def Compute(self):
n = 1
m = max(self.power, 3) + 7
manage.config.N, manage.config.M = n, m
impl = manage.config.EXPR_IMPL
manage.config.MAXPOWER = np.array([self.power])
self.SetStartSymbols(1)
target = None
for h_iter in itertools.combinations(xrange(m), self.power):
small_target = None
expr_vector = np.zeros((1, m))
for h in h_iter:
expr_vector[0, h] = 1
expr = impl([1], expr_vector)
if target is None:
target = expr
else:
target = target + expr
target = np.array([[target]])
matlab = '''n = 1;
m = 18;
A = randn(1, m);
sub = nchoosek(1:m, %s);
original = 0;
for i = 1:size(sub, 1)
original = original + prod(A(sub(i, :)));
end
''' % self.power
target = ExprMatrix(comp={THIS: ""}, expressions=target, powers=manage.config.MAXPOWER)
target = target.ElementwiseMultiply(120)
target.comp[MATLAB] = matlab
self.target_mat = target
def testFindLinearCombinationBroadcasting(self):
manage.config.MAXPOWER = np.array([10])
# mat1 mat2 target
# x1 | x1x2 x1 3x1 | 2x1x2 + x1
# 2x3 | x2^2 x3 5x3 | 2x2^2 + x3
mat1_11 = ExprSymbolic([1], np.array([[1, 0, 0]]))
mat1_12 = ExprSymbolic([1], np.array([[1, 1, 0]]))
mat1_21 = ExprSymbolic([2], np.array([[0, 0, 1]]))
mat1_22 = ExprSymbolic([1], np.array([[0, 2, 0]]))
mat2_11 = ExprSymbolic([1], np.array([[1, 0, 0]]))
mat2_21 = ExprSymbolic([1], np.array([[0, 0, 1]]))
target_11 = ExprSymbolic([3], np.array([[1, 0, 0]]))
target_12 = ExprSymbolic([2, 1], np.array([[1, 1, 0], [1, 0, 0]]))
target_21 = ExprSymbolic([5], np.array([[0, 0, 1]]))
target_22 = ExprSymbolic([2, 1], np.array([[0, 2, 0], [0, 0, 1]]))
mat1 = ExprMatrix("a",
np.array([[mat1_11, mat1_12], [mat1_21, mat1_22]]),
np.array([1]))
mat2 = ExprMatrix("b", np.array([[mat2_11], [mat2_21]]), np.array([1]))
target = ExprMatrix(
"target", np.array([[target_11, target_12], [target_21,
target_22]]),
np.array([1]))
expressions_list = [mat1, mat2]
weights = ExprSymbolic.FindLinearCombination(expressions_list,
target)[0]
self.assertEquals(2, len(weights))
self.assertAlmostEqual(2.0, weights[0])
self.assertAlmostEqual(1.0, weights[1])
def Compute(self):
n = 1
m = max(self.power, 3) + 7
manage.config.N, manage.config.M = n, m
impl = manage.config.EXPR_IMPL
manage.config.MAXPOWER = np.array([self.power])
self.SetStartSymbols(1)
target = None
for h_iter in itertools.combinations(xrange(m), self.power):
small_target = None
expr_vector = np.zeros((1, m))
for h in h_iter:
expr_vector[0, h] = 1
expr = impl([1], expr_vector)
if target is None:
target = expr
else:
target = target + expr
target = np.array([[target]])
matlab = '''n = 1;
m = 18;
A = randn(1, m);
sub = nchoosek(1:m, %s);
original = 0;
for i = 1:size(sub, 1)
original = original + prod(A(sub(i, :)));
end
''' % self.power
target = ExprMatrix(comp={THIS: ""},
expressions=target,
powers=manage.config.MAXPOWER)
target = target.ElementwiseMultiply(120)
target.comp[MATLAB] = matlab
self.target_mat = target
def GetMatricesSumMul(n, m, expr_impl):
manage.config.MAXPOWER = np.array([10, 10])
mat_a = []
