Problems

class ecyglpki.Problem

A GLPK problem

add_cols(int number)

Add new columns to problem object

Parameters:number (int) – the number of columns to add Returns:the index of the first column added Return type:int

add_named_cols(*names)

Add new columns to problem object

Parameters:names (tuple of str) – the names of the columns to add, none may exceed 255 bytes encoded as UTF-8

add_named_rows(*names)

Add new rows to problem object

Parameters:names (tuple of str) – the names of the rows to add, none may exceed 255 bytes encoded as UTF-8

add_rows(int number)

Add new rows to problem object

Parameters:number (int) – the number of rows to add Returns:the index of the first row added Return type:int

adv_basis()

Construct advanced initial LP basis

analyze_bound(ind, names_preferred=False)

Analyze active bound of non-basic variable

Parameters:names_preferred (bool) – whether to return row and column names or indices

analyze_coef(ind, names_preferred=False)

Analyze objective coefficient at basic variable

Parameters:names_preferred (bool) – whether to return row and column names or indices

bf_exists()

Check if LP basis factorization exists

Return type:bool

bf_updated()

Check if LP basis factorization has been updated

Return type:bool

btran(tuple rhs)

Perform backward transformation (solve system B’x = b)

check_cnfsat()

Check for CNF-SAT problem instance

Return type:bool

check_kkt(str solver, str condition, bool dual=False, names_preferred=False)

Check feasibility/optimality conditions

Parameters:names_preferred (bool) – whether to return the row or column name or index

clear_mat_col(col)

Clear column of the constraint matrix

Parameters:col (int or str) – the index or name of the column

clear_mat_row(row)

Clear row of the constraint matrix

Parameters:row (int or str) – the index or name of the row

clear_matrix()

Clear the whole constraint matrix

copy_prob(Problem source, bool copy_names)

Copy problem object content

Parameters:

• source (Problem) – the problem to copy
• copy_names (bool) – whether to copy problem component names or not

Returns:

the copied problem

Return type:

Problem

cpx_basis()

Construct Bixby’s initial LP basis

del_cols(*cols)

Delete specified columns from problem object

Parameters:cols (tuple of int or str) – the indices or the names of the columns

del_rows(*rows)

Delete specified rows from problem object

Parameters:rows (tuple of int or str) – the indices or names of the rows

dual_rtest(coeffs, int direction, double eps, names_preferred=False)

Perform dual ratio test

Parameters:names_preferred (bool) – whether to return row and column names or indices

erase_prob()

Erase problem object content

eval_tab_col(ind, names_preferred=False)

Compute column of the simplex tableau

Parameters:names_preferred (bool) – whether to return row and column names or indices

eval_tab_row(ind, names_preferred=False)

Compute row of the simplex tableau

Parameters:names_preferred (bool) – whether to return row and column names or indices

exact(SimplexControls controls)

Solve LP problem in exact arithmetic

factorize()

Compute LP basis factorization

find_col(str name)

Find column by its name

Parameters:name (str) – the name of the column Returns:the column index Return type:int

find_col_as_needed(col)

Parameters:col (int or str) – the index or name of the column Returns:the column index Return type:int

find_row(str name)

Find row by its name

Parameters:name (str) – the name of the row Returns:the row index Return type:int

find_row_as_needed(row)

Parameters:row (int or str) – the index or name of the row Returns:the row index Return type:int

find_row_or_col_as_needed(ind)

ftran(tuple rhs)

Perform forward transformation (solve system B*x = b)

get_bfcp()

Retrieve LP basis factorization control parameters

Returns:basis factorization control parameter object Return type:FactorizationControls

get_bhead(int k, names_preferred=False)

Retrieve LP basis header information

Parameters:names_preferred (bool) – whether to return the row or column name or index

get_col_bind(col)

Retrieve column index in the basis header

Parameters:col (int or str) – the index or name of the column Returns:basis header index Return type:int

get_col_dual(col)

retrieve column dual value (basic solution)

Parameters:col (int or str) – the index or name of the column Returns:the solution value Return type:float

get_col_kind(col)

Retrieve column kind

Parameters:col (int or str) – the index or name of the column Returns:the column kind, either 'continuous', 'integer', or 'binary' Return type:str

get_col_lb(col)

Retrieve column lower bound

Parameters:col (int or str) – the index or name of the column Returns:the lower bound Return type:float

get_col_name(int col)

