ó î&]\c @sdZddlZddljZddlmZddlm Z ddl m Z m Z m Z d„Zeeeeed„Zd d „Zd „Zd eeeeegd „Zd„Zeeeeeegdd„Zd„Zeeeeeegd ddeed„ ZdS(s9 Method agnostic utility functions for linear progamming iÿÿÿÿN(twarni(tOptimizeWarning(t_remove_redundancyt_remove_redundancy_sparset_remove_redundancy_densecCs¸|jdtƒ}|r6|dk r6tj|ƒ}n|rZ|dk rZtj|ƒ}n|jdtƒ}| r«tj|ƒs‘tj|ƒr«t|dc, Csn g}d} t} tj|jƒ} d} d} tj|ƒ}|dd…df}|dd…df}tj |tj|dƒtsumtflattentanyt logical_andtabsRt logical_nottisinfRtzipR"tdotRtallcloseR<thstacktnewaxisttolistR(R'RRRtlinalgt matrix_rankt ExceptionRR(,R-RR.RR/R0trrttoltundotc0tcompletetxtstatustmessageR7R8tm_eqtntm_ubR>RDtzero_rowR=tzero_colt singleton_rowtrowstcolstrowtcoltvalti_fti_nftresidualtslacktub_modtlb_modtx_zero_cR5tjtn_rows_Atredundancy_warningtsmall_nullspacetranktdim_row_nullspace((s;lib/python2.7/site-packages/scipy/optimize/_linprog_util.pyt _presolveTsrf      00"0///20 , 0    $"''     *+ *;      (     cCsŒ|dkri}nd„|jƒDƒ}t|||ƒ\}}}t||||||ƒ\}}}}}}|||||||fS(sz Parse the provided linear programming problem ``_parse_linprog`` employs two main steps ``_check_sparse_inputs`` and ``_clean_inputs``. ``_check_sparse_inputs`` checks for sparsity in the provided constraints (``A_ub`` and ``A_eq) and if these match the provided sparsity optional values. ``_clean inputs`` checks of the provided inputs. If no violations are identified the objective vector, upper bound constraints, equality constraints, and simple bounds are returned in the expected format. Parameters ---------- c : 1D array Coefficients of the linear objective function to be minimized. A_ub : 2D array, optional 2D array such that ``A_ub @ x`` gives the values of the upper-bound inequality constraints at ``x``. b_ub : 1D array, optional 1D array of values representing the upper-bound of each inequality constraint (row) in ``A_ub``. A_eq : 2D array, optional 2D array such that ``A_eq @ x`` gives the values of the equality constraints at ``x``. b_eq : 1D array, optional 1D array of values representing the RHS of each equality constraint (row) in ``A_eq``. bounds : sequence ``(min, max)`` pairs for each element in ``x``, defining the bounds on that parameter. Use None for one of ``min`` or ``max`` when there is no bound in that direction. By default bounds are ``(0, None)`` (non-negative). If a sequence containing a single tuple is provided, then ``min`` and ``max`` will be applied to all variables in the problem. options : dict A dictionary of solver options. All methods accept the following generic options: maxiter : int Maximum number of iterations to perform. disp : bool Set to True to print convergence messages. For method-specific options, see :func:`show_options('linprog')`. Returns ------- c : 1D array Coefficients of the linear objective function to be minimized. A_ub : 2D array, optional 2D array such that ``A_ub @ x`` gives the values of the upper-bound inequality constraints at ``x``. b_ub : 1D array, optional 1D array of values representing the upper-bound of each inequality constraint (row) in ``A_ub``. A_eq : 2D array, optional 2D array such that ``A_eq @ x`` gives the values of the equality constraints at ``x``. b_eq : 1D array, optional 1D array of values representing the RHS of each equality constraint (row) in ``A_eq``. bounds : sequence, optional ``(min, max)`` pairs for each element in ``x``, defining the bounds on that parameter. Use None for one of ``min`` or ``max`` when there is no bound in that direction. By default bounds are ``(0, None)`` (non-negative). If a sequence containing a single tuple is provided, then ``min`` and ``max`` will be applied to all variables in the problem. options : dict, optional A dictionary of solver options. All methods accept the following generic options: maxiter : int Maximum number of iterations to perform. disp : bool Set to True to print convergence messages. For method-specific options, see :func:`show_options('linprog')`. cSsi|]\}}||“qS(((t.0tktv((s;lib/python2.7/site-packages/scipy/optimize/_linprog_util.pys )s N(R titemsRR:(R-RR.RR/R0Rtsolver_options((s;lib/python2.7/site-packages/scipy/optimize/_linprog_util.pyt_parse_linprogÔsR  *ic%Csbtj|ƒrZt}tj|ƒ}tj|ƒ}d„} d„} tj} tj} n*t}tj} tj} tj } tj} t ƒ} t |ƒdkr²t |dƒ} ngt t |ƒƒD]}|| krÅ||^qÅ}tj |ƒ}|dd…df}|dd…df}|j\}}tj|dƒ}tj|dƒ}tj|ƒ}tj|ƒ}tj||ƒ}tj|ƒd}|| ||||<||= 0 by adding slack variables and making variable substitutions as necessary. Parameters ---------- c : 1D array Coefficients of the linear objective function to be minimized. Components corresponding with fixed variables have been eliminated. c0 : float Constant term in objective function due to fixed (and eliminated) variables. A_ub : 2D array, optional 2D array such that ``A_ub @ x`` gives the values of the upper-bound inequality constraints at ``x``. b_ub : 1D array, optional 1D array of values representing the upper-bound of each inequality constraint (row) in ``A_ub``. A_eq : 2D array, optional 2D array such that ``A_eq @ x`` gives the values of the equality constraints at ``x``. b_eq : 1D array, optional 1D array of values representing the RHS of each equality constraint (row) in ``A_eq``. bounds : sequence of tuples ``(min, max)`` pairs for each element in ``x``, defining the bounds on that parameter. Use None for each of ``min`` or ``max`` when there is no bound in that direction. Bounds have been tightened where possible. undo: list of tuples (`index`, `value`) pairs that record the original index and fixed value for each variable removed from the problem Returns ------- A : 2D array 2D array such that ``A`` @ ``x``, gives the values of the equality constraints at ``x``. b : 1D array 1D array of values representing the RHS of each equality constraint (row) in A (for standard form problem). c : 1D array Coefficients of the linear objective function to be minimized (for standard form problem). c0 : float Constant term in objective function due to fixed (and eliminated) variables. References ---------- .. [9] Bertsimas, Dimitris, and J. Tsitsiklis. "Introduction to linear programming." Athena Scientific 1 (1997): 997. cSstj|ddƒS(Ntformattlil(R RO(tblocks((s;lib/python2.7/site-packages/scipy/optimize/_linprog_util.pyRO‡scSstj|ddƒS(NR|R}(R RD(R~((s;lib/python2.7/site-packages/scipy/optimize/_linprog_util.pyRDŠsiNiiÿÿÿÿR?(R R Rt lil_matrixteyeRRRORDR#tsetRtrangeR%RRAR RJRHR<t count_nonzerot concatenatetarangeRBRRERttocsctdiagstravel(%R-RXRR.RR/R0RWRRORDR#R€tfixed_xR5tlbstubsR_R2tlb_nonetub_nonetlb_sometub_somet l_nolb_someubti_nolbti_newubtub_newubtn_boundstA1R4tl_freeti_freetn_freetA2R=ti_shifttlb_shift((s;lib/python2.7/site-packages/scipy/optimize/_linprog_util.pyt_get_Abc1s†Q         5" %  ( %7"9 3*cCs4|GH|dkr"dj|ƒGHndj|ƒGHdS(s› Print the termination summary of the linear program Parameters ---------- message : str A string descriptor of the exit status of the optimization. status : int An integer representing the exit status of the optimization:: 0 : Optimization terminated successfully 1 : Iteration limit reached 2 : Problem appears to be infeasible 3 : Problem appears to be unbounded 4 : Serious numerical difficulties encountered fun : float Value of the objective function. iteration : iteration The number of iterations performed. iis, Current function value: {0: <12.6f}s Iterations: {0:d}N(ii(R|(R\R[tfunt iteration((s;lib/python2.7/site-packages/scipy/optimize/_linprog_util.pyt_display_summaryës g:Œ0âŽyE>c Cs't|ƒ} tƒ} t|ƒdkrt|dƒ} |jƒ}x5t|d|dƒD]\} } |j| | ƒq[Wtj|ƒ}n| rX|dk rXd}x¯t|ƒD]ž\} }| | krÑq³n|\}}|dkr |dkr |d7}|| || |d|| =   $   !   c Csctj|ƒd}tj|ƒjƒp^tj|ƒp^tj|ƒjƒp^tj|ƒjƒ} | rpt} n…|||kjƒp™|||kjƒ} |dko¸|| kjƒ} |dkoßtj|ƒ|kjƒ} | pñ| pñ| } |dkr| rd}d}nB|dkr8| r8d}d}n!|dkrY| rYt|ƒ‚n||fS(s( Check the validity of the provided solution. A valid (optimal) solution satisfies all bounds, all slack variables are negative and all equality constraint residuals are strictly non-zero. Further, the lower-bounds, upper-bounds, slack and residuals contain no nan values. Parameters ---------- x : 1D array Solution vector to original linear programming problem fun: float optimal objective value for original problem status : int An integer representing the exit status of the optimization:: 0 : Optimization terminated successfully 1 : Iteration limit reached 2 : Problem appears to be infeasible 3 : Problem appears to be unbounded 4 : Serious numerical difficulties encountered slack : 1D array The (non-negative) slack in the upper bound constraints, that is, ``b_ub - A_ub @ x`` con : 1D array The (nominally zero) residuals of the equality constraints, that is, ``b - A_eq @ x`` lb : 1D array The lower bound constraints on the original variables ub: 1D array The upper bound constraints on the original variables message : str A string descriptor of the exit status of the optimization. tol : float Termination tolerance; see [1]_ Section 4.5. Returns ------- status : int An integer representing the exit status of the optimization:: 0 : Optimization terminated successfully 1 : Iteration limit reached 2 : Problem appears to be infeasible 3 : Problem appears to be unbounded 4 : Serious numerical difficulties encountered message : str A string descriptor of the exit status of the optimization. i iiisSThe solution does not satisfy the constraints, yet no errors were raised and there is no certificate of infeasibility or unboundedness. This is known to occur if the `presolve` option is False and the problem is infeasible. If you encounter this under different circumstances, please submit a bug report. Otherwise, please enable presolve.scNumerical difficulties were encountered but no errors were raised. This is known to occur if the 'presolve' option is False, 'sparse' is True, and A_eq includes redundant rows. If you encounter this under different circumstances, please submit a bug report. Otherwise, remove linearly dependent equations from your equality constraints or enable presolve.i(RtsqrttisnanRGRRIR (RZRR[RkR£R7R8RVR\t contains_nanst is_feasibletinvalid_boundst invalid_slackt invalid_con((s;lib/python2.7/site-packages/scipy/optimize/_linprog_util.pyt _check_resultvs(6 ,'  R;c Cs•t|||||||||| ƒ \}}}}}}t||| ||||| | ƒ \} } | rt| | || ƒn||||| | fS(sÓ Given solution x to presolved, standard form linear program x, add fixed variables back into the problem and undo the variable substitutions to get solution to original linear program. Also, calculate the objective function value, slack in original upper bound constraints, and residuals in original equality constraints. Parameters ---------- x : 1D array Solution vector to the standard-form problem. c : 1D array Original coefficients of the linear objective function to be minimized. A_ub : 2D array, optional 2D array such that ``A_ub @ x`` gives the values of the upper-bound inequality constraints at ``x``. b_ub : 1D array, optional 1D array of values representing the upper-bound of each inequality constraint (row) in ``A_ub``. A_eq : 2D array, optional 2D array such that ``A_eq @ x`` gives the values of the equality constraints at ``x``. b_eq : 1D array, optional 1D array of values representing the RHS of each equality constraint (row) in ``A_eq``. bounds : sequence of tuples Bounds, as modified in presolve complete : bool Whether the solution is was determined in presolve (``True`` if so) undo: list of tuples (`index`, `value`) pairs that record the original index and fixed value for each variable removed from the problem status : int An integer representing the exit status of the optimization:: 0 : Optimization terminated successfully 1 : Iteration limit reached 2 : Problem appears to be infeasible 3 : Problem appears to be unbounded 4 : Serious numerical difficulties encountered message : str A string descriptor of the exit status of the optimization. tol : float Termination tolerance; see [1]_ Section 4.5. Returns ------- x : 1D array Solution vector to original linear programming problem fun: float optimal objective value for original problem slack : 1D array The (non-negative) slack in the upper bound constraints, that is, ``b_ub - A_ub @ x`` con : 1D array The (nominally zero) residuals of the equality constraints, that is, ``b - A_eq @ x`` status : int An integer representing the exit status of the optimization:: 0 : Optimization terminated successfully 1 : Iteration limit reached 2 : Problem appears to be infeasible 3 : Problem appears to be unbounded 4 : Serious numerical difficulties encountered message : str A string descriptor of the exit status of the optimization. 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