""" klujax: a KLU solver for JAX """
__version__ = "0.2.10"
__author__ = "Floris Laporte"
__all__ = ["solve", "coo_mul_vec"]
# Imports =============================================================================
from functools import partial, wraps
from time import time
import jax
import jax.numpy as jnp
import numpy as np
from jax import core, lax
from jax.core import ShapedArray
from jax.interpreters import ad, batching
from jaxlib import xla_client
from jax._src.interpreters.xla import (
_backend_specific_translations,
)
import klujax_cpp
# Config ==============================================================================
jax.config.update("jax_enable_x64", True)
jax.config.update("jax_platform_name", "cpu")
# Constants ===========================================================================
COMPLEX_DTYPES = (
np.complex64,
np.complex128,
# np.complex256,
jnp.complex64,
jnp.complex128,
)
# Primitives ==========================================================================
solve_f64 = core.Primitive("solve_f64")
solve_c128 = core.Primitive("solve_c128")
coo_mul_vec_f64 = core.Primitive("coo_mul_vec_f64")
coo_mul_vec_c128 = core.Primitive("coo_mul_vec_c128")
# Helper Decorators ===================================================================
_cpu_translations = _backend_specific_translations["cpu"]
def _wrap_old_translation(f):
@wraps(f)
def wrapped(ctx, avals_in, avals_out, *args, **kw):
ans = f(ctx.builder, *args, **kw)
return [ans]
return wrapped
def xla_register_cpu(primitive, cpp_fun):
name = primitive.name.encode()
def decorator(fun):
xla_client.register_custom_call_target(
name,
cpp_fun(),
)
_cpu_translations[primitive] = _wrap_old_translation(partial(fun, name))
#mlir.register_lowering(primitive, partial(fun, name), 'cpu')
return fun
return decorator
def ad_register(primitive):
def decorator(fun):
ad.primitive_jvps[primitive] = fun
return fun
return decorator
def transpose_register(primitive):
def decorator(fun):
ad.primitive_transposes[primitive] = fun
return fun
return decorator
def vmap_register(primitive, operation):
def decorator(fun):
batching.primitive_batchers[primitive] = partial(fun, operation)
return fun
return decorator
# The Functions =======================================================================
[docs]@jax.jit # jitting by default allows for empty implementation definitions
def solve(Ai, Aj, Ax, b):
if any(x.dtype in COMPLEX_DTYPES for x in (Ax, b)):
result = solve_c128.bind(
Ai.astype(jnp.int32),
Aj.astype(jnp.int32),
Ax.astype(jnp.complex128),
b.astype(jnp.complex128),
)
else:
result = solve_f64.bind(
Ai.astype(jnp.int32),
Aj.astype(jnp.int32),
Ax.astype(jnp.float64),
b.astype(jnp.float64),
)
return result
[docs]@jax.jit # jitting by default allows for empty implementation definitions
def coo_mul_vec(Ai, Aj, Ax, b):
if any(x.dtype in COMPLEX_DTYPES for x in (Ax, b)):
result = coo_mul_vec_c128.bind(
Ai.astype(jnp.int32),
Aj.astype(jnp.int32),
Ax.astype(jnp.complex128),
b.astype(jnp.complex128),
)
else:
result = coo_mul_vec_f64.bind(
Ai.astype(jnp.int32),
Aj.astype(jnp.int32),
Ax.astype(jnp.float64),
b.astype(jnp.float64),
)
return result
# Implementation ======================================================================
@solve_f64.def_impl
@solve_c128.def_impl
@coo_mul_vec_f64.def_impl
@coo_mul_vec_c128.def_impl
def coo_vec_operation_impl(Ai, Aj, Ax, b):
# No implementations needed, as function is jitted by default (see above)
raise NotImplementedError
# Abstract Evaluations ================================================================
@solve_f64.def_abstract_eval
@solve_c128.def_abstract_eval
@coo_mul_vec_f64.def_abstract_eval
@coo_mul_vec_c128.def_abstract_eval
def coo_vec_operation_abstract_eval(Ai, Aj, Ax, b):
return ShapedArray(b.shape, b.dtype)
# XLA Implementations =================================================================
@xla_register_cpu(solve_f64, klujax_cpp.solve_f64)
@xla_register_cpu(solve_c128, klujax_cpp.solve_c128)
@xla_register_cpu(coo_mul_vec_f64, klujax_cpp.coo_mul_vec_f64)
@xla_register_cpu(coo_mul_vec_c128, klujax_cpp.coo_mul_vec_c128)
def coo_vec_operation_xla(primitive_name, c, Ai, Aj, Ax, b):
Ax_shape = c.get_shape(Ax)
Ai_shape = c.get_shape(Ai)
Aj_shape = c.get_shape(Aj)
b_shape = c.get_shape(b)
*_n_lhs_list, _Anz = Ax_shape.dimensions()
assert len(_n_lhs_list) < 2, "solve alows for maximum one batch dimension."