Retrieve column name

Parameters:col (int) – the index of the column Returns:the problem name Return type:str

get_col_name_if(int col, names_preferred=False)

Parameters:

• col (int) – the index of the column
• names_preferred (bool) – whether to return the column name or index

Returns:

the column name or index

Return type:

str or int

get_col_prim(col)

Retrieve column primal value (basic solution)

Parameters:col (int or str) – the index or name of the column Returns:the solution value Return type:float

get_col_stat(col)

Retrieve column status

Parameters:col (int or str) – the index or name of the column Returns:the column status, either 'basic', 'lower', 'upper', 'free', or 'fixed' Return type:str

get_col_type(col)

Retrieve column type

Parameters:col (int or str) – the index or name of the column Returns:the column type, either 'free', 'dominating', 'dominated', 'bounded', or 'fixed' Return type:str

get_col_ub(col)

Retrieve column upper bound

Parameters:col (int or str) – the index or name of the column Returns:the upper bound Return type:float

get_dual_stat()

Retrieve status of dual basic solution

get_mat_col(col, names_preferred=False)

Retrieve column of the constraint matrix

Parameters:

• col (int or str) – the index or name of the column
• names_preferred (bool) – whether to return row and column names or indices

Returns:

the column

Rtype coeffs:

Mapping from row names (str strings) to coefficient values (Real)

get_mat_row(row, names_preferred=False)

Retrieve row of the constraint matrix

Parameters:

• row (int or str) – the index or name of the row
• names_preferred (bool) – whether to return row and column names or indices

Returns:

the row

Rtype coeffs:

Mapping from column names (str strings) to coefficient values (Real)

get_num_bin()

Retrieve number of binary columns

Returns:the number of binary columns Return type:int

get_num_cols()

Retrieve number of columns

Returns:the number of columns Return type:int

get_num_int()

Retrieve number of integer columns

Returns:the number of integer columns Return type:int

get_num_nz()

Retrieve number of constraint coefficients

Returns:the number of (non-zero) constraint coefficients Return type:int

get_num_rows()

Retrieve number of rows

Returns:the number of rows Return type:int

get_obj_coef(col)

Retrieve obj. coefficient

Parameters:col (int or str) – the index or name of the column Returns:the coefficient value Return type:float

get_obj_const()

Retrieve obj. constant term

Returns:the constant value Return type:float

get_obj_dir()

Retrieve optimization direction flag

Returns:the objective direction, either 'minimize' or 'maximize' Return type:str

get_obj_name()

Retrieve objective function name

Returns:the objective name Return type:str

get_obj_val()

Retrieve objective value (basic solution)

Returns:the objective value of the basic solution Return type:float

get_prim_stat()

Retrieve status of primal basic solution

get_prob_name()

Retrieve problem name

Returns:the problem name Return type:str

get_rii(row)

Retrieve row scale factor

Parameters:row (int or str) – the index or name of the row Returns:the scale factor Return type:float

get_row_bind(row)

Retrieve row index in the basis header

Parameters:row (int or str) – the index or name of the row Returns:basis header index Return type:int

get_row_dual(row)

Retrieve row dual value (basic solution)

Parameters:row (int or str) – the index or name of the row Returns:the solution value Return type:float

get_row_lb(row)

Retrieve row lower bound

Parameters:row (int or str) – the index or name of the row Returns:the lower bound Return type:float

get_row_name(int row)

Retrieve row name

Parameters:row (int) – the index of the row Returns:the row name Return type:str

get_row_name_if(int row, names_preferred=False)

Parameters:

• row (int) – the index of the row
• names_preferred (bool) – whether to return the row name or index

Returns:

the row name or index

Return type:

str or int

get_row_or_col_name(int ind)

Retrieve row or column name

Parameters:ind (int) – the row/column index Returns:a pair, either 'row' or 'col' and the row or column name Return type:(str, str)

get_row_or_col_name_if(int ind, names_preferred=False)

Parameters:

• ind (int) – the row/column index
• names_preferred (bool) – whether to return the row or column name or index

Returns:

a pair, either 'row' or 'col' and the row or column name

Return type:

(str, str)

get_row_prim(row)

Retrieve row primal value (basic solution)

Parameters:row (int or str) – the index or name of the row Returns:the solution value Return type:float

get_row_stat(row)

