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        "author": "Julian Maerte",
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        "description": "# pysmps\n\nThis is a utility script for parsing MPS and SMPS file formats. It offers two main functions `load_mps` for loading mps files and `load_smps` for loading smps file directory.\n\n### `load_mps`\n\nThe `load_mps(path)` method takes a `path` variable as input. It should be a .cor or .mps file.\nIt opens the file with read-permissions and parses the described linear program into the following format:\n\n- `name`: The name given to the linear program (can't be blank)\n- `objective_name`: The name of the objective function value\n- `row_names`: list of row names\n- `col_names`: list of column names\n- `types`: list of constraint type indicators, i.e. either \"E\", \"L\" or \"G\" for equality, lower/equal or greater/equal constraint respectively.\n- `c`: the objective function coefficients\n- `A`: the constraint matrix\n- `rhs_names`: list of names of right hand sides (there can be multiple right hand side components be defined, seldom more than one though)\n- `rhs`: dictionary `(rhs_name) => b`, where `b` is the vector of constraint values for that given right hand side name.\n- `bnd_names`: list of names of box-bounds (seldom more than one)\n- `bnd`: dictionary `(bnd_name) => {\"LO\": v_l, \"UP\": v_u}` where `v_l` is the vector of lower bounds and `v_u` is the vector of upper bound values (defaults to `v_l = 0` and `v_u = +inf`).\n\nFinally this corresponds to the linear program\n\n```python\nmin \tc * x\n\ns.t.\tfor each rhs_name with corresponding b:\n\n\t\t\tA[types == \"E\",:] * x  = b[types == \"E\"]\n\t\t\tA[types == \"L\",:] * x <= b[types == \"L\"]\n\t\t\tA[types == \"G\",:] * x >= b[types == \"G\"]\n\n\t\tfor each bnd_name with corresponding v_l and v_u:\n\n\t\t\tv_l <= x < v_u\n\n```\n\n### `load_smps`\n\nThis function makes use of the `load_mps` function for parsing the .cor file. The SMPS file format consists of three files, a .cor, .tim and .sto file. The .cor file is in MPS format. Further the function expects a parameter `path` to be such that `path + \".cor\"` is the core file, `path + \".tim\"` the time file and `path + \".sto\"` is the stochastic file.\nIt *does not* support scenarios yet!\nIt returns a stochastic multi-stage problem in the following format\n\n- `name`: name of the program (must be the same in all 3 files)\n\n- `objective_name`: name of the objective function value\n\n- `constraints`: list of tuples `(name, period, type)` for each constraint. It gives a name, a period in which the constraints appears and a type, i.e. \"E\", \"L\" or \"G\" as in MPS.\n\n- `variables`: list of tuples `(name, period)` for each variable. It defines a name and a period in which the variable joins the program.\n\n- `c`: vector of objective function coefficients (of all periods)\n\n- `A`: matrix of constraint coefficients (of all periods)\n\n- `rhs_names`: list of rhs names as in MPS\n\n- `rhs`: dictionary as in MPS\n\n- `bounds`: dictionary as in MPS\n\n- `periods`: list of all periods appearing. `len(periods)` is the number stages.\n\n- `blocks`: dictionary of `Block`,`LinearTransform` or `SubRoutine` objects. Dependent on what the .sto file defined. `Blocks` are independent random variables (every case of a `Block` must be combined with each case of another `Block` to get all possible appearences; the probabilities multiply), `LinearTransform` are linear transformations of continuous random variables. The user needs to write the sample script on his own. `SubRoutine` is a left-out in the file; it presupposes the user to know what to do with these values.\n\n- `independent_variables`: dictionary `((i,j)) => {position, period, distrib}`, where `(i,j)` is the tuple of row/column indices. If one of them is `-1` this means that it's either an objective value or a rhs-value respectively. `position` is a dictionary adapting to where the entry is (objective value, rhs value or matrix value), `period` defines the period in which this variable is stochastic, `distrib` is either a definition of a continuous random variables\n\n  ```python\n  distrib: {type: \"N(mu, sigma**2)\"/\"U(a, b)\"/\"B(p, q)\"/\"G(p, b)\"/\"LN(mu, sigma**2)\", parameters}\n  ```\n\n  where parameters is a dictionary defining the required parameters. In the discrete case it is a list of tuples `(v,p)`, where `v` is the value of this position and `p` is the probability of it appearing.\n\nFor an example on how to use this format i recommand looking at the code for `load_2stage_problem`.\n\n### `load_2stage_problem`\n\nLoads a SMPS directory and tries to bring it into a 2-staged stochastic linear program with fixed recourse. Output is a dictionary containing the values\n\n- `c`: first stage objective function value\n- `A`: first stage (equality) constraint coefficient matrix\n- `b`: first stage constraint values\n- `q`: list of second stage objective function coefficients (each case one entry)\n- `h`: list of second stage constraint values (each case one entry)\n- `T`: list of second stage constraint values for deterministic variables (each case one entry)\n- `W`: recourse matrix (since it's fixed recourse this is not a list)\n- `p`: list of probabilities for each case\n\nThe constellations in which `(q,h,T,W)` appear are the realizations given by `(q[k], h[k], T[k], W)`.\nThe problem then resembles one of the form\n\n```python\nmin\t\tc * x + E_p[q * y]\n\ns.t.\tA * x         = b\n    \tT * x + W * y = h\n    \tx, y >= 0\n```\n\nwhich is a formal expression since T and h are also stochastic. In fact this notation means we assert the stochastic constraints inside of the expectation, making it a function of x only.\n\nFor casting the SMPS files into such a form we need to make certain assertments:\n\n- The upper right matrix needs to be zeroes only.\n- We only have one righthand side defined (`len(rhs_names) == 1`).\n- There are no boundaries or if we defined some they are the default values.\n- The first period parsed from the time file is the deterministic one, the other one is the stochastic one (especially there can only be two periods).\n- `A` and `W` are not stochastic.\n\nThis script however does\n\n- convert inequality constraints (deterministic and stochastic) into equality constraints by adding slack variables at the right places\n- calculate all combinations of independent accurances of stochastic components (BLOCKS and INDEP)\n- calculate the probabilities as products of independent elementary probabilities alongside.\n\n\n\n",
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