from __future__ import annotations
from typing import TYPE_CHECKING
import gamspy._algebra.expression as expression
import gamspy.utils as utils
from gamspy._symbols.implicits.implicit_symbol import ImplicitSymbol
from gamspy._symbols.symbol import Symbol
from gamspy.exceptions import ValidationError
if TYPE_CHECKING:
from gamspy import Alias, Set
from gamspy._algebra.expression import Expression
from gamspy._symbols.symbol import Symbol
class MathOp:
def __init__(
self,
op_name: str,
elements: tuple,
safe_cancel: bool = False,
):
self.op_name = op_name
self.elements = list(elements)
self.safe_cancel = safe_cancel
def gamsRepr(self) -> str:
operands_str = ",".join([_stringify(elem) for elem in self.elements])
return f"{self.op_name}({operands_str})"
def latexRepr(self) -> str:
"""
Representation of this MathOp in Latex.
Returns
-------
str
"""
op_map = {
"sqrt": "\\sqrt",
"floor": "\\floor",
"ceil": "\\lceil",
"abs": "\\lvert",
}
operands_str = ",".join([_stringify(elem) for elem in self.elements])
if self.op_name in op_map:
return f"{op_map[self.op_name]}{{{operands_str}}}"
return f"{self.op_name}({operands_str})"
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
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import abs
>>> m = Container()
>>> a = Parameter(m, "a", records=-3.8)
>>> b = Parameter(m, "b")
>>> b[...] = abs(a)
>>> b.toValue()
np.float64(3.8)
"""
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`` (i.e. ``ceil(4.1)`` returns ``5``)
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import ceil
>>> m = Container()
>>> a = Parameter(m, "a", records=3.2)
>>> b = Parameter(m, "b")
>>> b[...] = ceil(a)
>>> b.toValue()
np.float64(4.0)
"""
return expression.Expression(None, MathOp("ceil", (x,)), None)
[docs]
def div(
dividend: int | float | Symbol, divisor: int | float | Symbol
) -> Expression:
"""
Dividing operation, Error if the divisor is ``0``. To avoid the error, ``div0`` can be used instead.
Parameters
----------
dividend : int | float | Symbol
divisor : int | float | Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import div
>>> m = Container()
>>> a = Parameter(m, "a", records=210)
>>> b = Parameter(m, "b")
>>> b[...] = div(a, 3)
>>> b.toValue()
np.float64(70.0)
"""
return expression.Expression(
None, MathOp("div", (dividend, divisor)), None
)
[docs]
def div0(
dividend: int | float | Symbol, divisor: int | float | Symbol
) -> Expression:
"""
Dividing operation, returns ``1e+299`` if the divisor is ``0``
Parameters
----------
dividend : int | float | Symbol
divisor : int | float | Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import div0
>>> m = Container()
>>> a = Parameter(m, "a", records=210)
>>> b = Parameter(m, "b")
>>> b[...] = div0(a, 0)
>>> b.toValue()
np.float64(1e+299)
"""
return expression.Expression(
None, MathOp("div0", (dividend, divisor)), None
)
[docs]
def dist(
x1: int | float | Symbol,
x2: int | float | Symbol,
) -> Expression:
"""
Euclidean or L-2 Norm: ``sqrt(x1^2 + x2^2 + ... + xn^2)``
Returns
-------
Expression
Raises
------
Exception
In case both x1 and x2 are not a tuple or none.
