sofia.field.reductions

class sofia.field.reductions.Reduce(*args)

Bases: Function

Reduce a field to a scalar using the given operation (e.g. “min”, “max”, “mean”).

Supported operations: min, max, mean, sum, prod, all, any, std, var, median, norm.

For each operation there is also a short-hand available, e.g. Reduce(expr, “min”) is equivalent to Min(expr).

Parameters:

• expr – The expression containing fields to reduce.

• operation – The operation to use for the reduction.

classmethod eval(*args)

Returns a canonical form of cls applied to arguments args.

Explanation

The eval() method is called when the class cls is about to be instantiated and it should return either some simplified instance (possible of some other class), or if the class cls should be unmodified, return None.

Examples of eval() for the function “sign”

@classmethod
def eval(cls, arg):
    if arg is S.NaN:
        return S.NaN
    if arg.is_zero: return S.Zero
    if arg.is_positive: return S.One
    if arg.is_negative: return S.NegativeOne
    if isinstance(arg, Mul):
        coeff, terms = arg.as_coeff_Mul(rational=True)
        if coeff is not S.One:
            return cls(coeff) * cls(terms)

sofia.field.reductions.Min(expr: Expr, **kwargs) → Reduce

Compute the minimum of expr, returning a scalar.

sofia.field.reductions.Max(expr: Expr, **kwargs) → Reduce

Compute the maximum of expr, returning a scalar.

sofia.field.reductions.Mean(expr: Expr, **kwargs) → Reduce

Compute the arithmetic mean of expr, returning a scalar.

sofia.field.reductions.Sum(expr: Expr, **kwargs) → Reduce

Compute the sum of expr, returning a scalar.

sofia.field.reductions.Prod(expr: Expr, **kwargs) → Reduce

Compute the product of expr, returning a scalar.

sofia.field.reductions.All(expr: Expr, **kwargs) → Reduce

Compute the logical AND of expr, returning a scalar.

sofia.field.reductions.Any(expr: Expr, **kwargs) → Reduce

Compute the logical OR of expr, returning a scalar.

sofia.field.reductions.Std(expr: Expr, **kwargs) → Reduce

Compute the standard deviation of expr, returning a scalar.

sofia.field.reductions.Var(expr: Expr, **kwargs) → Reduce

Compute the variance of expr, returning a scalar.

sofia.field.reductions.Median(expr: Expr, **kwargs) → Reduce

Compute the median of expr, returning a scalar.

sofia.field.reductions.Norm(expr: Expr, **kwargs) → Reduce

Compute the entrywise 2-norm of expr, returning a scalar.