Retrieve row status

Parameters:row (int or str) – the index or name of the row Returns:the row status, either 'basic', 'lower', 'upper', 'free', or 'fixed' Return type:str

get_row_type(row)

Retrieve row type

Parameters:row (int or str) – the index or name of the row Returns:the row type, either 'free', 'dominating', 'dominated', 'bounded', or 'fixed' Return type:str

get_row_ub(row)

Retrieve row upper bound

Parameters:row (int or str) – the index or name of the row Returns:the upper bound Return type:float

get_sjj(col)

Retrieve column scale factor

Parameters:col (int or str) – the index or name of the column Returns:the scale factor Return type:float

get_status()

Retrieve generic status of basic solution

get_unbnd_ray(names_preferred=False)

Determine variable causing unboundedness

Parameters:names_preferred (bool) – whether to return the row or column name or index

interior(IPointControls controls)

Solve LP problem with the interior-point method

intfeas1(bool use_bound, int obj_bound)

Solve integer feasibility problem

intopt(IntOptControls controls)

Solve MIP problem with the branch-and-bound method

ipt_col_dual(col)

Retrieve column dual value (interior point)

Parameters:col (int or str) – the index or name of the column Returns:the solution value Return type:float

ipt_col_prim(col)

Retrieve column primal value (interior point)

Parameters:col (int or str) – the index or name of the column Returns:the solution value Return type:float

ipt_obj_val()

Retrieve objective value (interior point)

Returns:the objective value of the interior point solution Return type:float

ipt_row_dual(row)

Retrieve row dual value (interior point)

Parameters:row (int or str) – the index or name of the row Returns:the solution value Return type:float

ipt_row_prim(row)

Retrieve row primal value (interior point)

Parameters:row (int or str) – the index or name of the row Returns:the solution value Return type:float

ipt_status()

Retrieve status of interior-point solution

load_matrix(coeffs)

Load (replace) the whole constraint matrix

Parameters:coeffs – Mapping from row and column name (str string) pairs (length-2 tuple) to coefficient values (Real)

minisat1()

Solve CNF-SAT problem with MiniSat solver

mip_col_val(col)

Retrieve column value (MIP solution)

Parameters:col (int or str) – the index or name of the column Returns:the solution value Return type:float

mip_obj_val()

Retrieve objective value (MIP solution)

Returns:the objective value of the MIP solution Return type:float

mip_row_val(row)

Retrieve row value (MIP solution)

Parameters:row (int or str) – the index or name of the row Returns:the solution value Return type:float

mip_status()

Retrieve status of MIP solution

prim_rtest(coeffs, int direction, double eps, names_preferred=False)

Perform primal ratio test

Parameters:names_preferred (bool) – whether to return row and column names or indices

print_ipt(str fname)

Write interior-point solution in printable format

Parameters:fname (str) – file name

print_mip(str fname)

Write MIP solution in printable format

Parameters:fname (str) – file name

print_ranges(row_or_cols, str fname)

Print sensitivity analysis report

Parameters:fname (str) – file name

print_sol(str fname)

Write basic solution in printable format

Parameters:fname (str) – file name

read_cnfsat(str fname)

Read CNF-SAT problem data in DIMACS format

Parameters:fname (str) – file name Returns:the problem read Return type:Problem

read_ipt(str fname)

Read interior-point solution from text file

Parameters:fname (str) – file name

read_lp(str fname)

Read problem data in CPLEX LP format

Parameters:fname (str) – file name Returns:the problem read Return type:Problem

read_mip(str fname)

Read MIP solution from text file

Parameters:fname (str) – file name

read_mps(str format, str fname)

Read problem data in MPS format

Parameters:

• format (str) – the MPS file format, either 'fixed' or 'free'
• fname (str) – file name

Returns:

the problem read

Return type:

Problem

read_prob(str fname)

Read problem data in GLPK format

Parameters:fname (str) – file name Returns:the problem read Return type:Problem

read_sol(str fname)

Read basic solution from text file

Parameters:fname (str) – file name

scale_prob(*algorithms)

Scale problem data

Parameters:algorithms – the algorithms to apply, one or more from 'auto', 'skip', 'geometric', 'equilibration', 'round'

set_bfcp(FactorizationControls controls)

Change LP basis factorization control parameters

set_col_bnds(col, lower, upper)