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import dist
>>> m = Container()
>>> a = Parameter(m, "a", records=210)
>>> b = Parameter(m, "b")
>>> b[...] = dist(a, 100)
"""
return expression.Expression(None, MathOp("eDist", (x1, x2)), None)
[docs]
def factorial(x: int) -> Expression:
"""
Factorial of ``x``: ``x!``
Parameters
----------
x : int
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import factorial
>>> m = Container()
>>> b = Parameter(m, "b")
>>> b[...] = factorial(2)
"""
if not isinstance(x, int):
raise ValidationError("Factorial requires an integer")
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`` (i.e. ``floor(4.9)`` returns ``4``)
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import floor
>>> m = Container()
>>> a = Parameter(m, "a", records=3.9)
>>> b = Parameter(m, "b")
>>> b[...] = floor(a)
>>> b.toValue()
np.float64(3.0)
"""
return expression.Expression(None, MathOp("floor", (x,)), None)
[docs]
def fractional(x: int | float | Symbol) -> Expression:
"""
Returns the fractional part of ``x`` (i.e. ``fractional(3.9)`` returns ``0.9``)
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import fractional
>>> m = Container()
>>> a = Parameter(m, "a", records=3.9)
>>> b = Parameter(m, "b")
>>> b[...] = fractional(a)
>>> b.toValue()
np.float64(0.8999999999999999)
"""
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
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import Min
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> a = Parameter(m, "a", domain=i, records=[("i1", -2), ("i2", 0.3), ("i3", 2)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = Min(a[i], 1)
>>> b.toList()
[('i1', -2.0), ('i2', 0.3), ('i3', 1.0)]
"""
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
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import Max
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> a = Parameter(m, "a", domain=i, records=[("i1", 2), ("i2", 0.3), ("i3", 2.5)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = Max(a[i], 1)
>>> b.toList()
[('i1', 2.0), ('i2', 1.0), ('i3', 2.5)]
"""
return expression.Expression(None, MathOp("max", values), None)
[docs]
def mod(x: float | Symbol, y: float | Symbol) -> Expression:
"""
Remainder of ``x`` divided by ``y`` (i.e. ``mod(10, 3)`` returns ``1``)
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import mod
>>> m = Container()
>>> a = Parameter(m, "a", records=200)
>>> b = Parameter(m, "b")
>>> b[...] = mod(a, 3)
>>> b.toValue()
np.float64(2.0)
"""
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 (i.e. ``Round(3.14159, 2)`` returns ``3.14``)
Parameters
----------
x : float | Symbol
num_decimals : int, optional
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import Round, div
>>> m = Container()
>>> a = Parameter(m, "a", records=200)
>>> b = Parameter(m, "b")
>>> b[...] = Round(div(a, 3), 2)
>>> b.toValue()
np.float64(66.67)
"""
if not isinstance(num_decimals, int):
raise ValidationError("Round requires num_decimals to be an integer")
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
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import sign
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> a = Parameter(m, "a", domain=i, records=[("i1", 2), ("i2", -5.4), ("i3", 0)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = sign(a[i])
>>> b.toList()
[('i1', 1.0), ('i2', -1.0)]
"""
return expression.Expression(None, MathOp("sign", (x,)), None)
[docs]
def slexp(x: int | float | Symbol, S: int | float = 150) -> Expression:
"""
Smooth (linear) exponential where ``S <= 150``. (Default ``S = 150``)
Parameters
----------
x : int | float | Symbol
S : int | float, by default 150
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import slexp
>>> m = Container()
>>> a = Parameter(m, "a", records=3)
>>> b = Parameter(m, "b")
>>> b[...] = slexp(a)
>>> b.toValue()
np.float64(20.085536923187668)
"""
return expression.Expression(None, MathOp("slexp", (x, S)), None)
[docs]
def sqexp(x: int | float | Symbol, S: int | float = 150) -> Expression:
