prophys.symbolic

Symbolic expressions: parameters, inputs, operators and elementwise functions.

Every model quantity in prophys is an Expr, a lazily evaluated, differentiable expression graph. Leaves are constants (Const), fitted parameters (Param) and data placeholders (Input). Functions such as exp(), sqrt() or where() combine them elementwise. The special functions (erf(), ndtr(), owens_t(), …) are evaluated by optimized native kernels with exact gradients. The most common names are also exported at the top level (prp.exp, prp.Param, …).

Classes

Const	A fixed constant leaf holding a Python scalar, NumPy array or JAX array.
Expr	Base class of every symbolic expression node.
Op	An expression node that applies a pure function to the values of its child expressions.
Param	A named, learnable leaf fitted by calibration or optimization.
Input	A named placeholder for data supplied at evaluation time.
BinaryState	A learnable on/off design decision that stays differentiable.
CategoricalState	A learnable choice among k discrete states that stays differentiable.
Surrogate	Wrap an arbitrary pure callable, compatible with JAX, as a symbolic node.

Functions

op	Build an Op node applying a JAX function to expressions.
wrap	Return value as an expression, wrapping non-Expr values in a Const.
abs_	Elementwise absolute value of an expression (named abs_ to avoid shadowing the builtin).
arctan2	Elementwise arctangent of y / x over all four quadrants, in radians in [-pi, pi].
clip	Elementwise clamp of an expression to the interval [lo, hi].
concatenate	Join expressions along an existing axis.
cos	Elementwise cosine of an expression given in radians.
deg2rad	Elementwise conversion of an angle expression from degrees to radians.
dot	Dot product of two expressions, with jnp.dot semantics (inner product of vectors).
exp	Elementwise exponential e**x of an expression.
log	Elementwise natural logarithm of an expression.
log10	Elementwise base-10 logarithm of an expression.
logsumexp	Numerically stable log(sum(exp(x))) over axis (all elements when axis=None).
maximum	Elementwise maximum of two broadcastable expressions.
mean	Arithmetic mean of an expression over axis (all elements when axis=None).
minimum	Elementwise minimum of two broadcastable expressions.
norm	Euclidean (L2) norm of an expression along axis (the last axis by default).
prod	Product of an expression over axis (all elements when axis=None).
rad2deg	Elementwise conversion of an angle expression from radians to degrees.
relu	Elementwise rectified linear unit max(x, 0) of an expression.
sigmoid	Elementwise logistic sigmoid 1 / (1 + exp(-x)) of an expression.
tanh	Elementwise hyperbolic tangent of an expression.
sign	Elementwise sign of an expression: -1, 0 or +1.
sin	Elementwise sine of an expression given in radians.
softmax	Smooth, differentiable approximation of the maximum along axis.
softmin	Smooth, differentiable approximation of the minimum along axis.
softplus	Elementwise softplus log(1 + exp(x)) of an expression, a smooth positive ramp.
sqrt	Elementwise square root of an expression.
stack	Stack expressions of the same shape along a new axis.
sum_	Sum of an expression over axis (all elements when axis=None).
tan	Elementwise tangent of an expression given in radians.
where	Elementwise selection: a where cond is true, otherwise b.
erf	Elementwise error function erf(x) = 2/sqrt(pi) * integral_0^x exp(-t^2) dt.
erfc	Elementwise complementary error function 1 - erf(x), accurate far into the upper tail.
erfcx	Elementwise scaled complementary error function exp(x^2) erfc(x), free of underflow for large x.
ndtr	Elementwise standard normal cumulative distribution function Phi(x).
log_ndtr	Elementwise logarithm of the standard normal CDF, log Phi(x), accurate in the lower tail.
exp1	Elementwise exponential integral E1(x) for x > 0 (e.g. the Theis well function).
i0e	Elementwise exponentially scaled modified Bessel function of the first kind, exp(-|x|) I0(x).
i1e	Elementwise exponentially scaled modified Bessel function of the first kind, exp(-|x|) I1(x).
k0e	Elementwise scaled modified Bessel function of the second kind, exp(x) K0(x) for x > 0.
k1e	Elementwise scaled modified Bessel function of the second kind, exp(x) K1(x) for x > 0.
owens_t	Elementwise Owen's T function T(h, a).

Exceptions

ShapeError

Raised when shapes are incompatible, such as a distribution's sample shape and its parameters' batch shape.

Constants and objects

Env