def test_svd(self):
mtx = ch.array(np.random.randn(100).reshape((10, 10)))
# Get times for svd
from linalg import svd
u, s, v = svd(mtx)
def setup():
mtx.x = -mtx.x
def go_r():
_ = u.r
_ = s.r
_ = v.r
def go_dr():
_ = u.dr_wrt(mtx)
_ = s.dr_wrt(mtx)
_ = v.dr_wrt(mtx)
cht_r = timer(setup, go_r, 20)
cht_dr = timer(setup, go_dr, 1)
# Get times for numpy svd
def go():
u, s, v = np.linalg.svd(mtx.x)
npt = timer(setup=None, go=go, n=20)
# Compare
#print cht_r / npt
#print cht_dr / npt
self.assertLess(cht_r / npt, 3.3)
self.assertLess(cht_dr / npt, 2700)
def test_svd(self):
mtx = ch.array(np.random.randn(100).reshape((10,10)))
# Get times for svd
from linalg import svd
u, s, v = svd(mtx)
def setup():
mtx.x = -mtx.x
def go_r():
_ = u.r
_ = s.r
_ = v.r
def go_dr():
_ = u.dr_wrt(mtx)
_ = s.dr_wrt(mtx)
_ = v.dr_wrt(mtx)
cht_r = timer(setup, go_r, 20)
cht_dr = timer(setup, go_dr, 1)
# Get times for numpy svd
def go():
u,s,v = np.linalg.svd(mtx.x)
npt = timer(setup = None, go = go, n = 20)
# Compare
#print cht_r / npt
#print cht_dr / npt
self.assertLess(cht_r / npt, 3.3)
self.assertLess(cht_dr / npt, 2700)
def test_svd(self):
matrix = self.MATRIX_2
S,V,D = np.linalg.svd(matrix)
S2, V2, D2 = linalg.svd(matrix)
self.assertTrue(self.check_simmilarity(S, S2))
self.assertTrue(self.check_list(V, V2))
self.assertTrue(self.check_simmilarity(D, D2))
def check_simple_complex(self):
a = [[1,2,3],[1,2j,3],[2,5,6]]
u,s,vh = svd(a)
assert_array_almost_equal(dot(conj(transpose(u)),u),identity(3))
assert_array_almost_equal(dot(conj(transpose(vh)),vh),identity(3))
sigma = zeros((u.shape[0],vh.shape[0]),s.dtype.char)
for i in range(len(s)): sigma[i,i] = s[i]
assert_array_almost_equal(dot(dot(u,sigma),vh),a)
def check_simple_overdet(self):
a = [[1,2],[4,5],[3,4]]
u,s,vh = svd(a)
assert_array_almost_equal(dot(transpose(u),u),identity(3))
assert_array_almost_equal(dot(transpose(vh),vh),identity(2))
sigma = zeros((u.shape[0],vh.shape[0]),s.dtype.char)
for i in range(len(s)): sigma[i,i] = s[i]
assert_array_almost_equal(dot(dot(u,sigma),vh),a)
def check_random(self):
n = 20
m = 15
for i in range(3):
for a in [random([n,m]),random([m,n])]:
u,s,vh = svd(a)
assert_array_almost_equal(dot(transpose(u),u),identity(len(u)))
assert_array_almost_equal(dot(transpose(vh),vh),identity(len(vh)))
sigma = zeros((u.shape[0],vh.shape[0]),s.dtype.char)
for i in range(len(s)): sigma[i,i] = s[i]
assert_array_almost_equal(dot(dot(u,sigma),vh),a)
def check_random_complex(self):
n = 20
m = 15
for i in range(3):
for a in [random([n,m]),random([m,n])]:
a = a + 1j*random(list(a.shape))
u,s,vh = svd(a)
assert_array_almost_equal(dot(conj(transpose(u)),u),identity(len(u)))
# This fails when [m,n]
#assert_array_almost_equal(dot(conj(transpose(vh)),vh),identity(len(vh),dtype=vh.dtype.char))
sigma = zeros((u.shape[0],vh.shape[0]),s.dtype.char)
for i in range(len(s)): sigma[i,i] = s[i]
assert_array_almost_equal(dot(dot(u,sigma),vh),a)