"""
Smooth (quadratic) exponential where ``S <= 150``. (Default ``S = 150``)
Parameters
----------
x : int | float | Symbol
S : int | float, by default 150
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import sqexp
>>> m = Container()
>>> a = Parameter(m, "a", records=3)
>>> b = Parameter(m, "b")
>>> b[...] = sqexp(a)
>>> b.toValue()
np.float64(20.085536923187668)
"""
return expression.Expression(None, MathOp("sqexp", (x, S)), None)
[docs]
def sqrt(x: int | float | Symbol, safe_cancel: bool = False) -> Expression:
"""
Square root of ``x``
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import sqrt
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> a = Parameter(m, "a", domain=i, records=[("i1", 4), ("i2", 54), ("i3", 0)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = sqrt(a[i])
>>> b.toList()
[('i1', 2.0), ('i2', 7.3484692283495345)]
"""
return expression.Expression(
None, MathOp("sqrt", (x,), safe_cancel=safe_cancel), None
)
[docs]
def truncate(x: int | float | Symbol) -> Expression:
"""
Returns the integer part of ``x`` (i.e. ``truncate(3.9)`` returns ``3``)
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import truncate
>>> m = Container()
>>> a = Parameter(m, "a", records=3.9)
>>> b = Parameter(m, "b")
>>> b[...] = truncate(a)
>>> b.toValue()
np.float64(3.0)
"""
return expression.Expression(None, MathOp("trunc", (x,)), None)
[docs]
def beta(x: int | float | Symbol, y: int | float | Symbol) -> Expression:
"""
Beta function: ``B(x, y) = gamma(x) * gamma(y) / gamma(x + y) = (x-1)! * (y-1)! / (x + y - 1)!``
Parameters
----------
x : int | float | Symbol
y : int | float | Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import beta
>>> m = Container()
>>> a = Parameter(m, "a", records=3)
>>> b = Parameter(m, "b")
>>> b[...] = beta(a, 1)
>>> b.toValue()
np.float64(0.3333333333333333)
"""
return expression.Expression(None, MathOp("beta", (x, y)), None)
[docs]
def regularized_beta(
x: int | float, y: int | float, z: int | float
) -> Expression:
"""
Regularized Beta Function, See `MathWorld <https://mathworld.wolfram.com/RegularizedBetaFunction.html>`_
Parameters
----------
x : int | float
y : int | float
z : int | float
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import regularized_beta
>>> m = Container()
>>> a = Parameter(m, "a", records=3)
>>> b = Parameter(m, "b")
>>> b[...] = regularized_beta(0.5, a, 1)
>>> b.toValue()
np.float64(0.12500000000000003)
"""
return expression.Expression(None, MathOp("betaReg", (x, y, z)), None)
[docs]
def gamma(x: int | float | Symbol) -> Expression:
"""
Gamma function: ``gamma(x) = (x-1)!``
Parameters
----------
x : int | float
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import gamma
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> a = Parameter(m, "a", domain=i, records=[("i1", 4), ("i2", 7), ("i3", 0.5)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = gamma(a[i])
>>> b.toList()
[('i1', 6.0), ('i2', 720.0), ('i3', 1.772453850905516)]
"""
return expression.Expression(None, MathOp("gamma", (x,)), None)
[docs]
def regularized_gamma(x: int | float, a: int | float) -> Expression:
"""
Lower Incomplete Regularized Gamma function, See `MathWorld <https://mathworld.wolfram.com/RegularizedGammaFunction.html>`_
Parameters
----------
x : int | float
a : int | float
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import regularized_gamma
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> a = Parameter(m, "a", domain=i, records=[("i1", 4), ("i2", 1), ("i3", 0.5)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = regularized_gamma(0.5, a[i])
>>> b.toList()
[('i1', 0.001751622556290824), ('i2', 0.3934693402873665), ('i3', 0.6826894921370857)]
"""
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: ``ln(exp(x1) + exp(x2) + ... + exp(xn))``
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import lse_max
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> a = Parameter(m, "a", domain=i, records=[("i1", 4), ("i2", 10), ("i3", 0.5)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = lse_max(a[i], 5)