for r in xrange(n):
row = []
for c in xrange(m):
vec = [0] * (2 * n * m)
vec[r * m + c] = 1
row.append(expr_impl([1], np.array([vec])))
mat_a.append(row)
mat_b = []
for r in xrange(n):
row = []
for c in xrange(m):
vec = [0] * (2 * n * m)
vec[n * m + r * n + c] = 1
row.append(expr_impl([1], np.array([vec])))
mat_b.append(row)
A = ExprMatrix(comp='A',
expressions=np.array(mat_a),
powers=np.array([1, 0]))
B = ExprMatrix(comp='B',
expressions=np.array(mat_b),
powers=np.array([0, 1]))
return A, B
def testElementwiseMultiply(self):
manage.config.MAXPOWER = np.array([10, 10])
# a = x1 * x3
# b = x1 * x2^2
# c = x2^3 + x3^4
a = ExprSymbolic([1], np.array([[1, 0, 1]]))
b = ExprSymbolic([1], np.array([[1, 2, 0]]))
c = ExprSymbolic([1, 1], np.array([[0, 3, 0], [0, 0, 4]]))
expressions1 = np.array([[a, b], [c, a]])
expressions2 = np.array([[a, a], [a, a]])
# mat1:
# x1x3 | x1 * x2^2
# x2^3 + x3^4 | x1x3
mat1 = ExprMatrix('M1', expressions1, powers=np.array([1, 0]))
mat2 = ExprMatrix('M2', expressions2, powers=np.array([0, 1]))
mat1 = mat1.ElementwiseMultiply(mat2)
self.assertEquals((2, 2), mat1.expressions.shape)
elem = mat1.expressions[0, 0]
self.assertEquals(1, elem.expr_vectors.shape[0])
self.assertEquals(1, elem.quants[0])
self.assertTrue((np.array([2, 0, 2]) == elem.expr_vectors).all())
elem2 = mat1.expressions[1, 0] # x1x3 * (x2^3 + x3^4)
self.assertEquals(2, elem2.expr_vectors.shape[0])
self.assertTrue((np.array([1, 3, 1]) == elem2.expr_vectors).any())
self.assertTrue((np.array([1, 0, 5]) == elem2.expr_vectors).any())
self.assertTrue((np.array([1, 1]) == elem2.quants).any())
def testHashImmuneToConst(self):
manage.config.MAXPOWER = np.array([10])
a = ExprSymbolic([2, 3], np.array([[1, 2, 3], [4, 5, 6]]))
b = ExprSymbolic([4, 6], np.array([[1, 2, 3], [4, 5, 6]]))
self.assertNotEquals(a, b)
a = ExprMatrix("a", np.array([[a]]), np.array([1]))
b = ExprMatrix("b", np.array([[b]]), np.array([1]))
self.assertEquals(a, b)
def testMarginalizeBothAxis(self):
manage.config.MAXPOWER = np.array([10])
a = ExprZp([1], np.array([[1, 0, 0]]))
b = ExprZp([1], np.array([[0, 1, 0]]))
c = ExprZp([2], np.array([[0, 0, 1]]))
expressions = np.array([[a, b, c], [a, b, c]], dtype=np.object)
matrix = ExprMatrix('A', expressions, powers=np.array([1]))
matrix = matrix.Marginalize(axis=None)
self.assertEquals((1, 1), matrix.expressions.shape)
def testMarginalizeBothAxis(self):
a = ExprSymbolic([1], np.array([[1, 0, 0]]))
b = ExprSymbolic([1], np.array([[0, 1, 0]]))
c = ExprSymbolic([2], np.array([[0, 0, 1]]))
expressions = np.array([[a, b, c], [a, b, c]], dtype=np.object)
matrix = ExprMatrix('A', expressions, powers=np.array([1]))
matrix = matrix.Marginalize(axis=None)
self.assertEquals((1, 1), matrix.expressions.shape)
self.assertEquals(3, len(matrix.expressions.item(0, 0).quants))
self.assertEquals([2, 2, 4],
sorted(matrix.expressions.item(0, 0).quants))
def testSameHash(self):
manage.config.MAXPOWER = np.array([10])
a = ExprSymbolic([1], np.array([[1, 0, 0, 0]]))
