SparseDiffPy
Sparse Jacobians and Hessians of nonlinear expressions, computed by
SparseDiffEngine,
a C library that works out the sparsity pattern once and then only computes
the structural nonzeros. Results are scipy.sparse.csr_matrix.
Installation
pip install sparsediffpy
From source: git clone --recursive https://github.com/SparseDifferentiation/SparseDiffPy && pip install -e SparseDiffPy.
Quick start
import numpy as np
import sparsediffpy as sp
scope = sp.Scope() # owns the flat variable vector
x = scope.Variable(3, 1) # shapes are always 2-D: (rows, cols)
f = sp.exp(x) + 2.0 * x # build an expression with operators and sp.* atoms
fn = sp.compile(f) # analyze sparsity once
x.value = [1.0, 2.0, 3.0]
print(fn.forward()) # [[4.718] [11.389] [26.086]], shaped like f
print(fn.jacobian().toarray()) # diag(exp(x) + 2), a 3x3 csr_matrix
print(fn.hessian(np.ones(3))) # Hessian of w' f(x) for weights w
forward() has the shape of f, jacobian() has shape (f.size, n_vars)
and hessian(w) has shape (n_vars, n_vars), where n_vars is the total
size of all variables in the scope, in declaration order. Values must have
the exact shape of what they set: x.value takes an array shaped like x,
hessian(w) takes w shaped like f (for vectors a 1-D array also works),
and flat vectors such as scope.set_values(u) must be 1-D. Flat vectors (the
rows of the Jacobian, the scope values) are column-major. Reading x.value
gives a read-only copy, so assign to x.value to change it.
Parameters are data you can change without recompiling:
import numpy as np
import sparsediffpy as sp
scope = sp.Scope()
x = scope.Variable(3, 1)
A = scope.Parameter(2, 3, value=np.ones((2, 3)))
fn = sp.compile(sp.sin(A @ x))
x.value = [0.1, 0.2, 0.3]
J1 = fn.jacobian()
A.value = np.arange(6.0).reshape(2, 3) # no recompile needed
J2 = fn.jacobian()
Using it in a solver
sp.Problem(objective, constraints) exposes the callbacks NLP solvers ask for:
objective(), gradient(), constraints(), jacobian() and the Lagrangian
Hessian hessian(obj_factor, lagrange) = obj_factor * H_f + sum_i lagrange_i * H_gi.
Like compile, everything is evaluated at the scope's current values, so a solver
callback sets the flat point with scope.set_values(u) and then asks for what it
needs, in any order. Each stage runs once per point and its result is a read-only
array. Here it drives SciPy:
import numpy as np
from scipy.optimize import NonlinearConstraint, minimize
import sparsediffpy as sp
# minimize sum(exp(x) - c * x) subject to ||x||^2 <= 1
scope = sp.Scope()
x = scope.Variable(4, 1)
c = np.array([[1.0], [2.0], [3.0], [4.0]]) # constants are 2-D, like variables
prob = sp.Problem(sp.sum(sp.exp(x) - c * x), [sp.sum(x ** 2)])
def at(u, method, *args): # evaluate prob.method(*args) at the flat point u
scope.set_values(u)
return getattr(prob, method)(*args)
con = NonlinearConstraint(lambda u: at(u, "constraints"), -np.inf, 1.0,
jac=lambda u: at(u, "jacobian"),
hess=lambda u, v: at(u, "hessian", 0.0, v))
res = minimize(lambda u: at(u, "objective"), np.zeros(4),
jac=lambda u: at(u, "gradient"),
hess=lambda u: at(u, "hessian", 1.0, [0.0]),
method="trust-constr", constraints=con)
print(res.x) # approx. [0. 0.289 0.549 0.784], on the boundary ||x|| = 1
Supported operations
- Operators:
+ - * @ **,/by a constant,.T, and indexing with ints, slices and integer lists:x[1:3]on a vector,X[0, :]orX[[0, 2], 1]on a matrix (a matrix always takes two indices). Scalars, rows and columns broadcast. NumPy arrays andscipy.sparsematrices are accepted as constants; like every expression they must be 2-D, so passa[:, None]ora[None, :]for a 1-Da. - Elementwise:
sin cos tan exp log sinh tanh asinh atan atanh logistic normal_cdf entr xexp power atan2. - Affine:
sum prod reshape broadcast hstack vstack trace diag_vec index_flat. - Other:
quad_form quad_over_lin rel_entr.
log, tan, atanh, entr, atan2, rel_entr, quad_over_lin and prod
currently need plain Variables as arguments (an engine limitation).
The low-level C bindings remain available as sparsediffpy._sparsediffengine.
Free-threaded Python
Wheels are published for free-threaded CPython 3.14 (cp314t) as well as the
default builds. There is no cp313t wheel because NumPy ships none from 2.5
onwards, so that build would have to compile NumPy from source.
The extension declares that it does not need the GIL, so importing it leaves
free threading enabled. Distinct problems can be built and evaluated
concurrently from different threads: the engine keeps no mutable global state,
every problem and expression owns its own buffers, and all inputs and outputs
are copied at the boundary. This assumes a default build, since
SP_TRACK_MEMORY adds global allocation counters that are not thread-safe.
A single problem or expression capsule is not thread-safe. Do not call into
the same problem from two threads at once, and do not share expression capsules
between problems that are evaluated concurrently. Note that expr::refcount is
a plain int, so breaking this rule corrupts the heap rather than merely
interleaving calls, as it would under the GIL.
License
Apache License 2.0
1 maintainer
Metadata
1 maintainer
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| Download URL | sparsediffpy-0.9.0-cp311-cp311-macosx_10_9_universal2.whl |
|---|---|
| Size | 243.8 kB |
| Tags | CPython 3.11 macOS 10.9+ universal2 (ARM64, x86-64) |
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SHA-256 checksum How to use checksums |
8953970a834d949e0c107481b3371e657c579e2850ce40895bc72da0c824dfc1
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Yes |
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twine/7.0.0 CPython/3.13.16
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