>>> b.toList()
[('i1', 5.313261687518223), ('i2', 10.006715348489118), ('i3', 5.011047744848594)]
"""
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: ``lse_max_sc(T,x) = lse_max(Tx)/T``
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import lse_max_sc
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> a = Parameter(m, "a", domain=i, records=[("i1", 4), ("i2", 100), ("i3", 0.5)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = lse_max_sc(7.5, a[i], 10.5)
>>> b.toList()
[('i1', 10.50000153604837), ('i2', 10.5), ('i3', 10.902826555965506)]
"""
if len(xs) < 1:
raise ValidationError("lse_max_sc 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: ``-ln(exp(-x1) + exp(-x2) + ... + exp(-xn))``
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import lse_min
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> a = Parameter(m, "a", domain=i, records=[("i1", 4), ("i2", 10), ("i3", 0.5)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = lse_min(a[i], 5)
>>> b.toList()
[('i1', 3.686738312481777), ('i2', 4.993284651510882), ('i3', 0.4889522551514062)]
"""
if len(xs) < 1:
raise ValidationError("lse_min 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: ``lse_min_sc(T,x) = lse_min(Tx)/T``
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import lse_min_sc
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> a = Parameter(m, "a", domain=i, records=[("i1", 4), ("i2", 100), ("i3", 0.5)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = lse_min_sc(7.5, a[i], 10.5)
>>> b.toList()
[('i1', 4.0), ('i2', 10.5), ('i3', 0.5)]
"""
if len(xs) < 1:
raise ValidationError("lse_min_sc 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: ``x - z*ln(1 + exp((x-y)/z))``
Parameters
----------
x : Symbol
y : Symbol
z : int | float
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import ncp_cm
>>> m = Container()
>>> y = Parameter(m, "y", records=2)
>>> b = Parameter(m, "b")
>>> b[...] = ncp_cm(1, y, 0.5)
>>> b.toValue()
np.float64(0.9365359944785137)
"""
if not isinstance(z, (int, float)):
raise ValidationError("ncp_cm requires z to be an integer or a float")
if z <= 0:
raise ValidationError("ncp_cm requires z to be greater than 0")
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: ``sqrt(x^2 + y^2 + 2z) - x - y`` where ``z >= 0`` (default ``z = 0``)
Parameters
----------
x : Symbol
y : Symbol
z : int | float, optional
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import ncp_f
>>> m = Container()
>>> y = Parameter(m, "y", records=2)
>>> b = Parameter(m, "b")
>>> b[...] = ncp_f(1, y, 0.5)
>>> b.toValue()
np.float64(-0.5505102572168221)
"""
if not isinstance(z, (int, float)):
raise ValidationError("ncp_f requires z to be an integer or a float")
if z < 0:
raise ValidationError(
"ncp_f requires z to be greater than or equal to 0"
)
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
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import ncpVUpow
>>> m = Container()
>>> y = Parameter(m, "y", records=2)
>>> b = Parameter(m, "b")
>>> b[...] = ncpVUpow(1, y, 0.5)
>>> b.toValue()
np.float64(1.0)
"""
if not isinstance(mu, (int, float)):
raise ValidationError(
"ncpVUpow requires mu to be an integer or a float"
)
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
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import ncpVUsin
>>> m = Container()
>>> y = Parameter(m, "y", records=2)
>>> b = Parameter(m, "b")
>>> b[...] = ncpVUsin(1, y, 0.5)
>>> b.toValue()
np.float64(1.0)
"""
if not isinstance(mu, (int, float)):
raise ValidationError(
"ncpVUsin requires mu to be an integer or a float"
)
return expression.Expression(None, MathOp("ncpVUsin", (r, s, mu)), None)
[docs]
def poly(x, *args) -> Expression:
"""
Polynomial function: ``p(x) = A[0] + A[1]*x + A[2]*x^2 + ... + A[n-1]*x^(n-1)``
Returns
-------
Expression
Raises
------
ValidationError
If the number of arguments (args) is less than 3 or if any of args is not an integer or a float.