def get_graph_stoich(alpha, beta, complex_names = None, constant_names = None):
# number of reactions = number of columns of alpha
no_rxn = len(alpha[0])
# number of substance = number of rows of alpha
no_sub = len(alpha)
# stoichiometry matrix
stoich = []
for row_i in range(no_sub):
stoich_row = []
for col_i in range(no_rxn):
stoich_row.append(beta[row_i][col_i] - alpha[row_i][col_i])
stoich.append(stoich_row)
# rank of stoichiometry matrix
if no_sub < no_rxn:
# need to transpose stoich for svd call
stoich_tr = []
for i in range(no_rxn):
stoich_tr_row = []
for j in range(no_sub):
stoich_tr_row.append(stoich[j][i])
stoich_tr.append(stoich_tr_row)
matrix_U, sing_vals, matrix_V_t = linalg.svd(stoich_tr)
else:
matrix_U, sing_vals, matrix_V_t = linalg.svd(stoich)
# tol computation lent from NumPy
# https://github.com/numpy/numpy/blob/85b83e6938fa6f5176eaab8e8fd1652b27d53aa0/numpy/linalg/linalg.py#L1513
tol = max(sing_vals) * max(no_rxn, no_sub) * sys.float_info.epsilon
stoich_rank = sum([1 for s in sing_vals if s > tol])
# make directed graph
G = nx.DiGraph()
# add nodes to graph: add all reactions 'w' and substances 's'
if constant_names == None:
G.add_nodes_from(['w'+str(n) for n in range(1,no_rxn+1)], bipartite=1)
else:
G.add_nodes_from([constant_names[n-1] for n in range(1,no_rxn+1)], bipartite=1)
if complex_names == None:
G.add_nodes_from(['s'+str(n) for n in range(1,no_sub+1)], bipartite=0)
else:
G.add_nodes_from([complex_names[n-1] for n in range(1,no_sub+1)], bipartite=0)
# add ('s','w') edges, i.e. positive element in alpha
for row_i in range(no_sub):
curr_row = alpha[row_i]
for col_i in range(no_rxn):
curr_coeff = curr_row[col_i]
if curr_coeff > 0:
if constant_names == None and complex_names == None:
G.add_edge('s'+str(row_i+1), 'w'+str(col_i+1), coeff=curr_coeff)
elif constant_names == None and complex_names != None:
G.add_edge(complex_names[row_i], 'w'+str(col_i+1), coeff=curr_coeff)
elif constant_names != None and complex_names == None:
G.add_edge('s'+str(row_i+1), constant_names[col_i], coeff=curr_coeff)
elif constant_names != None and complex_names != None:
G.add_edge(complex_names[row_i], constant_names[col_i], coeff=curr_coeff)
else:
raise
# add ('w','s') edges, i.e. positive element in beta
for row_i in range(no_sub):
curr_row = beta[row_i]
for col_i in range(no_rxn):
curr_coeff = curr_row[col_i]
if curr_coeff > 0:
if constant_names == None and complex_names == None:
G.add_edge('w'+str(col_i+1), 's'+str(row_i+1), coeff=curr_coeff)
elif constant_names == None and complex_names != None:
G.add_edge('w'+str(col_i+1), complex_names[row_i], coeff=curr_coeff)
elif constant_names != None and complex_names == None:
G.add_edge(constant_names[col_i], 's'+str(row_i+1), coeff=curr_coeff)
elif constant_names != None and complex_names != None:
G.add_edge(constant_names[col_i], complex_names[row_i], coeff=curr_coeff)
else:
raise
return G, stoich, stoich_rank