b = ExprSymbolic([1], np.array([[0, 1, 0, 0]]))
c = ExprSymbolic([1], np.array([[0, 0, 1, 0]]))
d = ExprSymbolic([1], np.array([[0, 0, 0, 1]]))
expressions = np.array([[a, b], [c, d]], dtype=np.object)
matrix = ExprMatrix('A', expressions, powers=np.array([1]))
Q = matrix.Marginalize(axis=0).Marginalize(axis=1)
W = matrix.Marginalize(axis=1).Marginalize(axis=0)
self.assertEquals(Q, W)
def testHashIsComputed(self):
manage.config.MAXPOWER = np.array([10])
a = ExprZp(
[2, 3],
np.array([[1, 2, 3], [4, 5, 6]]))
b = ExprZp(
[2, 2],
np.array([[1, 2, 3], [4, 5, 6]]))
self.assertNotEquals(a, b)
a = ExprMatrix("a", np.array([[a]]), np.array([1]))
b = ExprMatrix("b", np.array([[b]]), np.array([1]))
self.assertNotEquals(a, b)
def Compute(self):
n = 1
m = max(self.power, 2) + 1
manage.config.N, manage.config.M = n, m
impl = manage.config.EXPR_IMPL
manage.config.MAXPOWER = np.array([self.power])
W = self.SetStartSymbols(1)[0]
zeros = np.array([0] * (n * m))
powers = [0]
# Target expression: sum (v^T W)^k
singles = []
for h_iter in range(0, pow(2, m)):
row = []
for mm in range(0, m):
if h_iter & pow(2, mm):
row.append([impl([1], np.array([zeros]))])
else:
row.append([impl([0], np.array([zeros]))])
h = ExprMatrix(comp="", \
expressions=np.array(row), powers=powers)
singles.append(W.Multiply(h).Power(self.power))
target = ExprAbstract.AddManyExpressions(singles)
matlab = '''n = 14;
m = 1;
A = randn(1, n);
nset = dec2bin(0:(2^(n) - 1));
original = 0;
for i = 1:size(nset, 1)
v = logical(nset(i, :) - '0');
original = original + (v * A') ^ %d;
end
''' % self.power
target.comp[MATLAB] = matlab
self.target_mat = target
def testElementwiseMultiply(self):
manage.config.MAXPOWER = np.array([10, 10])
# a = x1 * x3
# b = x1 * x2^2
# c = x2^3 + x3^4
a = ExprZp([1], np.array([[1, 0, 1]]))
b = ExprZp([1], np.array([[1, 2, 0]]))
c = ExprZp([1, 1], np.array([[0, 3, 0], [0, 0, 4]]))
expressions1 = np.array([[a, b], [c, a]])
expressions2 = np.array([[a, a], [a, a]])
# mat1:
# x1x3 | x1 * x2^2
# x2^3 + x3^4 | x1x3
mat1 = ExprMatrix('M1', expressions1, powers=np.array([1, 0]))
mat2 = ExprMatrix('M2', expressions2, powers=np.array([0, 1]))
mat1.ElementwiseMultiply(mat2)
self.assertEquals((2, 2), mat1.expressions.shape)
def testShapesAfterSumAreCorrec(self):
a = ExprSymbolic([1], np.array([[1, 0, 0]]))
b = ExprSymbolic([1], np.array([[0, 1, 0]]))
expressions = np.array([[a, a, a], [b, b, b]])
matrix = ExprMatrix('M', expressions, powers=np.array([1]))
# Exp matrix test
self.assertEquals((2, 3), matrix.expressions.shape)
m0 = copy.copy(matrix)
m0 = m0.Marginalize(axis=0)
self.assertEquals((1, 3), m0.expressions.shape)
self.assertEquals(a + b, m0.expressions[0, 0])
self.assertEquals(a + b, m0.expressions[0, 1])
m1 = copy.copy(matrix)
m1 = m1.Marginalize(axis=1)
self.assertEquals((2, 1), m1.expressions.shape)
self.assertEquals(a + a + a, m1.expressions[0, 0])
self.assertEquals(b + b + b, m1.expressions[1, 0])
def SetStartSymbols(self, nr):
n, m = manage.config.N, manage.config.M