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import poly
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> a = Parameter(m, "a", domain=i, records=[("i1", 4), ("i2", 10), ("i3", 0.5)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = poly(a[i], 15, 3, 4)
>>> b.toList()
[('i1', 91.0), ('i2', 445.0), ('i3', 17.5)]
"""
if len(args) < 3:
raise ValidationError("poly requires at least 3 arguments after x")
if not all(isinstance(arg, (int, float)) for arg in args):
raise ValidationError(
"poly requires all args to be integers or floats"
)
return expression.Expression(None, MathOp("poly", (x,) + args), None)
[docs]
def sigmoid(x: int | float | Symbol) -> Expression:
"""
Sigmoid of ``x`` (i.e. ``1 / (1 + exp(-x))``)
Parameters
----------
x : int | float | Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import sigmoid
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> a = Parameter(m, "a", domain=i, records=[("i1", 4), ("i2", -1), ("i3", 0.5)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = sigmoid(a[i])
>>> b.toList()
[('i1', 0.9820137900379085), ('i2', 0.2689414213699951), ('i3', 0.6224593312018546)]
"""
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
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import rand_binomial
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> p = Parameter(m, "p", domain=i, records=[("i1", 0.3), ("i2", 0.8), ("i3", 0.45)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = rand_binomial(75, p[i])
>>> b.toList()
[('i1', 21.0), ('i2', 63.0), ('i3', 25.0)]
"""
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 less than ``2 / (high - low)`` and greater than ``0``
Parameters
----------
low : int | float
slope : int | float
high : int | float
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import rand_linear
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> s = Parameter(m, "s", domain=i, records=[("i1", 0.03), ("i2", 0.008), ("i3", 0.04)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = rand_linear(75, s[i], 125)
>>> b.toList()
[('i1', 78.22119203430918), ('i2', 87.65662570307367), ('i3', 80.24583337516547)]
"""
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
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import rand_triangle
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> s = Parameter(m, "s", domain=i, records=[("i1", 103), ("i2", 80), ("i3", 115)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = rand_triangle(75, s[i], 125)
>>> b.toList()
[('i1', 90.50632080153123), ('i2', 106.22102486822031), ('i3', 108.17756338250294)]
"""
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
Examples
--------
>>> import gamspy as gp
>>> from gamspy.math import same_as
>>> m = gp.Container()
>>> i = gp.Set(m, name="i", records=["seattle", "san-diego"])
>>> j = gp.Set(m, name="j", records=["new-york", "seattle"])
>>> attr = gp.Parameter(m, "attr", domain = [i, j])
>>> attr[i,j] = same_as(i, j)
>>> attr.records.values.tolist()
[['seattle', 'seattle', 1.0]]
"""
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, where ``S >= 1e-10``. (Default ``S = 1e-10``)
Parameters
----------
x : int | float | Symbol
S : int | float, by default 1e-10
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import slrec
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> a = Parameter(m, "a", domain=i, records=[("i1", 1), ("i2", 0.8), ("i3", 15)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = slrec(a[i])
>>> b.toList()
[('i1', 1.0), ('i2', 1.25), ('i3', 0.06666666666666667)]
"""
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, where ``S >= 1e-10``. (Default ``S = 1e-10``)
Parameters
----------
x : int | float | Symbol
S : int | float, by default 1e-10
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import sqrec
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> a = Parameter(m, "a", domain=i, records=[("i1", 1), ("i2", 0.8), ("i3", 15)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = sqrec(a[i])
