def perform(self, matrix):
# linear independent checking
with B.NoTape():
rank = T.Rank()(matrix)
if rank.to_scalar() != matrix.columns:
return None
U = []
u_k = matrix[:, 1]
u_k_norm = T.L2Norm()(matrix[:, 1])
U.append(u_k / u_k_norm)
R = Matrix(np.zeros((matrix.columns, ) * 2), dtype=matrix.dtype)
R[1, 1] = u_k_norm
for col in range(2, matrix.columns + 1):
x_k = matrix[:, col]
u_k = B.copy(x_k)
for row, u in enumerate(U, 1):
c_k = (x_k.T * u).to_scalar()
R[row, col] = c_k
u_k -= c_k * u
u_k_norm = T.L2Norm()(u_k)
U.append(u_k / u_k_norm)
R[row + 1, col] = u_k_norm
return T.Cat(axis=-1)(*U), R
def perform(self, matrix):
if isinstance(self.other, Matrix):
result = matrix.matrix / self.other.matrix
result = B.copy(matrix, result, causal=True)
else:
with B.NoTape():
result = matrix / Matrix(self.other, dtype=matrix.dtype)
return result
def __build(self, *matrixs):
return_matrix = []
for matrix in matrixs:
if not self.eager:
new_matrix = B.copy(matrix, causal=self.causal)
else:
new_matrix = matrix
if self.tape_enabled and self.tape:
self.add_tape(new_matrix)
return_matrix.append(new_matrix)
return return_matrix
def perform(self, matrix):
if isinstance(self.other, Matrix):
result = matrix.matrix + self.other.matrix
result = B.copy(matrix, new_value=matrix.matrix + self.other.matrix, causal=True)
# binary operation tape
with B.LazyPerform():
self.other + matrix
else:
with B.NoTape():
result = matrix + Matrix(self.other, matrix.dtype)
return result
def perform(self, matrix):
if isinstance(self.other, Matrix):
if self.other.shape == (1, 1):
with B.NoTape():
result = matrix * self.other.to_scalar()
result = result.matrix
else:
result = matrix.matrix @ self.other.matrix
# binary operation tape
with B.LazyPerform():
self.other * matrix
elif isinstance(self.other, (int, float)):
result = matrix.matrix * self.other
else:
with B.NoTape():
result = matrix * Matrix(self.other, dtype=matrix.dtype)
result = B.copy(matrix, new_value=result, causal=True)
return result
def __build(self, *matrixs):
return_matrix = []
for matrix in matrixs:
new_matrix = B.copy(matrix)
return_matrix.append(new_matrix)
return return_matrix
def perform(self, matrix):
result = matrix.matrix.reshape(self.shape)
return B.copy(matrix, new_value=result, causal=True)
def perform(self, matrix):
return B.copy(matrix, new_type=self.new_type, causal=True)
def perform(self, matrix):
result = matrix.matrix[self.key]
return B.copy(matrix, new_value=result, causal=True)