feat: alternative matrix multiplication routine jack_matmul implemented

This commit is contained in:
Fabian Joswig 2021-11-17 16:57:08 +00:00
parent 972c8bd366
commit 865830af4c
2 changed files with 99 additions and 3 deletions

View file

@ -1,7 +1,7 @@
import numpy as np
from autograd import jacobian
import autograd.numpy as anp # Thinly-wrapped numpy
from .obs import derived_observable, CObs, Obs, _merge_idx, _expand_deltas_for_merge, _filter_zeroes
from .obs import derived_observable, CObs, Obs, _merge_idx, _expand_deltas_for_merge, _filter_zeroes, import_jackknife
from functools import partial
from autograd.extend import defvjp
@ -121,8 +121,13 @@ def derived_array(func, data, **kwargs):
def matmul(*operands):
"""Matrix multiply all operands.
Supports real and complex valued matrices and is faster compared to
standard multiplication via the @ operator.
Parameters
----------
operands : numpy.ndarray
Arbitrary number of 2d-numpy arrays which can be real or complex
Obs valued.
This implementation is faster compared to standard multiplication via the @ operator.
"""
if any(isinstance(o[0, 0], CObs) for o in operands):
extended_operands = []
@ -169,6 +174,56 @@ def matmul(*operands):
return derived_array(multi_dot, operands)
def jack_matmul(a, b):
"""Matrix multiply both operands making use of the jackknife approximation.
Parameters
----------
a : numpy.ndarray
First matrix, can be real or complex Obs valued
b : numpy.ndarray
Second matrix, can be real or complex Obs valued
For large matrices this is considerably faster compared to matmul.
"""
if any(isinstance(o[0, 0], CObs) for o in [a, b]):
def _exp_to_jack(matrix):
base_matrix = np.empty_like(matrix)
for (n, m), entry in np.ndenumerate(matrix):
base_matrix[n, m] = entry.real.export_jackknife() + 1j * entry.imag.export_jackknife()
return base_matrix
def _imp_from_jack(matrix, name):
base_matrix = np.empty_like(matrix)
for (n, m), entry in np.ndenumerate(matrix):
base_matrix[n, m] = CObs(import_jackknife(entry.real, name),
import_jackknife(entry.imag, name))
return base_matrix
j_a = _exp_to_jack(a)
j_b = _exp_to_jack(b)
r = j_a @ j_b
return _imp_from_jack(r, a.ravel()[0].real.names[0])
else:
def _exp_to_jack(matrix):
base_matrix = np.empty_like(matrix)
for (n, m), entry in np.ndenumerate(matrix):
base_matrix[n, m] = entry.export_jackknife()
return base_matrix
def _imp_from_jack(matrix, name):
base_matrix = np.empty_like(matrix)
for (n, m), entry in np.ndenumerate(matrix):
base_matrix[n, m] = import_jackknife(entry, name)
return base_matrix
j_a = _exp_to_jack(a)
j_b = _exp_to_jack(b)
r = j_a @ j_b
return _imp_from_jack(r, a.ravel()[0].names[0])
def inv(x):
"""Inverse of Obs or CObs valued matrices."""
return _mat_mat_op(anp.linalg.inv, x)

View file

@ -7,6 +7,27 @@ import pytest
np.random.seed(0)
def get_real_matrix(dimension):
base_matrix = np.empty((dimension, dimension), dtype=object)
for (n, m), entry in np.ndenumerate(base_matrix):
exponent_real = np.random.normal(0, 1)
exponent_imag = np.random.normal(0, 1)
base_matrix[n, m] = pe.Obs([np.random.normal(1.0, 0.1, 100)], ['t'])
return base_matrix
def get_complex_matrix(dimension):
base_matrix = np.empty((dimension, dimension), dtype=object)
for (n, m), entry in np.ndenumerate(base_matrix):
exponent_real = np.random.normal(0, 1)
exponent_imag = np.random.normal(0, 1)
base_matrix[n, m] = pe.CObs(pe.Obs([np.random.normal(1.0, 0.1, 100)], ['t']),
pe.Obs([np.random.normal(1.0, 0.1, 100)], ['t']))
return base_matrix
def test_matmul():
for dim in [4, 8]:
my_list = []
@ -29,6 +50,26 @@ def test_matmul():
assert e.is_zero(), t
def test_jack_matmul():
tt = get_real_matrix(8)
check1 = pe.linalg.jack_matmul(tt, tt) - pe.linalg.matmul(tt, tt)
[o.gamma_method() for o in check1.ravel()]
assert np.all([o.is_zero_within_error(0.1) for o in check1.ravel()])
trace1 = np.trace(check1)
trace1.gamma_method()
assert trace1.dvalue < 0.001
tt2 = get_complex_matrix(8)
check2 = pe.linalg.jack_matmul(tt2, tt2) - pe.linalg.matmul(tt2, tt2)
[o.gamma_method() for o in check2.ravel()]
assert np.all([o.real.is_zero_within_error(0.1) for o in check2.ravel()])
assert np.all([o.imag.is_zero_within_error(0.1) for o in check2.ravel()])
trace2 = np.trace(check2)
trace2.gamma_method()
assert trace2.real.dvalue < 0.001
assert trace2.imag.dvalue < 0.001
def test_multi_dot():
for dim in [4, 8]:
my_list = []