from __future__ import annotations
from typing import TYPE_CHECKING
import gamspy as gp
import gamspy._algebra.expression as expression
import gamspy._symbols.implicits as implicits
import gamspy.utils as utils
from gamspy.exceptions import ValidationError
if TYPE_CHECKING:
from gamspy import Alias, Set
from gamspy._algebra.expression import Expression
from gamspy._symbols.implicits.implicit_symbol import ImplicitSymbol
from gamspy._symbols.symbol import Symbol
class MathOp:
def __init__(
self,
op_name: str,
elements: tuple,
):
self.op_name = op_name
self.elements = elements
def gamsRepr(self):
operands_str = ",".join([_stringify(elem) for elem in self.elements])
return f"{self.op_name}({operands_str})"
def _find_variables(self):
variables = []
for elem in self.elements:
if isinstance(elem, gp.Variable):
variables.append(elem.name)
elif isinstance(elem, implicits.ImplicitVariable):
variables.append(elem.parent.name)
elif isinstance(elem, expression.Expression):
variables += elem._find_variables()
return variables
def __str__(self):
return self.gamsRepr()
def __len__(self):
return len(self.gamsRepr())
def _stringify(x: str | int | float | Symbol | ImplicitSymbol):
if isinstance(x, (int, float)):
x = utils._map_special_values(x)
return str(x)
elif isinstance(x, str):
return f'"{x}"'
return x.gamsRepr()
[docs]
def abs(x: int | float | Symbol) -> Expression:
"""
Absolute value of x (i.e. ``|x|``)
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("abs", (x,)), None)
[docs]
def ceil(x: int | float | Symbol) -> Expression:
"""
The smallest integer greater than or equal to x
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("ceil", (x,)), None)
[docs]
def div(
dividend: int | float | Symbol, divisor: int | float | Symbol
) -> Expression:
"""
Dividing operation
Parameters
----------
dividend : int | float | Symbol
divisor : int | float | Symbol
Returns
-------
Expression
"""
return expression.Expression(
None, MathOp("div", (dividend, divisor)), None
)
[docs]
def div0(
dividend: int | float | Symbol, divisor: int | float | Symbol
) -> Expression:
"""
Dividing operation
Parameters
----------
dividend : int | float | Symbol
divisor : int | float | Symbol
Returns
-------
Expression
"""
return expression.Expression(
None, MathOp("div0", (dividend, divisor)), None
)
[docs]
def dist(
x1: tuple[int, float] | Symbol,
x2: tuple[int, float] | Symbol,
) -> Expression:
"""
L2 norm
Returns
-------
Expression
Raises
------
Exception
In case both x1 and x2 are not a tuple or none.
"""
if isinstance(x1, tuple) or isinstance(x2, tuple):
raise ValidationError("Both should be a tuple or none")
return expression.Expression(None, MathOp("eDist", (x1, x2)), None)
[docs]
def factorial(x: int | Symbol) -> Expression:
"""
Factorial of x
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("fact", (x,)), None)
[docs]
def floor(x: int | float | Symbol) -> Expression:
"""
The greatest integer less than or equal to x
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("floor", (x,)), None)
[docs]
def fractional(x: int | float | Symbol) -> Expression:
"""
Returns the fractional part of x
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("frac", (x,)), None)
[docs]
def Min(*values) -> Expression:
"""
Minimum value of the values, where the number of values may vary.
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("min", values), None)
[docs]
def Max(*values) -> Expression:
"""
Maximum value of the values, where the number of values may vary.
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("max", values), None)
[docs]
def mod(x: float | Symbol, y: float | Symbol) -> Expression:
"""
Remainder of x divided by y.
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("mod", (x, y)), None)
[docs]
def Round(x: float | Symbol, num_decimals: int = 0) -> Expression:
"""
Round x to num_decimals decimal places.
