{
 "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": {
    "execution": {
     "iopub.execute_input": "2026-05-02T08:23:36.127831Z",
     "iopub.status.busy": "2026-05-02T08:23:36.127295Z",
     "iopub.status.idle": "2026-05-02T08:23:37.212098Z",
     "shell.execute_reply": "2026-05-02T08:23:37.211771Z"
    }
   },
   "outputs": [],
   "source": [
    "import ams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-02T08:23:37.213398Z",
     "iopub.status.busy": "2026-05-02T08:23:37.213284Z",
     "iopub.status.idle": "2026-05-02T08:23:37.215466Z",
     "shell.execute_reply": "2026-05-02T08:23:37.215206Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2026-05-02T08:23:37.216695Z",
     "iopub.status.busy": "2026-05-02T08:23:37.216620Z",
     "iopub.status.idle": "2026-05-02T08:23:37.325590Z",
     "shell.execute_reply": "2026-05-02T08:23:37.325324Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Working directory: \"/Users/jinningwang/work/ams/examples/demonstration\"\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "> Loaded config from file \"/Users/jinningwang/.ams/ams.rc\"\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Parsing input file \"/Users/jinningwang/work/ams/ams/cases/matpower/case14.m\"...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "CASE14    Power flow data for IEEE 14 bus test case.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Input file parsed in 0.0033 seconds.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Zero Line parameters detected, adjusted to default values: rate_a, rate_b, rate_c.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "System set up in 0.0017 seconds.\n"
     ]
    }
   ],
   "source": [
    "sp = ams.load(ams.get_case('matpower/case14.m'),\n",
    "              no_output=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-02T08:23:37.326675Z",
     "iopub.status.busy": "2026-05-02T08:23:37.326577Z",
     "iopub.status.idle": "2026-05-02T08:23:37.377477Z",
     "shell.execute_reply": "2026-05-02T08:23:37.377254Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Entering data check for <DCOPF>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " -> Data check passed\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Building system matrices\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<DCOPF> formulation: codegen=15/15\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Parsing OModel for <DCOPF>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Evaluating OModel for <DCOPF>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Finalizing OModel for <DCOPF>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<DCOPF> initialized in 0.0403 seconds.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<DCOPF> solved as optimal in 0.0070 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": {
    "execution": {
     "iopub.execute_input": "2026-05-02T08:23:37.378559Z",
     "iopub.status.busy": "2026-05-02T08:23:37.378468Z",
     "iopub.status.idle": "2026-05-02T08:23:37.380394Z",
     "shell.execute_reply": "2026-05-02T08:23:37.380191Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2026-05-02T08:23:37.381411Z",
     "iopub.status.busy": "2026-05-02T08:23:37.381343Z",
     "iopub.status.idle": "2026-05-02T08:23:37.383265Z",
     "shell.execute_reply": "2026-05-02T08:23:37.383052Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2026-05-02T08:23:37.384372Z",
     "iopub.status.busy": "2026-05-02T08:23:37.384281Z",
     "iopub.status.idle": "2026-05-02T08:23:37.386504Z",
     "shell.execute_reply": "2026-05-02T08:23:37.386277Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2026-05-02T08:23:37.387611Z",
     "iopub.status.busy": "2026-05-02T08:23:37.387521Z",
     "iopub.status.idle": "2026-05-02T08:23:37.391506Z",
     "shell.execute_reply": "2026-05-02T08:23:37.391287Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2026-05-02T08:23:37.392512Z",
     "iopub.status.busy": "2026-05-02T08:23:37.392430Z",
     "iopub.status.idle": "2026-05-02T08:23:37.394501Z",
     "shell.execute_reply": "2026-05-02T08:23:37.394312Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2026-05-02T08:23:37.395426Z",
     "iopub.status.busy": "2026-05-02T08:23:37.395357Z",
     "iopub.status.idle": "2026-05-02T08:23:37.404858Z",
     "shell.execute_reply": "2026-05-02T08:23:37.404639Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Entering data check for <DCOPF>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " -> Data check passed\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Disabled constraints: pglb, pgub\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<DCOPF> formulation: codegen=15/15\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Finalizing OModel for <DCOPF>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<DCOPF> initialized in 0.0022 seconds.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<DCOPF> solved as optimal in 0.0048 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": {
    "execution": {
     "iopub.execute_input": "2026-05-02T08:23:37.405993Z",
     "iopub.status.busy": "2026-05-02T08:23:37.405921Z",
     "iopub.status.idle": "2026-05-02T08:23:37.407873Z",
     "shell.execute_reply": "2026-05-02T08:23:37.407673Z"
    }
   },
   "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": [
    "## Why `Constraint.e` is always slack-from-zero\n",
    "\n",
    "Every routine constraint is authored in the **LHS-zero form** —\n",
    "all terms on the left, `<= 0` / `== 0` / `>= 0` on the right\n",
    "(post-v1.2.3; see the `is_eq` retirement migration). CVXPY then\n",
    "canonicalizes every inequality internally to `lhs - rhs <= 0`\n",
    "**regardless of operator direction**:\n",
    "\n",
    "```python\n",
    "import cvxpy as cp\n",
    "a = cp.Variable(3, name='a'); b = cp.Variable(3, name='b')\n",
    "(a <= b)._expr   # → a - b\n",
    "(b >= a)._expr   # → a - b   (same! __ge__ swaps operands)\n",
    "```\n",
    "\n",
    "`Constraint.e` (and `Constraint.v`) returns this canonical\n",
    "`lhs - rhs` value — i.e. the slack from zero. So:\n",
    "\n",
    "* **negative** = constraint is respected, with that much margin\n",
    "* **positive** = constraint is violated by that amount\n",
    "* **zero** = constraint is exactly tight\n",
    "\n",
    "The diagnostic is uniform across every constraint in every\n",
    "routine. For an infeasible problem, scanning each constraint's\n",
    "`.e` for positive entries pinpoints exactly which constraints\n",
    "fail and by how much. CVXPY rejects strict `<` / `>` (raises\n",
    "`NotImplementedError`), so only `<=`, `>=`, and `==` reach the\n",
    "solver — the canonicalization is total."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-02T08:23:37.408884Z",
     "iopub.status.busy": "2026-05-02T08:23:37.408821Z",
     "iopub.status.idle": "2026-05-02T08:23:37.411148Z",
     "shell.execute_reply": "2026-05-02T08:23:37.410946Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2026-05-02T08:23:37.412106Z",
     "iopub.status.busy": "2026-05-02T08:23:37.412037Z",
     "iopub.status.idle": "2026-05-02T08:23:37.413937Z",
     "shell.execute_reply": "2026-05-02T08:23:37.413769Z"
    }
   },
   "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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