feat: alternative matrix multiplication routine jack_matmul implemented

pyerrors/linalg.py

@@ -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)

tests/linalg_test.py

@@ -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 = []