Parameters
----------
x : float | Symbol
decimal : int, optional
Returns
-------
Expression
"""
return expression.Expression(
None, MathOp("round", (x, num_decimals)), None
)
[docs]
def sign(x: Symbol) -> Expression:
"""
Sign of x returns 1 if x > 0, -1 if x < 0, and 0 if x = 0
Parameters
----------
x : Symbol
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("sign", (x,)), None)
[docs]
def slexp(x: int | float | Symbol, S: int | float = 150) -> Expression:
"""
Smooth (linear) exponential
Parameters
----------
x : int | float | Symbol
S : int | float, by default 150
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("slexp", (x, S)), None)
[docs]
def sqexp(x: int | float | Symbol, S: int | float = 150) -> Expression:
"""
Smooth (quadratic) exponential
Parameters
----------
x : int | float | Symbol
S : int | float, by default 150
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("sqexp", (x, S)), None)
[docs]
def sqrt(x: int | float | Symbol) -> Expression:
"""
Square root of x
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("sqrt", (x,)), None)
[docs]
def truncate(x: int | float | Symbol) -> Expression:
"""
Returns the integer part of x
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("trunc", (x,)), None)
[docs]
def beta(x: int | float | Symbol, y: int | float | Symbol) -> Expression:
"""
Beta function
Parameters
----------
x : int | float | Symbol
y : int | float | Symbol
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("beta", (x, y)), None)
[docs]
def regularized_beta(
x: int | float, y: int | float, z: int | float
) -> Expression:
"""
Beta function
Parameters
----------
x : int | float
y : int | float
z : int | float
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("betaReg", (x, y, z)), None)
[docs]
def gamma(x: int | float | Symbol) -> Expression:
"""
Gamma function
Parameters
----------
x : int | float
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("gamma", (x,)), None)
[docs]
def regularized_gamma(x: int | float, a: int | float) -> Expression:
"""
Gamma function
Parameters
----------
x : int | float
a : int | float
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("gammaReg", (x, a)), None)
[docs]
def lse_max(*xs) -> Expression:
"""
Smoothed Max via the Logarithm of the Sum of Exponentials
Returns
-------
Expression
"""
if len(xs) < 1:
raise ValidationError("lse_max requires at least 1 x")
return expression.Expression(None, MathOp("lseMax", xs), None)
[docs]
def lse_max_sc(t, *xs) -> Expression:
"""
Scaled smoothed Max via the Logarithm of the Sum of Exponentials
Returns
-------
Expression
"""
if len(xs) < 1:
raise ValidationError("lse_max requires at least 1 x")
return expression.Expression(None, MathOp("lseMaxSc", xs + (t,)), None)
[docs]
def lse_min(*xs) -> Expression:
"""
Smoothed Min via the Logarithm of the Sum of Exponentials
Returns
-------
Expression
"""
if len(xs) < 1:
raise ValidationError("lse_max requires at least 1 x")
return expression.Expression(None, MathOp("lseMin", xs), None)
[docs]
def lse_min_sc(t, *xs) -> Expression:
"""
Scaled smoothed Min via the Logarithm of the Sum of Exponentials
Returns
-------
Expression
"""
if len(xs) < 1:
raise ValidationError("lse_max requires at least 1 x")
return expression.Expression(None, MathOp("lseMinSc", (t,) + xs), None)
[docs]
def ncp_cm(x: Symbol, y: Symbol, z: float | int) -> Expression:
"""
Chen-Mangasarian smoothing
Parameters
----------
x : Symbol
y : Symbol
z : int | float
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("ncpCM", (x, y, z)), None)
[docs]
def ncp_f(x: Symbol, y: Symbol, z: int | float = 0) -> Expression:
"""
Fisher-Burmeister smoothing
Parameters
----------
x : Symbol
y : Symbol
z : int | float, optional
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("ncpF", (x, y, z)), None)
[docs]
def ncpVUpow(
r: Symbol,
s: Symbol,
mu: int | float = 0,
) -> Expression:
"""
NCP Veelken-Ulbrich: smoothed min(r,s)
Parameters
----------
r : Symbol
s : Symbol
mu : int | float, optional
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("ncpVUpow", (r, s, mu)), None)
[docs]
def ncpVUsin(r: Symbol, s: Symbol, mu: int | float = 0) -> Expression:
"""
NCP Veelken-Ulbrich: smoothed min(r,s)
Parameters
----------
r : Symbol
s : Symbol
mu : int | float, optional
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("ncpVUsin", (r, s, mu)), None)
[docs]
def poly(x, *args) -> Expression:
"""
Polynomial function
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("poly", (x,) + args), None)
[docs]
def sigmoid(x: int | float | Symbol) -> Expression:
"""
Sigmoid of x
Parameters
----------
x : int | float | Symbol
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("sigmoid", (x,)), None)
[docs]
def rand_binomial(n: int | float, p: int | float) -> Expression:
"""
Generate a random number from the binomial distribution, where n is the
number of trials and p the probability of success for each trial
Parameters
----------
n : int | float
p : int | float
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("randBinomial", (n, p)), None)
[docs]
def rand_linear(
low: int | float, slope: int | float, high: int | float
) -> Expression:
"""
Generate a random number between low and high with linear distribution.
slope must be greater than 2 / (high - low)
Parameters
----------
low : int | float
slope : int | float
high : int | float
Returns
-------
Expression
"""
return expression.Expression(
None, MathOp("randLinear", (low, slope, high)), None
)
[docs]
def rand_triangle(
low: int | float, mid: int | float, high: int | float
) -> Expression:
"""
Generate a random number between low and high with triangular distribution.
mid is the most probable number.
