math#
- gamspy.math.cos(x: int | float | Symbol) Expression[source]#
Cosine of x.
- Returns:
- Expression
- gamspy.math.cosh(x: int | float | Symbol) Expression[source]#
Hyperbolic cosine of x.
- Returns:
- Expression
- gamspy.math.sin(x: float | Symbol) Expression[source]#
Sine of x.
- Returns:
- Expression
- gamspy.math.sinh(x: float | Symbol) Expression[source]#
Hyperbolic sine of x.
- Returns:
- Expression
- gamspy.math.acos(x: float | Symbol) Expression[source]#
Inverse cosine of x.
- Returns:
- Expresion | float
- gamspy.math.asin(x: float | Symbol) Expression[source]#
Inver sinus of x.
- Returns:
- Expression
- gamspy.math.tan(x: float | Symbol) Expression[source]#
Tangent of x.
- Returns:
- Expression
- gamspy.math.tanh(x: float | Symbol) Expression[source]#
Hyperbolic tangent of x.
- Returns:
- Expression
- gamspy.math.atan(x: float | Symbol) Expression[source]#
Inverse tangent of x.
- Returns:
- Expression
- gamspy.math.atan2(y: int | float | Symbol, x: int | float | Symbol) Expression[source]#
Four-quadrant arctan function
- Returns:
- Expression
- gamspy.math.exp(x: float | Symbol) Expression[source]#
Exponential of x (i.e. e^x)
- Returns:
- Expression
- gamspy.math.power(base: float | Symbol, exponent: float | Symbol) Expression[source]#
Base to the exponent power (i.e. base ^ exponent)
- Parameters:
- basefloat | Symbol
- exponentfloat | Symbol
- Returns:
- Expression
- gamspy.math.sqr(x: float | Symbol) Expression[source]#
Square of x
- Parameters:
- xfloat | Symbol
- Returns:
- Expression
- gamspy.math.sqrt(x: int | float | Symbol) Expression[source]#
Square root of x
- Returns:
- Expression
- gamspy.math.log(x: int | float | Symbol) Expression[source]#
Natural logarithm of x (i.e. logarithm base e of x)
- Returns:
- Expression
- gamspy.math.log2(x: float | Symbol) Expression[source]#
Binary logarithm (i.e. logarithm base 2 of x)
- Returns:
- Expression
- gamspy.math.log10(x: float | Symbol) Expression[source]#
Common logarithm (i.e. logarithm base 10 of x)
- Returns:
- Expression
- gamspy.math.log_beta(x: int | float | Symbol, y: int | float | Symbol) Expression[source]#
Log beta function
- Returns:
- Expression
- gamspy.math.log_gamma(x: int | float | Symbol, y: int | float | Symbol) Expression[source]#
Log gamma function
- Returns:
- Expression
- gamspy.math.logit(x: int | float | Symbol) Expression[source]#
Natural logarithm of x (i.e. logarithm base e of x)
- Returns:
- Expression
- gamspy.math.abs(x: int | float | Symbol) Expression[source]#
Absolute value of x (i.e.
|x|)- Returns:
- Expression
- gamspy.math.ceil(x: int | float | Symbol) Expression[source]#
The smallest integer greater than or equal to x
- Returns:
- Expression
- gamspy.math.dist(x1: tuple[int, float] | Symbol, x2: tuple[int, float] | Symbol) Expression[source]#
L2 norm
- Returns:
- Expression
- Raises:
- Exception
In case both x1 and x2 are not a tuple or none.
- gamspy.math.div(dividend: int | float | Symbol, divisor: int | float | Symbol) Expression[source]#
Dividing operation
- Parameters:
- dividendint | float | Symbol
- divisorint | float | Symbol
- Returns:
- Expression
- gamspy.math.div0(dividend: int | float | Symbol, divisor: int | float | Symbol) Expression[source]#
Dividing operation
- Parameters:
- dividendint | float | Symbol
- divisorint | float | Symbol
- Returns:
- Expression
- gamspy.math.factorial(x: int | Symbol) Expression[source]#
Factorial of x
- Returns:
- Expression
- gamspy.math.floor(x: int | float | Symbol) Expression[source]#
The greatest integer less than or equal to x
- Returns:
- Expression
- gamspy.math.fractional(x: int | float | Symbol) Expression[source]#
Returns the fractional part of x
- Returns:
- Expression
- gamspy.math.Min(*values) Expression[source]#
Minimum value of the values, where the number of values may vary.
- Returns:
- Expression
- gamspy.math.Max(*values) Expression[source]#
Maximum value of the values, where the number of values may vary.
- Returns:
- Expression
- gamspy.math.mod(x: float | Symbol, y: float | Symbol) Expression[source]#
Remainder of x divided by y.
- Returns:
- Expression
- gamspy.math.Round(x: float | Symbol, num_decimals: int = 0) Expression[source]#
Round x to num_decimals decimal places.