_n_lhs = int(np.prod(np.array(_n_lhs_list, np.int32)))
Ax = xla_client.ops.Reshape(Ax, (_n_lhs * _Anz,))
Ax_shape = c.get_shape(Ax)
if _n_lhs_list:
_n_lhs_b, _n_col, *_n_rhs_list = b_shape.dimensions()
else:
_n_col, *_n_rhs_list = b_shape.dimensions()
_n_lhs_b = 1
assert _n_lhs_b == _n_lhs, "Batch dimension of Ax and b don't match."
_n_col = int(_n_col)
_n_rhs = int(np.prod(np.array(_n_rhs_list, dtype=np.int32)))
b = xla_client.ops.Reshape(b, (_n_lhs, _n_col, _n_rhs))
b = xla_client.ops.Transpose(b, (0, 2, 1))
b = xla_client.ops.Reshape(b, (_n_lhs * _n_rhs * _n_col,))
b_shape = c.get_shape(b)
Anz = xla_client.ops.ConstantLiteral(c, np.int32(_Anz))
n_col = xla_client.ops.ConstantLiteral(c, np.int32(_n_col))
n_rhs = xla_client.ops.ConstantLiteral(c, np.int32(_n_rhs))
n_lhs = xla_client.ops.ConstantLiteral(c, np.int32(_n_lhs))
Anz_shape = xla_client.Shape.array_shape(np.dtype(np.int32), (), ())
n_col_shape = xla_client.Shape.array_shape(np.dtype(np.int32), (), ())
n_lhs_shape = xla_client.Shape.array_shape(np.dtype(np.int32), (), ())
n_rhs_shape = xla_client.Shape.array_shape(np.dtype(np.int32), (), ())
result = xla_client.ops.CustomCallWithLayout(
c,
primitive_name,
operands=(n_col, n_lhs, n_rhs, Anz, Ai, Aj, Ax, b),
operand_shapes_with_layout=(
n_col_shape,
n_lhs_shape,
n_rhs_shape,
Anz_shape,
Ai_shape,
Aj_shape,
Ax_shape,
b_shape,
),
shape_with_layout=b_shape,
)
result = xla_client.ops.Reshape(result, (_n_lhs, _n_rhs, _n_col))
result = xla_client.ops.Transpose(result, (0, 2, 1))
if _n_lhs_list:
result = xla_client.ops.Reshape(result, (_n_lhs, _n_col, *_n_rhs_list))
else:
result = xla_client.ops.Reshape(result, (_n_col, *_n_rhs_list))
return result
# Forward Gradients ===================================================================
@ad_register(solve_f64)
@ad_register(solve_c128)
def solve_value_and_jvp(arg_values, arg_tangents):
Ai, Aj, Ax, b = arg_values
dAi, dAj, dAx, db = arg_tangents
dAx = dAx if not isinstance(dAx, ad.Zero) else lax.zeros_like_array(Ax)
dAi = dAi if not isinstance(dAi, ad.Zero) else lax.zeros_like_array(Ai)
dAj = dAj if not isinstance(dAj, ad.Zero) else lax.zeros_like_array(Aj)
db = db if not isinstance(db, ad.Zero) else lax.zeros_like_array(b)
x = solve(Ai, Aj, Ax, b)
dA_x = coo_mul_vec(Ai, Aj, dAx, x)
invA_dA_x = solve(Ai, Aj, Ax, dA_x)
invA_db = solve(Ai, Aj, Ax, db)
return x, -invA_dA_x + invA_db
@ad_register(coo_mul_vec_f64)
@ad_register(coo_mul_vec_c128)
def coo_mul_vec_value_and_jvp(arg_values, arg_tangents):
Ai, Aj, Ax, b = arg_values
dAi, dAj, dAx, db = arg_tangents
dAx = dAx if not isinstance(dAx, ad.Zero) else lax.zeros_like_array(Ax)
dAi = dAi if not isinstance(dAi, ad.Zero) else lax.zeros_like_array(Ai)
dAj = dAj if not isinstance(dAj, ad.Zero) else lax.zeros_like_array(Aj)
db = db if not isinstance(db, ad.Zero) else lax.zeros_like_array(b)
x = coo_mul_vec(Ai, Aj, Ax, b)
dA_b = coo_mul_vec(Ai, Aj, dAx, b)
A_db = coo_mul_vec(Ai, Aj, Ax, db)
return x, dA_b + A_db
# Backward Gradients through Transposition ============================================
@transpose_register(solve_f64)
@transpose_register(solve_c128)
def solve_transpose(ct, Ai, Aj, Ax, b):
assert not ad.is_undefined_primal(Ai)
assert not ad.is_undefined_primal(Aj)
assert not ad.is_undefined_primal(Ax)
assert not ad.is_undefined_primal(Ax)
assert ad.is_undefined_primal(b)
return None, None, None, solve(Aj, Ai, Ax.conj(), ct) # = inv(A).H@ct [= ct@inv(A)]
@transpose_register(coo_mul_vec_f64)
@transpose_register(coo_mul_vec_c128)
def coo_mul_vec_transpose(ct, Ai, Aj, Ax, b):
assert not ad.is_undefined_primal(Ai)
assert not ad.is_undefined_primal(Aj)
assert ad.is_undefined_primal(Ax) != ad.is_undefined_primal(b) # xor
if ad.is_undefined_primal(b):
return None, None, None, coo_mul_vec(Aj, Ai, Ax.conj(), ct) # = A.T@ct [= ct@A]
else:
dA = ct[Ai] * b[Aj]
dA = dA.reshape(dA.shape[0], -1).sum(-1) # not sure about this...