Set (change) column bounds

Parameters:

• col (int or str) – the index or name of the column
• lower (Real or NoneType) – lower bound (None if unbounded from below)
• upper (Real or NoneType) – upper bound (None if unbounded from above)

set_col_kind(col, str kind)

Set (change) column kind

Parameters:

• col (int or str) – the index or name of the column
• kind (str) – the column kind, either 'continuous', 'integer', or 'binary'

set_col_name(col, str name)

Change column name

Parameters:

• col (int or str) – the index or name of the column
• name (str) – the name of the column, it may not exceed 255 bytes encoded as UTF-8

set_col_stat(col, str status)

Set (change) column status

Parameters:col (int or str) – the index or name of the column

set_mat_col(col, coeffs)

Set (replace) column of the constraint matrix

Parameters:

• col (int or str) – the index or name of the column
• coeffs – Mapping from row names (str strings) to coefficient values (Real)

set_mat_row(row, coeffs)

Set (replace) row of the constraint matrix

Parameters:

• row (int or str) – the index or name of the row
• coeffs – Mapping from column names (str strings) to coefficient values (Real)

set_obj_coef(col, double coeff)

Set (change) obj. coefficient

Parameters:

• col (int or str) – the index or name of the column
• coeff (Real) – the coefficient value

set_obj_const(double coeff)

Set (change) obj. constant term

Parameters:coeff (Real) – the coefficient value

set_obj_dir(str direction)

Set (change) optimization direction flag

Parameters:direction (str) – the objective direction, either 'minimize' or 'maximize'

set_obj_name(str name)

Assign (change) objective function name

Parameters:name (str) – the name of the objective, it may not exceed 255 bytes encoded as UTF-8

set_prob_name(str name)

Assign (change) problem name

Parameters:name (str) – the name of the problem, it may not exceed 255 bytes encoded as UTF-8

set_rii(row, double sf)

Set (change) row scale factor

Parameters:

• row (int or str) – the index or name of the row
• sf (Real) – the scale factor

set_row_bnds(row, lower, upper)

Set (change) row bounds

Parameters:

• row (int or str) – the index or name of the row
• lower (Real or NoneType) – lower bound (None if unbounded from below)
• upper (Real or NoneType) – upper bound (None if unbounded from above)

set_row_name(row, str name)

Change row name

Parameters:

• row (int or str) – the index or name of the row
• name (str) – the name of the row, it may not exceed 255 bytes encoded as UTF-8

set_row_stat(row, str status)

Set (change) row status

Parameters:row (int or str) – the index or name of the row

set_sjj(col, double sf)

Set (change) column scale factor

Parameters:

• col (int or str) – the index or name of the column
• sf (Real) – the scale factor

simplex(SimplexControls controls)

Solve LP problem with the simplex method

sort_matrix()

Sort elements of the constraint matrix

std_basis()

Construct standard initial LP basis

transform_col(coeffs, names_preferred=False)

Transform explicitly specified column

Parameters:

• coeffs – Mapping from row names (str strings) to coefficient values (Real)
• names_preferred (bool) – whether to return row and column names or indices

Returns:

transformed column

Return type:

Mapping from row and column names (str strings) to coefficient values (Real)

transform_row(coeffs, names_preferred=False)

Transform explicitly specified row

Parameters:

• coeffs – Mapping from column names (str strings) to coefficient values (Real)
• names_preferred (bool) – whether to return row and column names or indices

Returns:

transformed row

Return type:

Mapping from row and column names (str strings) to coefficient values (Real)

unscale_prob()

Unscale problem data

warm_up()

“Warm up” LP basis

write_cnfsat(str fname)

Write CNF-SAT problem data in DIMACS format

Parameters:fname (str) – file name

write_ipt(str fname)

Write interior-point solution to text file

Parameters:fname (str) – file name

write_lp(str fname)

Write problem data in CPLEX LP format

Parameters:fname (str) – file name

write_mip(str fname)

Write MIP solution to text file

Parameters:fname (str) – file name

write_mps(str format, str fname)

Write problem data in MPS format

Parameters:

• format (str) – the MPS file format, either 'fixed' or 'free'
• fname (str) – file name

write_prob(str fname)

Write problem data in GLPK format

Parameters:fname (str) – file name

write_sol(str fname)

Write basic solution to text file

Parameters:fname (str) – file name