def test_squareBlockMatrix():
n,m,l,k = symbols('n m l k', integer=True)
A = MatrixSymbol('A', n, n)
B = MatrixSymbol('B', n, m)
C = MatrixSymbol('C', m, n)
D = MatrixSymbol('D', m, m)
X = BlockMatrix([[A,B],[C,D]])
Y = BlockMatrix([[A]])
assert X.is_square
assert block_collapse(X+Identity(m+n)) == BlockMatrix(
[[A+Identity(n), B], [C, D+Identity(m)]])
Q = X+Identity(m+n)
assert block_collapse(Inverse(Q)) == Inverse(block_collapse(Q))
assert (X + MatrixSymbol('Q', n+m, n+m)).is_Add
assert (X * MatrixSymbol('Q', n+m, n+m)).is_Mul
assert Y.I[0,0] == A.I
assert Inverse(X, expand=True) == BlockMatrix([
[(-B*D.I*C + A).I, -A.I*B*(D+-C*A.I*B).I],
[-(D-C*A.I*B).I*C*A.I, (D-C*A.I*B).I]])
assert Inverse(X, expand=False).is_Inverse
assert X.inverse().is_Inverse
assert not X.is_Identity
Z = BlockMatrix([[Identity(n),B],[C,D]])
assert not Z.is_Identity
def test_squareBlockMatrix():
n, m, l, k = symbols('n m l k', integer=True)
A = MatrixSymbol('A', n, n)
B = MatrixSymbol('B', n, m)
C = MatrixSymbol('C', m, n)
D = MatrixSymbol('D', m, m)
X = BlockMatrix([[A, B], [C, D]])
Y = BlockMatrix([[A]])
assert X.is_square
assert block_collapse(X + Identity(m + n)) == BlockMatrix(
[[A + Identity(n), B], [C, D + Identity(m)]])
Q = X + Identity(m + n)
assert block_collapse(Inverse(Q)) == Inverse(block_collapse(Q))
assert (X + MatrixSymbol('Q', n + m, n + m)).is_Add
assert (X * MatrixSymbol('Q', n + m, n + m)).is_Mul
assert Y.I.blocks[0, 0] == A.I
assert Inverse(X, expand=True) == BlockMatrix([[
(-B * D.I * C + A).I, -A.I * B * (D + -C * A.I * B).I
], [-(D - C * A.I * B).I * C * A.I, (D - C * A.I * B).I]])
assert Inverse(X, expand=False).is_Inverse
assert X.inverse().is_Inverse
assert not X.is_Identity
Z = BlockMatrix([[Identity(n), B], [C, D]])
assert not Z.is_Identity
def gauss_cond(pdf, cond={}, **kw_cond):
cond = combine_dict_and_kwargs(cond, kw_cond)
new_cond = pdf.Cond.copy()
new_cond.update(cond)
scope = pdf.Scope.copy()
for var in cond:
del scope[var]
point_cond = {}
for var, value in list(cond.items()):
if value is not None:
point_cond[pdf.Vars[var]] = value
cond_vars = tuple(cond)
num_cond_vars = len(cond_vars)
scope_vars = tuple(set(pdf.VarsList) - set(cond))
num_scope_vars = len(scope_vars)
x_c = BlockMatrix((tuple(pdf.Vars[cond_var] for cond_var in cond_vars),))
m_c = BlockMatrix((tuple(pdf.Param[('Mean', cond_var)] for cond_var in cond_vars),))
m_s = BlockMatrix((tuple(pdf.Param[('Mean', scope_var)] for scope_var in scope_vars),))
S_c = [num_cond_vars * [None] for _ in range(num_cond_vars)] # careful not to create same mutable object
for i in range(num_cond_vars):
for j in range(i):
if ('Cov', cond_vars[i], cond_vars[j]) in pdf.Param:
S_c[i][j] = pdf.Param[('Cov', cond_vars[i], cond_vars[j])]
S_c[j][i] = S_c[i][j].T
else:
S_c[j][i] = pdf.Param[('Cov', cond_vars[j], cond_vars[i])]
S_c[i][j] = S_c[j][i].T
S_c[i][i] = pdf.Param[('Cov', cond_vars[i])]
S_c = BlockMatrix(S_c)
S_s = [num_scope_vars * [None] for _ in range(num_scope_vars)] # careful not to create same mutable object
for i in range(num_scope_vars):
for j in range(i):
if ('Cov', scope_vars[i], scope_vars[j]) in pdf.Param:
S_s[i][j] = pdf.Param[('Cov', scope_vars[i], scope_vars[j])]
S_s[j][i] = S_s[i][j].T
else:
S_s[j][i] = pdf.Param[('Cov', scope_vars[j], scope_vars[i])]
S_s[i][j] = S_s[j][i].T
S_s[i][i] = pdf.Param[('Cov', scope_vars[i])]
S_s = BlockMatrix(S_s)
S_cs = [num_scope_vars * [None] for _ in range(num_cond_vars)] # careful not to create same mutable object
for i, j in product(list(range(num_cond_vars)), list(range(num_scope_vars))):
if ('Cov', cond_vars[i], scope_vars[j]) in pdf.Param:
