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test_primitives.py
140 lines (96 loc) · 6.17 KB
/
test_primitives.py
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import unittest
import numpy as np
import matplotlib.pylab as plt
from ceviche.primitives import *
from ceviche.constants import *
import ceviche # use the ceviche wrapper for autograd derivatives
DECIMAL = 3 # number of decimals to check to
## Setup
class TestPlaneWave(unittest.TestCase):
""" Tests whether a plane wave has the right wavelength """
def setUp(self):
self.N = 8 # size of matrix dimensions. matrix shape = (N, N)
self.M = self.N**2 # number of non-zeros (make it dense for numerical stability)
# these are the default values used within the test functions
self.indices_const = make_rand_indeces(self.N, self.M)
self.entries_const = make_rand_complex(self.M)
self.x_const = make_rand_complex(self.N)
self.b_const = make_rand_complex(self.N)
def out_fn(self, output_vector):
# this function takes the output of each primitive and returns a real scalar (sort of like the objective function)
return npa.abs(npa.sum(output_vector))
def err_msg(self, fn_name, mode):
return '{}-mode gradients failed for fn: {}'.format(mode, fn_name)
def test_mult_entries(self):
def fn_mult_entries(entries):
# sparse matrix multiplication (Ax = b) as a function of matrix entries 'A(entries)'
b = sp_mult(entries, self.indices_const, self.x_const)
return self.out_fn(b)
## Testing Gradients of 'Mult Entries Reverse-mode'
entries = make_rand_complex(self.M)
grad_rev = ceviche.jacobian(fn_mult_entries, mode='reverse')(entries)[0]
grad_for = ceviche.jacobian(fn_mult_entries, mode='forward')(entries)[0]
grad_true = grad_num(fn_mult_entries, entries)
np.testing.assert_almost_equal(grad_rev, grad_true, decimal=DECIMAL, err_msg=self.err_msg('fn_mult_entries', 'reverse'))
np.testing.assert_almost_equal(grad_for, grad_true, decimal=DECIMAL, err_msg=self.err_msg('fn_mult_entries', 'forward'))
def test_mult_x(self):
def fn_mult_x(x):
# sparse matrix multiplication (Ax = b) as a function of dense vector 'x'
b = sp_mult(self.entries_const, self.indices_const, x)
return self.out_fn(b)
## Testing Gradients of 'Mult x Reverse-mode'
x = make_rand_complex(self.N)
grad_rev = ceviche.jacobian(fn_mult_x, mode='reverse')(x)[0]
grad_for = ceviche.jacobian(fn_mult_x, mode='forward')(x)[0]
grad_true = grad_num(fn_mult_x, x)
np.testing.assert_almost_equal(grad_rev, grad_true, decimal=DECIMAL, err_msg=self.err_msg('fn_mult_x', 'reverse'))
np.testing.assert_almost_equal(grad_for, grad_true, decimal=DECIMAL, err_msg=self.err_msg('fn_mult_x', 'forward'))
def test_solve_entries(self):
def fn_solve_entries(entries):
# sparse matrix solve (x = A^{-1}b) as a function of matrix entries 'A(entries)'
x = sp_solve(entries, self.indices_const, self.b_const)
return self.out_fn(x)
entries = make_rand_complex(self.M)
grad_rev = ceviche.jacobian(fn_solve_entries, mode='reverse')(entries)[0]
grad_for = ceviche.jacobian(fn_solve_entries, mode='forward')(entries)[0]
grad_true = grad_num(fn_solve_entries, entries)
np.testing.assert_almost_equal(grad_rev, grad_true, decimal=DECIMAL, err_msg=self.err_msg('fn_solve_entries', 'reverse'))
np.testing.assert_almost_equal(grad_for, grad_true, decimal=DECIMAL, err_msg=self.err_msg('fn_solve_entries', 'forward'))
def test_solve_b(self):
def fn_solve_b(b):
# sparse matrix solve (x = A^{-1}b) as a function of source 'b'
x = sp_solve(self.entries_const, self.indices_const, b)
return self.out_fn(x)
b = make_rand_complex(self.N)
grad_rev = ceviche.jacobian(fn_solve_b, mode='reverse')(b)[0]
grad_for = ceviche.jacobian(fn_solve_b, mode='forward')(b)[0]
grad_true = grad_num(fn_solve_b, b)
np.testing.assert_almost_equal(grad_rev, grad_true, decimal=DECIMAL, err_msg=self.err_msg('fn_solve_b', 'reverse'))
np.testing.assert_almost_equal(grad_for, grad_true, decimal=DECIMAL, err_msg=self.err_msg('fn_solve_b', 'forward'))
def test_spmut_entries(self):
def fn_spsp_entries_a(entries):
# sparse matrix - sparse matrix dot procut as function of entries into first matrix (A)
entries_c, indices_c = spsp_mult(entries, self.indices_const, self.entries_const, self.indices_const, N=self.N)
entries_c, indices_c = spsp_mult(entries_c, indices_c, self.entries_const, self.indices_const, N=self.N)
x = sp_solve(entries_c, indices_c, self.b_const)
return self.out_fn(x)
entries = make_rand_complex(self.M)
grad_rev = ceviche.jacobian(fn_spsp_entries_a, mode='reverse')(entries)[0]
grad_for = ceviche.jacobian(fn_spsp_entries_a, mode='forward')(entries)[0]
grad_true = grad_num(fn_spsp_entries_a, entries)
np.testing.assert_almost_equal(grad_rev, grad_true, decimal=DECIMAL, err_msg=self.err_msg('fn_solve_entries', 'reverse'))
np.testing.assert_almost_equal(grad_for, grad_true, decimal=DECIMAL, err_msg=self.err_msg('fn_solve_entries', 'forward'))
def test_spmut_entries2(self):
def fn_spsp_entries_x(entries):
# sparse matrix - sparse matrix dot procut as function of entries into second matrix (X)
entries_c, indices_c = spsp_mult(entries, self.indices_const, self.entries_const, self.indices_const, N=self.N)
x = sp_solve(entries_c, indices_c, self.b_const)
return self.out_fn(x)
entries = make_rand_complex(self.M)
grad_rev = ceviche.jacobian(fn_spsp_entries_x, mode='reverse')(entries)[0]
grad_for = ceviche.jacobian(fn_spsp_entries_x, mode='forward')(entries)[0]
grad_true = grad_num(fn_spsp_entries_x, entries)
np.testing.assert_almost_equal(grad_rev, grad_true, decimal=DECIMAL, err_msg=self.err_msg('fn_solve_entries', 'reverse'))
np.testing.assert_almost_equal(grad_for, grad_true, decimal=DECIMAL, err_msg=self.err_msg('fn_solve_entries', 'forward'))
if __name__ == '__main__':
unittest.main()