Parameters
----------
low : int | float
mid : int | float
high : int | float
Returns
-------
Expression
"""
return expression.Expression(
None, MathOp("randTriangle", (low, mid, high)), None
)
[docs]
def same_as(self: Set | Alias, other: Set | Alias | str) -> Expression:
"""
Evaluates to true if this set is identical to the given set or alias, false otherwise.
Parameters
----------
other : Set | Alias
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("sameAs", (self, other)), None)
[docs]
def slrec(x: int | float | Symbol, S: int | float = 1e-10) -> Expression:
"""
Smooth (linear) reciprocal
Parameters
----------
x : int | float | Symbol
S : int | float, by default 1e-10
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("slrec", (x, S)), None)
[docs]
def sqrec(x: int | float | Symbol, S: int | float = 1e-10) -> Expression:
"""
Smooth (quadratic) reciprocal
Parameters
----------
x : int | float | Symbol
S : int | float, by default 1e-10
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("sqrec", (x, S)), None)
[docs]
def entropy(x: int | float | Symbol) -> Expression:
"""
L2 Norm of x
Parameters
----------
x : int | float | Symbol
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("entropy", (x,)), None)
[docs]
def errorf(x: int | float | Symbol) -> Expression:
"""
Integral of the standard normal distribution
Parameters
----------
x : int, float, Symbol
Returns
-------
Expression
"""
return expression.Expression(None, MathOp("errorf", (x,)), None)
[docs]
def ifthen(
condition: Expression,
yes_return: float | Expression,
no_return: float | Expression,
) -> Expression:
"""
If the logical condition is true, the function returns iftrue,
else it returns else
Parameters
----------
condition : Expression
yes_return : float | Expression
no_return : float | Expression
Returns
-------
Expression
Examples
--------
>>> from gamspy.math import ifthen
>>> import gamspy as gp
>>> m = gp.Container()
>>> tt = gp.Parameter(m, "tt", records=2)
>>> y = gp.Parameter(m, "y", records=2)
>>> x = ifthen(tt == 2, 3, 4 + y)
"""
condition.representation = utils._replace_equality_signs(
condition.gamsRepr()
)
return expression.Expression(
None, MathOp("ifthen", (condition, yes_return, no_return)), None
)
[docs]
def bool_and(x: int | Symbol, y: int | Symbol) -> Expression:
return expression.Expression(None, MathOp("bool_and", (x, y)), None)
[docs]
def bool_eqv(x: int | Symbol, y: int | Symbol) -> Expression:
return expression.Expression(None, MathOp("bool_eqv", (x, y)), None)
[docs]
def bool_imp(x: int | Symbol, y: int | Symbol) -> Expression:
return expression.Expression(None, MathOp("bool_imp", (x, y)), None)
[docs]
def bool_not(x: int | Symbol) -> Expression:
return expression.Expression(None, MathOp("bool_not", (x,)), None)
[docs]
def bool_or(x: int | Symbol, y: int | Symbol) -> Expression:
return expression.Expression(None, MathOp("bool_or", (x, y)), None)
[docs]
def bool_xor(x: int | Symbol, y: int | Symbol) -> Expression:
return expression.Expression(None, MathOp("bool_xor", (x, y)), None)
[docs]
def rel_eq(x: int | Symbol, y: int | Symbol) -> Expression:
return expression.Expression(None, MathOp("rel_eq", (x, y)), None)
[docs]
def rel_ge(x: int | Symbol, y: int | Symbol) -> Expression:
return expression.Expression(None, MathOp("rel_ge", (x, y)), None)
[docs]
def rel_gt(x: int | Symbol, y: int | Symbol) -> Expression:
return expression.Expression(None, MathOp("rel_gt", (x, y)), None)
[docs]
def rel_le(x: int | Symbol, y: int | Symbol) -> Expression:
return expression.Expression(None, MathOp("rel_le", (x, y)), None)
[docs]
def rel_lt(x: int | Symbol, y: int | Symbol) -> Expression:
return expression.Expression(None, MathOp("rel_lt", (x, y)), None)
[docs]
def rel_ne(x: int | Symbol, y: int | Symbol) -> Expression:
return expression.Expression(None, MathOp("rel_ne", (x, y)), None)
