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import functools as ft
import sympy
import string
import random
# Special since need to reduce arguments.
MUL = 0
ADD = 1
_jnp_func_lookup = {
sympy.Mul: MUL,
sympy.Add: ADD,
sympy.div: "jnp.div",
sympy.Abs: "jnp.abs",
sympy.sign: "jnp.sign",
# Note: May raise error for ints.
sympy.ceiling: "jnp.ceil",
sympy.floor: "jnp.floor",
sympy.log: "jnp.log",
sympy.exp: "jnp.exp",
sympy.sqrt: "jnp.sqrt",
sympy.cos: "jnp.cos",
sympy.acos: "jnp.acos",
sympy.sin: "jnp.sin",
sympy.asin: "jnp.asin",
sympy.tan: "jnp.tan",
sympy.atan: "jnp.atan",
sympy.atan2: "jnp.atan2",
# Note: Also may give NaN for complex results.
sympy.cosh: "jnp.cosh",
sympy.acosh: "jnp.acosh",
sympy.sinh: "jnp.sinh",
sympy.asinh: "jnp.asinh",
sympy.tanh: "jnp.tanh",
sympy.atanh: "jnp.atanh",
sympy.Pow: "jnp.power",
sympy.re: "jnp.real",
sympy.im: "jnp.imag",
sympy.arg: "jnp.angle",
# Note: May raise error for ints and complexes
sympy.erf: "jsp.erf",
sympy.erfc: "jsp.erfc",
sympy.LessThan: "jnp.less",
sympy.GreaterThan: "jnp.greater",
sympy.And: "jnp.logical_and",
sympy.Or: "jnp.logical_or",
sympy.Not: "jnp.logical_not",
sympy.Max: "jnp.max",
sympy.Min: "jnp.min",
sympy.Mod: "jnp.mod",
}
def sympy2jaxtext(expr, parameters, symbols_in):
if issubclass(expr.func, sympy.Float):
parameters.append(float(expr))
return f"parameters[{len(parameters) - 1}]"
if issubclass(expr.func, sympy.Integer):
return f"{int(expr)}"
if issubclass(expr.func, sympy.Symbol):
return (
f"X[:, {[i for i in range(len(symbols_in)) if symbols_in[i] == expr][0]}]"
)
_func = _jnp_func_lookup[expr.func]
args = [sympy2jaxtext(arg, parameters, symbols_in) for arg in expr.args]
if _func == MUL:
return " * ".join(["(" + arg + ")" for arg in args])
if _func == ADD:
return " + ".join(["(" + arg + ")" for arg in args])
return f'{_func}({", ".join(args)})'
jax_initialized = False
jax = None
jnp = None
jsp = None
def _initialize_jax():
global jax_initialized
global jax
global jnp
global jsp
if not jax_initialized:
import jax as _jax
from jax import numpy as _jnp
from jax.scipy import special as _jsp
jax = _jax
jnp = _jnp
jsp = _jsp
def sympy2jax(expression, symbols_in, selection=None):
"""Returns a function f and its parameters;
the function takes an input matrix, and a list of arguments:
f(X, parameters)
where the parameters appear in the JAX equation.
# Examples:
Let's create a function in SymPy:
```python
x, y = symbols('x y')
cosx = 1.0 * sympy.cos(x) + 3.2 * y
```
Let's get the JAX version. We pass the equation, and
the symbols required.
```python
f, params = sympy2jax(cosx, [x, y])
```
The order you supply the symbols is the same order
you should supply the features when calling
the function `f` (shape `[nrows, nfeatures]`).
In this case, features=2 for x and y.
The `params` in this case will be
`jnp.array([1.0, 3.2])`. You pass these parameters
when calling the function, which will let you change them
and take gradients.
Let's generate some JAX data to pass:
```python
key = random.PRNGKey(0)
X = random.normal(key, (10, 2))
```
We can call the function with:
```python
f(X, params)
#> DeviceArray([-2.6080756 , 0.72633684, -6.7557726 , -0.2963162 ,
# 6.6014843 , 5.032483 , -0.810931 , 4.2520013 ,
# 3.5427954 , -2.7479894 ], dtype=float32)
```
We can take gradients with respect
to the parameters for each row with JAX
gradient parameters now:
```python
jac_f = jax.jacobian(f, argnums=1)
jac_f(X, params)
#> DeviceArray([[ 0.49364874, -0.9692889 ],
# [ 0.8283714 , -0.0318858 ],
# [-0.7447336 , -1.8784496 ],
# [ 0.70755106, -0.3137085 ],
# [ 0.944834 , 1.767703 ],
# [ 0.51673377, 1.4111717 ],
# [ 0.87347716, -0.52637756],
# [ 0.8760679 , 1.0549792 ],
# [ 0.9961824 , 0.79581654],
# [-0.88465923, -0.5822907 ]], dtype=float32)
```
We can also JIT-compile our function:
```python
compiled_f = jax.jit(f)
compiled_f(X, params)
#> DeviceArray([-2.6080756 , 0.72633684, -6.7557726 , -0.2963162 ,
# 6.6014843 , 5.032483 , -0.810931 , 4.2520013 ,
# 3.5427954 , -2.7479894 ], dtype=float32)
```
"""
_initialize_jax()
global jax_initialized
global jax
global jnp
global jsp
parameters = []
functional_form_text = sympy2jaxtext(expression, parameters, symbols_in)
hash_string = "A_" + str(abs(hash(str(expression) + str(symbols_in))))
text = f"def {hash_string}(X, parameters):\n"
if selection is not None:
# Impose the feature selection:
text += f" X = X[:, {list(selection)}]\n"
text += " return "
text += functional_form_text
ldict = {}
exec(text, globals(), ldict)
return ldict[hash_string], jnp.array(parameters)
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