def restored(A):
"""
@param A: full rank symmetric matrix whose rows sum to 1
@return: a doubly centered but otherwise full rank matrix
"""
assert_symmetric(A)
n = A.shape[0]
return A - ones_like(A) / n
def get_selection_S(F):
"""
The F and S notation is from Yang and Nielsen 2008.
@param F: a selection value for each codon, up to an additive constant
@return: selection differences F_j - F_i, also known as S_ij
"""
e = algopy.ones_like(F)
return algopy.outer(e, F) - algopy.outer(F, e)
def get_selection_S(F):
"""
The F and S notation is from Yang and Nielsen 2008.
@param F: a selection value for each codon, up to an additive constant
@return: selection differences F_j - F_i, also known as S_ij
"""
e = algopy.ones_like(F)
return algopy.outer(e, F) - algopy.outer(F, e)
def augmented(A):
"""
@param A: doubly centered symmetric nxn matrix of rank n-1
@return: full rank symmetric matrix whose rows sum to 1
"""
assert_square(A)
n = A.shape[0]
#assert_allclose(dot(ones(n), A), zeros(n), atol=1e-12)
#assert_allclose(dot(A, ones(n)), zeros(n), atol=1e-12)
return A + ones_like(A) / n
def get_selection_S(F):
"""
The F and S notation is from Yang and Nielsen 2008.
Speed matters.
@param F: a selection value for each codon, up to an additive constant
@return: selection differences F_j - F_i, also known as S_ij
"""
# FIXME: use algopy.ones_like when it becomes available
e = algopy.ones_like(F)
# # FIXME: instead of the following block
# e = algopy.zeros_like(F)
# for i in range(F.shape[0]):
# e[i] = 1.
return algopy.outer(e, F) - algopy.outer(F, e)