return None, None, dA, None
# Vectorization (vmap) ================================================================
@vmap_register(solve_f64, solve)
@vmap_register(solve_c128, solve)
@vmap_register(coo_mul_vec_f64, coo_mul_vec)
@vmap_register(coo_mul_vec_c128, coo_mul_vec)
def coo_vec_operation_vmap(operation, vector_arg_values, batch_axes):
aAi, aAj, aAx, ab = batch_axes
Ai, Aj, Ax, b = vector_arg_values
assert aAi is None, "Ai cannot be vectorized."
assert aAj is None, "Aj cannot be vectorized."
if aAx is not None and ab is not None:
assert isinstance(aAx, int) and isinstance(ab, int)
n_lhs = Ax.shape[aAx]
if ab != 0:
Ax = jnp.moveaxis(Ax, aAx, 0)
if ab != 0:
b = jnp.moveaxis(b, ab, 0)
result = operation(Ai, Aj, Ax, b)
return result, 0
if ab is None:
assert isinstance(aAx, int)
n_lhs = Ax.shape[aAx]
if aAx != 0:
Ax = jnp.moveaxis(Ax, aAx, 0)
b = jnp.broadcast_to(b[None], (Ax.shape[0], *b.shape))
result = operation(Ai, Aj, Ax, b)
return result, 0
if aAx is None:
assert isinstance(ab, int)
if ab != 0:
b = jnp.moveaxis(b, ab, 0)
n_lhs, n_col, *n_rhs_list = b.shape
n_rhs = np.prod(np.array(n_rhs_list, dtype=np.int32))
b = b.reshape(n_lhs, n_col, n_rhs).transpose((1, 0, 2)).reshape(n_col, -1)
result = operation(Ai, Aj, Ax, b)
result = result.reshape(n_col, n_lhs, *n_rhs_list)
return result, 1
raise ValueError("invalid arguments for vmap")
# Quick Tests =========================================================================
if __name__ == "__main__":
A = jnp.array(
[
[2 + 3j, 3, 0, 0, 0],
[3, 0, 4, 0, 6],
[0, -1, -3, 2, 0],
[0, 0, 1, 0, 0],
[0, 4, 2, 0, 1],
],
dtype=jnp.complex128,
)
A = jnp.array(
[
[2, 3, 0, 0, 0],
[3, 0, 4, 0, 6],
[0, -1, -3, 2, 0],
[0, 0, 1, 0, 0],
[0, 4, 2, 0, 1],
],
dtype=jnp.float64,
)
b = jnp.array([[8], [45], [-3], [3], [19]], dtype=jnp.float64)
b = jnp.array([[8, 7], [45, 44], [-3, -4], [3, 2], [19, 18]], dtype=jnp.float64)
b = jnp.array([3 + 8j, 8 + 45j, 23 + -3j, -7 - 3j, 13 + 19j], dtype=jnp.complex128)
b = jnp.array([8, 45, -3, 3, 19], dtype=jnp.float64)
Ai, Aj = jnp.where(abs(A) > 0)
Ax = A[Ai, Aj]
t = time()
result = solve(Ai, Aj, Ax, b)
print(f"{time()-t:.3e}", result)
t = time()
result = solve(Ai, Aj, Ax, b)
print(f"{time()-t:.3e}", result)
t = time()
result = solve(Ai, Aj, Ax, b)
print(f"{time()-t:.3e}", result)
def solve_sum(Ai, Aj, Ax, b):
return solve(Ai, Aj, Ax, b).sum()
solve_sum_grad = jax.grad(solve_sum, 2)
t = time()
result = solve_sum_grad(Ai, Aj, Ax, b)
print(f"{time()-t:.3e}", result)
def coo_mul_vec_sum(Ai, Aj, Ax, b):
return coo_mul_vec(Ai, Aj, Ax, b).sum()
coo_mul_vec_sum_grad = jax.grad(coo_mul_vec_sum, 3)
t = time()
result = coo_mul_vec_sum_grad(Ai, Aj, Ax, b)
print(f"{time()-t:.3e}", result)