>>> b.toList()
[('i1', 1.0), ('i2', 1.25), ('i3', 0.06666666666666667)]
"""
return expression.Expression(None, MathOp("sqrec", (x, S)), None)
[docs]
def entropy(x: int | float | Symbol) -> Expression:
"""
Entropy function: ``-x*ln(x)`` where ``x >= 0``
Parameters
----------
x : int | float | Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import entropy
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> a = Parameter(m, "a", domain=i, records=[("i1", 1), ("i2", 0.8), ("i3", 15)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = entropy(a[i])
>>> b.toList()
[('i2', 0.17851484105136778), ('i3', -40.62075301653315)]
"""
return expression.Expression(None, MathOp("entropy", (x,)), None)
[docs]
def errorf(x: int | float | Symbol) -> Expression:
"""
Integral of the standard normal distribution from negative infinity to ``x``
Parameters
----------
x : int, float, Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Set, Parameter
>>> from gamspy.math import errorf
>>> m = Container()
>>> i = Set(m, name="i", records=["i1", "i2", "i3"])
>>> a = Parameter(m, "a", domain=i, records=[("i1", -2.5), ("i2", 0.8), ("i3", 1.7)])
>>> b = Parameter(m, "b", domain=i)
>>> b[i] = errorf(a[i])
>>> b.toList()
[('i1', 0.0062096653257761375), ('i2', 0.7881446014166034), ('i3', 0.955434537241457)]
"""
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 ``yes_return``,
else it returns ``no_return``
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 | float | Symbol, y: int | float | Symbol) -> Expression:
"""
Returns ``true`` iff both ``x and y`` are true
Parameters
----------
x : int | float | Symbol
y : int | float | Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import bool_and
>>> m = Container()
>>> a = Parameter(m, "a", records=12)
>>> b = Parameter(m, "b", records=7)
>>> c = Parameter(m, "c")
>>> c[...] = bool_and(a > 10, b < 5)
>>> c.toValue()
np.float64(0.0)
"""
return expression.Expression(None, MathOp("bool_and", (x, y)), None)
[docs]
def bool_eqv(x: int | float | Symbol, y: int | float | Symbol) -> Expression:
"""
Returns ``false`` iff exactly one argument is false
Parameters
----------
x : int | float | Symbol
y : int | float | Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import bool_eqv
>>> m = Container()
>>> a = Parameter(m, "a", records=12)
>>> b = Parameter(m, "b", records=7)
>>> c = Parameter(m, "c")
>>> c[...] = bool_eqv(a > 10, b < 5)
>>> c.toValue()
np.float64(0.0)
"""
return expression.Expression(None, MathOp("bool_eqv", (x, y)), None)
[docs]
def bool_imp(x: int | float | Symbol, y: int | float | Symbol) -> Expression:
"""
Returns ``true`` iff ``x is false`` or ``y is true``
Parameters
----------
x : int | float | Symbol
y : int | float | Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import bool_imp
>>> m = Container()
>>> a = Parameter(m, "a", records=12)
>>> b = Parameter(m, "b", records=7)
>>> c = Parameter(m, "c")
>>> c[...] = bool_imp(a < 10, b > 5)
>>> c.toValue()
np.float64(1.0)
"""
return expression.Expression(None, MathOp("bool_imp", (x, y)), None)
[docs]
def bool_not(x: int | float | Symbol) -> Expression:
"""
Returns ``true`` iff ``x is false``
Parameters
----------
x : int | float | Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import bool_not
>>> m = Container()
>>> a = Parameter(m, "a", records=12)
>>> b = Parameter(m, "b", records=7)
>>> c = Parameter(m, "c")
>>> c[...] = bool_not(a > 10)
>>> c.toValue()
np.float64(0.0)
"""
return expression.Expression(None, MathOp("bool_not", (x,)), None)
[docs]
def bool_or(x: int | float | Symbol, y: int | float | Symbol) -> Expression:
"""
Returns ``true`` iff ``x is true`` or ``y is true``
Parameters
----------
x : int | float | Symbol
y : int | float | Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import bool_or