- Parameters:
- xfloat | Symbol
- decimalint, optional
- Returns:
- Expression
- gamspy.math.sign(x: Symbol) Expression[source]#
Sign of x returns 1 if x > 0, -1 if x < 0, and 0 if x = 0
- Parameters:
- xSymbol
- Returns:
- Expression
- gamspy.math.binomial(n: int | float | Symbol, k: int | float | Symbol) Expression[source]#
(Generalized) Binomial coefficient for n > -1, -1 < k < n + 1
- Parameters:
- nint | float | Symbol
- kint | float | Symbol
- Returns:
- Expression
- gamspy.math.centropy(x: int | float | Symbol, y: int | float | Symbol, z: float = 1e-20) Expression[source]#
Cross-entropy. x . ln((x + z) / (y + z)
- Parameters:
- xfloat | Symbol
- yfloat | Symbol
- zfloat, optional
- Returns:
- Expression
- Raises:
- ValueError
if z is smaller than 0
- gamspy.math.normal(mean: int | float, dev: int | float) Expression[source]#
Generate a random number from the normal distribution with mean mean and standard deviation dev.
- Parameters:
- meanint | float
- devint | float
- Returns:
- Expression
- gamspy.math.uniform(lower_bound: float | Expression, upper_bound: float | Expression) Expression[source]#
Generates a random number from the uniform distribution between lower_bound and higher_bound
- Parameters:
- lower_boundfloat
- upper_boundfloat
- Returns:
- Expression
- gamspy.math.uniformInt(lower_bound: int | float, upper_bound: int | float) Expression[source]#
Generates an integer random number from the discrete uniform distribution whose outcomes are the integers between lower_bound and higher_bound.
- Parameters:
- lower_boundint | float
- upper_boundint | float
- Returns
- ——-
- Expression
- gamspy.math.cv_power(base: float | Symbol, exponent: float | Symbol) Expression[source]#
Real power (i.e. base ^ exponent where X >= 0)
- Parameters:
- basefloat | Symbol
- exponentfloat | Symbol
- Returns:
- Expression
- gamspy.math.rpower(base: float | Symbol, exponent: float | Symbol)[source]#
Returns x^y for x > 0 and also for x = 0 and restricted values of y
- Parameters:
- basefloat | Symbol
- exponentfloat | Symbol
- Returns:
- Expression
- gamspy.math.sign_power(base: float | Symbol, exponent: float | Symbol)[source]#
Signed power for y > 0.
- Parameters:
- basefloat | Symbol
- exponentfloat | Symbol
- Returns:
- Expression
- gamspy.math.sllog10(x: int | float | Symbol, S: int | float = 1e-150) Expression[source]#
Smooth (linear) logarithm base 10
- Parameters:
- xint | float | Symbol
- Sint | float, by default 1.0e-150
- Returns:
- Expression
- gamspy.math.sqlog10(x: int | float | Symbol, S: int | float = 1e-150) Expression[source]#
Smooth (quadratic) logarithm base 10
- Parameters:
- xint | float | Symbol
- Sint | float, by default 1.0e-150
- Returns:
- Expression
- gamspy.math.vc_power(base: float | Symbol, exponent: float | Symbol)[source]#
Returns x^y for x >= 0
- Parameters:
- basefloat | Symbol
- exponentfloat | Symbol
- Returns:
- Expression
- gamspy.math.slexp(x: int | float | Symbol, S: int | float = 150) Expression[source]#
Smooth (linear) exponential
- Parameters:
- xint | float | Symbol
- Sint | float, by default 150
- Returns:
- Expression
- gamspy.math.sqexp(x: int | float | Symbol, S: int | float = 150) Expression[source]#
Smooth (quadratic) exponential
- Parameters:
- xint | float | Symbol
- Sint | float, by default 150
- Returns:
- Expression
- gamspy.math.truncate(x: int | float | Symbol) Expression[source]#
Returns the integer part of x
- Returns:
- Expression
- gamspy.math.ifthen(condition: Expression, yes_return: float | Expression, no_return: float | Expression) Expression[source]#
If the logical condition is true, the function returns iftrue, else it returns else
- Parameters:
- conditionExpression
- yes_returnfloat | Expression
- no_returnfloat | 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)
- gamspy.math.beta(x: int | float | Symbol, y: int | float | Symbol) Expression[source]#
Beta function
- Parameters:
- xint | float | Symbol
- yint | float | Symbol
- Returns:
- Expression
- gamspy.math.regularized_beta(x: int | float, y: int | float, z: int | float) Expression[source]#
Beta function
- Parameters:
- xint | float
- yint | float
- zint | float
- Returns:
- Expression
- gamspy.math.gamma(x: int | float | Symbol) Expression[source]#
Gamma function
- Parameters:
- xint | float
- Returns:
- Expression