S_cs[i][j] = pdf.Param[('Cov', cond_vars[i], scope_vars[j])]
else:
S_cs[i][j] = pdf.Param[('Cov', scope_vars[j], cond_vars[i])].T
S_cs = BlockMatrix(S_cs)
S_sc = S_cs.T
m = (m_s + (x_c - m_c) * S_c.inverse() * S_cs).xreplace(point_cond)
S = S_s - S_sc * S_c.inverse() * S_cs
param = {}
index_ranges_from = []
index_ranges_to = []
k = 0
for i in range(num_scope_vars):
l = k + pdf.Vars[scope_vars[i]].shape[1]
index_ranges_from += [k]
index_ranges_to += [l]
param[('Mean', scope_vars[i])] = m[0, index_ranges_from[i]:index_ranges_to[i]]
for j in range(i):
param[('Cov', scope_vars[j], scope_vars[i])] =\
S[index_ranges_from[j]:index_ranges_to[j], index_ranges_from[i]:index_ranges_to[i]]
param[('Cov', scope_vars[i])] =\
S[index_ranges_from[i]:index_ranges_to[i], index_ranges_from[i]:index_ranges_to[i]]
k = l
return GaussPDF(var_names_and_syms=pdf.Vars.copy(), param=param, cond=new_cond, scope=scope)
def gauss_cond(pdf, cond={}, **kw_cond):
cond = combine_dict_and_kwargs(cond, kw_cond)
new_cond = pdf.Cond.copy()
new_cond.update(cond)
scope = pdf.Scope.copy()
for var in cond:
del scope[var]
point_cond = {}
for var, value in cond.items():
if value is not None:
point_cond[pdf.Vars[var]] = value
cond_vars = tuple(cond)
num_cond_vars = len(cond_vars)
scope_vars = tuple(set(pdf.VarsList) - set(cond))
num_scope_vars = len(scope_vars)
x_c = BlockMatrix((tuple(pdf.Vars[cond_var] for cond_var in cond_vars),))
m_c = BlockMatrix((tuple(pdf.Param[('Mean', cond_var)] for cond_var in cond_vars),))
m_s = BlockMatrix((tuple(pdf.Param[('Mean', scope_var)] for scope_var in scope_vars),))
S_c = [num_cond_vars * [None] for _ in range(num_cond_vars)] # careful not to create same mutable object
for i in range(num_cond_vars):
for j in range(i):
if ('Cov', cond_vars[i], cond_vars[j]) in pdf.Param:
S_c[i][j] = pdf.Param[('Cov', cond_vars[i], cond_vars[j])]
S_c[j][i] = S_c[i][j].T
else:
S_c[j][i] = pdf.Param[('Cov', cond_vars[j], cond_vars[i])]
S_c[i][j] = S_c[j][i].T
S_c[i][i] = pdf.Param[('Cov', cond_vars[i])]
S_c = BlockMatrix(S_c)
S_s = [num_scope_vars * [None] for _ in range(num_scope_vars)] # careful not to create same mutable object
for i in range(num_scope_vars):
for j in range(i):
if ('Cov', scope_vars[i], scope_vars[j]) in pdf.Param:
S_s[i][j] = pdf.Param[('Cov', scope_vars[i], scope_vars[j])]
S_s[j][i] = S_s[i][j].T
else:
S_s[j][i] = pdf.Param[('Cov', scope_vars[j], scope_vars[i])]
S_s[i][j] = S_s[j][i].T
S_s[i][i] = pdf.Param[('Cov', scope_vars[i])]
S_s = BlockMatrix(S_s)
S_cs = [num_scope_vars * [None] for _ in range(num_cond_vars)] # careful not to create same mutable object
for i, j in product(range(num_cond_vars), range(num_scope_vars)):
if ('Cov', cond_vars[i], scope_vars[j]) in pdf.Param:
S_cs[i][j] = pdf.Param[('Cov', cond_vars[i], scope_vars[j])]
else:
S_cs[i][j] = pdf.Param[('Cov', scope_vars[j], cond_vars[i])].T
S_cs = BlockMatrix(S_cs)
S_sc = S_cs.T
m = (m_s + (x_c - m_c) * S_c.inverse() * S_cs).xreplace(point_cond)
S = S_s - S_sc * S_c.inverse() * S_cs
param = {}
index_ranges_from = []
index_ranges_to = []
k = 0
for i in range(num_scope_vars):
l = k + pdf.Vars[scope_vars[i]].shape[1]
index_ranges_from += [k]
index_ranges_to += [l]
param[('Mean', scope_vars[i])] = m[0, index_ranges_from[i]:index_ranges_to[i]]
for j in range(i):
param[('Cov', scope_vars[j], scope_vars[i])] =\
S[index_ranges_from[j]:index_ranges_to[j], index_ranges_from[i]:index_ranges_to[i]]
param[('Cov', scope_vars[i])] =\
S[index_ranges_from[i]:index_ranges_to[i], index_ranges_from[i]:index_ranges_to[i]]
k = l
return GaussPDF(var_names_and_syms=pdf.Vars.copy(), param=param, cond=new_cond, scope=scope)