>>> m = Container()
>>> a = Parameter(m, "a", records=12)
>>> b = Parameter(m, "b", records=7)
>>> c = Parameter(m, "c")
>>> c[...] = bool_or(a > 15, b < 5)
>>> c.toValue()
np.float64(0.0)
"""
return expression.Expression(None, MathOp("bool_or", (x, y)), None)
[docs]
def bool_xor(x: int | float | Symbol, y: int | float | Symbol) -> Expression:
"""
Returns ``true`` iff exactly one argument is ``false``
Parameters
----------
x : int | float | Symbol
y : int | float | Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import bool_xor
>>> m = Container()
>>> a = Parameter(m, "a", records=12)
>>> b = Parameter(m, "b", records=7)
>>> c = Parameter(m, "c")
>>> c[...] = bool_xor(a < 15, b > 5)
>>> c.toValue()
np.float64(0.0)
"""
return expression.Expression(None, MathOp("bool_xor", (x, y)), None)
[docs]
def rel_eq(x: int | float | Symbol, y: int | float | Symbol) -> Expression:
"""
Returns ``true`` iff ``x == y``
Parameters
----------
x : int | float | Symbol
y : int | float | Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import rel_eq
>>> m = Container()
>>> a = Parameter(m, "a", records=12)
>>> b = Parameter(m, "b", records=7)
>>> c = Parameter(m, "c")
>>> c[...] = rel_eq(a, b)
>>> c.toValue()
np.float64(0.0)
"""
return expression.Expression(None, MathOp("rel_eq", (x, y)), None)
[docs]
def rel_ge(x: int | float | Symbol, y: int | float | Symbol) -> Expression:
"""
Returns ``true`` iff ``x >= y``
Parameters
----------
x : int | float | Symbol
y : int | float | Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import rel_ge
>>> m = Container()
>>> a = Parameter(m, "a", records=12)
>>> b = Parameter(m, "b", records=7)
>>> c = Parameter(m, "c")
>>> c[...] = rel_ge(a, b)
>>> c.toValue()
np.float64(1.0)
"""
return expression.Expression(None, MathOp("rel_ge", (x, y)), None)
[docs]
def rel_gt(x: int | float | Symbol, y: int | float | Symbol) -> Expression:
"""
Returns ``true`` iff ``x > y``
Parameters
----------
x : int | float | Symbol
y : int | float | Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import rel_gt
>>> m = Container()
>>> a = Parameter(m, "a", records=7)
>>> b = Parameter(m, "b", records=7)
>>> c = Parameter(m, "c")
>>> c[...] = rel_gt(a, b)
>>> c.toValue()
np.float64(0.0)
"""
return expression.Expression(None, MathOp("rel_gt", (x, y)), None)
[docs]
def rel_le(x: int | float | Symbol, y: int | float | Symbol) -> Expression:
"""
Returns ``true`` iff ``x <= y``
Parameters
----------
x : int | float | Symbol
y : int | float | Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import rel_le
>>> m = Container()
>>> a = Parameter(m, "a", records=12)
>>> b = Parameter(m, "b", records=11)
>>> c = Parameter(m, "c")
>>> c[...] = rel_le(a, b)
>>> c.toValue()
np.float64(0.0)
"""
return expression.Expression(None, MathOp("rel_le", (x, y)), None)
[docs]
def rel_lt(x: int | float | Symbol, y: int | float | Symbol) -> Expression:
"""
Returns ``true`` iff ``x < y``
Parameters
----------
x : int | float | Symbol
y : int | float | Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import rel_lt
>>> m = Container()
>>> a = Parameter(m, "a", records=12)
>>> b = Parameter(m, "b", records=17)
>>> c = Parameter(m, "c")
>>> c[...] = rel_lt(a, b)
>>> c.toValue()
np.float64(1.0)
"""
return expression.Expression(None, MathOp("rel_lt", (x, y)), None)
[docs]
def rel_ne(x: int | float | Symbol, y: int | float | Symbol) -> Expression:
"""
Returns ``true`` iff ``x != y``
Parameters
----------
x : int | float | Symbol
y : int | float | Symbol
Returns
-------
Expression
Examples
--------
>>> from gamspy import Container, Parameter
>>> from gamspy.math import rel_ne
>>> m = Container()
>>> a = Parameter(m, "a", records=12)
>>> b = Parameter(m, "b", records=12)
>>> c = Parameter(m, "c")
>>> c[...] = rel_ne(a, b)
>>> c.toValue()
np.float64(0.0)
"""
return expression.Expression(None, MathOp("rel_ne", (x, y)), None)