- gamspy.math.regularized_gamma(x: int | float, a: int | float) Expression[source]#
Gamma function
- Parameters:
- xint | float
- aint | float
- Returns:
- Expression
- gamspy.math.entropy(x: int | float | Symbol) Expression[source]#
L2 Norm of x
- Parameters:
- xint | float | Symbol
- Returns:
- Expression
- gamspy.math.lse_max(*xs) Expression[source]#
Smoothed Max via the Logarithm of the Sum of Exponentials
- Returns:
- Expression
- gamspy.math.lse_max_sc(t, *xs) Expression[source]#
Scaled smoothed Max via the Logarithm of the Sum of Exponentials
- Returns:
- Expression
- gamspy.math.lse_min(*xs) Expression[source]#
Smoothed Min via the Logarithm of the Sum of Exponentials
- Returns:
- Expression
- gamspy.math.lse_min_sc(t, *xs) Expression[source]#
Scaled smoothed Min via the Logarithm of the Sum of Exponentials
- Returns:
- Expression
- gamspy.math.ncp_cm(x: Symbol, y: Symbol, z: float | int) Expression[source]#
Chen-Mangasarian smoothing
- Parameters:
- xSymbol
- ySymbol
- zint | float
- Returns:
- Expression
- gamspy.math.ncp_f(x: Symbol, y: Symbol, z: int | float = 0) Expression[source]#
Fisher-Burmeister smoothing
- Parameters:
- xSymbol
- ySymbol
- zint | float, optional
- Returns:
- Expression
- gamspy.math.ncpVUpow(r: Symbol, s: Symbol, mu: int | float = 0) Expression[source]#
NCP Veelken-Ulbrich: smoothed min(r,s)
- Parameters:
- rSymbol
- sSymbol
- muint | float, optional
- Returns:
- Expression
- gamspy.math.ncpVUsin(r: Symbol, s: Symbol, mu: int | float = 0) Expression[source]#
NCP Veelken-Ulbrich: smoothed min(r,s)
- Parameters:
- rSymbol
- sSymbol
- muint | float, optional
- Returns:
- Expression
- gamspy.math.poly(x, *args) Expression[source]#
Polynomial function
- Returns:
- Expression
- gamspy.math.rand_binomial(n: int | float, p: int | float) Expression[source]#
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:
- nint | float
- pint | float
- Returns:
- Expression
- gamspy.math.rand_linear(low: int | float, slope: int | float, high: int | float) Expression[source]#
Generate a random number between low and high with linear distribution. slope must be greater than 2 / (high - low)
- Parameters:
- lowint | float
- slopeint | float
- highint | float
- Returns:
- Expression
- gamspy.math.rand_triangle(low: int | float, mid: int | float, high: int | float) Expression[source]#
Generate a random number between low and high with triangular distribution. mid is the most probable number.
- Parameters:
- lowint | float
- midint | float
- highint | float
- Returns:
- Expression
- gamspy.math.slrec(x: int | float | Symbol, S: int | float = 1e-10) Expression[source]#
Smooth (linear) reciprocal
- Parameters:
- xint | float | Symbol
- Sint | float, by default 1e-10
- Returns:
- Expression
- gamspy.math.sqrec(x: int | float | Symbol, S: int | float = 1e-10) Expression[source]#
Smooth (quadratic) reciprocal
- Parameters:
- xint | float | Symbol
- Sint | float, by default 1e-10
- Returns:
- Expression
- gamspy.math.errorf(x: int | float | Symbol) Expression[source]#
Integral of the standard normal distribution
- Parameters:
- xint, float, Symbol
- Returns:
- Expression
- gamspy.math.same_as(self: Set | Alias, other: Set | Alias | str) Expression[source]#
Evaluates to true if this set is identical to the given set or alias, false otherwise.
- Parameters:
- otherSet | Alias
- Returns:
- Expression
- gamspy.math.sigmoid(x: int | float | Symbol) Expression[source]#
Sigmoid of x
- Parameters:
- xint | float | Symbol
- Returns:
- Expression
- gamspy.math.bool_and(x: int | Symbol, y: int | Symbol) Expression[source]#
- gamspy.math.bool_eqv(x: int | Symbol, y: int | Symbol) Expression[source]#
- gamspy.math.bool_imp(x: int | Symbol, y: int | Symbol) Expression[source]#
- gamspy.math.bool_not(x: int | Symbol) Expression[source]#
- gamspy.math.bool_or(x: int | Symbol, y: int | Symbol) Expression[source]#
- gamspy.math.bool_xor(x: int | Symbol, y: int | Symbol) Expression[source]#
- gamspy.math.rel_eq(x: int | Symbol, y: int | Symbol) Expression[source]#
- gamspy.math.rel_ge(x: int | Symbol, y: int | Symbol) Expression[source]#
- gamspy.math.rel_gt(x: int | Symbol, y: int | Symbol) Expression[source]#
- gamspy.math.rel_le(x: int | Symbol, y: int | Symbol) Expression[source]#
- gamspy.math.rel_lt(x: int | Symbol, y: int | Symbol) Expression[source]#
- gamspy.math.rel_ne(x: int | Symbol, y: int | Symbol) Expression[source]#