{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using LHS Value to Debug An Infeasible Problem\n",
    "\n",
    "This notebook aims to show how to use the left-hand side (LHS) value (`Constraint.e`) to debug an infeasible problem.\n",
    "\n",
    "The LHS value is the value of the left-hand side of the equation. It is useful to check which constraints are violated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import ams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "ams.config_logger(stream_level=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's solve a DCOPF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Parsing input file \"/Users/jinningwang/work/ams/ams/cases/matpower/case14.m\"...\n",
      "Input file parsed in 0.0070 seconds.\n",
      "Zero line rates detacted in rate_a, rate_b, rate_c, adjusted to 999.\n",
      "System set up in 0.0034 seconds.\n"
     ]
    }
   ],
   "source": [
    "sp = ams.load(ams.get_case('matpower/case14.m'),\n",
    "              no_output=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Building system matrices\n",
      "Parsing OModel for <DCOPF>\n",
      "Evaluating OModel for <DCOPF>\n",
      "Finalizing OModel for <DCOPF>\n",
      "<DCOPF> initialized in 0.0144 seconds.\n",
      "<DCOPF> solved as optimal in 0.0160 seconds, converged in 11 iterations with CLARABEL.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.DCOPF.run(solver='CLARABEL')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.21, 0.38, 0.  , 0.  , 0.  ])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.DCOPF.pg.v.round(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we can lower down the generator maximum output to create an infeasible problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.StaticGen.set(src='pmax', attr='v', idx=[1, 2, 3, 4, 5], value=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember to update the corresponding parameters in the routine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.DCOPF.update('pmax')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can see that the problem is infeasible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "DCOPF failed as infeasible in 9 iterations with CLARABEL!\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.DCOPF.run(solver='CLARABEL')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we can turn off some constraints and sovle it again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Turn off constraints: pglb, pgub\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.DCOPF.disable(['pglb', 'pgub'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that since there are some constraints touched, the OModel will be updated automatically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Disabled constraints: pglb, pgub\n",
      "Finalizing OModel for <DCOPF>\n",
      "<DCOPF> initialized in 0.0019 seconds.\n",
      "<DCOPF> solved as optimal in 0.0167 seconds, converged in 9 iterations with CLARABEL.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.DCOPF.run(solver='CLARABEL')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.31448356,  0.39836206, -0.04094854, -0.04094854, -0.04094854])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.DCOPF.pg.v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since all the inequality constraints are written in the form of $Ax -b \\leq 0$, we can check the violated constraints by finding the those with positive `Constraint.e`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.81448356, -0.10163794, -0.54094854, -0.54094854, -0.54094854])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.DCOPF.pgub.e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.31448356, -0.39836206,  0.04094854,  0.04094854,  0.04094854])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.DCOPF.pglb.e"
   ]
  }
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