build_functions as compiled_build_functions\n",
    "from pycalphad.core.constants import MIN_SITE_FRACTION\n",
    "from pycalphad.core.eqsolver import _solve_eq_at_conditions\n",
    "from sympy import Add, Symbol\n",
    "import dask\n",
    "from dask import delayed\n",
    "import dask.multiprocessing, dask.async\n",
    "from xarray import Dataset\n",
    "cimport numpy as np\n",
    "import numpy as np\n",
    "from collections import namedtuple, OrderedDict\n",
    "from datetime import datetime\n",
    "from pycalphad.core.phase_rec cimport PhaseRecord, obj, grad, hess\n",
    "cimport cython\n",
    "\n",
    "@cython.boundscheck(False)\n",
    "@cython.wraparound(False)\n",
    "def _build_multiphase_system(int[:] phase_dof, phases, cur_conds, double[:] site_fracs, double[:] phase_fracs,\n",
    "                              l_constraints, constraint_jac,\n",
    "                              np.ndarray[ndim=3, dtype=np.float64_t] constraint_hess,\n",
    "                              np.ndarray[ndim=1, dtype=np.float64_t] l_multipliers,\n",
    "                              phase_records):\n",
    "    cdef double[::1] obj_result =  np.empty(1)\n",
    "    cdef double[::1] obj_res = np.empty(1)\n",
    "    cdef int max_phase_dof = max(phase_dof)\n",
    "    cdef double[::1] grad_res = np.empty(2+max_phase_dof)\n",
    "    cdef double[::1,:] tmp_hess = np.empty((2+max_phase_dof, 2+max_phase_dof), order='F')\n",
    "    cdef double* tmp_hess_ptr = &tmp_hess[0,0]\n",
    "    cdef double[::1] dof = np.empty(2+max_phase_dof)\n",
    "    cdef double[::1,:] dof_2d_view = <double[:1:1, :dof.shape[0]]>&dof[0]\n",
    "    cdef int num_vars = len(site_fracs) + len(phases)\n",
    "    cdef double[::1,:] l_hessian = np.zeros((num_vars, num_vars), order='F')\n",
    "    cdef double[::1] gradient_term = np.zeros(num_vars)\n",
    "    cdef int var_offset = 0\n",
    "    cdef int phase_idx = 0\n",
    "    cdef int cur_phase_dof, constraint_idx, dof_x_idx, dof_y_idx, hess_x, hess_y, hess_idx\n",
    "    cdef double phase_frac\n",
    "    cdef PhaseRecord prn\n",
    "    dof[0] = cur_conds['P']\n",
    "    dof[1] = cur_conds['T']\n",
    "\n",
    "    for name, phase_frac in zip(phases, phase_fracs):\n",
    "        prn = phase_records[name]\n",
    "        with nogil:\n",
    "            cur_phase_dof = <int>phase_dof[phase_idx]\n",
    "            dof[2:2+cur_phase_dof] = site_fracs[var_offset:var_offset + cur_phase_dof]\n",
    "            obj(prn, obj_res, dof_2d_view, 1)\n",
    "            grad(prn, grad_res, dof)\n",
    "            hess(prn, tmp_hess, dof)\n",
    "            for dof_x_idx in range(cur_phase_dof):\n",
    "                gradient_term[var_offset + dof_x_idx] = \\\n",
    "                    phase_frac * grad_res[2+dof_x_idx]  # Remove P,T grad part\n",
    "            gradient_term[site_fracs.shape[0] + phase_idx] = obj_res[0]\n",
    "\n",
    "            for dof_x_idx in range(cur_phase_dof):\n",
    "                for dof_y_idx in range(dof_x_idx,cur_phase_dof):\n",
    "                    l_hessian[var_offset+dof_x_idx, var_offset+dof_y_idx] = \\\n",
    "                      phase_frac * tmp_hess_ptr[2+dof_x_idx + (2+cur_phase_dof)*(2+dof_y_idx)]\n",
    "                    l_hessian[var_offset+dof_y_idx, var_offset+dof_x_idx] = \\\n",
    "                      l_hessian[var_offset+dof_x_idx, var_offset+dof_y_idx]\n",
    "                # Phase fraction / site fraction cross derivative\n",
    "                l_hessian[site_fracs.shape[0] + phase_idx, var_offset + dof_x_idx] = \\\n",
    "                     grad_res[2+dof_x_idx] # Remove P,T grad part\n",
    "                l_hessian[var_offset + dof_x_idx, site_fracs.shape[0] + phase_idx] = grad_res[2+dof_x_idx]\n",
    "            var_offset += cur_phase_dof\n",
    "            phase_idx += 1\n",
    "    l_hessian -= np.einsum('i,ijk->jk', l_multipliers, constraint_hess, order='F')\n",
    "    return np.asarray(l_hessian), np.asarray(gradient_term)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The line_profiler extension is already loaded. To reload it, use:\n",
      "  %reload_ext line_profiler\n"
     ]
    }
   ],
   "source": [
    "%load_ext line_profiler\n",
    "%lprun -f _build_multiphase_system equilibrium(dbf, ['AL', 'FE', 'VA'], list(dbf.phases.keys()), {v.T: 700, v.X('AL'): (0,1,0.02), v.P: 101325}, model=models, build_multiphase_system=_build_multiphase_system)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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