self.start_symbols = []
for k in range(nr):
mat = []
for r in xrange(n):
row = []
for c in xrange(m):
vec = np.array([0] * nr * (n * m))
vec[k * n * m + r * m + c] = 1
row.append(manage.config.EXPR_IMPL([1], np.array([vec])))
mat.append(row)
powers = np.array([0] * nr)
powers[k] = 1
expr_mat = ExprMatrix(comp=chr(ord('A') + k),
expressions=np.array(mat),
powers=powers)
self.start_symbols.append(expr_mat)
return self.start_symbols
def SetStartSymbolsWithShapes(self, mat_shapes):
self.start_symbols = []
total_variables = sum(n * m for n, m in mat_shapes)
variables_so_far = 0
for k, (n, m) in enumerate(mat_shapes):
mat = []
for r in xrange(n):
row = []
for c in xrange(m):
vec = np.array([0] * total_variables)
vec[variables_so_far + r * m + c] = 1
row.append(manage.config.EXPR_IMPL([1], np.array([vec])))
mat.append(row)
powers = np.array([0] * len(mat_shapes))
powers[k] = 1
expr_mat = ExprMatrix(comp=chr(ord('A') + k),
expressions=np.array(mat),
powers=powers)
self.start_symbols.append(expr_mat)
variables_so_far += n * m
assert variables_so_far == total_variables
return self.start_symbols
def Compute(self):
n = max(self.power, 2)
m = n + 1
manage.config.N, manage.config.M = n, m
impl = manage.config.EXPR_IMPL
manage.config.MAXPOWER = np.array([self.power])
W = self.SetStartSymbols(1)[0]
zeros = np.array([0] * (n * m))
powers = [0]
# Target expression: sum (v^T W h)^k
singles = []
vs = []
vWs = []
hs = []
for v_iter in range(0, pow(2, n)):
col = []
col01 = []
for nn in range(0, n):
if v_iter & pow(2, nn):
col.append(impl([1], np.array([zeros])))
col01.append(1)
else:
col.append(impl([0], np.array([zeros])))
col01.append(0)
v = ExprMatrix(comp="np.array([%s])" % str(col01), \
expressions=np.array([col]), powers=powers)
vs.append(v)
vWs.append(v.Multiply(W))
for h_iter in range(0, pow(2, m)):
row = []
row01 = []
for mm in range(0, m):
if h_iter & pow(2, mm):
row.append([impl([1], np.array([zeros]))])
row01.append(1)
else:
row.append([impl([0], np.array([zeros]))])
row01.append(0)
hs.append(ExprMatrix(comp="np.array([%s]).transpose()" % str(row01), \
expressions=np.array(row), powers=powers))
for v_iter in range(0, pow(2, n)):
v = vs[v_iter]
vW = vWs[v_iter]
for h_iter in range(0, pow(2, m)):
h = hs[h_iter]
singles.append(vW.Multiply(h).Power(self.power))
target = ExprAbstract.AddManyExpressions(singles)
matlab = '''n = 7;
m = 8;
A = randn(n, m);
nset = dec2bin(0:(2^(n) - 1));
mset = dec2bin(0:(2^(m) - 1));
original = 0;
for i = 1:size(nset, 1)
for j = 1:size(mset, 1)
v = logical(nset(i, :) - '0');
h = logical(mset(j, :) - '0');
original = original + (v * A * h') ^ %d;
end
end
''' % self.power
target.comp[MATLAB] = matlab
self.target_mat = target
def testAddOne(self):
manage.config.MAXPOWER = np.array([10])
a = ExprSymbolic([5], np.array([[0, 0, 0, 0]]))
expressions = np.array([[a]], dtype=np.object)
matrix = ExprMatrix('A', expressions, powers=np.array([1]))
self.assertTrue(matrix.Add(4).expressions[0, 0].quants.shape[0] == 1)
